Details

Time bar (total: 3.7s)

analyze97.0ms (2.6%)

Algorithm
1×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)

sample1.9s (50.4%)

Results
1.9s8256×body128valid
Compiler

Compiled 100 to 72 computations (28% saved)

preprocess29.0ms (0.8%)

Algorithm
2×egg-herbie
Rules
654×associate-/l*_binary32
635×associate-/l/_binary32
596×times-frac_binary32
556×associate-*r/_binary32
486×associate-/r/_binary32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
041106
111786
244670
3187364
022
Stop Event
1×saturated
1×node limit
Compiler

Compiled 35 to 25 computations (28.6% saved)

simplify23.0ms (0.6%)

Algorithm
1×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
1×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)))
1.7b
(*.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)

localize78.0ms (2.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.2b
(*.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)

series27.0ms (0.7%)

Counts
4 → 84
Calls

21 calls:

2.0ms
(*.f32 (*.f32 (*.f32 6 (PI.f32)) s) r)
r
0
2.0ms
(*.f32 (*.f32 2 (PI.f32)) s)
s
inf
2.0ms
(/.f32 (neg.f32 r) (*.f32 3 s))
r
0
1.0ms
(/.f32 (neg.f32 r) (*.f32 3 s))
r
inf
1.0ms
(*.f32 (*.f32 (*.f32 6 (PI.f32)) s) r)
s
0

rewrite57.0ms (1.5%)

Algorithm
1×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
1×node limit
Counts
4 → 92

simplify25.0ms (0.7%)

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

Useful iterations: 0 (0.0ms)

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

prune206.0ms (5.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New93598
Fresh011
Picked101
Done000
Total946100
Error
0.0b
Counts
100 → 6
Alt Table
StatusErrorProgram
16.4b
(+.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)))) (pow.f32 (pow.f32 (*.f32 (*.f32 r 6) (*.f32 (PI.f32) s)) 3) 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)))) (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)))) (*.f32 (PI.f32) (*.f32 6 (*.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 r (/.f32 -1/3 s)))) (*.f32 (*.f32 (*.f32 6 (PI.f32)) s) r)))
▶0.1b
(+.f32 (/.f32 (*.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (*.f32 2 (*.f32 s (*.f32 (PI.f32) r)))) (/.f32 (*.f32 3/4 (exp.f32 (/.f32 (neg.f32 r) (*.f32 3 s)))) (*.f32 (*.f32 (*.f32 6 (PI.f32)) s) r)))
1.7b
(*.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 3951 to 2454 computations (37.9% saved)

localize87.0ms (2.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
✓0.2b
(*.f32 s (*.f32 (PI.f32) r))
0.2b
(*.f32 (*.f32 (*.f32 6 (PI.f32)) s) r)
0.3b
(/.f32 (neg.f32 r) (*.f32 3 s))
✓0.4b
(*.f32 (PI.f32) r)

series9.0ms (0.2%)

Counts
2 → 0
Calls

9 calls:

1.0ms
(*.f32 s (*.f32 (PI.f32) r))
r
-inf
1.0ms
(*.f32 s (*.f32 (PI.f32) r))
s
-inf
1.0ms
(*.f32 s (*.f32 (PI.f32) r))
r
inf
1.0ms
(*.f32 s (*.f32 (PI.f32) r))
s
inf
1.0ms
(*.f32 s (*.f32 (PI.f32) r))
s
0

rewrite36.0ms (1%)

Algorithm
1×batch-egg-rewrite
Rules
532×log1p-expm1-u_binary32
532×expm1-log1p-u_binary32
437×unpow-prod-down_binary32
330×log-prod_binary32
160×pow2_binary32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0613
111913
2146713
Stop Event
1×node limit
Counts
2 → 34

simplify6.0ms (0.2%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
000
Stop Event
1×saturated
Counts
34 → 34

prune142.0ms (3.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New99099
Fresh055
Picked011
Done000
Total996105
Error
0.0b
Counts
105 → 6
Alt Table
StatusErrorProgram
16.4b
(+.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)))) (pow.f32 (pow.f32 (*.f32 (*.f32 r 6) (*.f32 (PI.f32) s)) 3) 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)))) (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)))) (*.f32 (PI.f32) (*.f32 6 (*.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 r (/.f32 -1/3 s)))) (*.f32 (*.f32 (*.f32 6 (PI.f32)) s) r)))
✓0.1b
(+.f32 (/.f32 (*.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (*.f32 2 (*.f32 s (*.f32 (PI.f32) r)))) (/.f32 (*.f32 3/4 (exp.f32 (/.f32 (neg.f32 r) (*.f32 3 s)))) (*.f32 (*.f32 (*.f32 6 (PI.f32)) s) r)))
1.7b
(*.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 3989 to 2277 computations (42.9% saved)

localize104.0ms (2.8%)

Local error

Found 4 expressions with local error:

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

series13.0ms (0.3%)

Counts
2 → 24
Calls

12 calls:

2.0ms
(*.f32 (PI.f32) (*.f32 6 (*.f32 s r)))
s
0
1.0ms
(*.f32 (PI.f32) (*.f32 6 (*.f32 s r)))
s
inf
1.0ms
(*.f32 (PI.f32) (*.f32 6 (*.f32 s r)))
r
-inf
1.0ms
(*.f32 (PI.f32) (*.f32 6 (*.f32 s r)))
s
-inf
1.0ms
(*.f32 (PI.f32) (*.f32 6 (*.f32 s r)))
r
inf

rewrite42.0ms (1.1%)

Algorithm
1×batch-egg-rewrite
Rules
707×log1p-expm1-u_binary32
707×expm1-log1p-u_binary32
146×expm1-udef_binary32
146×log1p-udef_binary32
130×log-pow_binary32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0818
116218
2193918
Stop Event
1×node limit
Counts
2 → 28

simplify14.0ms (0.4%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
08264
115264
237264
372264
483264
Stop Event
1×saturated
Counts
52 → 30

prune126.0ms (3.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New62163
Fresh044
Picked101
Done011
Total63669
Error
0.0b
Counts
69 → 6
Alt Table
StatusErrorProgram
16.4b
(+.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)))) (pow.f32 (pow.f32 (*.f32 (*.f32 r 6) (*.f32 (PI.f32) s)) 3) 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 (PI.f32) (exp.f32 (log.f32 (*.f32 6 (*.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 r (/.f32 -1/3 s)))) (*.f32 (*.f32 (*.f32 6 (PI.f32)) s) r)))
✓0.1b
(+.f32 (/.f32 (*.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (*.f32 2 (*.f32 s (*.f32 (PI.f32) r)))) (/.f32 (*.f32 3/4 (exp.f32 (/.f32 (neg.f32 r) (*.f32 3 s)))) (*.f32 (*.f32 (*.f32 6 (PI.f32)) s) r)))
1.7b
(*.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 2638 to 1597 computations (39.5% saved)

localize90.0ms (2.4%)

Local error

Found 4 expressions with local error:

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

series89.0ms (2.4%)

Counts
3 → 36
Calls

15 calls:

22.0ms
(pow.f32 (cbrt.f32 (*.f32 (*.f32 r 6) (*.f32 (PI.f32) s))) 3)
s
-inf
20.0ms
(pow.f32 (cbrt.f32 (*.f32 (*.f32 r 6) (*.f32 (PI.f32) s))) 3)
r
-inf
10.0ms
(pow.f32 (cbrt.f32 (*.f32 (*.f32 r 6) (*.f32 (PI.f32) s))) 3)
r
inf
9.0ms
(pow.f32 (cbrt.f32 (*.f32 (*.f32 r 6) (*.f32 (PI.f32) s))) 3)
s
0
8.0ms
(pow.f32 (cbrt.f32 (*.f32 (*.f32 r 6) (*.f32 (PI.f32) s))) 3)
r
0

rewrite51.0ms (1.4%)

Algorithm
1×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
1×node limit
Counts
3 → 79

simplify16.0ms (0.4%)

Algorithm
1×egg-herbie
Rules
26×associate-*l*_binary32
20×associate-*r*_binary32
15×*-commutative_binary32
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
09324
116324
237324
372324
481324
Stop Event
1×saturated
Counts
115 → 71

prune194.0ms (5.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New85287
Fresh134
Picked011
Done011
Total86793
Error
0.0b
Counts
93 → 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 (PI.f32) (exp.f32 (log.f32 (*.f32 6 (*.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 s (*.f32 6 (*.f32 r (PI.f32))))))
✓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 r (/.f32 -1/3 s)))) (*.f32 (*.f32 (*.f32 6 (PI.f32)) s) r)))
✓0.1b
(+.f32 (/.f32 (*.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (*.f32 2 (*.f32 s (*.f32 (PI.f32) r)))) (/.f32 (*.f32 3/4 (exp.f32 (/.f32 (neg.f32 r) (*.f32 3 s)))) (*.f32 (*.f32 (*.f32 6 (PI.f32)) s) r)))
1.7b
(*.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 3674 to 2259 computations (38.5% saved)

regimes122.0ms (3.3%)

Accuracy

Total 0.1b remaining (36.9%)

Threshold costs 0.1b (36.9%)

Counts
31 → 1
Compiler

Compiled 3427 to 2488 computations (27.4% saved)

simplify4.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
02653
14453
25053
35553
45753
Stop Event
1×saturated

end164.0ms (4.4%)

Stop Event
1×fuel
Compiler

Compiled 322 to 234 computations (27.3% saved)

Profiling

Loading profile data...