premature optimization xkcd

(Multiply vs. shift, etc). This comic is a flowchart making fun of the difference between prematurely optimizing and doing things right in the first place: it tells you that if you are using it to decide whether you are optimizing prematurely, then you're optimizing prematurely. Third, make it fast. ), but the usage suggested here is more appropriately covered by instinct, common sense, and observation of the behavior of the completed program. "Premature optimization" is a phrase used to describe a situation where a programmer lets performance considerations affect the design of a piece of code. (Score: 5, Informative) by LichtSpektren on Wednesday June 08, 2016 @11:48AM Sandboxing all of FF's plugins is good security practice. 141.101.98.47 08:33, 8 June 2016 (UTC) Yay! In my experience, most optimization problems can be solved at either the architecture/design or data-structure/algorithm level. For example whereas a little tweaking might give you a 10% increase of speed with optimization, changing fundamentally the way your program works might make it 10x faster. If you're actually applying whatever you're doing in areas that are genuinely needed and they genuinely benefit from it, then you're doing just great in the eyes of Knuth. We should forgot about small My advice: Try to only pay the cost of optimisation when you can quantify the benefit. Its source is credited to Donald Knuth. It is far less costly to design correctly considering the optimal code for the situation you expect than to wait until the there are a million users and people are screaming becasue you used cursors throughout the application. calls for ignoring efficiency in the small; but I believe this is It's relatively common to include assertions for certain invariants because it can potentially allow compilers to make better optimizations, though this is usually a sign of premature optimization. The point of the maxim is that, typically, optimization is convoluted and complex. I prefer to schedule performance, scalability, and similar issues with dedicated stories (see Performance Optimization in Chapter 9). Secondly, it's not obvious that user's time is more valuable than programmer's time. Optimize for memory, trying to fit more code/data in the cache. I don't think that recognized best practices are premature optimizations. So expecting some help to clarify these two concept with the difference between them. What he deemed "premature optimizations" were optimizations applied by people who effectively didn't know what they were doing: didn't know if the optimization was really needed, didn't measure with proper tools, maybe didn't understand the nature of their compiler or computer architecture, and most of all, were "pennywise-and-pound-foolish", meaning they overlooked the big opportunities to optimize (save millions of dollars) by trying to pinch pennies, and all while creating code they can no longer effectively debug and maintain. This work is licensed under a Creative Commons Attribution-NonCommercial 2.5 License. There is a reason why quick and dirty is called that. Another layer of humor is provided by the minimalism and directness of the flowchart, which suggests that it has itself been (prematurely?) Also note how he isn't just criticizing these "pennywise-and-pound-foolish" programmers, but also the people who react by suggesting you should always ignore small inefficiencies. Accordingly, understanding what premature optimization is and how to avoid it can be beneficial in many areas of life. If you come-up with some examples, It will be more benefit for others. Optimization can happen at different levels of granularity, from very high-level to very low-level: Start with a good architecture, loose coupling, modularity, etc. technique is different but not Today's analogical equivalent might be like, "People shouldn't be taking blind stabs at optimizing their software, but custom memory allocators can make a huge difference when applied in key areas to improve locality of reference," or, "Handwritten SIMD code using an SoA rep is really hard to maintain and you shouldn't be using it all over the place, but it can consume memory much faster when applied appropriately by an experienced and guided hand.". Premature optimization to me means trying to improve the efficiency of your code before you have a working system, and before you have actually profiled it and know where the bottleneck is. Even after that, readability and maintainability should come before optimization in many cases. But, the speedup from using more sophisticated algorithms was orders of magnitude more than that. Yet it was a quote in favor of appropriately applied micro-optimizations when used by an experienced hand holding a profiler. I apologize for this unfortunate omission, and hope that the readers will forgive me : ) What you seem to be talking about is optimization like using a hash-based lookup container vs an indexed one like an array when a lot of key lookups will be done. “Premature optimization is the root of all evil” is a famous saying among software developers. In an ideal world, you could optimize everything. Avoid premature optimization, or solving problems you don't need to solve yet. Optimization can prove to have been a waste of time if parts of the program are later changed or discarded, or if the optimized … So you have two techniques ready at hand, identical in cost (same effort to use, read, modify) and one is more efficient. designed to provide all programmers with feedback indicating what Of This page was last edited on 7 December 2019, at 20:30. However, the trick is to spend the extra cost only where it counts to the performance of the application and where the additional cost outweighs the performance hit. Knuth also says it is always better to, instead of optimizing, change the algorithms your program uses, the approach it takes to a problem. To quote the immortal words of xkcd: “Premature optimization is the root of all evil.” EDIT: It has been pointed out to me the the original author of the “premature optimization” quote is in fact Donald Knuth, not xkcd. If you are consulting flowchart, you are either the kind of person who does everything methodically and waste gigantic amount of time by it, especially if trying to optimize, or you lack the experience and common sense needed to distinguish when the optimization is premature, and statistically are more likely to optimize incorrect part of code. Optimization should never be done without metrics. Many problems of scaling can be solved just by throwing more hardware at the problem. I had a 20k rep user today tell me that using a HashSet instead of a List was premature optimization. Any code change that is done before stage #3 is definitely premature. Premature optimization [xkcd.com] Re:Honestly? It's only premature if you do so without first optimizing the architecture, data structures, algorithms, memory footprint, and flow-control. The title text's root of all evil refers to Donald Knuth's paper "Structured Programming with Goto statements" (1974)[1] in which he wrote: "There is no doubt that the grail of efficiency leads to abuse. Flowcharts are often used in xkcd including the (mostly) non-farcical 1688: Map Age Guide one week prior to this comic. Choose the right data structures and algorithms for the problem. Just like how heroin gets abused, a lot of programmers suffer from what I call Premature Optimization Syndrome. particularly obscure or obfuscated, of all evil. Rules 3 and 4 are instances of the design philosophy KISS. should be supplied automatically unless it has been specifically It's more about burning time on the what ifs that are potential performance problems depending on the usage scenarios. While there are things where you shouldn’t compromise, such as documenting your code, is it really necessary for your script to finish in 5 minutes instead of 15? Premature optimization is the act of trying to make things more efficient at a stage when it is too early to do so. The point of avoiding premature optimization isn't to excuse low performance code. simply an overreaction to the abuses they see being practiced by No, using the more efficient one would not, in that case, be premature. Yet we should not pass up our opportunities in that critical 3%. statements in this context]. More details. Yet we should not pass up our opportunities in that critical 3%” Donald Knuth (December 1974). Premature optimization is (still) bad. But it's rarely necessary to optimize the flow control & expression logic. ACM Journal Computing Surveys 6 (4): 268. Interrupting your code-writing to look for alternatives to common programming constructs / library routines on the off-chance that there's a more efficient version hanging around somewhere even though for all you know the relative speed of what you're writing will never actually matter... That's premature. I try to only optimise when a performance issue is confirmed. optimizations [using gotos] are not difficult to learn and, as I have Recently comparativists history migration essay on pattern in world have expressed commitment to democratic institutions than the market. The kind of optimization the Knuth rule is about is minimizing the length the most common codepaths, optimizing the code that is run most by for example rewriting in assembly or simplifying the code, making it less general. The humorous conclusion is that if there is any doubt whether an optimization is premature, then it is premature! The title text may also be poking fun at the comic, since the comic itself may be the "system" used to determine premature optimization. Computing Surveys, Vol 6, No 4, December 1974: http://web.archive.org/web/20130731202547/http://pplab.snu.ac.kr/courses/adv_pl05/papers/p261-knuth.pdf, https://www.explainxkcd.com/wiki/index.php?title=1691:_Optimization&oldid=184316. Second, verify that the code is correct. In reaction to a lot of the other comments posted on this question: algorithm selection != optimization. Any time you're trying to promote carefully-applied micro-optimizations as Knuth promoted above, it's good to throw in a disclaimer to discourage novices from getting too excited and blindly taking stabs at optimization, like rewriting their entire software to use goto. While there are things where you shouldn’t compromise, such as documenting your code, is it really necessary for your script to finish in 5 minutes instead of 15? We should forget about small efficiencies, say about 97% of the time: premature optimization is the root of all evil. And in those cases where it actually is necessary, it's rarely sufficient. A) You can reach the goal performance threshold by performing high-level optimizations, so it's not necessary to fiddle with the expressions. the premature optimization definition xkcd why root java example evil optimization - When is optimisation premature? The point is to keep the code clear and concise throughout the development process, until the benefits of performance outweigh the induced costs of writing and maintaining the optimizations. So what’s my footnote? Within each function, make appropriate use of flow-control statements. Remember: "Premature optimization is the root of all evil" (Donald Knuth). His quote was a caveat he added to justify his rationale for using goto in order to speed up those critical loops. ), Within each statement, use the most efficient expressions yielding the correct result. Professor Donald Knuth, 1974. is performed about a million or so times in the program. can that really be considered a Oleksandr Kaleniuk, “Premature optimization is the root of all evil” is the root of evil, September 2016 The figure is due to the irrepressible Randall Munroe. Databases do not refactor easily. In the past I've worked on some time critical code (an RSA implementation) where looking at the assembler that the compiler produced and removing a single unnecessary instruction in an inner loop gave a 30% speedup. measured improvement in server performance. Also frankly when you understand performance tuning in databases, you can write code that is more likely to perform well in the same time or less than it takes to write code which doesn't perform well. From a database perspective, not to consider optimal design at the design stage is foolhardy at best. Among these are: Optimisation (going for performance) often comes at the expense of other parameters, and must be balanced against the "loss" in these areas. This work is licensed under a Creative Commons Attribution-NonCommercial 2.5 License. turned off. People have misused his quote all over the place, often suggesting that micro-optimizations are premature when his entire paper was advocating micro-optimizations! Other teams include "Performance" and "Scalability" in their "done done" list, but these can lead to premature optimization. "Premature optimization" is the practice of trying to optimize parts of a program before such optimization has been shown to be needed. First, get the code working. bunderbunder on Nov 16, 2017. Put the most common value first in a switch/case, etc. Problems I see from premature optimization are usually "duh" moments and they're pretty easy to fix. Premature, unproven optimizations are bad, as the infamous Donald Knuth once said: Any coding practice that makes your code harder to understand in the name of performance is a premature optimization. Actually finish projects. Inefficiency (another xkcd theme) was featured in the comic prior to this one. And of course, any optimization is premature if you don't define a goal performance threshold. However, there are many other ways in which premature optimization can take place, and there are some optimizations which are not premature, so this is a robust and fruit laden branch. If speed really is mission critical, get the algorithm working first (and write all your test cases), before tackling optimization. “Premature optimization is the root of all evil” goes one of the most famous quotes in CS. "Structured Programming with go to Statements". Programmers waste enormous amounts of time thinking about, or worrying about, the speed of noncritical parts of their programs, and these attempts at efficiency actually have a strong negative impact when debugging and maintenance are considered. (Actually second time, but first time I didn't save it in time.) That's in part what he was doing. attempts at efficiency actually have a strong negative impact when Even after that, readability and maintainability should come before optimization in many cases. Randall Hyde, The Fallacy of Premature Optimization, ACM Ubiquity Magazine, February 2009 — Hyde and a few other authors mistakenly attribute the Knuth quote to Tony Hoare, but it is Knuth’s statement. It has been optimized, by pruning branches which cannot apply. In other words, will Moore's law make your optimisation irrelevant before too long. How to Be "Done Done" Make a little progress on every aspect of your work every day. image credit: xkcd “ Premature optimization is the root of all evil “: the famous Knuth-ism that we all know and… well, that we all know.It’s hard to go a day of reading programming blogs without someone referencing this and leaving their particular footnote on it.I suppose today I am that someone. In established engineering disciplines a their "optimized" programs. Optimization (alt-text) Premature optimization is the root of all evil, so to start this project I'd better come up with a system that can determine whether a possible optimization is premature or not. In some fields, such as compilers or database design, such tools can be useful and productive (the 3% mentioned by Knuth? As Knuth said, We should forget about small efficiencies, say about 97% of the time: premature optimization is the root of all evil. When you have the option of choosing well-known algorithms that perform well, the cost of "optimising" up-front is often acceptable. Premature optimization may lead to code that is difficult to modify, maintain, and read. Premature optimization is spending a lot of time on something that you may not actually need. Here is the full quote from his book The Art of Computer Programming: Posted on 12 September 2016 by ecoquant. So, the first line is only true because the very fact that you are asking a question about whether or not optimization is premature means that you are not sure that you need optimization, which by definition makes it premature. Herb Sutter's C++ coding standards says to avoid Premature optimization and Premature pessimization.But I feel both is doing the same thing. ... premature optimization is the root of all evil (or at least most of it) in programming.'' XKCD tells it all. Are you consulting a flow chart cannot be answered no while consulting the flow chart, so the entire branch structure resulting from a no answer has been eliminated. This is not premature optimization, but something you should decide in the design phase. The standard answer to these optimisation-tips questions is to profile your code and see if it's a problem first, and if it's not, then therefore your new technique is unneeded. L_226 on Nov 16, 2017. step 1 - don't use pandas. awesome incremental search Crucially, before embarking on a grand optimization adventure, make sure that the functions you are optimizing are actually the functions that you will want to use in the long run. Yet we should not pass up our opportunities in that critical 3%.". Certain idioms that were introduced in the name of optimization have … “Premature optimization is the root of all evil” goes one of the most famous quotes in CS. A primary goal of software development teams is delivering valuable features and products as quickly and effectively as possible.One way they can optimize how quickly they deliver software is by leveraging methodologies … Not taking the time to learn what is good performing database design is developer laziness, not best practice. Ken Thompson rephrased Pike's rules 3 and 4 as "When in doubt, use brute force.". programmers who have been using measurement tools has been that their to restrict myself to tools that deny me such efficiencies [i.e., goto notice. [...] again, this is a noticeable saving in the overall running speed, The use case in question was a statically initialized collection thats sole purpose was to serve as a look-up table. edit: Incidentally, regarding the linked article, I would question many of the assumptions made. Most users are (to say the least) not frantically using every CPU cycle available anyhow, they are probably waiting for the network to do something. I don't think I'm wrong in saying there is a distinction in selecting the right tool for the job versus premature optimization. The memory subsystem is 10 to 100 times slower than the CPU, and if your data gets paged to disk, it's 1000 to 10,000 times slower. said, they are appropriate in just a small part of a program, yet they It pokes fun at time-wasting behavior by obsessively perfectionist coders who develop tools to analyze aspects of their software, such as performance. the premature optimization definition xkcd why root java example evil optimization - When is optimisation premature? Therefore, this flowchart has been prematurely optimized.173.245.56.69 11:02, 8 June 2016 (UTC), Is this also an implicit reference to https://xkcd.com/1205/ (Is It Worth the Time)?Dani (talk) 11:44, 8 June 2016 (UTC). So what’s my footnote? Making toys/playable demos is great when learning new concepts but you need to actually finish games to understand what's required to make something start to finish. As Knuth said, We should forget about small efficiencies, say about 97% of the time: premature optimization is the root of all evil. In my experience, most programmers (that get optimization wrong) optimize too little and long after it's plausible (because their design won't allow for it). Another question to ask yourself when optimising is "am I doing the equivalent of optimising for a 300 baud modem here?". But doing this has no use until you are certain which parts of code need this kind of optimization and optimizing will (could?) More details.. One of the groups of people he was criticizing who echo this "conventional wisdom" as he put of always ignoring efficiencies in the small are often misusing his quote which was originally directed, in part, against such types who discourage all forms of micro-optimization. Keep in mind how he used "optimized" in quotes (the software probably isn't actually efficient). Once they are poorly designed (this is what a design that doesn't consider optimization is no matter how you might try to hide behind the nonsense of premature optimization), is almost never able to recover from that becasue the database is too basic to the operation of the whole system. efficiencies, say 97% of the time; premature optimization is the root ... and then some more about the importance of profiling tools: It is often a mistake to make a priori judgments about what parts of a When programming, a number of parameters are vital. Remember: “Premature optimization is the root of all evil” (Donald Knuth). Premature optimization to me means trying to improve the efficiency of your code before you have a working system, and before you have actually profiled it and know where the bottleneck is. image credit: xkcd “ Premature optimization is the root of all evil “: the famous Knuth-ism that we all know and… well, that we all know.It’s hard to go a day of reading programming blogs without someone referencing this and leaving their particular footnote on it.I suppose today I am that someone. If you don't fit in the "pennywise-and-pound-foolish" category, then you aren't prematurely optimizing by Knuth's standards, even if you're using a goto in order to speed up a critical loop (something which is unlikely to help much against today's optimizers, but if it did, and in a genuinely critical area, then you wouldn't be prematurely optimizing). First time starting a page's explanation! (and so on). Probably not Douglas Hofstadter ( talk ) 15:11, 11 September 2019 (UTC) If premature optimization is the root of all evil, then the lack of planned performance during the design and implementation phases is the trunk, branches, and leaves of all evil. Also, first comment! Remember: “Premature optimization is the root of all evil” (Donald Knuth). pennywise-and-pound-foolish programmers, who can't debug or maintain 12% improvement, easily obtained, is never considered marginal; and I We should forget about small efficiencies, say about 97% of the time: premature optimization is the root of all evil. Other optimizations such as using sargeable code, selecting what look to be the best possible indexes, etc. but when it's a question of preparing quality programs, I don't want A good example: If you burn a week trying to optimize reflecting over an object before you have proof that it is a bottleneck you are prematurely optimizing. The way I see it is, if you optimize something without knowing how much performance you can gain in different scenario IS a premature optimization. believe the same viewpoint should prevail in software engineering. Don Knuth started the literate programming movement because he believed that the most important function of computer code is to communicate the programmer's intent to a human reader.Any coding practice that makes your code harder to understand in the name of performance is a premature optimization. Optimisations often introduce additional complexity into code which increases both the development and maintenance cost of that code. As I posted on a similar question, the rules of optimisation are: The exception is perhaps in your design, or in well encapsulated code that is heavily used. How to Be "Done Done" Make a little progress on every aspect of your work every day. Optimization can prove to have been a waste of time if parts of the program are later changed or discarded, or if the optimized code is only a small part of the workload. The goal of code should really making it easiest for human to read. This means you're free to copy and share these comics (but not to sell them). This means you're free to copy and share these comics (but not to sell them). We should forget about small efficiencies, say about 97% of the time: premature optimization is the root of all evil. Optimizing for space instead of speed in C++. premature optimization is the root of all evil. Making a routine 10 times faster doesn't help much if that routine is only consuming 1% of the running time to begin with and it may result in more complicated and buggier code. So what’s my footnote? Avoiding premature optimization is about picking your battles. Anything longer than that isn't usually optimisation, it's bug fixing. This is something which often comes up in Stack Overflow answers to questions like "which is the most efficient loop mechanism", "SQL optimisation techniques?" Firstly it's not true that Moore's law stopped working in the 90s. There is most definitely a time and place for optimisation. javascript required to view this site. often yield substantial savings. His quote was effectively a part of a big disclaimer, just like someone doing a motorcycle jump over a flaming fire pit might add a disclaimer that amateurs shouldn't try this at home while simultaneously criticizing those who try without proper knowledge and equipment and get hurt. I prefer to schedule performance, scalability, and similar issues with dedicated stories (see Performance Optimization in Chapter 9). Since it would be handy to keep that branch in mind, its removal is clearly premature. Rule 5 was previously stated by Fred Brooks in The Mythical Man-Month. XKCD tells it all. Alerted to the existence of the image by Tamino. Such loop There's something really offensive about attributing "premature optimization..." to xkcd, even as a joke. “Premature optimization is the root of all evil.” That quote by Donald Knuth gets repeated a lot in programming circles. My question is, if a particular Optimizing for memory footprint is often (though not always) called for. optimized. Plus there is an opportunity cost when programmer's time is diverted from implementing something else, to shaving a few milliseconds off something that the program does while the user is on the phone. Premature optimization can often end up backfiring, and cause you to waste a lot of resources, such as time, money, and effort, while also increasing the likelihood that you will create future problems. In, the federal definition of optimization in levels. intuitive guesses fail. Finally, to the frequently-quoted part: There is no doubt that the grail of efficiency leads to abuse. optimization - xkcd - When is optimisation premature? [...]. program are really critical, since the universal experience of if, say, the average value of n is about 20, and if the search routine But optimized code takes longer to write, and longer to maintain, and in this subideal world, we have limited time to spend on code. 过早优化效应 (Premature Optimization Effect) 普特定律 (Putt's Law) 里德定律 (Reed's Law) 复杂性守恒定律 (The Law of Conservation of Complexity or Tesler's Law) 得墨忒耳定律 (The Law of Demeter) ... XKCD 386: "Duty Calls" 邓巴数字 (Dunbar's Number) And typically, you the architect/designer/programmer/maintainer need clear and concise code in order to understand what is going on. Being cautious about memory consumption is more likely to provide major gains than optimizing individual instructions. image credit: xkcd “ Premature optimization is the root of all evil “: the famous Knuth-ism that we all know and… well, that we all know.It’s hard to go a day of reading programming blogs without someone referencing this and leaving their particular footnote on it.I suppose today I am that someone. debugging and maintenance are considered. My definition of premature optimisation is 'effort wasted on code that is not known to be a performance problem.' If I understand correctly, Mozilla is re-writing their layout engine in Rust, which should be considerably more secure than Blink (Chrome's engine). why. (Move immutable expressions outside of the loop body. So, the first line is only true because the very fact that you are asking a question about whether or not optimization is premature means that you are not sure that you need optimization, which by definition makes it premature. Phew. And those problems are hard to fix. If it's web application you're talking about, you can run it under load to see where the bottlenecks are - but the likelihood is that you will have the same scaling problems as most other sites, and the same solutions will apply. For example, premature optimization could involve someone spending a lot of time and money picking out the best possible gear for a certain hobby, despite the fact that they haven’t actually tried out that hobby to make sure they enjoy it. Posted on 12 September 2016 by ecoquant. Certain idioms that were introduced in the name of optimization have become so popular that everyone understands them and they have become expected, not premature. Their code actually needs tuning, or; Their techniques actually work. Pike's rules 1 and 2 restate Tony Hoare's famous maxim "Premature optimization is the root of all evil." Nit-picking about whether to use a divide expression or a shift expression isn't necessarily premature optimization. Last updated on November 12, 2020 Plutora Blog - Release Management Lean Software Development and the 7 Principles That Drive It Reading time 6 minutes. The figure is due to the irrepressible Randall Munroe. about, the speed of noncritical parts of their programs, and these It's worth noting that Knuth's original quote came from a paper he wrote promoting the use of goto in carefully selected and measured areas as a way to eliminate hotspots. Because it can't work well ever, so don't use quickness as a substitute for good code. Note that 'efficient' code is not necessarily the same as 'optimised' code. Programmers waste enormous amounts of time thinking about, or worrying Other teams include "Performance" and "Scalability" in their "done done" list, but these can lead to premature optimization. The conventional wisdom shared by many of today's software engineers ... premature optimization is the root of all evil (or at least most of it) in … parts of their programs are costing the most; indeed, this feedback The flow chart has no branches. Improve INSERT-per-second performance of SQLite? To quote the immortal words of xkcd: “ Premature optimization is the root of all evil. Here's a related article by Randall Hyde called The Fallacy of Premature Optimization. code that performs its intended function, quickly and completely with simplest logic reasonable.) – Jörg W Mittag Jul 27 '16 at 0:49 After working with such tools for seven years, premature optimisation? make the code harder to understand or maintain, hence "premature optimization is the root of all evil". Premature Optimizations means trying to optimize code without knowing if. In computing, program optimization is the practice of making a computer program work as quickly as possible, typically by designing it to perform the fewest calculations. only make sense to do at design time. I am not entirely sure how to classify design choices made before that (like using well-suited data structures), but I prefer to veer towards using abstractions taht are easy to program with rather than those who are well-performing, until I am at a stage where I can start using profiling and having a correct (though frequently slow) reference implementation to compare results with. Phew. B) Even after performing all possible optimizations, you won't meet your goal performance threshold, and the low-level optimizations don't make enough difference in performance to justify the loss of readability. course I wouldn't bother making such optimizations on a oneshot job, The first time I have ever heard about the concept of premature optimization was in one of my first year computer science classes. I've become convinced that all compilers written from now on should be My question is, if a particular technique is different but not particularly obscure or obfuscated, can that really be considered a premature optimisation? Last but not least it's premature to optimise before the program is going too slowly. Alerted to the existence of the image by Tamino. – Jörg W Mittag Jul 27 '16 at 0:49 The title text takes the joke a step further by proposing optimizing a brand new project by introducing a procedure to determine whether a possible optimization is premature - which is obviously a premature optimization. If a particular optimization is clear and concise, feel free to experiment with it (but do go back and check whether that optimization is effective). " Premature optimization " is the practice of trying to optimize parts of a program before such optimization has been shown to be needed. When writing code (or a DB query) I strive to write 'efficient' code (i.e. Don’t optimize unless you …

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