Details

Time bar (total: 6.8s)

analyze1.1s (16.5%)

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
0%99.9%0.1%5
0%93.7%6.3%6
6.2%84.3%9.5%7
6.2%82.7%11%8
7.8%78%14.1%9
10.1%73%16.9%10
11.3%70%18.6%11
11.7%69.2%19.1%12
12.2%67.7%20.1%13
12.2%67%20.9%14
Compiler

Compiled 22 to 12 computations (45.5% saved)

sample3.3s (49%)

Results
2.1s3237×body8192exit
1.1s8256×body128valid
29.0ms227×body128invalid
Compiler

Compiled 43 to 23 computations (46.5% saved)

simplify127.0ms (1.9%)

Algorithm
egg-herbie
Rules
680×unsub-neg_binary64
594×fma-neg_binary64
560×sub-neg_binary64
520×fma-def_binary64
399×cancel-sign-sub-inv_binary64
Counts
1 → 2
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01226
13025
27123
319416
457314
5177914
6304814
7413714
8461514
9474914
10478414
11490714
12499814

prune3.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
7.6b
Counts
3 → 2
Alt Table
StatusErrorProgram
7.7b
(*.f64 x.re (fma.f64 x.re x.re (*.f64 (*.f64 x.im x.im) -3)))
7.7b
(-.f64 (*.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) x.re) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.im))
Compiler

Compiled 97 to 51 computations (47.4% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re))
0.1b
(*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.im)
0.2b
(-.f64 (*.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) x.re) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.im))
7.2b
(*.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) x.re)

series44.0ms (0.6%)

Counts
4 → 96
Calls

4 calls:

15.0ms
(-.f64 (*.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) x.re) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.im))
12.0ms
(*.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) x.re)
11.0ms
(*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.im)
6.0ms
(+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re))

rewrite24.0ms (0.3%)

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 → 79
Calls

4 calls:

6.0ms
(-.f64 (*.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) x.re) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.im))
5.0ms
(*.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) x.re)
5.0ms
(*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.im)
3.0ms
(+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re))

simplify119.0ms (1.8%)

Algorithm
egg-herbie
Rules
245×times-frac_binary64
240×associate-*l*_binary64
214×associate-*r*_binary64
210×distribute-rgt-out_binary64
204×fma-neg_binary64
Counts
175 → 142
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01562898
14452551
217552377
335402365
447762365
550892365

prune121.0ms (1.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1357142
Fresh011
Picked101
Done000
Total1368144
Error
0.0b
Counts
144 → 8
Alt Table
StatusErrorProgram
7.6b
(fma.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) x.re (neg.f64 (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.im)))
8.1b
(-.f64 (*.f64 (*.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) (*.f64 (cbrt.f64 x.re) (cbrt.f64 x.re))) (cbrt.f64 x.re)) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.im))
0.2b
(-.f64 (*.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.re)) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.im))
7.7b
(*.f64 x.re (fma.f64 x.re x.re (*.f64 (*.f64 x.im x.im) -3)))
8.1b
(-.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.re)) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.im))
8.3b
(*.f64 (*.f64 (cbrt.f64 (*.f64 x.re (-.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) (*.f64 x.im (+.f64 x.im x.im))))) (cbrt.f64 (*.f64 x.re (-.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) (*.f64 x.im (+.f64 x.im x.im)))))) (cbrt.f64 (*.f64 x.re (-.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) (*.f64 x.im (+.f64 x.im x.im))))))
30.7b
(cbrt.f64 (*.f64 (*.f64 (-.f64 (*.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) x.re) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.im)) (-.f64 (*.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) x.re) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.im))) (-.f64 (*.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) x.re) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.im))))
7.6b
(-.f64 (pow.f64 x.re 3) (*.f64 3 (*.f64 x.re (pow.f64 x.im 2))))
Compiler

Compiled 4544 to 929 computations (79.6% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re))
0.1b
(*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.im)
0.2b
(-.f64 (*.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.re)) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.im))
0.2b
(*.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.re))

series26.0ms (0.4%)

Counts
2 → 48
Calls

2 calls:

15.0ms
(-.f64 (*.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.re)) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.im))
11.0ms
(*.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.re))

rewrite28.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
40×associate-*l/_binary64
17×flip-+_binary64
17×flip3-+_binary64
16×frac-sub_binary64
12×frac-times_binary64
Counts
2 → 61
Calls

2 calls:

10.0ms
(-.f64 (*.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.re)) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.im))
8.0ms
(*.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.re))

simplify101.0ms (1.5%)

Algorithm
egg-herbie
Rules
567×fma-neg_binary64
525×associate-*l*_binary64
507×associate-*r*_binary64
326×neg-sub0_binary64
325×neg-mul-1_binary64
Counts
109 → 107
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01833168
17322601
234242376
340952376
447022376

prune170.0ms (2.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1636169
Fresh437
Picked101
Done000
Total1689177
Error
0b
Counts
177 → 9
Alt Table
StatusErrorProgram
0.6b
(-.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.re))) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.im))
8.1b
(-.f64 (*.f64 (*.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) (*.f64 (cbrt.f64 x.re) (cbrt.f64 x.re))) (cbrt.f64 x.re)) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.im))
7.7b
(-.f64 (*.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.re)) (*.f64 2 (*.f64 x.re (*.f64 x.im x.im))))
0.6b
(-.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.re))) (cbrt.f64 (*.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.re)))) (cbrt.f64 (*.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.re)))) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.im))
7.7b
(*.f64 x.re (fma.f64 x.re x.re (*.f64 (*.f64 x.im x.im) -3)))
24.7b
(*.f64 (sqrt.f64 (-.f64 (*.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.re)) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.im))) (sqrt.f64 (-.f64 (*.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.re)) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.im))))
1.0b
(*.f64 (*.f64 (cbrt.f64 (-.f64 (*.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.re)) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.im))) (cbrt.f64 (-.f64 (*.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.re)) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.im)))) (cbrt.f64 (-.f64 (*.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.re)) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.im))))
0.2b
(fma.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.re) (neg.f64 (*.f64 x.im (*.f64 2 (*.f64 x.re x.im)))))
7.6b
(-.f64 (pow.f64 x.re 3) (*.f64 3 (*.f64 x.re (pow.f64 x.im 2))))
Compiler

Compiled 6362 to 1420 computations (77.7% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(*.f64 (-.f64 x.re x.im) x.re)
0.0b
(*.f64 2 (*.f64 x.re x.im))
0.1b
(*.f64 x.im (*.f64 2 (*.f64 x.re x.im)))
0.2b
(fma.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.re) (neg.f64 (*.f64 x.im (*.f64 2 (*.f64 x.re x.im)))))

series38.0ms (0.6%)

Counts
4 → 72
Calls

4 calls:

16.0ms
(fma.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.re) (neg.f64 (*.f64 x.im (*.f64 2 (*.f64 x.re x.im)))))
12.0ms
(*.f64 x.im (*.f64 2 (*.f64 x.re x.im)))
5.0ms
(*.f64 (-.f64 x.re x.im) x.re)
5.0ms
(*.f64 2 (*.f64 x.re x.im))

rewrite19.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
20×add-cbrt-cube_binary64
20×add-exp-log_binary64
20×pow1_binary64
12×add-sqr-sqrt_binary64
11×associate-*l*_binary64
Counts
4 → 77
Calls

4 calls:

6.0ms
(*.f64 (-.f64 x.re x.im) x.re)
5.0ms
(*.f64 x.im (*.f64 2 (*.f64 x.re x.im)))
4.0ms
(*.f64 2 (*.f64 x.re x.im))
0.0ms
(fma.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.re) (neg.f64 (*.f64 x.im (*.f64 2 (*.f64 x.re x.im)))))

simplify90.0ms (1.3%)

Algorithm
egg-herbie
Rules
798×fma-def_binary64
590×fma-neg_binary64
401×*-commutative_binary64
288×unswap-sqr_binary64
263×associate-+l+_binary64
Counts
149 → 117
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01221941
12841669
29441623
319581541
447861541
552511541

prune137.0ms (2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New1134117
Fresh628
Picked011
Done000
Total1197126
Error
0b
Counts
126 → 7
Alt Table
StatusErrorProgram
0.7b
(fma.f64 (+.f64 x.re x.im) (*.f64 (*.f64 (-.f64 x.re x.im) (*.f64 (cbrt.f64 x.re) (cbrt.f64 x.re))) (cbrt.f64 x.re)) (neg.f64 (*.f64 x.im (*.f64 2 (*.f64 x.re x.im)))))
0.5b
(fma.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.re) (neg.f64 (*.f64 (*.f64 (cbrt.f64 x.im) (cbrt.f64 x.im)) (*.f64 (cbrt.f64 x.im) (*.f64 2 (*.f64 x.re x.im))))))
18.4b
(fma.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.re) (neg.f64 (*.f64 (sqrt.f64 (*.f64 x.im (*.f64 2 (*.f64 x.re x.im)))) (sqrt.f64 (*.f64 x.im (*.f64 2 (*.f64 x.re x.im)))))))
7.7b
(*.f64 x.re (fma.f64 x.re x.re (*.f64 (*.f64 x.im x.im) -3)))
1.0b
(*.f64 (*.f64 (cbrt.f64 (fma.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.re) (neg.f64 (*.f64 x.im (*.f64 2 (*.f64 x.re x.im)))))) (cbrt.f64 (fma.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.re) (neg.f64 (*.f64 x.im (*.f64 2 (*.f64 x.re x.im))))))) (cbrt.f64 (fma.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.re) (neg.f64 (*.f64 x.im (*.f64 2 (*.f64 x.re x.im)))))))
0.2b
(fma.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.re) (neg.f64 (*.f64 x.im (*.f64 2 (*.f64 x.re x.im)))))
7.6b
(-.f64 (pow.f64 x.re 3) (*.f64 3 (*.f64 x.re (pow.f64 x.im 2))))
Compiler

Compiled 2913 to 1136 computations (61% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 (*.f64 (cbrt.f64 x.im) (cbrt.f64 x.im)) (*.f64 (cbrt.f64 x.im) (*.f64 2 (*.f64 x.re x.im))))
0.3b
(*.f64 (cbrt.f64 x.im) (*.f64 2 (*.f64 x.re x.im)))
0.5b
(*.f64 (cbrt.f64 x.im) (cbrt.f64 x.im))
0.6b
(cbrt.f64 x.im)

series456.0ms (6.7%)

Counts
4 → 72
Calls

4 calls:

359.0ms
(*.f64 (cbrt.f64 x.im) (*.f64 2 (*.f64 x.re x.im)))
36.0ms
(*.f64 (cbrt.f64 x.im) (cbrt.f64 x.im))
36.0ms
(cbrt.f64 x.im)
25.0ms
(*.f64 (*.f64 (cbrt.f64 x.im) (cbrt.f64 x.im)) (*.f64 (cbrt.f64 x.im) (*.f64 2 (*.f64 x.re x.im))))

rewrite33.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
52×pow1_binary64
47×add-exp-log_binary64
32×pow-prod-down_binary64
31×cbrt-unprod_binary64
31×prod-exp_binary64
Counts
4 → 117
Calls

4 calls:

14.0ms
(*.f64 (*.f64 (cbrt.f64 x.im) (cbrt.f64 x.im)) (*.f64 (cbrt.f64 x.im) (*.f64 2 (*.f64 x.re x.im))))
6.0ms
(*.f64 (cbrt.f64 x.im) (*.f64 2 (*.f64 x.re x.im)))
5.0ms
(*.f64 (cbrt.f64 x.im) (cbrt.f64 x.im))
1.0ms
(cbrt.f64 x.im)

simplify118.0ms (1.7%)

Algorithm
egg-herbie
Rules
975×fma-def_binary64
318×associate-*r*_binary64
298×log-prod_binary64
295×associate-*l*_binary64
289×exp-prod_binary64
Counts
189 → 158
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01402286
12961877
212081826
320051753
435051741
549871741
650081741

prune176.0ms (2.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New1951196
Fresh145
Picked011
Done011
Total1967203
Error
0b
Counts
203 → 7
Alt Table
StatusErrorProgram
0.7b
(fma.f64 (+.f64 x.re x.im) (*.f64 (*.f64 (-.f64 x.re x.im) (*.f64 (cbrt.f64 x.re) (cbrt.f64 x.re))) (cbrt.f64 x.re)) (neg.f64 (*.f64 x.im (*.f64 2 (*.f64 x.re x.im)))))
0.5b
(fma.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.re) (neg.f64 (*.f64 (*.f64 (cbrt.f64 x.im) (cbrt.f64 x.im)) (*.f64 (cbrt.f64 x.im) (*.f64 2 (*.f64 x.re x.im))))))
7.7b
(*.f64 x.re (fma.f64 x.re x.re (*.f64 (*.f64 x.im x.im) -3)))
1.0b
(*.f64 (*.f64 (cbrt.f64 (fma.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.re) (neg.f64 (*.f64 x.im (*.f64 2 (*.f64 x.re x.im)))))) (cbrt.f64 (fma.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.re) (neg.f64 (*.f64 x.im (*.f64 2 (*.f64 x.re x.im))))))) (cbrt.f64 (fma.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.re) (neg.f64 (*.f64 x.im (*.f64 2 (*.f64 x.re x.im)))))))
7.7b
(fma.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.re) (neg.f64 (*.f64 2 (*.f64 x.re (pow.f64 x.im 2)))))
0.2b
(fma.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.re) (neg.f64 (*.f64 x.im (*.f64 2 (*.f64 x.re x.im)))))
7.6b
(-.f64 (pow.f64 x.re 3) (*.f64 3 (*.f64 x.re (pow.f64 x.im 2))))
Compiler

Compiled 5841 to 1903 computations (67.4% saved)

regimes340.0ms (5%)

Accuracy

Total 0.2b remaining (89%)

Threshold costs 0.2b (89%)

Counts
100 → 1
Compiler

Compiled 8973 to 4306 computations (52% saved)

simplify4.0ms (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
01558
12958
24058
35258
45758
56058
66158
76158

end108.0ms (1.6%)

Compiler

Compiled 255 to 120 computations (52.9% saved)

Profiling

Loading profile data...