Details

Time bar (total: 29.8s)

analyze240.0ms (0.8%)

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)

sample139.0ms (0.5%)

Algorithm
intervals
Results
38.0ms256×body128valid
7.0ms256×pre128true
Compiler

Compiled 95 to 73 computations (23.2% saved)

simplify73.0ms (0.2%)

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

prune4.0ms (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)

localize76.0ms (0.3%)

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)
0.3b
(*.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)))
0.3b
(/.f32 (PI.f32) s)
0.3b
(/.f32 (neg.f32 (PI.f32)) s)

series1.2s (4%)

Counts
4 → 60
Calls

4 calls:

1.0s
(*.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)))
143.0ms
(+.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)
3.0ms
(/.f32 (neg.f32 (PI.f32)) s)
2.0ms
(/.f32 (PI.f32) s)

rewrite112.0ms (0.4%)

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:

42.0ms
(*.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)))
40.0ms
(+.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)
4.0ms
(/.f32 (neg.f32 (PI.f32)) s)
2.0ms
(/.f32 (PI.f32) s)

simplify193.0ms (0.7%)

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

prune410.0ms (1.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New2738281
Fresh000
Picked101
Done000
Total2748282
Error
0b
Counts
282 → 8
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))))
0.8b
(*.f32 (*.f32 (cbrt.f32 (*.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)))) (cbrt.f32 (*.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))))) (cbrt.f32 (*.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 (neg.f32 s) (log.f32 (*.f32 (sqrt.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)) (sqrt.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)))))
0.5b
(+.f32 (*.f32 (log.f32 (*.f32 (cbrt.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 (+.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 (cbrt.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))) (neg.f32 s)))
0.6b
(*.f32 (sqrt.f32 s) (*.f32 (neg.f32 (sqrt.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))))
0.4b
(+.f32 (*.f32 (neg.f32 s) (log1p.f32 (/.f32 1 (sqrt.f32 (+.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 (+.f32 (/.f32 1 (sqrt.f32 (+.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))))
0.3b
(*.f32 (neg.f32 s) (log.f32 (fma.f32 (/.f32 1 (+.f32 (pow.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) 3) (pow.f32 (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))) 3))) (+.f32 (*.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s))))) (-.f32 (*.f32 (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (*.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)))
0.8b
(*.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 19010 to 10590 computations (44.3% saved)

localize111.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(/.f32 1 (+.f32 (pow.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) 3) (pow.f32 (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))) 3)))
0.3b
(/.f32 (PI.f32) s)
0.3b
(/.f32 (neg.f32 (PI.f32)) s)
0.4b
(fma.f32 (/.f32 1 (+.f32 (pow.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) 3) (pow.f32 (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))) 3))) (+.f32 (*.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s))))) (-.f32 (*.f32 (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (*.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)

series1.9s (6.2%)

Counts
2 → 48
Calls

2 calls:

1.3s
(fma.f32 (/.f32 1 (+.f32 (pow.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) 3) (pow.f32 (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))) 3))) (+.f32 (*.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s))))) (-.f32 (*.f32 (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (*.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)
589.0ms
(/.f32 1 (+.f32 (pow.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) 3) (pow.f32 (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))) 3)))

rewrite169.0ms (0.6%)

Algorithm
rewrite-expression-head
Rules
792×*-un-lft-identity_binary32
379×times-frac_binary32
276×distribute-lft-out_binary32
144×cube-prod_binary32
144×unpow-prod-down_binary32
Counts
2 → 198
Calls

2 calls:

104.0ms
(/.f32 1 (+.f32 (pow.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) 3) (pow.f32 (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))) 3)))
0.0ms
(fma.f32 (/.f32 1 (+.f32 (pow.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) 3) (pow.f32 (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))) 3))) (+.f32 (*.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s))))) (-.f32 (*.f32 (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (*.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)

simplify428.0ms (1.4%)

Algorithm
egg-herbie
Rules
414×+-commutative_binary32
359×associate-+r+_binary32
328×*-commutative_binary32
325×fma-def_binary32
219×distribute-rgt-in_binary32
Counts
246 → 157
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0114332735
1399231352
2521731352

prune2.2s (7.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New5890589
Fresh077
Picked011
Done000
Total5898597
Error
0b
Counts
597 → 8
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))))
0.8b
(*.f32 (*.f32 (cbrt.f32 (*.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)))) (cbrt.f32 (*.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))))) (cbrt.f32 (*.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 (neg.f32 s) (log.f32 (*.f32 (sqrt.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)) (sqrt.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)))))
0.5b
(+.f32 (*.f32 (log.f32 (*.f32 (cbrt.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 (+.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 (cbrt.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))) (neg.f32 s)))
0.6b
(*.f32 (sqrt.f32 s) (*.f32 (neg.f32 (sqrt.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))))
0.4b
(+.f32 (*.f32 (neg.f32 s) (log1p.f32 (/.f32 1 (sqrt.f32 (+.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 (+.f32 (/.f32 1 (sqrt.f32 (+.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))))
0.3b
(*.f32 (neg.f32 s) (log.f32 (fma.f32 (/.f32 1 (+.f32 (pow.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) 3) (pow.f32 (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))) 3))) (+.f32 (*.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s))))) (-.f32 (*.f32 (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (*.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)))
0.8b
(*.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 81714 to 45111 computations (44.8% saved)

localize82.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(*.f32 (neg.f32 s) (log.f32 (*.f32 (sqrt.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)) (sqrt.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)
0.5b
(*.f32 (sqrt.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)) (sqrt.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)))

series1.2s (3.9%)

Counts
2 → 48
Calls

2 calls:

1.0s
(*.f32 (neg.f32 s) (log.f32 (*.f32 (sqrt.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)) (sqrt.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)))))
156.0ms
(*.f32 (sqrt.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)) (sqrt.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)))

rewrite210.0ms (0.7%)

Algorithm
rewrite-expression-head
Rules
50×sqrt-prod_binary32
48×add-sqr-sqrt_binary32
46×*-un-lft-identity_binary32
35×pow1_binary32
28×associate-*r*_binary32
Counts
2 → 126
Calls

2 calls:

94.0ms
(*.f32 (neg.f32 s) (log.f32 (*.f32 (sqrt.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)) (sqrt.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)))))
90.0ms
(*.f32 (sqrt.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)) (sqrt.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)))

simplify233.0ms (0.8%)

Algorithm
egg-herbie
Rules
641×associate-/l*_binary32
638×associate-/r*_binary32
445×fma-def_binary32
194×+-commutative_binary32
192×*-commutative_binary32
Counts
174 → 220
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
070015503
1231114695
2552614695

prune938.0ms (3.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New4351436
Fresh156
Picked101
Done011
Total4377444
Error
0b
Counts
444 → 7
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))))
0.8b
(*.f32 (*.f32 (cbrt.f32 (*.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)))) (cbrt.f32 (*.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))))) (cbrt.f32 (*.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)))))
0.6b
(*.f32 (sqrt.f32 s) (*.f32 (neg.f32 (sqrt.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))))
0.4b
(*.f32 (neg.f32 s) (log.f32 (*.f32 (sqrt.f32 (sqrt.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))) (pow.f32 (sqrt.f32 (sqrt.f32 (+.f32 -1 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (neg.f32 (/.f32 (PI.f32) s))))) (/.f32 (-.f32 1 u) (+.f32 (exp.f32 (/.f32 (PI.f32) s)) 1))))))) 3))))
0.4b
(+.f32 (*.f32 (neg.f32 s) (log1p.f32 (/.f32 1 (sqrt.f32 (+.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 (+.f32 (/.f32 1 (sqrt.f32 (+.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))))
0.3b
(*.f32 (neg.f32 s) (log.f32 (fma.f32 (/.f32 1 (+.f32 (pow.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) 3) (pow.f32 (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))) 3))) (+.f32 (*.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s))))) (-.f32 (*.f32 (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (*.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)))
0.8b
(*.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 34134 to 19151 computations (43.9% saved)

localize87.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f32 (neg.f32 s) (log.f32 (+.f32 (/.f32 1 (sqrt.f32 (+.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)))
0.3b
(/.f32 1 (sqrt.f32 (+.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)
0.3b
(*.f32 (neg.f32 s) (log1p.f32 (/.f32 1 (sqrt.f32 (+.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)))))))))

series12.7s (42.8%)

Counts
3 → 50
Calls

3 calls:

6.2s
(*.f32 (neg.f32 s) (log1p.f32 (/.f32 1 (sqrt.f32 (+.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)))))))))
5.6s
(*.f32 (neg.f32 s) (log.f32 (+.f32 (/.f32 1 (sqrt.f32 (+.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)))
864.0ms
(/.f32 1 (sqrt.f32 (+.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)))))))

rewrite110.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
231×*-un-lft-identity_binary32
117×times-frac_binary32
72×distribute-lft-out_binary32
55×add-sqr-sqrt_binary32
52×sqrt-prod_binary32
Counts
3 → 163
Calls

3 calls:

47.0ms
(*.f32 (neg.f32 s) (log.f32 (+.f32 (/.f32 1 (sqrt.f32 (+.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)))
33.0ms
(/.f32 1 (sqrt.f32 (+.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)))))))
4.0ms
(*.f32 (neg.f32 s) (log1p.f32 (/.f32 1 (sqrt.f32 (+.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)))))))))

simplify518.0ms (1.7%)

Algorithm
egg-herbie
Rules
725×fma-def_binary32
380×associate-/l*_binary32
336×associate-/r*_binary32
308×times-frac_binary32
34×sqr-pow_binary32
Counts
213 → 184
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0250357019
1516157019

prune2.0s (6.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New3880388
Fresh055
Picked011
Done011
Total3887395
Error
0b
Counts
395 → 7
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))))
0.8b
(*.f32 (*.f32 (cbrt.f32 (*.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)))) (cbrt.f32 (*.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))))) (cbrt.f32 (*.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)))))
0.6b
(*.f32 (sqrt.f32 s) (*.f32 (neg.f32 (sqrt.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))))
0.4b
(*.f32 (neg.f32 s) (log.f32 (*.f32 (sqrt.f32 (sqrt.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))) (pow.f32 (sqrt.f32 (sqrt.f32 (+.f32 -1 (/.f32 1 (+.f32 (/.f32 u (+.f32 1 (exp.f32 (neg.f32 (/.f32 (PI.f32) s))))) (/.f32 (-.f32 1 u) (+.f32 (exp.f32 (/.f32 (PI.f32) s)) 1))))))) 3))))
0.4b
(+.f32 (*.f32 (neg.f32 s) (log1p.f32 (/.f32 1 (sqrt.f32 (+.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 (+.f32 (/.f32 1 (sqrt.f32 (+.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))))
0.3b
(*.f32 (neg.f32 s) (log.f32 (fma.f32 (/.f32 1 (+.f32 (pow.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) 3) (pow.f32 (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))) 3))) (+.f32 (*.f32 (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s)))) (/.f32 u (+.f32 1 (exp.f32 (/.f32 (neg.f32 (PI.f32)) s))))) (-.f32 (*.f32 (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s)))) (/.f32 (-.f32 1 u) (+.f32 1 (exp.f32 (/.f32 (PI.f32) s))))) (*.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)))
0.8b
(*.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 88681 to 51670 computations (41.7% saved)

regimes2.2s (7.5%)

Accuracy

Total 0.3b remaining (83.1%)

Threshold costs 0.3b (83.1%)

Counts
388 → 1
Compiler

Compiled 67344 to 47996 computations (28.7% saved)

simplify18.0ms (0.1%)

Algorithm
egg-herbie
Rules
37×cancel-sign-sub-inv_binary32
32×distribute-rgt-neg-in_binary32
29×neg-sub0_binary32
29×neg-mul-1_binary32
22×distribute-lft-neg-in_binary32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
030155
152155
275155
394155
4109155
5123155
6127155
7144155
8159155
9171155
10189155
11200155
12214155
13228155
14240155
15247155
16249155
17245155

end1.0ms (0%)

Compiler

Compiled 96 to 57 computations (40.6% saved)

sample2.2s (7.5%)

Algorithm
intervals
Results
1.3s8000×body128valid
226.0ms8000×pre128true
Compiler

Compiled 615 to 411 computations (33.2% saved)

Profiling

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