Diff for "WesterBenchmarks"

Problem Key

→

simplify

A(...)

assume ...

S(...,x)

solve ... for x

T(...,x=b)

Taylor series of ... based at b

(p.v.)

principal value

(div)

divergent

Performance Key

×

wrong answer/cannot do the problem

s sec/ms/μs

performs correctly in time s

>s sec/ms/μs

does not finish in time s

>.<,s or >.<,×

very difficult to convince system to do what you want (regardless of performance)

Problem

Maple

Mathematica

GiNaC

Maxima

Sage

Symbolics

Notes (such as code used/version etc.)

√2√3+4→1+√3 

2∞−3→∞

ex−1ex/2+1→ex/2−1

A(x≥y,y≥z,z≥x);x=z?

A(x>y,y>0);2x2>2y2?

cosxcos(3x)→cos2x−3sin2x

cosxcos(3x)→2cos(2x)−1

A(x,y>0);x1/ny1/n−(xy)1/n→0

log(tan(21x+4π))−sinh−1(tan(x))→0

log2√r+1√4r+4√r+1→0

√x|z|√xy|z|2→√x√xy/→√y

Note √x=±√x

2x=0+1→2x+1=1

S(e2x+2ex+1=z,x)

S((x+1)(sin2x+1)2cos3(3x)=0,x)

M−1, where M=[[x,1],[y,ez]]

∑nk=1k3→4n2(n+1)2

∑∞k=1(1k2+1k3)→6π2+ζ(3)

∏nk=1k→n!

limn→∞(1+n1)n→e

limx→0xsinx→1

limx→0x21−cosx→21

d2dx2y(x(t))→dx2d2y(dtdx)2+dxdydt2d2x

ddx(∫1x3+2dx)→1x3+2 

∫1a+bcosxdx(a<b) 

ddx∫1a+bcosxdx=1a+bcosx 

ddx|x|→x|x|

∫|x|dx→2x|x| 

∫x√1+x+√1−xdx→3(1+x)3/2+(1−x)3/2 

∫2√1+x+√1−xdx→3(1+x)3/2+(1−x)3/2 

∫1−1x1dx→0  (p.v.)

∫1−11x2dx→  (div)

∫01√x+x1−2dx→34 

∫12√x+x1−2dx→34−√8 

∫02√x+x1−2dx→38−√8 

A(a>0); \int_{-\infty}^\infty\frac{\cos x}{x^2+a^2}dx \rightarrow \frac\pi ae^{-a}

A(0 < a < 1); \int_0^\infty\frac{t^{a-1}}{t+1}dt \rightarrow \frac{\pi}{\sin(\pi a)}

T(\frac1\sqrt{1-(x/c)^2},x=0)

T((\log x)^ae^{-bx},x=1)

T(\log(\sinh z) + \log(\cosh(z + w)))

T(\log(\frac{\sin x}{x}), x=0)