Details

Time bar (total: 9.1s)

analyze88.0ms (1%)

Algorithm
search
Search
TrueOtherFalseIter
0%2.1%97.9%0
0%2.1%97.9%1
1%1%97.9%2
1%1%97.9%3
1.5%0.5%97.9%4
1.5%0.5%97.9%5
1.8%0.3%97.9%6
1.8%0.3%97.9%7
1.9%0.1%97.9%8
1.9%0.1%97.9%9
2%0.1%97.9%10
2%0.1%97.9%11
2%0%97.9%12
2%0%97.9%13
2%0%97.9%14
Compiler

Compiled 50 to 36 computations (28% saved)

sample111.0ms (1.2%)

Algorithm
intervals
Results
31.0ms256×body128valid
9.0ms256×pre128true
Compiler

Compiled 87 to 63 computations (27.6% saved)

simplify59.0ms (0.6%)

Algorithm
egg-herbie
Rules
672×fma-neg_binary32
634×associate-*l*_binary32
530×associate-*r*_binary32
445×associate-/r*_binary32
406×*-commutative_binary32
Counts
1 → 2
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02653
16643
223735
386432
4257232
5389032
6429332
7487132
8487032

prune5.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
0.1b
Counts
3 → 2
Alt Table
StatusErrorProgram
0.6b
(*.f32 (/.f32 (/.f32 1/8 (*.f32 s (PI.f32))) r) (+.f32 (exp.f32 (/.f32 (neg.f32 r) s)) (pow.f32 (exp.f32 (/.f32 r s)) -1/3)))
0.2b
(+.f32 (/.f32 (*.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (*.f32 (*.f32 (*.f32 2 (PI.f32)) s) r)) (/.f32 (*.f32 3/4 (exp.f32 (/.f32 (neg.f32 r) (*.f32 3 s)))) (*.f32 (*.f32 (*.f32 6 (PI.f32)) s) r)))
Compiler

Compiled 169 to 117 computations (30.8% saved)

localize120.0ms (1.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(*.f32 (*.f32 (*.f32 2 (PI.f32)) s) r)
0.3b
(/.f32 (neg.f32 r) (*.f32 3 s))
0.3b
(*.f32 (*.f32 (*.f32 6 (PI.f32)) s) r)
0.3b
(*.f32 (*.f32 2 (PI.f32)) s)

series30.0ms (0.3%)

Counts
4 → 84
Calls

4 calls:

10.0ms
(/.f32 (neg.f32 r) (*.f32 3 s))
8.0ms
(*.f32 (*.f32 (*.f32 2 (PI.f32)) s) r)
8.0ms
(*.f32 (*.f32 (*.f32 6 (PI.f32)) s) r)
3.0ms
(*.f32 (*.f32 2 (PI.f32)) s)

rewrite24.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
32×add-cbrt-cube_binary32
32×add-exp-log_binary32
27×pow1_binary32
16×cbrt-unprod_binary32
16×prod-exp_binary32
Counts
4 → 105
Calls

4 calls:

6.0ms
(*.f32 (*.f32 (*.f32 6 (PI.f32)) s) r)
5.0ms
(*.f32 (*.f32 (*.f32 2 (PI.f32)) s) r)
4.0ms
(*.f32 (*.f32 2 (PI.f32)) s)
4.0ms
(/.f32 (neg.f32 r) (*.f32 3 s))

simplify88.0ms (1%)

Algorithm
egg-herbie
Rules
512×associate-/l*_binary32
418×associate-*l*_binary32
326×associate-/r*_binary32
318×distribute-rgt-neg-out_binary32
310×associate-*r*_binary32
Counts
189 → 153
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01872248
14421951
218851945
345711945
449351945

prune280.0ms (3.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New1485153
Fresh011
Picked101
Done000
Total1496155
Error
0.1b
Counts
155 → 6
Alt Table
StatusErrorProgram
0.1b
(+.f32 (/.f32 (*.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (*.f32 (*.f32 (*.f32 2 (PI.f32)) s) r)) (/.f32 (*.f32 3/4 (exp.f32 (/.f32 (neg.f32 (sqrt.f32 r)) (/.f32 s (/.f32 (sqrt.f32 r) 3))))) (*.f32 (*.f32 (*.f32 6 (PI.f32)) s) r)))
0.6b
(*.f32 (/.f32 (/.f32 1/8 (*.f32 s (PI.f32))) r) (+.f32 (exp.f32 (/.f32 (neg.f32 r) s)) (pow.f32 (exp.f32 (/.f32 r s)) -1/3)))
0.2b
(+.f32 (/.f32 (*.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (*.f32 (*.f32 (*.f32 (*.f32 2 (PI.f32)) (sqrt.f32 s)) (sqrt.f32 s)) r)) (/.f32 (*.f32 3/4 (exp.f32 (/.f32 (neg.f32 r) (*.f32 3 s)))) (*.f32 (*.f32 (*.f32 6 (PI.f32)) s) r)))
0.2b
(+.f32 (/.f32 (*.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (*.f32 (*.f32 (*.f32 2 (PI.f32)) s) r)) (/.f32 (*.f32 3/4 (exp.f32 (/.f32 (neg.f32 r) (*.f32 3 s)))) (*.f32 (*.f32 6 (PI.f32)) (*.f32 s r))))
0.2b
(+.f32 (/.f32 (*.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (*.f32 (*.f32 (*.f32 2 (PI.f32)) s) r)) (/.f32 (*.f32 3/4 (exp.f32 (/.f32 (neg.f32 r) (*.f32 3 s)))) (*.f32 (sqrt.f32 (*.f32 6 (*.f32 s (*.f32 (PI.f32) r)))) (sqrt.f32 (*.f32 6 (*.f32 s (*.f32 (PI.f32) r)))))))
0.1b
(+.f32 (/.f32 (*.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (*.f32 (*.f32 (*.f32 2 (PI.f32)) s) r)) (/.f32 (*.f32 3/4 (exp.f32 (*.f32 (neg.f32 r) (/.f32 1/3 s)))) (*.f32 (*.f32 (*.f32 6 (PI.f32)) s) r)))
Compiler

Compiled 6238 to 3599 computations (42.3% saved)

localize79.0ms (0.9%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(*.f32 (neg.f32 r) (/.f32 1/3 s))
0.3b
(*.f32 (*.f32 (*.f32 6 (PI.f32)) s) r)
0.3b
(*.f32 (*.f32 2 (PI.f32)) s)
0.4b
(/.f32 1/3 s)

series8.0ms (0.1%)

Counts
2 → 24
Calls

2 calls:

7.0ms
(*.f32 (neg.f32 r) (/.f32 1/3 s))
2.0ms
(/.f32 1/3 s)

rewrite12.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt_binary32
20×*-un-lft-identity_binary32
20×add-cube-cbrt_binary32
19×times-frac_binary32
13×associate-*r*_binary32
Counts
2 → 71
Calls

2 calls:

7.0ms
(*.f32 (neg.f32 r) (/.f32 1/3 s))
2.0ms
(/.f32 1/3 s)

simplify69.0ms (0.8%)

Algorithm
egg-herbie
Rules
711×fma-def_binary32
578×neg-mul-1_binary32
370×div-sub_binary32
356×distribute-rgt-neg-out_binary32
350×distribute-lft-neg-out_binary32
Counts
95 → 103
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0103975
1247880
2829876
32408876
43912876
55205876

prune309.0ms (3.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1603163
Fresh145
Picked101
Done000
Total1627169
Error
0.1b
Counts
169 → 7
Alt Table
StatusErrorProgram
24.6b
(+.f32 (/.f32 (*.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (*.f32 (*.f32 (*.f32 2 (PI.f32)) s) r)) (/.f32 (*.f32 3/4 (exp.f32 (*.f32 (neg.f32 r) (/.f32 1/3 s)))) (log.f32 (exp.f32 (*.f32 6 (*.f32 s (*.f32 (PI.f32) r)))))))
0.2b
(+.f32 (/.f32 (*.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (*.f32 (*.f32 (*.f32 (*.f32 2 (PI.f32)) (sqrt.f32 s)) (sqrt.f32 s)) r)) (/.f32 (*.f32 3/4 (exp.f32 (/.f32 (neg.f32 r) (*.f32 3 s)))) (*.f32 (*.f32 (*.f32 6 (PI.f32)) s) r)))
0.2b
(+.f32 (/.f32 (*.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (*.f32 (*.f32 (*.f32 2 (PI.f32)) s) r)) (/.f32 (*.f32 3/4 (exp.f32 (*.f32 (neg.f32 r) (/.f32 1/3 s)))) (*.f32 (*.f32 (*.f32 s (*.f32 (PI.f32) 6)) (*.f32 (cbrt.f32 r) (cbrt.f32 r))) (cbrt.f32 r))))
0.2b
(+.f32 (/.f32 (*.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (*.f32 (*.f32 (*.f32 2 (PI.f32)) s) r)) (/.f32 (*.f32 3/4 (exp.f32 (/.f32 (neg.f32 r) (*.f32 3 s)))) (*.f32 (sqrt.f32 (*.f32 6 (*.f32 s (*.f32 (PI.f32) r)))) (sqrt.f32 (*.f32 6 (*.f32 s (*.f32 (PI.f32) r)))))))
0.1b
(+.f32 (/.f32 (*.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (*.f32 (*.f32 (*.f32 2 (PI.f32)) s) r)) (/.f32 (*.f32 3/4 (exp.f32 (/.f32 (neg.f32 (sqrt.f32 r)) (/.f32 s (/.f32 (sqrt.f32 r) 3))))) (*.f32 (*.f32 (*.f32 6 (PI.f32)) s) r)))
0.6b
(*.f32 (/.f32 (/.f32 1/8 (*.f32 s (PI.f32))) r) (+.f32 (exp.f32 (/.f32 (neg.f32 r) s)) (pow.f32 (exp.f32 (/.f32 r s)) -1/3)))
0.1b
(+.f32 (/.f32 (*.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (*.f32 (*.f32 (*.f32 2 (PI.f32)) s) r)) (/.f32 (*.f32 3/4 (exp.f32 (*.f32 (neg.f32 r) (/.f32 1/3 s)))) (*.f32 (*.f32 6 (PI.f32)) (*.f32 s r))))
Compiler

Compiled 6810 to 4019 computations (41% saved)

localize76.0ms (0.8%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(*.f32 (*.f32 6 (PI.f32)) (*.f32 s r))
0.3b
(*.f32 (neg.f32 r) (/.f32 1/3 s))
0.3b
(*.f32 (*.f32 2 (PI.f32)) s)
0.4b
(/.f32 1/3 s)

series9.0ms (0.1%)

Counts
1 → 24
Calls

1 calls:

8.0ms
(*.f32 (*.f32 6 (PI.f32)) (*.f32 s r))

rewrite6.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
13×add-cbrt-cube_binary32
13×add-exp-log_binary32
13×pow1_binary32
cbrt-unprod_binary32
prod-exp_binary32
Counts
1 → 24
Calls

1 calls:

5.0ms
(*.f32 (*.f32 6 (PI.f32)) (*.f32 s r))

simplify66.0ms (0.7%)

Algorithm
egg-herbie
Rules
407×associate-/l/_binary32
395×*-commutative_binary32
338×sqr-pow_binary32
336×associate-/l*_binary32
287×associate-*r/_binary32
Counts
48 → 30
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
054665
1132565
2487565
3756565
41012565
51447565
62224565
73813565
84955565

prune324.0ms (3.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1601161
Fresh066
Picked101
Done000
Total1617168
Error
0.1b
Counts
168 → 7
Alt Table
StatusErrorProgram
24.6b
(+.f32 (/.f32 (*.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (*.f32 (*.f32 (*.f32 2 (PI.f32)) s) r)) (/.f32 (*.f32 3/4 (exp.f32 (*.f32 (neg.f32 r) (/.f32 1/3 s)))) (log.f32 (exp.f32 (*.f32 6 (*.f32 s (*.f32 (PI.f32) r)))))))
0.2b
(+.f32 (/.f32 (*.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (*.f32 (*.f32 (*.f32 (*.f32 2 (PI.f32)) (sqrt.f32 s)) (sqrt.f32 s)) r)) (/.f32 (*.f32 3/4 (exp.f32 (/.f32 (neg.f32 r) (*.f32 3 s)))) (*.f32 (*.f32 (*.f32 6 (PI.f32)) s) r)))
0.2b
(+.f32 (/.f32 (*.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (*.f32 (*.f32 (*.f32 2 (PI.f32)) s) r)) (/.f32 (*.f32 3/4 (exp.f32 (*.f32 (neg.f32 r) (/.f32 1/3 s)))) (*.f32 (*.f32 (*.f32 s (*.f32 (PI.f32) 6)) (*.f32 (cbrt.f32 r) (cbrt.f32 r))) (cbrt.f32 r))))
0.2b
(+.f32 (/.f32 (*.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (*.f32 (*.f32 (*.f32 2 (PI.f32)) s) r)) (/.f32 (*.f32 3/4 (exp.f32 (/.f32 (neg.f32 r) (*.f32 3 s)))) (*.f32 (sqrt.f32 (*.f32 6 (*.f32 s (*.f32 (PI.f32) r)))) (sqrt.f32 (*.f32 6 (*.f32 s (*.f32 (PI.f32) r)))))))
0.1b
(+.f32 (/.f32 (*.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (*.f32 (*.f32 (*.f32 2 (PI.f32)) s) r)) (/.f32 (*.f32 3/4 (exp.f32 (/.f32 (neg.f32 (sqrt.f32 r)) (/.f32 s (/.f32 (sqrt.f32 r) 3))))) (*.f32 (*.f32 (*.f32 6 (PI.f32)) s) r)))
0.6b
(*.f32 (/.f32 (/.f32 1/8 (*.f32 s (PI.f32))) r) (+.f32 (exp.f32 (/.f32 (neg.f32 r) s)) (pow.f32 (exp.f32 (/.f32 r s)) -1/3)))
0.2b
(+.f32 (/.f32 (*.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (*.f32 (*.f32 (*.f32 2 (PI.f32)) s) r)) (/.f32 (*.f32 3/4 (exp.f32 (*.f32 (*.f32 -1/3 r) (/.f32 1 s)))) (*.f32 (*.f32 6 (PI.f32)) (*.f32 s r))))
Compiler

Compiled 6743 to 3835 computations (43.1% saved)

localize89.0ms (1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(*.f32 (*.f32 (*.f32 6 (PI.f32)) s) r)
0.3b
(/.f32 (sqrt.f32 r) 3)
0.3b
(*.f32 (*.f32 2 (PI.f32)) s)
0.3b
(/.f32 (neg.f32 (sqrt.f32 r)) (/.f32 s (/.f32 (sqrt.f32 r) 3)))

series16.0ms (0.2%)

Counts
2 → 20
Calls

2 calls:

10.0ms
(/.f32 (neg.f32 (sqrt.f32 r)) (/.f32 s (/.f32 (sqrt.f32 r) 3)))
6.0ms
(/.f32 (sqrt.f32 r) 3)

rewrite293.0ms (3.2%)

Algorithm
rewrite-expression-head
Rules
3194×times-frac_binary32
1431×*-un-lft-identity_binary32
1431×add-sqr-sqrt_binary32
1431×add-cube-cbrt_binary32
903×sqrt-prod_binary32
Counts
2 → 1285
Calls

2 calls:

28.0ms
(/.f32 (neg.f32 (sqrt.f32 r)) (/.f32 s (/.f32 (sqrt.f32 r) 3)))
5.0ms
(/.f32 (sqrt.f32 r) 3)

simplify1.2s (13%)

Algorithm
egg-herbie
Rules
1021×associate-/r/_binary32
755×times-frac_binary32
490×div-sub_binary32
382×distribute-frac-neg_binary32
376×neg-mul-1_binary32
Counts
1305 → 1395
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0123048510
1305448017
2515848017

prune3.5s (38.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New145411455
Fresh066
Picked011
Done000
Total145481462
Error
0.1b
Counts
1462 → 8
Alt Table
StatusErrorProgram
24.6b
(+.f32 (/.f32 (*.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (*.f32 (*.f32 (*.f32 2 (PI.f32)) s) r)) (/.f32 (*.f32 3/4 (exp.f32 (*.f32 (neg.f32 r) (/.f32 1/3 s)))) (log.f32 (exp.f32 (*.f32 6 (*.f32 s (*.f32 (PI.f32) r)))))))
0.2b
(+.f32 (/.f32 (*.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (*.f32 (*.f32 (*.f32 (*.f32 2 (PI.f32)) (sqrt.f32 s)) (sqrt.f32 s)) r)) (/.f32 (*.f32 3/4 (exp.f32 (/.f32 (neg.f32 r) (*.f32 3 s)))) (*.f32 (*.f32 (*.f32 6 (PI.f32)) s) r)))
0.2b
(+.f32 (/.f32 (*.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (*.f32 (*.f32 (*.f32 2 (PI.f32)) s) r)) (/.f32 (*.f32 3/4 (exp.f32 (*.f32 (neg.f32 r) (/.f32 1/3 s)))) (*.f32 (*.f32 (*.f32 s (*.f32 (PI.f32) 6)) (*.f32 (cbrt.f32 r) (cbrt.f32 r))) (cbrt.f32 r))))
0.2b
(+.f32 (/.f32 (*.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (*.f32 (*.f32 (*.f32 2 (PI.f32)) s) r)) (/.f32 (*.f32 3/4 (exp.f32 (/.f32 (neg.f32 r) (*.f32 3 s)))) (*.f32 (sqrt.f32 (*.f32 6 (*.f32 s (*.f32 (PI.f32) r)))) (sqrt.f32 (*.f32 6 (*.f32 s (*.f32 (PI.f32) r)))))))
0.1b
(+.f32 (/.f32 (*.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (*.f32 (*.f32 (*.f32 2 (PI.f32)) s) r)) (/.f32 (*.f32 3/4 (exp.f32 (/.f32 (neg.f32 (sqrt.f32 r)) (/.f32 s (/.f32 (sqrt.f32 r) 3))))) (*.f32 (*.f32 (*.f32 6 (PI.f32)) s) r)))
0.3b
(+.f32 (/.f32 (*.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (*.f32 (*.f32 (*.f32 2 (PI.f32)) s) r)) (/.f32 (*.f32 3/4 (exp.f32 (/.f32 (neg.f32 (sqrt.f32 r)) (/.f32 s (/.f32 (sqrt.f32 r) 3))))) (exp.f32 (+.f32 (+.f32 (log.f32 (*.f32 6 (PI.f32))) (log.f32 s)) (log.f32 r)))))
0.6b
(*.f32 (/.f32 (/.f32 1/8 (*.f32 s (PI.f32))) r) (+.f32 (exp.f32 (/.f32 (neg.f32 r) s)) (pow.f32 (exp.f32 (/.f32 r s)) -1/3)))
0.2b
(+.f32 (/.f32 (*.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (*.f32 (*.f32 (*.f32 2 (PI.f32)) s) r)) (/.f32 (*.f32 3/4 (exp.f32 (*.f32 (*.f32 -1/3 r) (/.f32 1 s)))) (*.f32 (*.f32 6 (PI.f32)) (*.f32 s r))))
Compiler

Compiled 77065 to 39219 computations (49.1% saved)

regimes407.0ms (4.5%)

Accuracy

Total 0.1b remaining (54%)

Threshold costs 0.1b (54%)

Counts
104 → 1
Compiler

Compiled 12151 to 8752 computations (28% saved)

simplify4.0ms (0%)

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

Useful iterations: 2 (0.0ms)

IterNodesCost
02960
15060
26558
38058
48658
58858
68758

end1.0ms (0%)

Compiler

Compiled 38 to 27 computations (28.9% saved)

sample1.9s (20.4%)

Algorithm
intervals
Results
1.0s8000×body128valid
208.0ms8000×pre128true
Compiler

Compiled 393 to 280 computations (28.8% saved)

Profiling

Loading profile data...