Details

Time bar (total: 11.3s)

analyze558.0ms (5%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
50%50%0.1%5
50%50%0.1%6
50%40.6%9.5%7
50%39%11%8
50%33.6%16.5%9
50%32.4%17.7%10
50%29.5%20.6%11
50%28.8%21.3%12
50%27.3%22.8%13
50%26.9%23.1%14
Compiler

Compiled 14 to 11 computations (21.4% saved)

sample6.7s (59.4%)

Results
3.1s4201×body1024valid
1.3s1926×body1024invalid
888.0ms2090×body512valid
422.0ms1006×body512invalid
293.0ms1049×body256valid
223.0ms210×body2048valid
146.0ms545×body256invalid
124.0ms706×body128valid
120.0ms792×body128invalid
Compiler

Compiled 41 to 32 computations (22% saved)

simplify113.0ms (1%)

Algorithm
egg-herbie
Rules
454×fma-def_binary64
444×times-frac_binary64
419×sub-neg_binary64
365×distribute-rgt-neg-in_binary64
340×fma-neg_binary64
Counts
1 → 2
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01118
12318
24918
310618
422517
544917
696217
7171317
8358817
9428217
10477317
11492317
12495717
13474817

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New112
Fresh011
Picked000
Done000
Total123
Error
42.5b
Counts
3 → 1
Alt Table
StatusErrorProgram
42.5b
(*.f64 (*.f64 1/2 (sin.f64 re)) (-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
Compiler

Compiled 50 to 35 computations (30% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(exp.f64 im)
0.0b
(*.f64 (*.f64 1/2 (sin.f64 re)) (-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
6.0b
(-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))

series20.0ms (0.2%)

Counts
3 → 36
Calls

3 calls:

17.0ms
(*.f64 (*.f64 1/2 (sin.f64 re)) (-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
2.0ms
(-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))
1.0ms
(exp.f64 im)

rewrite20.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
31×*-un-lft-identity_binary64
31×add-sqr-sqrt_binary64
27×prod-diff_binary64
27×add-cube-cbrt_binary64
13×distribute-lft-in_binary64
Counts
3 → 93
Calls

3 calls:

8.0ms
(*.f64 (*.f64 1/2 (sin.f64 re)) (-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
5.0ms
(-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))
1.0ms
(exp.f64 im)

simplify102.0ms (0.9%)

Algorithm
egg-herbie
Rules
602×fma-neg_binary64
384×distribute-rgt-in_binary64
362×cancel-sign-sub-inv_binary64
281×associate-*r*_binary64
278×associate-*l*_binary64
Counts
129 → 146
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02432746
15852447
221352232
342902227
448822227

prune78.0ms (0.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New1442146
Fresh000
Picked011
Done000
Total1443147
Error
0.1b
Counts
147 → 3
Alt Table
StatusErrorProgram
42.7b
(*.f64 (*.f64 1/2 (sin.f64 re)) (-.f64 (exp.f64 (neg.f64 im)) (log.f64 (exp.f64 (exp.f64 im)))))
0.5b
(*.f64 (sin.f64 re) (-.f64 (neg.f64 im) (*.f64 (pow.f64 im 3) 1/6)))
42.5b
(*.f64 (*.f64 1/2 (sin.f64 re)) (-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
Compiler

Compiled 3548 to 1285 computations (63.8% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.1b
(*.f64 (sin.f64 re) (-.f64 (neg.f64 im) (*.f64 (pow.f64 im 3) 1/6)))
0.1b
(*.f64 (pow.f64 im 3) 1/6)

series49.0ms (0.4%)

Counts
2 → 36
Calls

2 calls:

46.0ms
(*.f64 (sin.f64 re) (-.f64 (neg.f64 im) (*.f64 (pow.f64 im 3) 1/6)))
3.0ms
(*.f64 (pow.f64 im 3) 1/6)

rewrite17.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt_binary64
20×prod-diff_binary64
15×associate-*l*_binary64
14×*-un-lft-identity_binary64
14×add-cube-cbrt_binary64
Counts
2 → 79
Calls

2 calls:

8.0ms
(*.f64 (sin.f64 re) (-.f64 (neg.f64 im) (*.f64 (pow.f64 im 3) 1/6)))
4.0ms
(*.f64 (pow.f64 im 3) 1/6)

simplify88.0ms (0.8%)

Algorithm
egg-herbie
Rules
760×fma-def_binary64
481×fma-neg_binary64
382×cancel-sign-sub-inv_binary64
354×exp-prod_binary64
273×unswap-sqr_binary64
Counts
115 → 122
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01922142
14451909
217051772
342231772
449661772

prune131.0ms (1.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New1166122
Fresh011
Picked011
Done011
Total1169125
Error
0.0b
Counts
125 → 9
Alt Table
StatusErrorProgram
1.5b
(*.f64 (*.f64 (sin.f64 re) (*.f64 (cbrt.f64 (neg.f64 (fma.f64 1/6 (pow.f64 im 3) im))) (cbrt.f64 (neg.f64 (fma.f64 1/6 (pow.f64 im 3) im))))) (cbrt.f64 (-.f64 (neg.f64 im) (*.f64 (pow.f64 im 3) 1/6))))
42.7b
(*.f64 (*.f64 1/2 (sin.f64 re)) (-.f64 (exp.f64 (neg.f64 im)) (log.f64 (exp.f64 (exp.f64 im)))))
33.6b
(cbrt.f64 (*.f64 (*.f64 (*.f64 (sin.f64 re) (sin.f64 re)) (sin.f64 re)) (*.f64 (*.f64 (-.f64 (neg.f64 im) (*.f64 (pow.f64 im 3) 1/6)) (-.f64 (neg.f64 im) (*.f64 (pow.f64 im 3) 1/6))) (-.f64 (neg.f64 im) (*.f64 (pow.f64 im 3) 1/6)))))
0.5b
(*.f64 (sin.f64 re) (-.f64 (neg.f64 im) (*.f64 (pow.f64 im 3) 1/6)))
31.6b
(*.f64 (*.f64 (sin.f64 re) (sqrt.f64 (neg.f64 (fma.f64 1/6 (pow.f64 im 3) im)))) (sqrt.f64 (-.f64 (neg.f64 im) (*.f64 (pow.f64 im 3) 1/6))))
24.5b
(*.f64 (sqrt.f64 (neg.f64 (*.f64 (fma.f64 1/6 (pow.f64 im 3) im) (sin.f64 re)))) (sqrt.f64 (neg.f64 (*.f64 (fma.f64 1/6 (pow.f64 im 3) im) (sin.f64 re)))))
34.4b
(*.f64 (sqrt.f64 (sin.f64 re)) (*.f64 (neg.f64 (fma.f64 1/6 (pow.f64 im 3) im)) (sqrt.f64 (sin.f64 re))))
42.5b
(*.f64 (*.f64 1/2 (sin.f64 re)) (-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
23.7b
(/.f64 (*.f64 (sin.f64 re) (fma.f64 (pow.f64 im 6) -1/36 (*.f64 im im))) (+.f64 (neg.f64 im) (*.f64 (pow.f64 im 3) 1/6)))
Compiler

Compiled 2881 to 1837 computations (36.2% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(*.f64 (*.f64 (sin.f64 re) (*.f64 (cbrt.f64 (neg.f64 (fma.f64 1/6 (pow.f64 im 3) im))) (cbrt.f64 (neg.f64 (fma.f64 1/6 (pow.f64 im 3) im))))) (cbrt.f64 (-.f64 (neg.f64 im) (*.f64 (pow.f64 im 3) 1/6))))
0.5b
(*.f64 (cbrt.f64 (neg.f64 (fma.f64 1/6 (pow.f64 im 3) im))) (cbrt.f64 (neg.f64 (fma.f64 1/6 (pow.f64 im 3) im))))
0.7b
(cbrt.f64 (-.f64 (neg.f64 im) (*.f64 (pow.f64 im 3) 1/6)))
0.7b
(cbrt.f64 (neg.f64 (fma.f64 1/6 (pow.f64 im 3) im)))

series538.0ms (4.8%)

Counts
4 → 60
Calls

4 calls:

445.0ms
(*.f64 (*.f64 (sin.f64 re) (*.f64 (cbrt.f64 (neg.f64 (fma.f64 1/6 (pow.f64 im 3) im))) (cbrt.f64 (neg.f64 (fma.f64 1/6 (pow.f64 im 3) im))))) (cbrt.f64 (-.f64 (neg.f64 im) (*.f64 (pow.f64 im 3) 1/6))))
42.0ms
(*.f64 (cbrt.f64 (neg.f64 (fma.f64 1/6 (pow.f64 im 3) im))) (cbrt.f64 (neg.f64 (fma.f64 1/6 (pow.f64 im 3) im))))
29.0ms
(cbrt.f64 (neg.f64 (fma.f64 1/6 (pow.f64 im 3) im)))
22.0ms
(cbrt.f64 (-.f64 (neg.f64 im) (*.f64 (pow.f64 im 3) 1/6)))

rewrite38.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
64×cbrt-prod_binary64
34×add-sqr-sqrt_binary64
30×*-un-lft-identity_binary64
26×add-cube-cbrt_binary64
20×pow1_binary64
Counts
4 → 128
Calls

4 calls:

12.0ms
(*.f64 (*.f64 (sin.f64 re) (*.f64 (cbrt.f64 (neg.f64 (fma.f64 1/6 (pow.f64 im 3) im))) (cbrt.f64 (neg.f64 (fma.f64 1/6 (pow.f64 im 3) im))))) (cbrt.f64 (-.f64 (neg.f64 im) (*.f64 (pow.f64 im 3) 1/6))))
11.0ms
(*.f64 (cbrt.f64 (neg.f64 (fma.f64 1/6 (pow.f64 im 3) im))) (cbrt.f64 (neg.f64 (fma.f64 1/6 (pow.f64 im 3) im))))
3.0ms
(cbrt.f64 (-.f64 (neg.f64 im) (*.f64 (pow.f64 im 3) 1/6)))
1.0ms
(cbrt.f64 (neg.f64 (fma.f64 1/6 (pow.f64 im 3) im)))

simplify176.0ms (1.6%)

Algorithm
egg-herbie
Rules
422×cancel-sign-sub-inv_binary64
359×associate-*r*_binary64
349×fma-neg_binary64
325×associate-*l*_binary64
204×fma-def_binary64
Counts
188 → 242
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03627148
19946145
233655749
349695749
449845749

prune601.0ms (5.3%)

Pruning

12 alts after pruning (9 fresh and 3 done)

PrunedKeptTotal
New2844288
Fresh156
Picked011
Done022
Total28512297
Error
0.0b
Counts
297 → 12
Alt Table
StatusErrorProgram
1.5b
(*.f64 (*.f64 (sin.f64 re) (*.f64 (cbrt.f64 (neg.f64 (fma.f64 1/6 (pow.f64 im 3) im))) (cbrt.f64 (neg.f64 (fma.f64 1/6 (pow.f64 im 3) im))))) (cbrt.f64 (-.f64 (neg.f64 im) (*.f64 (pow.f64 im 3) 1/6))))
42.7b
(*.f64 (*.f64 1/2 (sin.f64 re)) (-.f64 (exp.f64 (neg.f64 im)) (log.f64 (exp.f64 (exp.f64 im)))))
24.5b
(*.f64 (sqrt.f64 (neg.f64 (*.f64 (fma.f64 1/6 (pow.f64 im 3) im) (sin.f64 re)))) (sqrt.f64 (neg.f64 (*.f64 (fma.f64 1/6 (pow.f64 im 3) im) (sin.f64 re)))))
2.4b
(*.f64 (*.f64 (sin.f64 re) (*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (neg.f64 (fma.f64 1/6 (pow.f64 im 3) im)))) 4) (pow.f64 (cbrt.f64 (cbrt.f64 (neg.f64 (fma.f64 1/6 (pow.f64 im 3) im)))) 4))) (cbrt.f64 (cbrt.f64 (-.f64 (neg.f64 im) (*.f64 (pow.f64 im 3) 1/6)))))
33.6b
(cbrt.f64 (*.f64 (*.f64 (*.f64 (sin.f64 re) (sin.f64 re)) (sin.f64 re)) (*.f64 (*.f64 (-.f64 (neg.f64 im) (*.f64 (pow.f64 im 3) 1/6)) (-.f64 (neg.f64 im) (*.f64 (pow.f64 im 3) 1/6))) (-.f64 (neg.f64 im) (*.f64 (pow.f64 im 3) 1/6)))))
0.5b
(*.f64 (sin.f64 re) (-.f64 (neg.f64 im) (*.f64 (pow.f64 im 3) 1/6)))
31.9b
(*.f64 (*.f64 (sin.f64 re) (*.f64 (cbrt.f64 (neg.f64 (fma.f64 1/6 (pow.f64 im 3) im))) (*.f64 (cbrt.f64 (sqrt.f64 (neg.f64 (fma.f64 1/6 (pow.f64 im 3) im)))) (cbrt.f64 (sqrt.f64 (neg.f64 (fma.f64 1/6 (pow.f64 im 3) im))))))) (cbrt.f64 (-.f64 (neg.f64 im) (*.f64 (pow.f64 im 3) 1/6))))
1.8b
(*.f64 (*.f64 (sin.f64 re) (*.f64 (*.f64 (cbrt.f64 (neg.f64 (fma.f64 1/6 (pow.f64 im 3) im))) (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (neg.f64 (fma.f64 1/6 (pow.f64 im 3) im)))) 6))) (cbrt.f64 (cbrt.f64 (neg.f64 (fma.f64 1/6 (pow.f64 im 3) im)))))) (cbrt.f64 (-.f64 (neg.f64 im) (*.f64 (pow.f64 im 3) 1/6))))
31.6b
(*.f64 (*.f64 (sin.f64 re) (sqrt.f64 (neg.f64 (fma.f64 1/6 (pow.f64 im 3) im)))) (sqrt.f64 (-.f64 (neg.f64 im) (*.f64 (pow.f64 im 3) 1/6))))
2.1b
(*.f64 (*.f64 (sin.f64 re) (pow.f64 (cbrt.f64 (cbrt.f64 (neg.f64 (fma.f64 1/6 (pow.f64 im 3) im)))) 6)) (cbrt.f64 (-.f64 (neg.f64 im) (*.f64 (pow.f64 im 3) 1/6))))
34.4b
(*.f64 (sqrt.f64 (sin.f64 re)) (*.f64 (neg.f64 (fma.f64 1/6 (pow.f64 im 3) im)) (sqrt.f64 (sin.f64 re))))
42.5b
(*.f64 (*.f64 1/2 (sin.f64 re)) (-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
Compiler

Compiled 13136 to 9955 computations (24.2% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.6b
(cbrt.f64 (cbrt.f64 (neg.f64 (fma.f64 1/6 (pow.f64 im 3) im))))
0.7b
(cbrt.f64 (neg.f64 (fma.f64 1/6 (pow.f64 im 3) im)))
0.7b
(cbrt.f64 (-.f64 (neg.f64 im) (*.f64 (pow.f64 im 3) 1/6)))
1.2b
(pow.f64 (cbrt.f64 (cbrt.f64 (neg.f64 (fma.f64 1/6 (pow.f64 im 3) im)))) 6)

series189.0ms (1.7%)

Counts
2 → 24
Calls

2 calls:

145.0ms
(pow.f64 (cbrt.f64 (cbrt.f64 (neg.f64 (fma.f64 1/6 (pow.f64 im 3) im)))) 6)
44.0ms
(cbrt.f64 (cbrt.f64 (neg.f64 (fma.f64 1/6 (pow.f64 im 3) im))))

rewrite11.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
46×cbrt-prod_binary64
16×unpow-prod-down_binary64
12×*-un-lft-identity_binary64
12×add-sqr-sqrt_binary64
12×add-cube-cbrt_binary64
Counts
2 → 56
Calls

2 calls:

3.0ms
(pow.f64 (cbrt.f64 (cbrt.f64 (neg.f64 (fma.f64 1/6 (pow.f64 im 3) im)))) 6)
2.0ms
(cbrt.f64 (cbrt.f64 (neg.f64 (fma.f64 1/6 (pow.f64 im 3) im))))

simplify97.0ms (0.9%)

Algorithm
egg-herbie
Rules
627×fma-def_binary64
425×associate-/r*_binary64
419×associate-/l*_binary64
217×fma-neg_binary64
197×unswap-sqr_binary64
Counts
80 → 117
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02193144
15603000
216412627
347952627
449652627

prune620.0ms (5.5%)

Pruning

12 alts after pruning (8 fresh and 4 done)

PrunedKeptTotal
New3310331
Fresh088
Picked011
Done033
Total33112343
Error
0.0b
Counts
343 → 12
Alt Table
StatusErrorProgram
1.5b
(*.f64 (*.f64 (sin.f64 re) (*.f64 (cbrt.f64 (neg.f64 (fma.f64 1/6 (pow.f64 im 3) im))) (cbrt.f64 (neg.f64 (fma.f64 1/6 (pow.f64 im 3) im))))) (cbrt.f64 (-.f64 (neg.f64 im) (*.f64 (pow.f64 im 3) 1/6))))
42.7b
(*.f64 (*.f64 1/2 (sin.f64 re)) (-.f64 (exp.f64 (neg.f64 im)) (log.f64 (exp.f64 (exp.f64 im)))))
24.5b
(*.f64 (sqrt.f64 (neg.f64 (*.f64 (fma.f64 1/6 (pow.f64 im 3) im) (sin.f64 re)))) (sqrt.f64 (neg.f64 (*.f64 (fma.f64 1/6 (pow.f64 im 3) im) (sin.f64 re)))))
2.4b
(*.f64 (*.f64 (sin.f64 re) (*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (neg.f64 (fma.f64 1/6 (pow.f64 im 3) im)))) 4) (pow.f64 (cbrt.f64 (cbrt.f64 (neg.f64 (fma.f64 1/6 (pow.f64 im 3) im)))) 4))) (cbrt.f64 (cbrt.f64 (-.f64 (neg.f64 im) (*.f64 (pow.f64 im 3) 1/6)))))
33.6b
(cbrt.f64 (*.f64 (*.f64 (*.f64 (sin.f64 re) (sin.f64 re)) (sin.f64 re)) (*.f64 (*.f64 (-.f64 (neg.f64 im) (*.f64 (pow.f64 im 3) 1/6)) (-.f64 (neg.f64 im) (*.f64 (pow.f64 im 3) 1/6))) (-.f64 (neg.f64 im) (*.f64 (pow.f64 im 3) 1/6)))))
0.5b
(*.f64 (sin.f64 re) (-.f64 (neg.f64 im) (*.f64 (pow.f64 im 3) 1/6)))
31.9b
(*.f64 (*.f64 (sin.f64 re) (*.f64 (cbrt.f64 (neg.f64 (fma.f64 1/6 (pow.f64 im 3) im))) (*.f64 (cbrt.f64 (sqrt.f64 (neg.f64 (fma.f64 1/6 (pow.f64 im 3) im)))) (cbrt.f64 (sqrt.f64 (neg.f64 (fma.f64 1/6 (pow.f64 im 3) im))))))) (cbrt.f64 (-.f64 (neg.f64 im) (*.f64 (pow.f64 im 3) 1/6))))
1.8b
(*.f64 (*.f64 (sin.f64 re) (*.f64 (*.f64 (cbrt.f64 (neg.f64 (fma.f64 1/6 (pow.f64 im 3) im))) (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (neg.f64 (fma.f64 1/6 (pow.f64 im 3) im)))) 6))) (cbrt.f64 (cbrt.f64 (neg.f64 (fma.f64 1/6 (pow.f64 im 3) im)))))) (cbrt.f64 (-.f64 (neg.f64 im) (*.f64 (pow.f64 im 3) 1/6))))
31.6b
(*.f64 (*.f64 (sin.f64 re) (sqrt.f64 (neg.f64 (fma.f64 1/6 (pow.f64 im 3) im)))) (sqrt.f64 (-.f64 (neg.f64 im) (*.f64 (pow.f64 im 3) 1/6))))
2.1b
(*.f64 (*.f64 (sin.f64 re) (pow.f64 (cbrt.f64 (cbrt.f64 (neg.f64 (fma.f64 1/6 (pow.f64 im 3) im)))) 6)) (cbrt.f64 (-.f64 (neg.f64 im) (*.f64 (pow.f64 im 3) 1/6))))
34.4b
(*.f64 (sqrt.f64 (sin.f64 re)) (*.f64 (neg.f64 (fma.f64 1/6 (pow.f64 im 3) im)) (sqrt.f64 (sin.f64 re))))
42.5b
(*.f64 (*.f64 1/2 (sin.f64 re)) (-.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
Compiler

Compiled 21225 to 16818 computations (20.8% saved)

regimes808.0ms (7.2%)

Accuracy

Total 0.8b remaining (89.2%)

Threshold costs 0.8b (89.2%)

Counts
92 → 1
Compiler

Compiled 18375 to 14024 computations (23.7% saved)

simplify3.0ms (0%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
+-commutative_binary64
sub-neg_binary64
neg-sub0_binary64
neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01015
11715
22415
33015
43315
53415
63415

end254.0ms (2.3%)

Compiler

Compiled 354 to 271 computations (23.4% saved)

Profiling

Loading profile data...