Details

Time bar (total: 5.1s)

analyze87.0ms (1.7%)

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)

sample123.0ms (2.4%)

Algorithm
1×intervals
Results
30.0ms256×body128valid
8.0ms256×pre128true
Compiler

Compiled 87 to 63 computations (27.6% saved)

simplify58.0ms (1.1%)

Algorithm
1×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
0.6b
(*.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 (neg.f32 r) (*.f32 3 s)))) (*.f32 (*.f32 (*.f32 6 (PI.f32)) s) r)))
Compiler

Compiled 169 to 117 computations (30.8% saved)

localize79.0ms (1.6%)

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

series28.0ms (0.5%)

Counts
4 → 84
Calls

4 calls:

9.0ms
(*.f32 (*.f32 (*.f32 6 (PI.f32)) s) r)
8.0ms
(*.f32 (*.f32 (*.f32 2 (PI.f32)) s) r)
7.0ms
(/.f32 (neg.f32 r) (*.f32 3 s))
3.0ms
(*.f32 (*.f32 2 (PI.f32)) s)

rewrite25.0ms (0.5%)

Algorithm
1×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:

6.0ms
(*.f32 (*.f32 (*.f32 2 (PI.f32)) s) r)
5.0ms
(*.f32 (*.f32 (*.f32 6 (PI.f32)) s) r)
4.0ms
(/.f32 (neg.f32 r) (*.f32 3 s))
4.0ms
(*.f32 (*.f32 2 (PI.f32)) s)

simplify97.0ms (1.9%)

Algorithm
1×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 → 157
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01872248
14421951
218851945
345711945
449351945

prune263.0ms (5.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1516157
Fresh011
Picked101
Done000
Total1527159
Error
0.1b
Counts
159 → 7
Alt Table
StatusErrorProgram
0.6b
(*.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 (*.f32 2 (PI.f32)) (sqrt.f32 s)) (sqrt.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 (neg.f32 r) (*.f32 3 s)))) (*.f32 (*.f32 6 (PI.f32)) (*.f32 s r))))
24.7b
(+.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)))) (log.f32 (exp.f32 (*.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 r (*.f32 s (PI.f32))) 6)))))
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 (*.f32 (cbrt.f32 r) (cbrt.f32 r)) 3) (/.f32 (neg.f32 (cbrt.f32 r)) 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 (*.f32 2 (PI.f32)) s) (*.f32 (cbrt.f32 r) (cbrt.f32 r))) (cbrt.f32 r))) (/.f32 (*.f32 3/4 (exp.f32 (/.f32 (neg.f32 r) (*.f32 3 s)))) (*.f32 (*.f32 (*.f32 6 (PI.f32)) s) r)))
Compiler

Compiled 6448 to 3738 computations (42% saved)

localize90.0ms (1.8%)

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

series9.0ms (0.2%)

Counts
1 → 24
Calls

1 calls:

9.0ms
(*.f32 (*.f32 6 (PI.f32)) (*.f32 s r))

rewrite7.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
13×add-cbrt-cube_binary32
13×add-exp-log_binary32
13×pow1_binary32
8×cbrt-unprod_binary32
8×prod-exp_binary32
Counts
1 → 24
Calls

1 calls:

6.0ms
(*.f32 (*.f32 6 (PI.f32)) (*.f32 s r))

simplify69.0ms (1.4%)

Algorithm
1×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

prune276.0ms (5.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New1512153
Fresh246
Picked101
Done000
Total1546160
Error
0.0b
Counts
160 → 6
Alt Table
StatusErrorProgram
0.6b
(*.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 (cbrt.f32 r) (cbrt.f32 r)) (*.f32 -3 (/.f32 s (cbrt.f32 r)))))) (*.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 (*.f32 2 (PI.f32)) (sqrt.f32 s)) (sqrt.f32 s)) r)) (/.f32 (*.f32 3/4 (exp.f32 (/.f32 (neg.f32 r) (*.f32 3 s)))) (*.f32 (*.f32 6 (PI.f32)) (*.f32 s r))))
24.7b
(+.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)))) (log.f32 (exp.f32 (*.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 r (*.f32 s (PI.f32))) 6)))))
0.1b
(+.f32 (/.f32 (*.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (*.f32 (*.f32 (*.f32 (*.f32 2 (PI.f32)) s) (*.f32 (cbrt.f32 r) (cbrt.f32 r))) (cbrt.f32 r))) (/.f32 (*.f32 3/4 (exp.f32 (/.f32 (neg.f32 r) (*.f32 3 s)))) (*.f32 (*.f32 (*.f32 6 (PI.f32)) s) r)))
Compiler

Compiled 6241 to 3470 computations (44.4% saved)

localize85.0ms (1.7%)

Local error

Found 4 expressions with local error:

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

series17.0ms (0.3%)

Counts
2 → 8
Calls

2 calls:

11.0ms
(*.f32 (*.f32 2 (PI.f32)) (sqrt.f32 s))
6.0ms
(*.f32 (*.f32 (*.f32 2 (PI.f32)) (sqrt.f32 s)) (sqrt.f32 s))

rewrite15.0ms (0.3%)

Algorithm
1×rewrite-expression-head
Rules
16×add-cbrt-cube_binary32
16×add-exp-log_binary32
16×pow1_binary32
12×associate-*r*_binary32
9×cbrt-unprod_binary32
Counts
2 → 49
Calls

2 calls:

7.0ms
(*.f32 (*.f32 (*.f32 2 (PI.f32)) (sqrt.f32 s)) (sqrt.f32 s))
5.0ms
(*.f32 (*.f32 2 (PI.f32)) (sqrt.f32 s))

simplify71.0ms (1.4%)

Algorithm
1×egg-herbie
Rules
744×fma-def_binary32
682×associate-*l/_binary32
376×*-commutative_binary32
255×log-div_binary32
228×distribute-rgt-in_binary32
Counts
57 → 59
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
071704
1171615
2615615
3885615
41123615
51501615
63981615
74985615

prune268.0ms (5.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New1482150
Fresh145
Picked101
Done000
Total1506156
Error
0.0b
Counts
156 → 6
Alt Table
StatusErrorProgram
0.1b
(+.f32 (/.f32 (*.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (*.f32 (*.f32 (*.f32 (*.f32 (*.f32 2 (PI.f32)) (*.f32 (cbrt.f32 (sqrt.f32 s)) (cbrt.f32 (sqrt.f32 s)))) (cbrt.f32 (sqrt.f32 s))) (sqrt.f32 s)) r)) (/.f32 (*.f32 3/4 (exp.f32 (/.f32 (neg.f32 r) (*.f32 3 s)))) (*.f32 (*.f32 6 (PI.f32)) (*.f32 s r))))
24.7b
(+.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)))) (log.f32 (exp.f32 (*.f32 (*.f32 (*.f32 6 (PI.f32)) s) r)))))
0.6b
(*.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 (cbrt.f32 r) (cbrt.f32 r)) (*.f32 -3 (/.f32 s (cbrt.f32 r)))))) (*.f32 (*.f32 6 (PI.f32)) (*.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 r (*.f32 s (PI.f32))) 6)))))
▶0.1b
(+.f32 (/.f32 (*.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (*.f32 (*.f32 (expm1.f32 (log1p.f32 (*.f32 (*.f32 2 (PI.f32)) (sqrt.f32 s)))) (sqrt.f32 s)) r)) (/.f32 (*.f32 3/4 (exp.f32 (/.f32 (neg.f32 r) (*.f32 3 s)))) (*.f32 (*.f32 6 (PI.f32)) (*.f32 s r))))
Compiler

Compiled 6751 to 3569 computations (47.1% saved)

localize93.0ms (1.8%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(*.f32 (*.f32 6 (PI.f32)) (*.f32 s r))
0.3b
(/.f32 (neg.f32 r) (*.f32 3 s))
✓0.4b
(*.f32 (expm1.f32 (log1p.f32 (*.f32 (*.f32 2 (PI.f32)) (sqrt.f32 s)))) (sqrt.f32 s))
0.4b
(*.f32 (*.f32 2 (PI.f32)) (sqrt.f32 s))

series7.0ms (0.1%)

Counts
1 → 8
Calls

1 calls:

7.0ms
(*.f32 (expm1.f32 (log1p.f32 (*.f32 (*.f32 2 (PI.f32)) (sqrt.f32 s)))) (sqrt.f32 s))

rewrite5.0ms (0.1%)

Algorithm
1×rewrite-expression-head
Rules
8×add-sqr-sqrt_binary32
6×associate-*r*_binary32
4×sqrt-prod_binary32
4×*-un-lft-identity_binary32
4×add-cube-cbrt_binary32
Counts
1 → 24
Calls

1 calls:

4.0ms
(*.f32 (expm1.f32 (log1p.f32 (*.f32 (*.f32 2 (PI.f32)) (sqrt.f32 s)))) (sqrt.f32 s))

simplify77.0ms (1.5%)

Algorithm
1×egg-herbie
Rules
489×associate-*l*_binary32
386×fma-def_binary32
323×associate-*r*_binary32
306×log-div_binary32
272×log-prod_binary32
Counts
32 → 37
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
046541
185409
2310409
31169409
41344409
51705409
62751409
74667409
84999409

prune275.0ms (5.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New1501151
Fresh145
Picked101
Done000
Total1525157
Error
0.0b
Counts
157 → 5
Alt Table
StatusErrorProgram
0.6b
(*.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 (cbrt.f32 r) (cbrt.f32 r)) (*.f32 -3 (/.f32 s (cbrt.f32 r)))))) (*.f32 (*.f32 6 (PI.f32)) (*.f32 s r))))
0.1b
(+.f32 (/.f32 (*.f32 1/4 (exp.f32 (/.f32 (neg.f32 r) s))) (*.f32 (*.f32 (expm1.f32 (log1p.f32 (*.f32 (*.f32 (*.f32 2 (PI.f32)) (sqrt.f32 (sqrt.f32 s))) (sqrt.f32 (sqrt.f32 s))))) (sqrt.f32 s)) r)) (/.f32 (*.f32 3/4 (exp.f32 (/.f32 (neg.f32 r) (*.f32 3 s)))) (*.f32 (*.f32 6 (PI.f32)) (*.f32 s r))))
24.7b
(+.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)))) (log.f32 (exp.f32 (*.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 r (*.f32 s (PI.f32))) 6)))))
Compiler

Compiled 6846 to 3733 computations (45.5% saved)

regimes1.0s (20.2%)

Accuracy

Total 0.0b remaining (33%)

Threshold costs 0.0b (33%)

Counts
212 → 1
Compiler

Compiled 24928 to 17965 computations (27.9% saved)

simplify4.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
02860
14660
25460
36160
46560
56660
66660

end1.0ms (0%)

Compiler

Compiled 39 to 27 computations (30.8% saved)

sample1.9s (37.7%)

Algorithm
1×intervals
Results
1.1s8000×body128valid
233.0ms8000×pre128true
Compiler

Compiled 274 to 194 computations (29.2% saved)

Profiling

Loading profile data...