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| = The Symbolic Benchmark Challenge Suite = | See also [:SymbolicBenchmarks: this other page]. = The Symbolic Benchmark Suite = The conditions for something to be listed here: (a) it must be resemble an ''actual'' computation somebody actually wanted to do in Sage, and (b) the question must be precisely formulated with Sage code that uses the Sage symbolics in a straightforward way (i.e., don't cleverly use number fields). Do ''not'' post any "synthetic" benchmarks. This page is supposed to be about nailing down exactly why people consider the sage symbolics at present "so slow as to be completely useless for anything but fast float". == Problem 1 == SETUP: Define a function $f(z) = \sqrt{1/3}\cdot z^2 + i/3$. COMPUTATION: Compute the real part of $f(f(f(...(f(i/2))...)$ iterated $10$ times. {{{ # setup def f(z): return sqrt(1/3)*z^2 + i/3 # computation real(f(f(f(f(f(f(f(f(f(f(i/2))))))))))) // -15323490199844318074242473679071410934833494247466385771803570370858961112774390851798166656796902695599442662754502211584226105508648298600018090510170430216881977761279503642801008178271982531042720727178135881702924595044672634313417239327304576652633321095875724771887486594852083526001648217317718794685379391946143663292907934545842931411982264788766619812559999515408813796287448784343854980686798782575952258163992236113752353237705088451481168691158059505161807961082162315225057299394348203539002582692884735745377391416638540520323363224931163680324690025802009761307137504963304640835891588925883135078996398616361571065941964628043214890356454145039464055430143/(160959987592246947739944859375773744043416001841910423046466880402863187009126824419781711398533250016237703449459397319370100476216445123130147322940019839927628599479294678599689928643570237983736966305423831947366332466878486992676823215303312139985015592974537721140932243906832125049776934072927576666849331956351862828567668505777388133331284248870175178634054430823171923639987569211668426477739974572402853248951261366399284257908177157179099041115431335587887276292978004143353025122721401971549897673882099546646236790739903146970578001092018346524464799146331225822142880459202800229013082033028722077703362360159827236163041299500992177627657014103138377287073792*sqrt(3)) Time: CPU 0.11 s, Wall: 0.34 s }}} == Problem 2 == {{{ def hermite(n,y): if n == 1: return 2*y if n == 0: return 1 return 2*y*hermite(n-1,y) - 2*(n-1)*hermite(n-2,y) def phi(n,y): return 1/(sqrt(2^n*factorial(n))*pi^(1/4))*exp(-y^2/2)*hermite(n,y) time a = phi(25,4) // Time: CPU 0.59 s, Wall: 0.60 s }}} == Problem 3 == {{{ sage: var('x,y,z') sage: f = x+y+z sage: time for _ in range(10): a = bool(f==f) // CPU time: 0.09 s, Wall time: 0.52 s }}} |
See also [:SymbolicBenchmarks: this other page].
The Symbolic Benchmark Suite
The conditions for something to be listed here: (a) it must be resemble an actual computation somebody actually wanted to do in Sage, and (b) the question must be precisely formulated with Sage code that uses the Sage symbolics in a straightforward way (i.e., don't cleverly use number fields). Do not post any "synthetic" benchmarks. This page is supposed to be about nailing down exactly why people consider the sage symbolics at present "so slow as to be completely useless for anything but fast float".
Problem 1
SETUP: Define a function f(z) = \sqrt{1/3}\cdot z^2 + i/3. COMPUTATION: Compute the real part of f(f(f(...(f(i/2))...) iterated 10 times.
# setup def f(z): return sqrt(1/3)*z^2 + i/3 # computation real(f(f(f(f(f(f(f(f(f(f(i/2))))))))))) // -15323490199844318074242473679071410934833494247466385771803570370858961112774390851798166656796902695599442662754502211584226105508648298600018090510170430216881977761279503642801008178271982531042720727178135881702924595044672634313417239327304576652633321095875724771887486594852083526001648217317718794685379391946143663292907934545842931411982264788766619812559999515408813796287448784343854980686798782575952258163992236113752353237705088451481168691158059505161807961082162315225057299394348203539002582692884735745377391416638540520323363224931163680324690025802009761307137504963304640835891588925883135078996398616361571065941964628043214890356454145039464055430143/(160959987592246947739944859375773744043416001841910423046466880402863187009126824419781711398533250016237703449459397319370100476216445123130147322940019839927628599479294678599689928643570237983736966305423831947366332466878486992676823215303312139985015592974537721140932243906832125049776934072927576666849331956351862828567668505777388133331284248870175178634054430823171923639987569211668426477739974572402853248951261366399284257908177157179099041115431335587887276292978004143353025122721401971549897673882099546646236790739903146970578001092018346524464799146331225822142880459202800229013082033028722077703362360159827236163041299500992177627657014103138377287073792*sqrt(3)) Time: CPU 0.11 s, Wall: 0.34 s
Problem 2
def hermite(n,y):
if n == 1:
return 2*y
if n == 0:
return 1
return 2*y*hermite(n-1,y) - 2*(n-1)*hermite(n-2,y)
def phi(n,y):
return 1/(sqrt(2^n*factorial(n))*pi^(1/4))*exp(-y^2/2)*hermite(n,y)
time a = phi(25,4)
//
Time: CPU 0.59 s, Wall: 0.60 s
Problem 3
sage: var('x,y,z')
sage: f = x+y+z
sage: time for _ in range(10): a = bool(f==f)
//
CPU time: 0.09 s, Wall time: 0.52 s