Details

Time bar (total: 4.7s)

analyze105.0ms (2.2%)

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)

sample2.2s (46.1%)

Results
2.1s8256×body128valid
Compiler

Compiled 135 to 97 computations (28.1% saved)

simplify58.0ms (1.2%)

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
0.2b
Counts
3 → 2
Alt Table
StatusErrorProgram
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))))
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)

localize91.0ms (1.9%)

Local error

Found 4 expressions with local error:

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

series31.0ms (0.6%)

Counts
4 → 84
Calls

4 calls:

12.0ms
(*.f32 (*.f32 (*.f32 6 (PI.f32)) s) r)
8.0ms
(*.f32 (*.f32 (*.f32 2 (PI.f32)) s) r)
8.0ms
(/.f32 (neg.f32 r) (*.f32 3 s))
3.0ms
(*.f32 (*.f32 2 (PI.f32)) s)

rewrite66.0ms (1.4%)

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:

64.0ms
(*.f32 (*.f32 (*.f32 6 (PI.f32)) s) r)
64.0ms
(*.f32 (*.f32 (*.f32 2 (PI.f32)) s) r)
64.0ms
(*.f32 (*.f32 2 (PI.f32)) s)
64.0ms
(/.f32 (neg.f32 r) (*.f32 3 s))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01639
133937
2387137
3499237
000
100

simplify28.0ms (0.6%)

Algorithm
egg-herbie
Rules
51×associate-*l*_binary32
35×associate-*r*_binary32
29×*-commutative_binary32
associate-/l*_binary32
associate-*r/_binary32
Counts
181 → 102
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
015792
130792
269792
3107792
4108792
5108792

prune148.0ms (3.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New966102
Fresh011
Picked101
Done000
Total977104
Error
0.1b
Counts
104 → 7
Alt Table
StatusErrorProgram
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))))
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)))) (pow.f32 (cbrt.f32 (*.f32 r (*.f32 s (*.f32 (PI.f32) 6)))) 3)))
25.4b
(+.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)))) (log.f32 (+.f32 1 (expm1.f32 (*.f32 r (*.f32 s (*.f32 (PI.f32) 6))))))))
18.0b
(+.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)))
0.3b
(+.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 (/.f32 -1 (pow.f32 (cbrt.f32 (*.f32 3 s)) 2)) (/.f32 r (cbrt.f32 (*.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 r (*.f32 s (PI.f32))) 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 (neg.f32 r) (*.f32 3 s)))) (exp.f32 (log.f32 (*.f32 r (*.f32 s (*.f32 (PI.f32) 6)))))))
Compiler

Compiled 4190 to 2632 computations (37.2% saved)

localize93.0ms (2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f32 (*.f32 (*.f32 2 (PI.f32)) s) r)
0.2b
(*.f32 (*.f32 2 (PI.f32)) s)
0.2b
(/.f32 (neg.f32 r) (*.f32 3 s))
0.6b
(pow.f32 (cbrt.f32 (*.f32 r (*.f32 s (*.f32 (PI.f32) 6)))) 3)

series484.0ms (10.3%)

Counts
1 → 24
Calls

1 calls:

484.0ms
(pow.f32 (cbrt.f32 (*.f32 r (*.f32 s (*.f32 (PI.f32) 6)))) 3)

rewrite46.0ms (1%)

Algorithm
batch-egg-rewrite
Rules
888×log1p-expm1-u_binary32
888×expm1-log1p-u_binary32
100×add-sqr-sqrt_binary32
98×associate-*r*_binary32
94×add-cbrt-cube_binary32
Counts
1 → 46
Calls

1 calls:

45.0ms
(pow.f32 (cbrt.f32 (*.f32 r (*.f32 s (*.f32 (PI.f32) 6)))) 3)
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01111
121111
2234911
3534311
000
100

simplify85.0ms (1.8%)

Algorithm
egg-herbie
Rules
683×fma-neg_binary32
604×associate-*l*_binary32
458×associate-*r*_binary32
374×exp-sum_binary32
264×unsub-neg_binary32
Counts
70 → 54
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
059576
1148576
2270552
3889288
43298288
54345288
64971288
74885288

prune219.0ms (4.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New1353138
Fresh336
Picked011
Done000
Total1387145
Error
0.1b
Counts
145 → 7
Alt Table
StatusErrorProgram
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))))
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)))) (pow.f32 (cbrt.f32 (*.f32 r (*.f32 s (*.f32 (PI.f32) 6)))) 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 (pow.f32 (pow.f32 (*.f32 r (*.f32 s (*.f32 (PI.f32) 6))) 1/6) 3) (pow.f32 (pow.f32 (*.f32 r (*.f32 s (*.f32 (PI.f32) 6))) 1/6) 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)))) (exp.f32 (log.f32 (*.f32 r (*.f32 s (*.f32 (PI.f32) 6)))))))
18.0b
(+.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)))
0.2b
(+.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 s (*.f32 (*.f32 (PI.f32) 6) 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 r) (*.f32 3 s)))) (*.f32 6 (pow.f32 (exp.f32 (*.f32 1/3 (+.f32 (log.f32 r) (log.f32 (*.f32 s (PI.f32)))))) 3))))
Compiler

Compiled 5940 to 3783 computations (36.3% saved)

localize81.0ms (1.7%)

Local error

Found 4 expressions with local error:

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

series8.0ms (0.2%)

Counts
1 → 24
Calls

1 calls:

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

rewrite51.0ms (1.1%)

Algorithm
batch-egg-rewrite
Rules
710×log1p-expm1-u_binary32
710×expm1-log1p-u_binary32
146×expm1-udef_binary32
146×log1p-udef_binary32
130×log-pow_binary32
Counts
1 → 16
Calls

1 calls:

50.0ms
(*.f32 s (*.f32 (*.f32 (PI.f32) 6) r))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0811
116211
2187911
3495811
000
100

simplify13.0ms (0.3%)

Algorithm
egg-herbie
Rules
26×associate-*l*_binary32
20×associate-*r*_binary32
17×*-commutative_binary32
Counts
40 → 17
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
08264
115264
235264
355264
455264
555264

prune146.0ms (3.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New1010101
Fresh055
Picked011
Done011
Total1017108
Error
0.1b
Counts
108 → 7
Alt Table
StatusErrorProgram
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))))
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)))) (pow.f32 (cbrt.f32 (*.f32 r (*.f32 s (*.f32 (PI.f32) 6)))) 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 (pow.f32 (pow.f32 (*.f32 r (*.f32 s (*.f32 (PI.f32) 6))) 1/6) 3) (pow.f32 (pow.f32 (*.f32 r (*.f32 s (*.f32 (PI.f32) 6))) 1/6) 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)))) (exp.f32 (log.f32 (*.f32 r (*.f32 s (*.f32 (PI.f32) 6)))))))
18.0b
(+.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)))
0.2b
(+.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 s (*.f32 (*.f32 (PI.f32) 6) 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 r) (*.f32 3 s)))) (*.f32 6 (pow.f32 (exp.f32 (*.f32 1/3 (+.f32 (log.f32 r) (log.f32 (*.f32 s (PI.f32)))))) 3))))
Compiler

Compiled 4104 to 2575 computations (37.3% saved)

localize92.0ms (1.9%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f32 (*.f32 (*.f32 2 (PI.f32)) s) r)
0.2b
(*.f32 (*.f32 2 (PI.f32)) s)
0.2b
(/.f32 (neg.f32 r) (*.f32 3 s))
2.7b
(exp.f32 (log.f32 (*.f32 r (*.f32 s (*.f32 (PI.f32) 6)))))

series10.0ms (0.2%)

Counts
1 → 24
Calls

1 calls:

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

rewrite43.0ms (0.9%)

Algorithm
batch-egg-rewrite
Rules
792×log1p-expm1-u_binary32
792×expm1-log1p-u_binary32
160×log1p-udef_binary32
94×associate-*r*_binary32
89×add-sqr-sqrt_binary32
Counts
1 → 42
Calls

1 calls:

42.0ms
(exp.f32 (log.f32 (*.f32 r (*.f32 s (*.f32 (PI.f32) 6)))))
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01011
117911
2208011
3516411
000
100

simplify13.0ms (0.3%)

Algorithm
egg-herbie
Rules
26×associate-*l*_binary32
20×associate-*r*_binary32
17×*-commutative_binary32
Counts
66 → 43
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
08264
115264
235264
355264
455264
555264

prune177.0ms (3.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New1252127
Fresh134
Picked101
Done022
Total1277134
Error
0.1b
Counts
134 → 7
Alt Table
StatusErrorProgram
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 r) (*.f32 3 s)))) (*.f32 6 (pow.f32 (exp.f32 (*.f32 1/3 (+.f32 (log.f32 r) (log.f32 (*.f32 s (PI.f32)))))) 3))))
24.7b
(+.f32 (/.f32 (*.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (*.f32 (log.f32 (+.f32 1 (expm1.f32 (*.f32 s (*.f32 2 (PI.f32)))))) 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)))))))
0.3b
(+.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 r) (*.f32 3 s)))) (pow.f32 (exp.f32 (pow.f32 (cbrt.f32 (log.f32 (*.f32 r (*.f32 s (*.f32 (PI.f32) 6))))) 2)) (cbrt.f32 (log.f32 (*.f32 r (*.f32 s (*.f32 (PI.f32) 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 (neg.f32 r) (*.f32 3 s)))) (pow.f32 (cbrt.f32 (*.f32 r (*.f32 s (*.f32 (PI.f32) 6)))) 3)))
18.0b
(+.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)))
0.2b
(+.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 (pow.f32 (pow.f32 (*.f32 r (*.f32 s (*.f32 (PI.f32) 6))) 1/6) 3) (pow.f32 (pow.f32 (*.f32 r (*.f32 s (*.f32 (PI.f32) 6))) 1/6) 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 s (*.f32 (*.f32 (PI.f32) 6) r))))
Compiler

Compiled 5107 to 3209 computations (37.2% saved)

regimes275.0ms (5.8%)

Accuracy

Total 0.1b remaining (35.7%)

Threshold costs 0.1b (35.7%)

Counts
72 → 1
Compiler

Compiled 8377 to 6205 computations (25.9% 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
02858
14658
25258
35758
45958
55958

end171.0ms (3.6%)

Compiler

Compiled 372 to 276 computations (25.8% saved)

Profiling

Loading profile data...