Details

Time bar (total: 7.6s)

analyze95.0ms (1.3%)

Algorithm
search
Search
TrueOtherFalseIter
0%24.7%75.3%0
0%24.7%75.3%1
0%24.7%75.3%2
12.4%12.4%75.3%3
12.4%12.4%75.3%4
18.5%6.2%75.3%5
18.5%6.2%75.3%6
21.6%3.1%75.3%7
21.6%3.1%75.3%8
23.2%1.5%75.3%9
23.2%1.5%75.3%10
23.9%0.8%75.3%11
23.9%0.8%75.3%12
24.3%0.4%75.3%13
24.3%0.4%75.3%14
Compiler

Compiled 18 to 14 computations (22.2% saved)

sample1.3s (17.7%)

Results
1.3s8256×body128valid
Compiler

Compiled 47 to 37 computations (21.3% saved)

simplify56.0ms (0.7%)

Algorithm
egg-herbie
Rules
944×fma-neg_binary32
518×unswap-sqr_binary32
432×exp-prod_binary32
340×times-frac_binary32
333×associate-*l*_binary32
Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0914
11714
22714
33614
45014
57914
614714
726114
852814
9167614
10316014
11412114
12485014

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
0.1b
Counts
2 → 1
Alt Table
StatusErrorProgram
0.1b
(/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))
Compiler

Compiled 33 to 27 computations (18.2% saved)

localize21.0ms (0.3%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s)))
0.0b
(exp.f32 (/.f32 (neg.f32 x) s))
0.0b
(/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))

series33.0ms (0.4%)

Counts
3 → 72
Calls

3 calls:

22.0ms
(/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))
6.0ms
(+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s)))
5.0ms
(exp.f32 (/.f32 (neg.f32 x) s))

rewrite21.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
43×*-un-lft-identity_binary32
42×times-frac_binary32
34×exp-prod_binary32
33×add-sqr-sqrt_binary32
33×add-cube-cbrt_binary32
Counts
3 → 102
Calls

3 calls:

6.0ms
(exp.f32 (/.f32 (neg.f32 x) s))
6.0ms
(/.f32 1 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))
4.0ms
(+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s)))

simplify102.0ms (1.4%)

Algorithm
egg-herbie
Rules
727×fma-neg_binary32
322×associate-/l/_binary32
269×associate-/r/_binary32
197×distribute-rgt-neg-in_binary32
190×distribute-lft-neg-in_binary32
Counts
174 → 161
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01702521
13462365
28062311
324142287
448502287
550892287

prune185.0ms (2.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New1574161
Fresh000
Picked101
Done000
Total1584162
Error
0.0b
Counts
162 → 4
Alt Table
StatusErrorProgram
12.1b
(*.f32 (/.f32 1 (+.f32 1 (pow.f32 (exp.f32 (/.f32 x s)) -3))) (+.f32 (*.f32 1 1) (-.f32 (*.f32 (exp.f32 (/.f32 (neg.f32 x) s)) (exp.f32 (/.f32 (neg.f32 x) s))) (*.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))))
0.0b
(cbrt.f32 (/.f32 (*.f32 (*.f32 1 1) 1) (*.f32 (*.f32 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))) (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s)))) (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))))
23.4b
(fma.f32 (pow.f32 (/.f32 x s) 3) -1/48 (fma.f32 1/4 (/.f32 x s) 1/2))
12.1b
(*.f32 (/.f32 1 (+.f32 (pow.f32 1 3) (pow.f32 (exp.f32 (/.f32 (neg.f32 x) s)) 3))) (+.f32 (*.f32 1 1) (-.f32 (*.f32 (exp.f32 (/.f32 (neg.f32 x) s)) (exp.f32 (/.f32 (neg.f32 x) s))) (*.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))))
Compiler

Compiled 2859 to 1523 computations (46.7% saved)

localize44.0ms (0.6%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(exp.f32 (/.f32 (neg.f32 x) s))
0.0b
(/.f32 (*.f32 (*.f32 1 1) 1) (*.f32 (*.f32 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))) (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s)))) (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s)))))
0.0b
(*.f32 (*.f32 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))) (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s)))) (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))
0.0b
(*.f32 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))) (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))

series89.0ms (1.2%)

Counts
3 → 72
Calls

3 calls:

59.0ms
(/.f32 (*.f32 (*.f32 1 1) 1) (*.f32 (*.f32 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))) (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s)))) (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s)))))
17.0ms
(*.f32 (*.f32 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))) (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s)))) (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))
13.0ms
(*.f32 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))) (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))

rewrite83.0ms (1.1%)

Algorithm
rewrite-expression-head
Rules
124×add-exp-log_binary32
91×prod-exp_binary32
60×flip-+_binary32
60×frac-times_binary32
60×flip3-+_binary32
Counts
3 → 185
Calls

3 calls:

23.0ms
(/.f32 (*.f32 (*.f32 1 1) 1) (*.f32 (*.f32 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))) (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s)))) (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s)))))
16.0ms
(*.f32 (*.f32 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))) (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s)))) (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))
12.0ms
(*.f32 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))) (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))

simplify146.0ms (1.9%)

Algorithm
egg-herbie
Rules
470×times-frac_binary32
374×associate-+l+_binary32
367×associate-/r*_binary32
249×associate-/l*_binary32
227×distribute-rgt-in_binary32
Counts
257 → 261
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02117526
15436073
217865818
351335818

prune585.0ms (7.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New4584462
Fresh213
Picked101
Done000
Total4615466
Error
0.0b
Counts
466 → 5
Alt Table
StatusErrorProgram
15.7b
(cbrt.f32 (/.f32 (*.f32 (*.f32 1 1) 1) (*.f32 (*.f32 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))) (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s)))) (+.f32 1 (pow.f32 (exp.f32 (sqrt.f32 (neg.f32 (/.f32 x s)))) (sqrt.f32 (/.f32 (neg.f32 x) s)))))))
0.5b
(cbrt.f32 (log.f32 (exp.f32 (/.f32 1 (pow.f32 (+.f32 1 (exp.f32 (neg.f32 (/.f32 x s)))) 3)))))
12.1b
(*.f32 (/.f32 1 (+.f32 1 (pow.f32 (exp.f32 (/.f32 x s)) -3))) (+.f32 (*.f32 1 1) (-.f32 (*.f32 (exp.f32 (/.f32 (neg.f32 x) s)) (exp.f32 (/.f32 (neg.f32 x) s))) (*.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))))))
0.1b
(cbrt.f32 (/.f32 (*.f32 (*.f32 1 1) 1) (*.f32 (pow.f32 (sqrt.f32 (+.f32 1 (exp.f32 (neg.f32 (/.f32 x s))))) 3) (pow.f32 (sqrt.f32 (+.f32 1 (exp.f32 (neg.f32 (/.f32 x s))))) 3))))
0.0b
(cbrt.f32 (/.f32 (*.f32 (*.f32 1 1) 1) (exp.f32 (*.f32 3 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))))))
Compiler

Compiled 19639 to 9694 computations (50.6% saved)

localize42.0ms (0.6%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(/.f32 (*.f32 (*.f32 1 1) 1) (exp.f32 (*.f32 3 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s)))))))
0.0b
(*.f32 3 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s)))))
0.1b
(exp.f32 (*.f32 3 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))))
1.3b
(log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))

series1.5s (19.6%)

Counts
4 → 96
Calls

4 calls:

421.0ms
(*.f32 3 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s)))))
398.0ms
(/.f32 (*.f32 (*.f32 1 1) 1) (exp.f32 (*.f32 3 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s)))))))
332.0ms
(log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))
330.0ms
(exp.f32 (*.f32 3 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))))

rewrite16.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
22×add-exp-log_binary32
19×prod-exp_binary32
15×add-cbrt-cube_binary32
13×1-exp_binary32
11×div-exp_binary32
Counts
4 → 76
Calls

4 calls:

7.0ms
(/.f32 (*.f32 (*.f32 1 1) 1) (exp.f32 (*.f32 3 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s)))))))
3.0ms
(*.f32 3 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s)))))
1.0ms
(exp.f32 (*.f32 3 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))))
0.0ms
(log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))

simplify112.0ms (1.5%)

Algorithm
egg-herbie
Rules
845×fma-def_binary32
612×fma-neg_binary32
247×distribute-rgt-neg-in_binary32
242×distribute-lft-neg-in_binary32
198×distribute-neg-frac_binary32
Counts
172 → 146
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01423106
13232729
27362583
325232510
447922510
549202510

prune208.0ms (2.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New1433146
Fresh314
Picked101
Done000
Total1474151
Error
0.0b
Counts
151 → 4
Alt Table
StatusErrorProgram
15.7b
(cbrt.f32 (/.f32 (*.f32 (*.f32 1 1) 1) (*.f32 (*.f32 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))) (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s)))) (+.f32 1 (pow.f32 (exp.f32 (sqrt.f32 (neg.f32 (/.f32 x s)))) (sqrt.f32 (/.f32 (neg.f32 x) s)))))))
0.0b
(cbrt.f32 (/.f32 (/.f32 1 (pow.f32 (+.f32 1 (exp.f32 (neg.f32 (/.f32 x s)))) 3/2)) (sqrt.f32 (exp.f32 (*.f32 3 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s)))))))))
0.0b
(cbrt.f32 (*.f32 (sqrt.f32 (pow.f32 (+.f32 1 (exp.f32 (neg.f32 (/.f32 x s)))) -3)) (sqrt.f32 (pow.f32 (+.f32 1 (exp.f32 (neg.f32 (/.f32 x s)))) -3))))
0.1b
(cbrt.f32 (/.f32 (*.f32 (*.f32 1 1) 1) (exp.f32 (expm1.f32 (log1p.f32 (*.f32 3 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))))))))
Compiler

Compiled 3313 to 2126 computations (35.8% saved)

localize51.0ms (0.7%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(/.f32 1 (pow.f32 (+.f32 1 (exp.f32 (neg.f32 (/.f32 x s)))) 3/2))
0.0b
(*.f32 3 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s)))))
0.1b
(exp.f32 (*.f32 3 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))))
1.3b
(log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))

series73.0ms (1%)

Counts
1 → 24
Calls

1 calls:

73.0ms
(/.f32 1 (pow.f32 (+.f32 1 (exp.f32 (neg.f32 (/.f32 x s)))) 3/2))

rewrite10.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
26×*-un-lft-identity_binary32
24×times-frac_binary32
18×add-sqr-sqrt_binary32
18×add-cube-cbrt_binary32
16×unpow-prod-down_binary32
Counts
1 → 59
Calls

1 calls:

7.0ms
(/.f32 1 (pow.f32 (+.f32 1 (exp.f32 (neg.f32 (/.f32 x s)))) 3/2))

simplify102.0ms (1.4%)

Algorithm
egg-herbie
Rules
765×times-frac_binary32
636×fma-neg_binary32
383×associate-/l*_binary32
303×associate-/r*_binary32
234×associate-*r*_binary32
Counts
83 → 72
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01082208
12302138
27022014
341591963
449871963
549291963

prune343.0ms (4.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New1591160
Fresh033
Picked011
Done000
Total1595164
Error
0.0b
Counts
164 → 5
Alt Table
StatusErrorProgram
15.7b
(cbrt.f32 (/.f32 (*.f32 (*.f32 1 1) 1) (*.f32 (*.f32 (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s))) (+.f32 1 (exp.f32 (/.f32 (neg.f32 x) s)))) (+.f32 1 (pow.f32 (exp.f32 (sqrt.f32 (neg.f32 (/.f32 x s)))) (sqrt.f32 (/.f32 (neg.f32 x) s)))))))
0.0b
(cbrt.f32 (/.f32 (/.f32 1 (pow.f32 (+.f32 1 (exp.f32 (neg.f32 (/.f32 x s)))) 3/2)) (sqrt.f32 (exp.f32 (*.f32 3 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s)))))))))
0.2b
(cbrt.f32 (/.f32 (*.f32 (/.f32 1 (pow.f32 (*.f32 (cbrt.f32 (+.f32 1 (exp.f32 (neg.f32 (/.f32 x s))))) (cbrt.f32 (+.f32 1 (exp.f32 (neg.f32 (/.f32 x s)))))) 3/2)) (/.f32 1 (pow.f32 (cbrt.f32 (+.f32 1 (exp.f32 (neg.f32 (/.f32 x s))))) 3/2))) (sqrt.f32 (exp.f32 (*.f32 3 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s)))))))))
0.0b
(cbrt.f32 (*.f32 (sqrt.f32 (pow.f32 (+.f32 1 (exp.f32 (neg.f32 (/.f32 x s)))) -3)) (sqrt.f32 (pow.f32 (+.f32 1 (exp.f32 (neg.f32 (/.f32 x s)))) -3))))
0.1b
(cbrt.f32 (/.f32 (*.f32 (*.f32 1 1) 1) (exp.f32 (expm1.f32 (log1p.f32 (*.f32 3 (log1p.f32 (exp.f32 (neg.f32 (/.f32 x s))))))))))
Compiler

Compiled 5129 to 2975 computations (42% saved)

regimes2.2s (29.3%)

Accuracy

Total 0.0b remaining (13.1%)

Threshold costs 0.0b (13.1%)

Counts
264 → 1
Compiler

Compiled 46602 to 34340 computations (26.3% saved)

simplify3.0ms (0%)

Algorithm
egg-herbie
Rules
*-commutative_binary32
+-commutative_binary32
sub-neg_binary32
neg-sub0_binary32
neg-mul-1_binary32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01533
12533
22933
33233
43333
53233

end107.0ms (1.4%)

Compiler

Compiled 200 to 140 computations (30% saved)

Profiling

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