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⇤ ← Revision 1 as of 2008-08-12 09:13:38
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| Describe SymbolicBenchmarks here. | ||<-2> Problem Key || || $\rightarrow$ || simplify || || $A(...)$ || assume ... || ||<-2> Performance Key || || $\times$ || wrong answer/cannot do the problem || || $s\ sec/ms/\mu s$ || performs correctly in time $s$ || || $>.<, s$ || performs correctly in time $s$, very difficult to convince system to do what you want || || Problem || Maple || Mathematica || GiNaC || Maxima || Sage || Symbolics || Notes (such as code used/version etc.) || || $\sqrt{2\sqrt{3} + 4} \rightarrow 1 + \sqrt{3}$ || || || || || || || || || $2\infty - 3 \rightarrow \infty$ || || || || || || || || || $\frac{e^x-1}{e^{x/2}+1} \rightarrow e^{x/2} - 1$ || || || || || || || || || $A(x \geq y, y \geq z, z \geq x); x = z?$ || || || || || || || || || $A(x > y, y > 0); 2x^2 > 2y^2?$ || || || || || || || || || $\frac{\cos(3x)}{\cos x} \rightarrow \cos^2 x - 3\sin^2 x$ || || || || || || || || || $\frac{\cos(3x)}{\cos x} \rightarrow 2\cos(2x) - 1$ || || || || || || || || || $A(x,y > 0); x^{1/n}y^{1/n} - (xy)^{1/n} \rightarrow 0$ || || || || || || || || || $\log(\tan(\frac{1}{2}x + \frac{\pi}{4})) - \sinh^{-1}(\tan(x)) \rightarrow 0$ || || || || || || || || || $\log\frac{2\sqrt{r} + 1}{\sqrt{4r + 4\sqrt{r} + 1}} \rightarrow 0$ || || || || || || || || |
Problem Key |
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\rightarrow |
simplify |
A(...) |
assume ... |
Performance Key |
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\times |
wrong answer/cannot do the problem |
s\ sec/ms/\mu s |
performs correctly in time s |
>.<, s |
performs correctly in time s, very difficult to convince system to do what you want |
Problem |
Maple |
Mathematica |
GiNaC |
Maxima |
Sage |
Symbolics |
Notes (such as code used/version etc.) |
\sqrt{2\sqrt{3} + 4} \rightarrow 1 + \sqrt{3} |
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2\infty - 3 \rightarrow \infty |
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\frac{e^x-1}{e^{x/2}+1} \rightarrow e^{x/2} - 1 |
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A(x \geq y, y \geq z, z \geq x); x = z? |
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A(x > y, y > 0); 2x^2 > 2y^2? |
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\frac{\cos(3x)}{\cos x} \rightarrow \cos^2 x - 3\sin^2 x |
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\frac{\cos(3x)}{\cos x} \rightarrow 2\cos(2x) - 1 |
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A(x,y > 0); x^{1/n}y^{1/n} - (xy)^{1/n} \rightarrow 0 |
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\log(\tan(\frac{1}{2}x + \frac{\pi}{4})) - \sinh^{-1}(\tan(x)) \rightarrow 0 |
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\log\frac{2\sqrt{r} + 1}{\sqrt{4r + 4\sqrt{r} + 1}} \rightarrow 0 |
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