Details

Time bar (total: 6.1s)

analyze94.0ms (1.5%)

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)

sample2.0s (33.4%)

Results
2.0s8256×body128valid
Compiler

Compiled 135 to 97 computations (28.1% saved)

simplify57.0ms (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)))
0.7b
(*.f32 (/.f32 (/.f32 1/8 (*.f32 s (PI.f32))) r) (+.f32 (exp.f32 (/.f32 (neg.f32 r) s)) (pow.f32 (exp.f32 -1/3) (/.f32 r s))))
Compiler

Compiled 169 to 117 computations (30.8% saved)

localize79.0ms (1.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
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)

series27.0ms (0.4%)

Counts
4 → 84
Calls

4 calls:

9.0ms
(*.f32 (*.f32 (*.f32 2 (PI.f32)) s) r)
8.0ms
(*.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)

rewrite70.0ms (1.1%)

Algorithm
batch-egg-rewrite
Rules
276×expm1-udef_binary32
276×log1p-udef_binary32
239×log-pow_binary32
166×associate-*r*_binary32
166×add-sqr-sqrt_binary32
Counts
4 → 97
Calls

4 calls:

68.0ms
(/.f32 (neg.f32 r) (*.f32 3 s))
68.0ms
(*.f32 (*.f32 (*.f32 6 (PI.f32)) s) r)
68.0ms
(*.f32 (*.f32 (*.f32 2 (PI.f32)) s) r)
68.0ms
(*.f32 (*.f32 2 (PI.f32)) s)
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01639
133937
2387137
3499237

simplify28.0ms (0.5%)

Algorithm
egg-herbie
Rules
51×associate-*l*_binary32
35×associate-*r*_binary32
29×*-commutative_binary32
associate-/l*_binary32
associate-*r/_binary32
Counts
181 → 101
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
015792
130792
269792
3107792
4108792
5108792

prune135.0ms (2.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New947101
Fresh101
Picked101
Done000
Total967103
Error
0.0b
Counts
103 → 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 (log.f32 (/.f32 1 (+.f32 1 (expm1.f32 (/.f32 r (*.f32 s 3)))))))) (*.f32 (*.f32 (*.f32 6 (PI.f32)) s) r)))
19.0b
(+.f32 (/.f32 (*.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (pow.f32 (pow.f32 (*.f32 (*.f32 (*.f32 2 (PI.f32)) s) r) 3) 1/3)) (/.f32 (*.f32 3/4 (exp.f32 (/.f32 (neg.f32 r) (*.f32 3 s)))) (*.f32 (*.f32 (*.f32 6 (PI.f32)) s) r)))
19.7b
(+.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)))) (cbrt.f32 (*.f32 (pow.f32 r 3) (pow.f32 (*.f32 s (*.f32 (PI.f32) 6)) 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)))) (pow.f32 (sqrt.f32 (*.f32 r (*.f32 s (*.f32 (PI.f32) 6)))) 2)))
18.7b
(+.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)))) (pow.f32 (pow.f32 (*.f32 r (*.f32 s (*.f32 (PI.f32) 6))) 3) 1/3)))
0.1b
(+.f32 (/.f32 (*.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (pow.f32 (cbrt.f32 (*.f32 (*.f32 (*.f32 2 (PI.f32)) s) r)) 3)) (/.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 (exp.f32 (log.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 4191 to 2642 computations (37% saved)

localize94.0ms (1.5%)

Local error

Found 4 expressions with local error:

NewErrorProgram
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)
5.6b
(log.f32 (/.f32 1 (+.f32 1 (expm1.f32 (/.f32 r (*.f32 s 3))))))

series1.4s (23.7%)

Counts
1 → 24
Calls

1 calls:

1.4s
(log.f32 (/.f32 1 (+.f32 1 (expm1.f32 (/.f32 r (*.f32 s 3))))))

rewrite79.0ms (1.3%)

Algorithm
batch-egg-rewrite
Rules
459×log-prod_binary32
202×fma-def_binary32
189×prod-diff_binary32
167×expm1-udef_binary32
167×log1p-udef_binary32
Counts
1 → 90
Calls

1 calls:

78.0ms
(log.f32 (/.f32 1 (+.f32 1 (expm1.f32 (/.f32 r (*.f32 s 3))))))
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01116
12307
224587
349367
449047

simplify50.0ms (0.8%)

Algorithm
egg-herbie
Rules
749×fma-neg_binary32
561×log-prod_binary32
490×times-frac_binary32
478×associate-/l/_binary32
450×associate-/l*_binary32
Counts
114 → 92
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
012168
128168
249168
394168
4213168
5512168
61335168
73943168
85182168

prune184.0ms (3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New1440144
Fresh066
Picked011
Done000
Total1447151
Error
0.0b
Counts
151 → 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 (log.f32 (/.f32 1 (+.f32 1 (expm1.f32 (/.f32 r (*.f32 s 3)))))))) (*.f32 (*.f32 (*.f32 6 (PI.f32)) s) r)))
19.0b
(+.f32 (/.f32 (*.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (pow.f32 (pow.f32 (*.f32 (*.f32 (*.f32 2 (PI.f32)) s) r) 3) 1/3)) (/.f32 (*.f32 3/4 (exp.f32 (/.f32 (neg.f32 r) (*.f32 3 s)))) (*.f32 (*.f32 (*.f32 6 (PI.f32)) s) r)))
19.7b
(+.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)))) (cbrt.f32 (*.f32 (pow.f32 r 3) (pow.f32 (*.f32 s (*.f32 (PI.f32) 6)) 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)))) (pow.f32 (sqrt.f32 (*.f32 r (*.f32 s (*.f32 (PI.f32) 6)))) 2)))
18.7b
(+.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)))) (pow.f32 (pow.f32 (*.f32 r (*.f32 s (*.f32 (PI.f32) 6))) 3) 1/3)))
0.1b
(+.f32 (/.f32 (*.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (pow.f32 (cbrt.f32 (*.f32 (*.f32 (*.f32 2 (PI.f32)) s) r)) 3)) (/.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 (exp.f32 (log.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 6242 to 4084 computations (34.6% saved)

localize87.0ms (1.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(*.f32 r (*.f32 s (*.f32 (PI.f32) 6)))
0.3b
(*.f32 (*.f32 (*.f32 2 (PI.f32)) s) r)
0.3b
(*.f32 (*.f32 2 (PI.f32)) s)
0.5b
(pow.f32 (sqrt.f32 (*.f32 r (*.f32 s (*.f32 (PI.f32) 6)))) 2)

series58.0ms (1%)

Counts
2 → 24
Calls

2 calls:

50.0ms
(pow.f32 (sqrt.f32 (*.f32 r (*.f32 s (*.f32 (PI.f32) 6)))) 2)
8.0ms
(*.f32 r (*.f32 s (*.f32 (PI.f32) 6)))

rewrite48.0ms (0.8%)

Algorithm
batch-egg-rewrite
Rules
859×log1p-expm1-u_binary32
859×expm1-log1p-u_binary32
98×add-sqr-sqrt_binary32
96×associate-*r*_binary32
93×add-log-exp_binary32
Counts
2 → 60
Calls

2 calls:

47.0ms
(*.f32 r (*.f32 s (*.f32 (PI.f32) 6)))
47.0ms
(pow.f32 (sqrt.f32 (*.f32 r (*.f32 s (*.f32 (PI.f32) 6)))) 2)
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01122
120922
2227622
3519922

simplify13.0ms (0.2%)

Algorithm
egg-herbie
Rules
26×associate-*l*_binary32
20×associate-*r*_binary32
17×*-commutative_binary32
Counts
84 → 49
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
08264
115264
235264
355264
455264
555264

prune158.0ms (2.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New80383
Fresh325
Picked101
Done011
Total84690
Error
0.0b
Counts
90 → 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 (log.f32 (/.f32 1 (+.f32 1 (expm1.f32 (/.f32 r (*.f32 s 3)))))))) (*.f32 (*.f32 (*.f32 6 (PI.f32)) s) r)))
19.0b
(+.f32 (/.f32 (*.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (pow.f32 (pow.f32 (*.f32 (*.f32 (*.f32 2 (PI.f32)) s) r) 3) 1/3)) (/.f32 (*.f32 3/4 (exp.f32 (/.f32 (neg.f32 r) (*.f32 3 s)))) (*.f32 (*.f32 (*.f32 6 (PI.f32)) s) r)))
18.7b
(+.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)))) (pow.f32 (pow.f32 (*.f32 r (*.f32 s (*.f32 (PI.f32) 6))) 3) 1/3)))
24.2b
(+.f32 (/.f32 (*.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (*.f32 (-.f32 (exp.f32 (log1p.f32 (*.f32 (*.f32 2 (PI.f32)) s))) 1) r)) (/.f32 (*.f32 3/4 (exp.f32 (/.f32 (neg.f32 r) (*.f32 3 s)))) (pow.f32 (sqrt.f32 (*.f32 r (*.f32 s (*.f32 (PI.f32) 6)))) 2)))
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 s (PI.f32)) (*.f32 6 r))))
0.1b
(+.f32 (/.f32 (*.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (pow.f32 (cbrt.f32 (*.f32 (*.f32 (*.f32 2 (PI.f32)) s) r)) 3)) (/.f32 (*.f32 3/4 (exp.f32 (/.f32 (neg.f32 r) (*.f32 3 s)))) (pow.f32 (sqrt.f32 (*.f32 r (*.f32 s (*.f32 (PI.f32) 6)))) 2)))
Compiler

Compiled 3655 to 2317 computations (36.6% saved)

localize102.0ms (1.7%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(*.f32 (*.f32 (*.f32 2 (PI.f32)) s) r)
0.3b
(*.f32 (*.f32 2 (PI.f32)) s)
0.5b
(pow.f32 (sqrt.f32 (*.f32 r (*.f32 s (*.f32 (PI.f32) 6)))) 2)
0.7b
(pow.f32 (cbrt.f32 (*.f32 (*.f32 (*.f32 2 (PI.f32)) s) r)) 3)

series488.0ms (8%)

Counts
1 → 24
Calls

1 calls:

488.0ms
(pow.f32 (cbrt.f32 (*.f32 (*.f32 (*.f32 2 (PI.f32)) s) r)) 3)

rewrite47.0ms (0.8%)

Algorithm
batch-egg-rewrite
Rules
867×log1p-expm1-u_binary32
867×expm1-log1p-u_binary32
98×add-sqr-sqrt_binary32
93×associate-*r*_binary32
93×add-log-exp_binary32
Counts
1 → 45
Calls

1 calls:

46.0ms
(pow.f32 (cbrt.f32 (*.f32 (*.f32 (*.f32 2 (PI.f32)) s) r)) 3)
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01111
121011
2230311
3523311

simplify82.0ms (1.3%)

Algorithm
egg-herbie
Rules
683×fma-neg_binary32
602×associate-*l*_binary32
446×associate-*r*_binary32
374×exp-sum_binary32
264×unsub-neg_binary32
Counts
69 → 53
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
058880
1147576
2271552
3888288
43297288
54344288
64970288
74884288

prune224.0ms (3.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New1291130
Fresh134
Picked101
Done011
Total1315136
Error
0.0b
Counts
136 → 5
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 (log.f32 (/.f32 1 (+.f32 1 (expm1.f32 (/.f32 r (*.f32 s 3)))))))) (*.f32 (*.f32 (*.f32 6 (PI.f32)) s) r)))
0.1b
(+.f32 (/.f32 (*.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (pow.f32 (cbrt.f32 (*.f32 (*.f32 (*.f32 2 (PI.f32)) s) r)) 3)) (/.f32 (*.f32 3/4 (exp.f32 (/.f32 (neg.f32 r) (*.f32 3 s)))) (*.f32 (*.f32 s (PI.f32)) (*.f32 6 r))))
19.0b
(+.f32 (/.f32 (*.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (pow.f32 (pow.f32 (*.f32 (*.f32 (*.f32 2 (PI.f32)) s) r) 3) 1/3)) (/.f32 (*.f32 3/4 (exp.f32 (/.f32 (neg.f32 r) (*.f32 3 s)))) (*.f32 (*.f32 (*.f32 6 (PI.f32)) s) r)))
18.7b
(+.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)))) (pow.f32 (pow.f32 (*.f32 r (*.f32 s (*.f32 (PI.f32) 6))) 3) 1/3)))
24.2b
(+.f32 (/.f32 (*.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (*.f32 (-.f32 (exp.f32 (log1p.f32 (*.f32 (*.f32 2 (PI.f32)) s))) 1) r)) (/.f32 (*.f32 3/4 (exp.f32 (/.f32 (neg.f32 r) (*.f32 3 s)))) (pow.f32 (sqrt.f32 (*.f32 r (*.f32 s (*.f32 (PI.f32) 6)))) 2)))
Compiler

Compiled 5702 to 3670 computations (35.6% saved)

regimes269.0ms (4.4%)

Accuracy

Total 0.0b remaining (21.2%)

Threshold costs 0.0b (21.2%)

Counts
74 → 1
Compiler

Compiled 8452 to 6244 computations (26.1% saved)

simplify3.0ms (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
02653
14453
25053
35553
45753
55753

end131.0ms (2.1%)

Compiler

Compiled 268 to 199 computations (25.7% saved)

Profiling

Loading profile data...