Details

Time bar (total: 13.2s)

analyze306.0ms (2.3%)

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 44 to 32 computations (27.3% saved)

sample117.0ms (0.9%)

Algorithm
intervals
Results
73.0ms256×body128valid
10.0ms256×pre128true
Compiler

Compiled 81 to 59 computations (27.2% saved)

simplify123.0ms (0.9%)

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

Useful iterations: 3 (0.0ms)

IterNodesCost
02653
16645
223535
385032
4252432
5376232
6402932
7442632
8475632
9485732
10478332

prune18.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
0.1b
Counts
2 → 2
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 r) (*.f32 3 s)))) (*.f32 (*.f32 (*.f32 6 PI.f32) s) r)))
1.3b
(*.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)))
Compiler

Compiled 136 to 98 computations (27.9% saved)

localize216.0ms (1.6%)

Local error

Found 4 expressions with local error:

0.2b
(/.f32 (neg.f32 r) (*.f32 3 s))
0.3b
(*.f32 (*.f32 (*.f32 6 PI.f32) s) r)
0.3b
(*.f32 (*.f32 (*.f32 2 PI.f32) s) r)
0.3b
(*.f32 (*.f32 2 PI.f32) s)

rewrite602.0ms (4.6%)

Algorithm
rewrite-expression-head
Error
0.1b
Rules
32×add-cbrt-cube_binary32
32×add-exp-log_binary32
27×pow1_binary32
16×cbrt-unprod_binary32
16×prod-exp_binary32
Counts
4 → 97
Calls

4 calls:

11.0ms
(*.f32 (*.f32 (*.f32 2 PI.f32) s) r)
11.0ms
(*.f32 (*.f32 (*.f32 6 PI.f32) s) r)
9.0ms
(/.f32 (neg.f32 r) (*.f32 3 s))
8.0ms
(*.f32 (*.f32 2 PI.f32) s)
Compiler

Compiled 3367 to 1941 computations (42.4% saved)

series259.0ms (2%)

Error
0.1b
Counts
4 → 21
Calls

4 calls:

64.0ms
(*.f32 (*.f32 (*.f32 6 PI.f32) s) r)
62.0ms
(*.f32 (*.f32 (*.f32 2 PI.f32) s) r)
60.0ms
(/.f32 (neg.f32 r) (*.f32 3 s))
30.0ms
(*.f32 (*.f32 2 PI.f32) s)
Compiler

Compiled 1591 to 1130 computations (29% saved)

simplify144.0ms (1.1%)

Algorithm
egg-herbie
Rules
802×associate-/l*_binary32
420×associate-*l*_binary32
342×distribute-rgt-neg-out_binary32
309×associate-*r*_binary32
223×distribute-lft-neg-out_binary32
Counts
118 → 101
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01972412
14901951
221641798
351491798

prune361.0ms (2.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New965101
Fresh011
Picked101
Done000
Total976103
Error
0.1b
Counts
103 → 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 (cbrt.f32 (*.f32 -1/27 (pow.f32 (/.f32 r s) 3))))) (*.f32 (*.f32 (*.f32 6 PI.f32) s) 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 3 s)))) (*.f32 (*.f32 (*.f32 s (*.f32 PI.f32 6)) (sqrt.f32 r)) (sqrt.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 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)))) (exp.f32 (log.f32 (*.f32 r (*.f32 s (*.f32 PI.f32 6)))))))
0.2b
(*.f32 (/.f32 1/8 (*.f32 s PI.f32)) (+.f32 (/.f32 (exp.f32 (/.f32 (neg.f32 r) s)) r) (/.f32 (pow.f32 (exp.f32 -1/3) (/.f32 r s)) r)))
1.3b
(*.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)))
Compiler

Compiled 2276 to 1354 computations (40.5% saved)

localize226.0ms (1.7%)

Local error

Found 4 expressions with local error:

0.3b
(*.f32 (*.f32 (*.f32 2 PI.f32) s) r)
0.3b
(*.f32 (*.f32 2 PI.f32) s)
0.5b
(*.f32 -1/27 (pow.f32 (/.f32 r s) 3))
16.4b
(cbrt.f32 (*.f32 -1/27 (pow.f32 (/.f32 r s) 3)))

rewrite560.0ms (4.2%)

Algorithm
rewrite-expression-head
Error
0.1b
Rules
38×associate-*r*_binary32
35×add-sqr-sqrt_binary32
26×add-exp-log_binary32
22×*-un-lft-identity_binary32
22×add-cube-cbrt_binary32
Counts
4 → 104
Calls

4 calls:

23.0ms
(*.f32 -1/27 (pow.f32 (/.f32 r s) 3))
15.0ms
(cbrt.f32 (*.f32 -1/27 (pow.f32 (/.f32 r s) 3)))
13.0ms
(*.f32 (*.f32 (*.f32 2 PI.f32) s) r)
8.0ms
(*.f32 (*.f32 2 PI.f32) s)
Compiler

Compiled 3420 to 2080 computations (39.2% saved)

series321.0ms (2.4%)

Error
0.1b
Counts
4 → 21
Calls

4 calls:

100.0ms
(cbrt.f32 (*.f32 -1/27 (pow.f32 (/.f32 r s) 3)))
89.0ms
(*.f32 -1/27 (pow.f32 (/.f32 r s) 3))
69.0ms
(*.f32 (*.f32 (*.f32 2 PI.f32) s) r)
32.0ms
(*.f32 (*.f32 2 PI.f32) s)
Compiler

Compiled 1739 to 1299 computations (25.3% saved)

simplify159.0ms (1.2%)

Algorithm
egg-herbie
Rules
829×times-frac_binary32
681×associate-/l*_binary32
331×associate-*l*_binary32
267×associate-*r*_binary32
140×associate-/l/_binary32
Counts
125 → 90
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02052585
14852322
221232056
351042056

prune273.0ms (2.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New89190
Fresh145
Picked011
Done000
Total90696
Error
0.1b
Counts
96 → 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 (cbrt.f32 (*.f32 -1/27 (pow.f32 (/.f32 r s) 3))))) (*.f32 (*.f32 (*.f32 6 PI.f32) s) 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 3 s)))) (*.f32 (*.f32 (*.f32 s (*.f32 PI.f32 6)) (sqrt.f32 r)) (sqrt.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 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)))) (exp.f32 (log.f32 (*.f32 r (*.f32 s (*.f32 PI.f32 6)))))))
1.3b
(*.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 1/8 (*.f32 s PI.f32)) (+.f32 (/.f32 (exp.f32 (/.f32 (neg.f32 r) s)) r) (/.f32 (exp.f32 (cbrt.f32 (*.f32 -1/27 (pow.f32 (/.f32 r s) 3)))) r)))
Compiler

Compiled 1929 to 1200 computations (37.8% saved)

localize154.0ms (1.2%)

Local error

Found 4 expressions with local error:

0.3b
(pow.f32 (/.f32 r s) 3)
0.3b
(*.f32 s PI.f32)
0.5b
(*.f32 -1/27 (pow.f32 (/.f32 r s) 3))
16.4b
(cbrt.f32 (*.f32 -1/27 (pow.f32 (/.f32 r s) 3)))

rewrite532.0ms (4%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
52×add-sqr-sqrt_binary32
38×times-frac_binary32
37×*-un-lft-identity_binary32
37×add-cube-cbrt_binary32
35×associate-*r*_binary32
Counts
4 → 129
Calls

4 calls:

21.0ms
(*.f32 -1/27 (pow.f32 (/.f32 r s) 3))
12.0ms
(cbrt.f32 (*.f32 -1/27 (pow.f32 (/.f32 r s) 3)))
9.0ms
(*.f32 s PI.f32)
8.0ms
(pow.f32 (/.f32 r s) 3)
Compiler

Compiled 3012 to 1434 computations (52.4% saved)

series268.0ms (2%)

Error
0.1b
Counts
4 → 21
Calls

4 calls:

85.0ms
(cbrt.f32 (*.f32 -1/27 (pow.f32 (/.f32 r s) 3)))
76.0ms
(*.f32 -1/27 (pow.f32 (/.f32 r s) 3))
65.0ms
(pow.f32 (/.f32 r s) 3)
25.0ms
(*.f32 s PI.f32)
Compiler

Compiled 1268 to 928 computations (26.8% saved)

simplify331.0ms (2.5%)

Algorithm
egg-herbie
Rules
732×associate-/l*_binary32
655×associate-/r*_binary32
346×unswap-sqr_binary32
221×associate-/l/_binary32
151×associate-*l*_binary32
Counts
150 → 102
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01882484
14472283
216862243
351022243

prune235.0ms (1.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New1011102
Fresh044
Picked011
Done101
Total1026108
Error
0.1b
Counts
108 → 6
Alt Table
StatusErrorProgram
0.2b
(*.f32 (/.f32 1/8 (*.f32 (*.f32 (cbrt.f32 s) (cbrt.f32 s)) (*.f32 PI.f32 (cbrt.f32 s)))) (+.f32 (/.f32 (exp.f32 (/.f32 (neg.f32 r) s)) r) (/.f32 (exp.f32 (cbrt.f32 (*.f32 -1/27 (pow.f32 (/.f32 r s) 3)))) r)))
0.1b
(*.f32 (/.f32 1/8 (*.f32 s PI.f32)) (+.f32 (/.f32 (exp.f32 (/.f32 (neg.f32 r) s)) r) (/.f32 (exp.f32 (cbrt.f32 (*.f32 -1/27 (pow.f32 (/.f32 r s) 3)))) 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 3 s)))) (*.f32 (*.f32 (*.f32 s (*.f32 PI.f32 6)) (sqrt.f32 r)) (sqrt.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 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)))) (exp.f32 (log.f32 (*.f32 r (*.f32 s (*.f32 PI.f32 6)))))))
1.3b
(*.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)))
Compiler

Compiled 1570 to 812 computations (48.3% saved)

localize224.0ms (1.7%)

Local error

Found 4 expressions with local error:

0.3b
(*.f32 (*.f32 (*.f32 2 PI.f32) s) r)
0.3b
(*.f32 (*.f32 s (*.f32 PI.f32 6)) (sqrt.f32 r))
0.3b
(*.f32 (*.f32 (*.f32 s (*.f32 PI.f32 6)) (sqrt.f32 r)) (sqrt.f32 r))
0.3b
(*.f32 (*.f32 2 PI.f32) s)

rewrite545.0ms (4.1%)

Algorithm
rewrite-expression-head
Error
0.0b
Rules
41×add-cbrt-cube_binary32
41×add-exp-log_binary32
41×pow1_binary32
25×cbrt-unprod_binary32
25×prod-exp_binary32
Counts
4 → 90
Calls

4 calls:

17.0ms
(*.f32 (*.f32 (*.f32 s (*.f32 PI.f32 6)) (sqrt.f32 r)) (sqrt.f32 r))
14.0ms
(*.f32 (*.f32 s (*.f32 PI.f32 6)) (sqrt.f32 r))
10.0ms
(*.f32 (*.f32 (*.f32 2 PI.f32) s) r)
9.0ms
(*.f32 (*.f32 2 PI.f32) s)
Compiler

Compiled 3408 to 1838 computations (46.1% saved)

series316.0ms (2.4%)

Error
0.1b
Counts
4 → 21
Calls

4 calls:

96.0ms
(*.f32 (*.f32 2 PI.f32) s)
67.0ms
(*.f32 (*.f32 s (*.f32 PI.f32 6)) (sqrt.f32 r))
65.0ms
(*.f32 (*.f32 (*.f32 s (*.f32 PI.f32 6)) (sqrt.f32 r)) (sqrt.f32 r))
64.0ms
(*.f32 (*.f32 (*.f32 2 PI.f32) s) r)
Compiler

Compiled 1788 to 1241 computations (30.6% saved)

simplify216.0ms (1.6%)

Algorithm
egg-herbie
Rules
595×times-frac_binary32
570×associate-*l*_binary32
486×associate-/l*_binary32
400×associate-*r*_binary32
215×exp-prod_binary32
Counts
111 → 83
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01832523
15102077
222322068
344612068
449492068
549432068

prune179.0ms (1.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New82183
Fresh134
Picked101
Done011
Total84589
Error
0.1b
Counts
89 → 5
Alt Table
StatusErrorProgram
0.2b
(*.f32 (/.f32 1/8 (*.f32 (*.f32 (cbrt.f32 s) (cbrt.f32 s)) (*.f32 PI.f32 (cbrt.f32 s)))) (+.f32 (/.f32 (exp.f32 (/.f32 (neg.f32 r) s)) r) (/.f32 (exp.f32 (cbrt.f32 (*.f32 -1/27 (pow.f32 (/.f32 r s) 3)))) r)))
0.1b
(*.f32 (/.f32 1/8 (*.f32 s PI.f32)) (+.f32 (/.f32 (exp.f32 (/.f32 (neg.f32 r) s)) r) (/.f32 (exp.f32 (cbrt.f32 (*.f32 -1/27 (pow.f32 (/.f32 r s) 3)))) 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)))) (exp.f32 (log.f32 (*.f32 r (*.f32 s (*.f32 PI.f32 6)))))))
1.3b
(*.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 3 s)))) (*.f32 (*.f32 (*.f32 (*.f32 s (*.f32 PI.f32 6)) (fabs.f32 (cbrt.f32 r))) (sqrt.f32 (cbrt.f32 r))) (sqrt.f32 r))))
Compiler

Compiled 1334 to 766 computations (42.6% saved)

regimes2.4s (18.5%)

Accuracy

Total 0.0b remaining (30.8%)

Threshold costs 0.0b (30.8%)

Compiler

Compiled 16783 to 11965 computations (28.7% saved)

simplify31.0ms (0.2%)

Algorithm
egg-herbie
Rules
84×distribute-rgt-neg-in_binary32
54×distribute-lft-neg-in_binary32
52×distribute-lft-neg-out_binary32
46×cancel-sign-sub-inv_binary32
42×neg-sub0_binary32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03567
16067
28067
310267
413267
515867
619767
724767
828167
931067
1033567
1135167
1236967
1337867
1438067
1536867

end4.0ms (0%)

Compiler

Compiled 44 to 30 computations (31.8% saved)

sample4.1s (30.7%)

Algorithm
intervals
Results
2.1s8000×body128valid
388.0ms8000×pre128true
Compiler

Compiled 254 to 181 computations (28.7% saved)

Profiling

Loading profile data...