Details

Time bar (total: 5.4s)

analyze92.0ms (1.7%)

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)

sample2.3s (42.9%)

Results
2.3s8256×body128valid
Compiler

Compiled 135 to 97 computations (28.1% saved)

simplify26.0ms (0.5%)

Algorithm
egg-herbie
Rules
622×associate-*l*_binary32
523×associate-*r*_binary32
423×associate-/r*_binary32
364×associate-/l*_binary32
320×associate-/l/_binary32
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02653
16643
224435
3102632
4341732
Stop Event
node limit
Counts
1 → 2

prune4.0ms (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 (/.f32 1/8 s) (PI.f32)) r) (+.f32 (exp.f32 (/.f32 (neg.f32 r) s)) (pow.f32 (exp.f32 r) (/.f32 -1/3 s))))
Compiler

Compiled 169 to 117 computations (30.8% saved)

localize115.0ms (2.1%)

Local error

Found 4 expressions with local error:

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

series37.0ms (0.7%)

Counts
4 → 84
Calls

4 calls:

13.0ms
(*.f32 (*.f32 2 (PI.f32)) s)
9.0ms
(*.f32 (*.f32 (*.f32 2 (PI.f32)) s) r)
8.0ms
(*.f32 (*.f32 (*.f32 6 (PI.f32)) s) r)
7.0ms
(/.f32 (neg.f32 r) (*.f32 3 s))

rewrite63.0ms (1.2%)

Algorithm
batch-egg-rewrite
Rules
276×expm1-udef_binary32
276×log1p-udef_binary32
166×associate-*r*_binary32
166×add-sqr-sqrt_binary32
155×log1p-expm1-u_binary32
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01639
133937
2445237
Stop Event
node limit
Counts
4 → 92
Calls

4 calls:

61.0ms
(*.f32 (*.f32 (*.f32 6 (PI.f32)) s) r)
61.0ms
(/.f32 (neg.f32 r) (*.f32 3 s))
61.0ms
(*.f32 (*.f32 (*.f32 2 (PI.f32)) s) r)
61.0ms
(*.f32 (*.f32 2 (PI.f32)) s)

simplify27.0ms (0.5%)

Algorithm
egg-herbie
Rules
50×associate-*l*_binary32
34×associate-*r*_binary32
28×*-commutative_binary32
associate-/l*_binary32
associate-*r/_binary32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
015792
130792
273792
3142792
4156792
Stop Event
saturated
Counts
176 → 98

prune704.0ms (13%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New92698
Fresh011
Picked101
Done000
Total937100
Error
0.0b
Counts
100 → 7
Alt Table
StatusErrorProgram
17.8b
(+.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 (PI.f32) (*.f32 6 s)) 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 -1 s) (*.f32 r 1/3)))) (*.f32 (*.f32 (*.f32 6 (PI.f32)) s) r)))
17.3b
(+.f32 (/.f32 (*.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (*.f32 (cbrt.f32 (*.f32 (pow.f32 (*.f32 2 (PI.f32)) 3) (pow.f32 s 3))) 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 (neg.f32 r) (*.f32 3 s)))) (pow.f32 (cbrt.f32 (*.f32 (*.f32 r 6) (*.f32 (PI.f32) s))) 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)))) (expm1.f32 (log1p.f32 (*.f32 (*.f32 r 6) (*.f32 (PI.f32) s))))))
1.0b
(*.f32 (/.f32 (/.f32 (/.f32 1/8 s) (PI.f32)) r) (+.f32 (exp.f32 (/.f32 (neg.f32 r) s)) (pow.f32 (exp.f32 r) (/.f32 -1/3 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)))) (exp.f32 (log.f32 (*.f32 (*.f32 r 6) (*.f32 (PI.f32) s))))))
Compiler

Compiled 4045 to 2528 computations (37.5% saved)

localize92.0ms (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)
0.3b
(*.f32 r 1/3)
0.4b
(*.f32 (/.f32 -1 s) (*.f32 r 1/3))

series12.0ms (0.2%)

Counts
2 → 36
Calls

2 calls:

11.0ms
(*.f32 (/.f32 -1 s) (*.f32 r 1/3))
1.0ms
(*.f32 r 1/3)

rewrite36.0ms (0.7%)

Algorithm
batch-egg-rewrite
Rules
709×log1p-expm1-u_binary32
709×expm1-log1p-u_binary32
143×expm1-udef_binary32
143×log1p-udef_binary32
80×add-sqr-sqrt_binary32
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0814
116411
2195411
Stop Event
node limit
Counts
2 → 37
Calls

2 calls:

35.0ms
(*.f32 r 1/3)
35.0ms
(*.f32 (/.f32 -1 s) (*.f32 r 1/3))

simplify13.0ms (0.2%)

Algorithm
egg-herbie
Rules
*-commutative_binary32
associate-/l*_binary32
associate-*r/_binary32
associate-*l/_binary32
associate-/r/_binary32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
08216
112216
216216
320216
421216
Stop Event
saturated
Counts
73 → 41

prune166.0ms (3.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New74074
Fresh066
Picked011
Done000
Total74781
Error
0.0b
Counts
81 → 7
Alt Table
StatusErrorProgram
17.8b
(+.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 (PI.f32) (*.f32 6 s)) 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 -1 s) (*.f32 r 1/3)))) (*.f32 (*.f32 (*.f32 6 (PI.f32)) s) r)))
17.3b
(+.f32 (/.f32 (*.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (*.f32 (cbrt.f32 (*.f32 (pow.f32 (*.f32 2 (PI.f32)) 3) (pow.f32 s 3))) 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 (neg.f32 r) (*.f32 3 s)))) (pow.f32 (cbrt.f32 (*.f32 (*.f32 r 6) (*.f32 (PI.f32) s))) 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)))) (expm1.f32 (log1p.f32 (*.f32 (*.f32 r 6) (*.f32 (PI.f32) s))))))
1.0b
(*.f32 (/.f32 (/.f32 (/.f32 1/8 s) (PI.f32)) r) (+.f32 (exp.f32 (/.f32 (neg.f32 r) s)) (pow.f32 (exp.f32 r) (/.f32 -1/3 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)))) (exp.f32 (log.f32 (*.f32 (*.f32 r 6) (*.f32 (PI.f32) s))))))
Compiler

Compiled 3137 to 2051 computations (34.6% saved)

localize121.0ms (2.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(*.f32 (PI.f32) s)
0.3b
(*.f32 (*.f32 2 (PI.f32)) s)
0.4b
(*.f32 (*.f32 r 6) (*.f32 (PI.f32) s))
0.7b
(pow.f32 (cbrt.f32 (*.f32 (*.f32 r 6) (*.f32 (PI.f32) s))) 3)

series556.0ms (10.2%)

Counts
3 → 60
Calls

3 calls:

545.0ms
(pow.f32 (cbrt.f32 (*.f32 (*.f32 r 6) (*.f32 (PI.f32) s))) 3)
8.0ms
(*.f32 (*.f32 r 6) (*.f32 (PI.f32) s))
3.0ms
(*.f32 (PI.f32) s)

rewrite46.0ms (0.9%)

Algorithm
batch-egg-rewrite
Rules
885×log1p-expm1-u_binary32
885×expm1-log1p-u_binary32
100×add-sqr-sqrt_binary32
96×associate-*r*_binary32
94×add-cbrt-cube_binary32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01127
122427
2246827
Stop Event
node limit
Counts
3 → 79
Calls

3 calls:

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

simplify36.0ms (0.7%)

Algorithm
egg-herbie
Rules
664×associate-*l*_binary32
508×associate-*r*_binary32
259×fma-def_binary32
182×*-commutative_binary32
176×associate-+l+_binary32
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0611188
11621188
24391140
31207612
Stop Event
node limit
Counts
139 → 79

prune225.0ms (4.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New91495
Fresh235
Picked101
Done011
Total948102
Error
0.0b
Counts
102 → 8
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 (/.f32 -1 s) (*.f32 r 1/3)))) (*.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 (pow.f32 (pow.f32 (*.f32 r (*.f32 (*.f32 6 s) (PI.f32))) 1/6) 3) (pow.f32 (pow.f32 (*.f32 r (*.f32 (*.f32 6 s) (PI.f32))) 1/6) 3))))
17.3b
(+.f32 (/.f32 (*.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (*.f32 (cbrt.f32 (*.f32 (pow.f32 (*.f32 2 (PI.f32)) 3) (pow.f32 s 3))) 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 (neg.f32 r) (*.f32 3 s)))) (*.f32 (*.f32 (*.f32 6 s) (PI.f32)) r)))
1.0b
(*.f32 (/.f32 (/.f32 (/.f32 1/8 s) (PI.f32)) r) (+.f32 (exp.f32 (/.f32 (neg.f32 r) s)) (pow.f32 (exp.f32 r) (/.f32 -1/3 s))))
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 (pow.f32 (cbrt.f32 r) 2) (*.f32 (cbrt.f32 r) (*.f32 (*.f32 6 s) (PI.f32))))))
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 r 6) (*.f32 (PI.f32) s))))))
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 (cbrt.f32 (*.f32 (*.f32 r 6) (pow.f32 (cbrt.f32 (*.f32 (PI.f32) s)) 3))) 3)))
Compiler

Compiled 4319 to 2692 computations (37.7% saved)

localize77.0ms (1.4%)

Local error

Found 4 expressions with local error:

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

series3.0ms (0.1%)

Counts
1 → 12
Calls

1 calls:

3.0ms
(*.f32 (*.f32 6 s) (PI.f32))

rewrite31.0ms (0.6%)

Algorithm
batch-egg-rewrite
Rules
514×log1p-expm1-u_binary32
514×expm1-log1p-u_binary32
379×unpow-prod-down_binary32
298×log-prod_binary32
154×pow2_binary32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
068
11218
214108
Stop Event
node limit
Counts
1 → 17
Calls

1 calls:

31.0ms
(*.f32 (*.f32 6 s) (PI.f32))

simplify8.0ms (0.2%)

Algorithm
egg-herbie
Rules
*-commutative_binary32
associate-*r*_binary32
associate-*l*_binary32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0696
11096
21796
31996
Stop Event
saturated
Counts
29 → 19

prune162.0ms (3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New991100
Fresh156
Picked011
Done011
Total1008108
Error
0.0b
Counts
108 → 8
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 (/.f32 -1 s) (*.f32 r 1/3)))) (*.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 (pow.f32 (pow.f32 (*.f32 r (*.f32 (*.f32 6 s) (PI.f32))) 1/6) 3) (pow.f32 (pow.f32 (*.f32 r (*.f32 (*.f32 6 s) (PI.f32))) 1/6) 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)))) (*.f32 (*.f32 (*.f32 6 s) (PI.f32)) r)))
1.0b
(*.f32 (/.f32 (/.f32 (/.f32 1/8 s) (PI.f32)) r) (+.f32 (exp.f32 (/.f32 (neg.f32 r) s)) (pow.f32 (exp.f32 r) (/.f32 -1/3 s))))
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 (pow.f32 (cbrt.f32 (*.f32 s (*.f32 6 (PI.f32)))) 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 (pow.f32 (cbrt.f32 r) 2) (*.f32 (cbrt.f32 r) (*.f32 (*.f32 6 s) (PI.f32))))))
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 r 6) (*.f32 (PI.f32) s))))))
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 (cbrt.f32 (*.f32 (*.f32 r 6) (pow.f32 (cbrt.f32 (*.f32 (PI.f32) s)) 3))) 3)))
Compiler

Compiled 3934 to 2443 computations (37.9% saved)

regimes270.0ms (5%)

Accuracy

Total 0.1b remaining (47.6%)

Threshold costs 0.1b (47.6%)

Counts
75 → 1
Compiler

Compiled 8455 to 6211 computations (26.5% 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
03058
14658
25058
35358
45458
Stop Event
saturated

end175.0ms (3.2%)

Compiler

Compiled 377 to 279 computations (26% saved)

Profiling

Loading profile data...