Details

Time bar (total: 5.7s)

analyze311.0ms (5.4%)

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
25%74.9%0.1%5
25%74.9%0.1%6
31.2%50%18.8%7
34.3%43.7%22%8
45.3%26.5%28.2%9
46.8%23.4%29.8%10
48.8%14%37.2%11
49.8%12.1%38.1%12
52.8%7.1%40.1%13
53.3%6.1%40.6%14
Compiler

Compiled 22 to 12 computations (45.5% saved)

sample49.0ms (0.9%)

Algorithm
intervals
Results
30.0ms256×body128valid
3.0ms16×body128invalid
Compiler

Compiled 45 to 25 computations (44.4% saved)

simplify145.0ms (2.5%)

Algorithm
egg-herbie
Rules
613×sub-neg_binary64
578×fma-neg_binary64
529×neg-mul-1_binary64
501×neg-sub0_binary64
455×unsub-neg_binary64
Counts
1 → 2
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01224
12623
26023
313016
433516
588116
6149616
7351116
8406116
9397716
10461416
11477116
12491816
13491416

prune6.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
7.2b
Counts
3 → 2
Alt Table
StatusErrorProgram
7.2b
(+.f64 (*.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) x.im) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.re))
7.2b
(*.f64 x.im (fma.f64 x.re (*.f64 x.re 3) (neg.f64 (*.f64 x.im x.im))))
Compiler

Compiled 100 to 54 computations (46% saved)

localize22.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re))
0.2b
(+.f64 (*.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) x.im) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.re))
0.2b
(*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.re)
6.8b
(*.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) x.im)

series118.0ms (2.1%)

Counts
4 → 96
Calls

4 calls:

50.0ms
(*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.re)
30.0ms
(+.f64 (*.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) x.im) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.re))
26.0ms
(*.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) x.im)
11.0ms
(+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re))

rewrite50.0ms (0.9%)

Algorithm
rewrite-expression-head
Rules
12×associate-*l/_binary64
12×add-sqr-sqrt_binary64
*-un-lft-identity_binary64
add-cube-cbrt_binary64
add-cbrt-cube_binary64
Counts
4 → 77
Calls

4 calls:

14.0ms
(+.f64 (*.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) x.im) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.re))
10.0ms
(*.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) x.im)
10.0ms
(*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.re)
6.0ms
(+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re))

simplify129.0ms (2.2%)

Algorithm
egg-herbie
Rules
727×distribute-rgt-in_binary64
685×distribute-lft-in_binary64
245×associate-*l*_binary64
206×associate-*r*_binary64
181×distribute-rgt-out_binary64
Counts
173 → 139
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01462758
14272398
216752360
348222360

prune219.0ms (3.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1336139
Fresh011
Picked101
Done000
Total1347141
Error
0.0b
Counts
141 → 7
Alt Table
StatusErrorProgram
7.6b
(+.f64 (*.f64 (*.f64 (cbrt.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im))) (cbrt.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)))) (*.f64 (cbrt.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im))) x.im)) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.re))
7.2b
(fma.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) x.im (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.re))
0.3b
(+.f64 (*.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.im)) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.re))
7.5b
(+.f64 (*.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) x.im) (*.f64 (*.f64 (cbrt.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re))) (cbrt.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)))) (*.f64 x.re (cbrt.f64 (*.f64 2 (*.f64 x.im x.re))))))
24.3b
(+.f64 (neg.f64 (pow.f64 x.im 3)) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.re))
7.7b
(+.f64 (*.f64 (*.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) (*.f64 (cbrt.f64 x.im) (cbrt.f64 x.im))) (cbrt.f64 x.im)) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.re))
7.2b
(*.f64 x.im (fma.f64 x.re (*.f64 x.re 3) (neg.f64 (*.f64 x.im x.im))))
Compiler

Compiled 4349 to 961 computations (77.9% saved)

localize22.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re))
0.2b
(+.f64 (*.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.im)) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.re))
0.2b
(*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.re)
0.2b
(*.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.im))

series51.0ms (0.9%)

Counts
2 → 48
Calls

2 calls:

28.0ms
(+.f64 (*.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.im)) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.re))
23.0ms
(*.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.im))

rewrite54.0ms (0.9%)

Algorithm
rewrite-expression-head
Rules
40×associate-*l/_binary64
18×flip-+_binary64
18×flip3-+_binary64
16×frac-add_binary64
12×frac-times_binary64
Counts
2 → 59
Calls

2 calls:

20.0ms
(+.f64 (*.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.im)) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.re))
16.0ms
(*.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.im))

simplify163.0ms (2.8%)

Algorithm
egg-herbie
Rules
535×associate-*l*_binary64
483×associate-*r*_binary64
427×fma-neg_binary64
304×distribute-rgt-out_binary64
299×distribute-rgt-in_binary64
Counts
107 → 103
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01733975
16673223
231762270
343042268
446752268

prune317.0ms (5.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1597166
Fresh336
Picked101
Done000
Total16310173
Error
0.0b
Counts
173 → 10
Alt Table
StatusErrorProgram
7.2b
(fma.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) x.im (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.re))
0.7b
(+.f64 (*.f64 (*.f64 (cbrt.f64 (+.f64 x.re x.im)) (cbrt.f64 (+.f64 x.re x.im))) (*.f64 (cbrt.f64 (+.f64 x.re x.im)) (*.f64 (-.f64 x.re x.im) x.im))) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.re))
0.5b
(+.f64 (*.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.im)) (*.f64 (*.f64 (*.f64 2 (*.f64 x.im x.re)) (*.f64 (cbrt.f64 x.re) (cbrt.f64 x.re))) (cbrt.f64 x.re)))
7.5b
(+.f64 (*.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) x.im) (*.f64 (*.f64 (cbrt.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re))) (cbrt.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)))) (*.f64 x.re (cbrt.f64 (*.f64 2 (*.f64 x.im x.re))))))
38.9b
(/.f64 (-.f64 (*.f64 (*.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.im)) (*.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.im))) (*.f64 (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.re) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.re))) (-.f64 (*.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.im)) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.re)))
0.2b
(fma.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.im) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.re))
1.0b
(*.f64 (*.f64 (cbrt.f64 (+.f64 (*.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.im)) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.re))) (cbrt.f64 (+.f64 (*.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.im)) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.re)))) (cbrt.f64 (+.f64 (*.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.im)) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.re))))
0.6b
(+.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.im))) (cbrt.f64 (*.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.im)))) (cbrt.f64 (*.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.im)))) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.re))
7.2b
(-.f64 (*.f64 3 (*.f64 x.im (*.f64 x.re x.re))) (pow.f64 x.im 3))
7.2b
(*.f64 x.im (fma.f64 x.re (*.f64 x.re 3) (neg.f64 (*.f64 x.im x.im))))
Compiler

Compiled 6361 to 1412 computations (77.8% saved)

localize21.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(*.f64 (-.f64 x.re x.im) x.im)
0.0b
(+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re))
0.2b
(*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.re)
0.2b
(fma.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.im) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.re))

series44.0ms (0.8%)

Counts
2 → 48
Calls

2 calls:

33.0ms
(fma.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.im) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.re))
10.0ms
(*.f64 (-.f64 x.re x.im) x.im)

rewrite13.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
add-sqr-sqrt_binary64
*-un-lft-identity_binary64
associate-*l*_binary64
add-cube-cbrt_binary64
add-cbrt-cube_binary64
Counts
2 → 34
Calls

2 calls:

10.0ms
(*.f64 (-.f64 x.re x.im) x.im)
1.0ms
(fma.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.im) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.re))

simplify111.0ms (1.9%)

Algorithm
egg-herbie
Rules
834×fma-def_binary64
381×*-commutative_binary64
379×exp-prod_binary64
293×fma-neg_binary64
252×associate-*l*_binary64
Counts
82 → 65
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0711147
1144995
2409995
31394925
43300925
54985925
64958925

prune278.0ms (4.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New1244128
Fresh729
Picked011
Done000
Total1317138
Error
0b
Counts
138 → 7
Alt Table
StatusErrorProgram
0.5b
(fma.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.im) (*.f64 (*.f64 (*.f64 2 (*.f64 x.im x.re)) (*.f64 (cbrt.f64 x.re) (cbrt.f64 x.re))) (cbrt.f64 x.re)))
0.6b
(fma.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.im) (*.f64 (*.f64 (cbrt.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re))) (cbrt.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)))) (*.f64 x.re (cbrt.f64 (*.f64 2 (*.f64 x.im x.re))))))
1.0b
(*.f64 (*.f64 (cbrt.f64 (fma.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.im) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.re))) (cbrt.f64 (fma.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.im) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.re)))) (cbrt.f64 (fma.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.im) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.re))))
0.7b
(fma.f64 (+.f64 x.re x.im) (*.f64 (*.f64 (-.f64 x.re x.im) (*.f64 (cbrt.f64 x.im) (cbrt.f64 x.im))) (cbrt.f64 x.im)) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.re))
7.2b
(-.f64 (*.f64 3 (*.f64 x.im (*.f64 x.re x.re))) (pow.f64 x.im 3))
0.2b
(fma.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.im) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.re))
7.2b
(*.f64 x.im (fma.f64 x.re (*.f64 x.re 3) (neg.f64 (*.f64 x.im x.im))))
Compiler

Compiled 3359 to 771 computations (77% saved)

localize25.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(fma.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.im) (*.f64 (*.f64 (*.f64 2 (*.f64 x.im x.re)) (*.f64 (cbrt.f64 x.re) (cbrt.f64 x.re))) (cbrt.f64 x.re)))
0.2b
(*.f64 (*.f64 2 (*.f64 x.im x.re)) (*.f64 (cbrt.f64 x.re) (cbrt.f64 x.re)))
0.5b
(*.f64 (cbrt.f64 x.re) (cbrt.f64 x.re))
0.6b
(cbrt.f64 x.re)

series908.0ms (15.8%)

Counts
4 → 72
Calls

4 calls:

712.0ms
(*.f64 (*.f64 2 (*.f64 x.im x.re)) (*.f64 (cbrt.f64 x.re) (cbrt.f64 x.re)))
72.0ms
(*.f64 (cbrt.f64 x.re) (cbrt.f64 x.re))
68.0ms
(cbrt.f64 x.re)
55.0ms
(fma.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.im) (*.f64 (*.f64 (*.f64 2 (*.f64 x.im x.re)) (*.f64 (cbrt.f64 x.re) (cbrt.f64 x.re))) (cbrt.f64 x.re)))

rewrite41.0ms (0.7%)

Algorithm
rewrite-expression-head
Rules
32×pow1_binary64
27×add-exp-log_binary64
21×add-sqr-sqrt_binary64
19×cbrt-prod_binary64
19×add-cbrt-cube_binary64
Counts
4 → 95
Calls

4 calls:

18.0ms
(*.f64 (*.f64 2 (*.f64 x.im x.re)) (*.f64 (cbrt.f64 x.re) (cbrt.f64 x.re)))
9.0ms
(*.f64 (cbrt.f64 x.re) (cbrt.f64 x.re))
1.0ms
(cbrt.f64 x.re)
1.0ms
(fma.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.im) (*.f64 (*.f64 (*.f64 2 (*.f64 x.im x.re)) (*.f64 (cbrt.f64 x.re) (cbrt.f64 x.re))) (cbrt.f64 x.re)))

simplify203.0ms (3.5%)

Algorithm
egg-herbie
Rules
583×*-commutative_binary64
508×fma-def_binary64
426×exp-prod_binary64
279×distribute-rgt-in_binary64
261×log-prod_binary64
Counts
167 → 136
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01392282
12991921
211661796
322131782
443521690
548051690
649141690

prune294.0ms (5.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New1702172
Fresh235
Picked011
Done011
Total1727179
Error
0b
Counts
179 → 7
Alt Table
StatusErrorProgram
0.2b
(fma.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.im) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.re))
7.4b
(fma.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.im) (*.f64 (*.f64 (*.f64 2 (*.f64 x.im x.re)) (cbrt.f64 (*.f64 x.re x.re))) (cbrt.f64 x.re)))
0.5b
(fma.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.im) (*.f64 (*.f64 (*.f64 2 (*.f64 x.im x.re)) (*.f64 (cbrt.f64 x.re) (cbrt.f64 x.re))) (cbrt.f64 x.re)))
0.7b
(fma.f64 (+.f64 x.re x.im) (*.f64 (*.f64 (-.f64 x.re x.im) (*.f64 (cbrt.f64 x.im) (cbrt.f64 x.im))) (cbrt.f64 x.im)) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.re))
7.2b
(-.f64 (*.f64 3 (*.f64 x.im (*.f64 x.re x.re))) (pow.f64 x.im 3))
7.2b
(*.f64 x.im (fma.f64 x.re (*.f64 x.re 3) (neg.f64 (*.f64 x.im x.im))))
0.6b
(fma.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.im) (*.f64 (*.f64 (*.f64 2 (*.f64 x.im x.re)) (*.f64 (cbrt.f64 x.re) (cbrt.f64 x.re))) (*.f64 (cbrt.f64 (*.f64 (cbrt.f64 x.re) (cbrt.f64 x.re))) (cbrt.f64 (cbrt.f64 x.re)))))
Compiler

Compiled 4844 to 1500 computations (69% saved)

regimes570.0ms (9.9%)

Accuracy

Total 0.2b remaining (88.2%)

Threshold costs 0.2b (88.2%)

Counts
107 → 1
Compiler

Compiled 8145 to 4005 computations (50.8% saved)

simplify7.0ms (0.1%)

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
01123
11823
22323
32523
42623
52623

end1.0ms (0%)

Compiler

Compiled 18 to 10 computations (44.4% saved)

sample1.6s (27.2%)

Algorithm
intervals
Results
894.0ms8000×body128valid
63.0ms564×body128invalid
Compiler

Compiled 197 to 107 computations (45.7% saved)

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