Details

Time bar (total: 7.2s)

analyze91.0ms (1.3%)

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 50 to 36 computations (28% saved)

sample117.0ms (1.6%)

Algorithm
intervals
Results
30.0ms256×body128valid
6.0ms256×pre128true
Compiler

Compiled 87 to 63 computations (27.6% saved)

simplify65.0ms (0.9%)

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
0.1b
(+.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)))
1.0b
(*.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 169 to 117 computations (30.8% saved)

localize89.0ms (1.2%)

Local error

Found 4 expressions with local error:

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

series43.0ms (0.6%)

Counts
4 → 84
Calls

4 calls:

23.0ms
(*.f32 (*.f32 (*.f32 2 (PI.f32)) s) r)
10.0ms
(*.f32 (*.f32 (*.f32 6 (PI.f32)) s) r)
6.0ms
(/.f32 (neg.f32 r) (*.f32 3 s))
3.0ms
(*.f32 (*.f32 2 (PI.f32)) s)

rewrite28.0ms (0.4%)

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:

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

simplify99.0ms (1.4%)

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 → 154
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01872248
14421951
218851945
345711945
449351945

prune295.0ms (4.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1486154
Fresh011
Picked101
Done000
Total1497156
Error
0.0b
Counts
156 → 7
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 (*.f32 6 (PI.f32)) s) (*.f32 (cbrt.f32 r) (cbrt.f32 r))) (cbrt.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 6 (PI.f32)) (*.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 (sqrt.f32 (*.f32 (*.f32 s (*.f32 (PI.f32) r)) 6)) (sqrt.f32 (*.f32 (*.f32 s (*.f32 (PI.f32) r)) 6)))))
0.1b
(+.f32 (/.f32 (*.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (*.f32 (*.f32 (*.f32 (*.f32 2 (PI.f32)) (*.f32 (cbrt.f32 s) (cbrt.f32 s))) (cbrt.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)))) (exp.f32 (log.f32 (*.f32 (*.f32 (*.f32 6 (PI.f32)) s) r)))))
1.0b
(*.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 (/.f32 (neg.f32 r) 3) s))) (*.f32 (*.f32 (*.f32 6 (PI.f32)) s) r)))
Compiler

Compiled 6357 to 3672 computations (42.2% saved)

localize84.0ms (1.2%)

Local error

Found 4 expressions with local error:

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

series9.0ms (0.1%)

Counts
1 → 24
Calls

1 calls:

9.0ms
(/.f32 (/.f32 (neg.f32 r) 3) s)

rewrite26.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
222×times-frac_binary32
116×*-un-lft-identity_binary32
116×add-sqr-sqrt_binary32
116×add-cube-cbrt_binary32
36×distribute-lft-neg-in_binary32
Counts
1 → 158
Calls

1 calls:

8.0ms
(/.f32 (/.f32 (neg.f32 r) 3) s)

simplify162.0ms (2.3%)

Algorithm
egg-herbie
Rules
756×div-sub_binary32
455×neg-mul-1_binary32
340×associate-/l/_binary32
290×associate-/r/_binary32
269×distribute-frac-neg_binary32
Counts
182 → 220
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02973491
16353398
217343326
332323326
442353326
549723326
648703326

prune727.0ms (10.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New3112313
Fresh246
Picked101
Done000
Total3146320
Error
0.0b
Counts
320 → 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 r) (*.f32 3 s)))) (*.f32 (sqrt.f32 (*.f32 (*.f32 s (*.f32 (PI.f32) r)) 6)) (sqrt.f32 (*.f32 (*.f32 s (*.f32 (PI.f32) r)) 6)))))
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 (neg.f32 r) 3) s))) (exp.f32 (log.f32 (*.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 (*.f32 6 (PI.f32)) s) (*.f32 (cbrt.f32 r) (cbrt.f32 r))) (cbrt.f32 r))))
0.1b
(+.f32 (/.f32 (*.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (*.f32 (*.f32 (*.f32 (*.f32 2 (PI.f32)) (*.f32 (cbrt.f32 s) (cbrt.f32 s))) (cbrt.f32 s)) r)) (/.f32 (*.f32 3/4 (exp.f32 (/.f32 (neg.f32 r) (*.f32 3 s)))) (*.f32 (*.f32 (*.f32 6 (PI.f32)) s) r)))
0.1b
(+.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 (/.f32 (neg.f32 r) 3) s))) (*.f32 (*.f32 6 (PI.f32)) (*.f32 s r))))
1.0b
(*.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 13449 to 7702 computations (42.7% saved)

localize83.0ms (1.2%)

Local error

Found 4 expressions with local error:

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

series10.0ms (0.1%)

Counts
1 → 24
Calls

1 calls:

10.0ms
(*.f32 (*.f32 6 (PI.f32)) (*.f32 s r))

rewrite8.0ms (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:

7.0ms
(*.f32 (*.f32 6 (PI.f32)) (*.f32 s r))

simplify73.0ms (1%)

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

prune648.0ms (9.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New3082310
Fresh145
Picked101
Done000
Total3106316
Error
0.0b
Counts
316 → 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 r) (*.f32 3 s)))) (*.f32 (sqrt.f32 (*.f32 (*.f32 s (*.f32 (PI.f32) r)) 6)) (sqrt.f32 (*.f32 (*.f32 s (*.f32 (PI.f32) r)) 6)))))
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 (neg.f32 r) 3) s))) (exp.f32 (log.f32 (*.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 (*.f32 6 (PI.f32)) s) (*.f32 (cbrt.f32 r) (cbrt.f32 r))) (cbrt.f32 r))))
18.2b
(+.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 (neg.f32 r) 3) s))) (cbrt.f32 (*.f32 (*.f32 (*.f32 (*.f32 6 (PI.f32)) (*.f32 6 (PI.f32))) (*.f32 6 (PI.f32))) (*.f32 (*.f32 (*.f32 s r) (*.f32 s r)) (*.f32 s r))))))
0.1b
(+.f32 (/.f32 (*.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (*.f32 (*.f32 (*.f32 (*.f32 2 (PI.f32)) (*.f32 (cbrt.f32 s) (cbrt.f32 s))) (cbrt.f32 s)) r)) (/.f32 (*.f32 3/4 (exp.f32 (/.f32 (/.f32 (neg.f32 r) 3) s))) (*.f32 (*.f32 6 (PI.f32)) (*.f32 s r))))
1.0b
(*.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 13381 to 7366 computations (45% saved)

localize94.0ms (1.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(*.f32 (*.f32 (*.f32 2 (PI.f32)) (*.f32 (cbrt.f32 s) (cbrt.f32 s))) (cbrt.f32 s))
0.3b
(*.f32 (*.f32 6 (PI.f32)) (*.f32 s r))
0.4b
(*.f32 (*.f32 2 (PI.f32)) (*.f32 (cbrt.f32 s) (cbrt.f32 s)))
0.5b
(*.f32 (cbrt.f32 s) (cbrt.f32 s))

series120.0ms (1.7%)

Counts
3 → 36
Calls

3 calls:

61.0ms
(*.f32 (*.f32 2 (PI.f32)) (*.f32 (cbrt.f32 s) (cbrt.f32 s)))
43.0ms
(*.f32 (cbrt.f32 s) (cbrt.f32 s))
15.0ms
(*.f32 (*.f32 (*.f32 2 (PI.f32)) (*.f32 (cbrt.f32 s) (cbrt.f32 s))) (cbrt.f32 s))

rewrite30.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
40×pow1_binary32
35×add-exp-log_binary32
23×pow-prod-down_binary32
22×cbrt-unprod_binary32
22×prod-exp_binary32
Counts
3 → 98
Calls

3 calls:

12.0ms
(*.f32 (*.f32 (*.f32 2 (PI.f32)) (*.f32 (cbrt.f32 s) (cbrt.f32 s))) (cbrt.f32 s))
7.0ms
(*.f32 (*.f32 2 (PI.f32)) (*.f32 (cbrt.f32 s) (cbrt.f32 s)))
5.0ms
(*.f32 (cbrt.f32 s) (cbrt.f32 s))

simplify161.0ms (2.2%)

Algorithm
egg-herbie
Rules
981×fma-def_binary32
507×*-commutative_binary32
418×unswap-sqr_binary32
346×associate-/l*_binary32
320×sqr-pow_binary32
Counts
134 → 130
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01181723
12431479
29421413
315471379
429821287
543261287
648891287

prune599.0ms (8.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New1600160
Fresh055
Picked011
Done000
Total1606166
Error
0.0b
Counts
166 → 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 r) (*.f32 3 s)))) (*.f32 (sqrt.f32 (*.f32 (*.f32 s (*.f32 (PI.f32) r)) 6)) (sqrt.f32 (*.f32 (*.f32 s (*.f32 (PI.f32) r)) 6)))))
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 (neg.f32 r) 3) s))) (exp.f32 (log.f32 (*.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 (*.f32 6 (PI.f32)) s) (*.f32 (cbrt.f32 r) (cbrt.f32 r))) (cbrt.f32 r))))
18.2b
(+.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 (neg.f32 r) 3) s))) (cbrt.f32 (*.f32 (*.f32 (*.f32 (*.f32 6 (PI.f32)) (*.f32 6 (PI.f32))) (*.f32 6 (PI.f32))) (*.f32 (*.f32 (*.f32 s r) (*.f32 s r)) (*.f32 s r))))))
0.1b
(+.f32 (/.f32 (*.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (*.f32 (*.f32 (*.f32 (*.f32 2 (PI.f32)) (*.f32 (cbrt.f32 s) (cbrt.f32 s))) (cbrt.f32 s)) r)) (/.f32 (*.f32 3/4 (exp.f32 (/.f32 (/.f32 (neg.f32 r) 3) s))) (*.f32 (*.f32 6 (PI.f32)) (*.f32 s r))))
1.0b
(*.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 7427 to 3686 computations (50.4% saved)

regimes1.7s (23.1%)

Accuracy

Total 0.1b remaining (45.9%)

Threshold costs 0.1b (45.9%)

Counts
333 → 1
Compiler

Compiled 42406 to 30358 computations (28.4% saved)

simplify5.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
02853
14653
25453
36153
46553
56653
66553

end1.0ms (0%)

Compiler

Compiled 35 to 25 computations (28.6% saved)

sample1.8s (25.6%)

Algorithm
intervals
Results
1.1s8000×body128valid
195.0ms8000×pre128true
Compiler

Compiled 327 to 226 computations (30.9% saved)

Profiling

Loading profile data...