Details

Time bar (total: 2.5min)

analyze474.0ms (0.3%)

Algorithm
search
Search
TrueOtherFalseIter
0%1.6%98.4%0
0%1.6%98.4%1
0%1.6%98.4%2
0.4%1.2%98.4%3
0.6%1%98.4%4
0.9%0.7%98.4%5
1%0.5%98.4%6
1.2%0.4%98.4%7
1.3%0.3%98.4%8
1.4%0.2%98.4%9
1.4%0.1%98.4%10
1.5%0.1%98.4%11
1.5%0.1%98.4%12
1.5%0%98.4%13
1.5%0%98.4%14
Compiler

Compiled 54 to 41 computations (24.1% saved)

sample2.9s (2%)

Results
2.8s8256×body128valid
Compiler

Compiled 147 to 112 computations (23.8% saved)

simplify94.0ms (0.1%)

Algorithm
egg-herbie
Rules
1145×fma-def_binary32
518×unswap-sqr_binary32
445×fma-neg_binary32
420×times-frac_binary32
354×associate-*l*_binary32
Counts
1 → 2
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
02259
14259
27259
312051
417948
531946
650546
778846
8124946
9258446
10441946
11483246
12482746

prune8.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
0.3b
Counts
3 → 1
Alt Table
StatusErrorProgram
0.3b
(*.f32 (neg.f32 s) (log.f32 (+.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1)))
Compiler

Compiled 127 to 93 computations (26.8% saved)

localize146.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(+.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1)
0.2b
(*.f32 (neg.f32 s) (log.f32 (+.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1)))
0.3b
(/.f32 (PI.f32) s)
0.3b
(/.f32 (neg.f32 (PI.f32)) s)

series1.8s (1.2%)

Counts
4 → 60
Calls

4 calls:

1.5s
(*.f32 (neg.f32 s) (log.f32 (+.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1)))
295.0ms
(+.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1)
5.0ms
(/.f32 (neg.f32 (PI.f32)) s)
4.0ms
(/.f32 (PI.f32) s)

rewrite214.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
207×*-un-lft-identity_binary32
129×times-frac_binary32
71×add-sqr-sqrt_binary32
57×distribute-lft-out_binary32
57×add-cube-cbrt_binary32
Counts
4 → 194
Calls

4 calls:

81.0ms
(+.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1)
74.0ms
(*.f32 (neg.f32 s) (log.f32 (+.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1)))
7.0ms
(/.f32 (neg.f32 (PI.f32)) s)
4.0ms
(/.f32 (PI.f32) s)

simplify236.0ms (0.2%)

Algorithm
egg-herbie
Rules
708×associate-/l*_binary32
454×fma-def_binary32
194×+-commutative_binary32
185×*-commutative_binary32
152×associate-+r+_binary32
Counts
254 → 281
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
076413367
1245812878
2504712878

prune738.0ms (0.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New2729281
Fresh000
Picked101
Done000
Total2739282
Error
0.0b
Counts
282 → 9
Alt Table
StatusErrorProgram
0.8b
(*.f32 (*.f32 (cbrt.f32 s) (cbrt.f32 s)) (*.f32 (neg.f32 (cbrt.f32 s)) (log.f32 (+.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1))))
16.6b
(cbrt.f32 (*.f32 (*.f32 (*.f32 (neg.f32 s) (neg.f32 s)) (neg.f32 s)) (*.f32 (*.f32 (log.f32 (+.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1)) (log.f32 (+.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1))) (log.f32 (+.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1)))))
0.3b
(*.f32 (neg.f32 s) (log.f32 (*.f32 (+.f32 (sqrt.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))))) 1) (-.f32 (sqrt.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))))) 1))))
0.3b
(*.f32 (neg.f32 s) (log.f32 (+.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (exp.f32 (log.f32 (/.f32 (PI.f32) s)))))))) -1)))
0.4b
(+.f32 (*.f32 (neg.f32 s) (*.f32 2 (log.f32 (cbrt.f32 (+.f32 -1 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (neg.f32 (/.f32 (PI.f32) s))))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))))))))) (*.f32 (neg.f32 s) (log.f32 (cbrt.f32 (+.f32 -1 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (neg.f32 (/.f32 (PI.f32) s))))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))))))))
0.4b
(+.f32 (*.f32 (log.f32 (+.f32 (sqrt.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))))) 1)) (neg.f32 s)) (*.f32 (log.f32 (-.f32 (sqrt.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))))) 1)) (neg.f32 s)))
0.3b
(*.f32 (neg.f32 s) (log.f32 (/.f32 (+.f32 (/.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (neg.f32 (/.f32 (PI.f32) s))))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) (+.f32 (/.f32 u (+.f32 1 (exp.f32 (neg.f32 (/.f32 (PI.f32) s))))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1) (+.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (neg.f32 (/.f32 (PI.f32) s))))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) 1))))
24.3b
(*.f32 (neg.f32 s) (log.f32 (log.f32 (exp.f32 (+.f32 -1 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (neg.f32 (/.f32 (PI.f32) s))))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))))))))
0.9b
(*.f32 (*.f32 (neg.f32 s) (*.f32 (cbrt.f32 (log.f32 (+.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1))) (cbrt.f32 (log.f32 (+.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1))))) (cbrt.f32 (log.f32 (+.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1))))
Compiler

Compiled 18982 to 10594 computations (44.2% saved)

localize185.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(/.f32 (PI.f32) s)
0.3b
(/.f32 (neg.f32 (PI.f32)) s)
0.4b
(log.f32 (/.f32 (PI.f32) s))
3.0b
(exp.f32 (log.f32 (/.f32 (PI.f32) s)))

series476.0ms (0.3%)

Counts
2 → 24
Calls

2 calls:

470.0ms
(log.f32 (/.f32 (PI.f32) s))
5.0ms
(exp.f32 (log.f32 (/.f32 (PI.f32) s)))

rewrite16.0ms (0%)

Algorithm
rewrite-expression-head
Rules
26×log-prod_binary32
18×times-frac_binary32
17×*-un-lft-identity_binary32
17×add-sqr-sqrt_binary32
17×add-cube-cbrt_binary32
Counts
2 → 54
Calls

2 calls:

6.0ms
(exp.f32 (log.f32 (/.f32 (PI.f32) s)))
4.0ms
(log.f32 (/.f32 (PI.f32) s))

simplify166.0ms (0.1%)

Algorithm
egg-herbie
Rules
752×fma-def_binary32
703×unsub-neg_binary32
465×fma-neg_binary32
331×distribute-rgt-in_binary32
281×times-frac_binary32
Counts
78 → 81
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
0106875
1151839
2307821
3659810
41751790
53609790
64885790
74965790
84962790

prune569.0ms (0.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1890189
Fresh088
Picked011
Done000
Total1899198
Error
0.0b
Counts
198 → 9
Alt Table
StatusErrorProgram
0.8b
(*.f32 (*.f32 (cbrt.f32 s) (cbrt.f32 s)) (*.f32 (neg.f32 (cbrt.f32 s)) (log.f32 (+.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1))))
16.6b
(cbrt.f32 (*.f32 (*.f32 (*.f32 (neg.f32 s) (neg.f32 s)) (neg.f32 s)) (*.f32 (*.f32 (log.f32 (+.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1)) (log.f32 (+.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1))) (log.f32 (+.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1)))))
0.3b
(*.f32 (neg.f32 s) (log.f32 (*.f32 (+.f32 (sqrt.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))))) 1) (-.f32 (sqrt.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))))) 1))))
0.3b
(*.f32 (neg.f32 s) (log.f32 (+.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (exp.f32 (log.f32 (/.f32 (PI.f32) s)))))))) -1)))
0.4b
(+.f32 (*.f32 (neg.f32 s) (*.f32 2 (log.f32 (cbrt.f32 (+.f32 -1 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (neg.f32 (/.f32 (PI.f32) s))))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))))))))) (*.f32 (neg.f32 s) (log.f32 (cbrt.f32 (+.f32 -1 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (neg.f32 (/.f32 (PI.f32) s))))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))))))))
0.4b
(+.f32 (*.f32 (log.f32 (+.f32 (sqrt.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))))) 1)) (neg.f32 s)) (*.f32 (log.f32 (-.f32 (sqrt.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))))) 1)) (neg.f32 s)))
0.3b
(*.f32 (neg.f32 s) (log.f32 (/.f32 (+.f32 (/.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (neg.f32 (/.f32 (PI.f32) s))))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) (+.f32 (/.f32 u (+.f32 1 (exp.f32 (neg.f32 (/.f32 (PI.f32) s))))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1) (+.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (neg.f32 (/.f32 (PI.f32) s))))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) 1))))
24.3b
(*.f32 (neg.f32 s) (log.f32 (log.f32 (exp.f32 (+.f32 -1 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (neg.f32 (/.f32 (PI.f32) s))))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))))))))
0.9b
(*.f32 (*.f32 (neg.f32 s) (*.f32 (cbrt.f32 (log.f32 (+.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1))) (cbrt.f32 (log.f32 (+.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1))))) (cbrt.f32 (log.f32 (+.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1))))
Compiler

Compiled 7825 to 4328 computations (44.7% saved)

localize94.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f32 (neg.f32 s) (log.f32 (/.f32 (+.f32 (/.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (neg.f32 (/.f32 (PI.f32) s))))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) (+.f32 (/.f32 u (+.f32 1 (exp.f32 (neg.f32 (/.f32 (PI.f32) s))))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1) (+.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (neg.f32 (/.f32 (PI.f32) s))))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) 1))))
0.2b
(/.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (neg.f32 (/.f32 (PI.f32) s))))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) (+.f32 (/.f32 u (+.f32 1 (exp.f32 (neg.f32 (/.f32 (PI.f32) s))))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))))
0.3b
(/.f32 (PI.f32) s)
0.5b
(/.f32 (+.f32 (/.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (neg.f32 (/.f32 (PI.f32) s))))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) (+.f32 (/.f32 u (+.f32 1 (exp.f32 (neg.f32 (/.f32 (PI.f32) s))))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1) (+.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (neg.f32 (/.f32 (PI.f32) s))))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) 1))

series2.4min (94.6%)

Calls

2 calls:

7.5s
(/.f32 (+.f32 (/.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (neg.f32 (/.f32 (PI.f32) s))))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) (+.f32 (/.f32 u (+.f32 1 (exp.f32 (neg.f32 (/.f32 (PI.f32) s))))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) -1) (+.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (neg.f32 (/.f32 (PI.f32) s))))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) 1))
1.2s
(/.f32 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (neg.f32 (/.f32 (PI.f32) s))))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))))) (+.f32 (/.f32 u (+.f32 1 (exp.f32 (neg.f32 (/.f32 (PI.f32) s))))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))))

Profiling

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