Details

Time bar (total: 4.6s)

analyze2.0ms (0%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
99.9%0%0.1%1
Compiler

Compiled 22 to 12 computations (45.5% saved)

sample1.5s (31.3%)

Results
1.3s8256×body128valid
Compiler

Compiled 65 to 35 computations (46.2% saved)

simplify198.0ms (4.3%)

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

prune7.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
6.6b
Counts
3 → 2
Alt Table
StatusErrorProgram
6.7b
(*.f64 x.im (fma.f64 x.re (*.f64 x.re 3) (neg.f64 (*.f64 x.im x.im))))
11.1b
(+.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))
Compiler

Compiled 100 to 54 computations (46% saved)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

NewErrorProgram
2.9b
(fma.f64 x.re (*.f64 x.re 3) (neg.f64 (*.f64 x.im x.im)))
3.9b
(*.f64 x.im (fma.f64 x.re (*.f64 x.re 3) (neg.f64 (*.f64 x.im x.im))))

series44.0ms (1%)

Counts
2 → 48
Calls

2 calls:

29.0ms
(*.f64 x.im (fma.f64 x.re (*.f64 x.re 3) (neg.f64 (*.f64 x.im x.im))))
15.0ms
(fma.f64 x.re (*.f64 x.re 3) (neg.f64 (*.f64 x.im x.im)))

rewrite15.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
add-sqr-sqrt_binary64
*-un-lft-identity_binary64
add-cube-cbrt_binary64
add-cbrt-cube_binary64
add-exp-log_binary64
Counts
2 → 32
Calls

2 calls:

11.0ms
(*.f64 x.im (fma.f64 x.re (*.f64 x.re 3) (neg.f64 (*.f64 x.im x.im))))
1.0ms
(fma.f64 x.re (*.f64 x.re 3) (neg.f64 (*.f64 x.im x.im)))

simplify196.0ms (4.2%)

Algorithm
egg-herbie
Rules
435×exp-prod_binary64
356×unswap-sqr_binary64
355×fma-def_binary64
319×*-commutative_binary64
271×associate-*l*_binary64
Counts
80 → 66
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0571276
11161183
23361183
311361183
421051183
544651183
649491183
749161183

prune114.0ms (2.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New62466
Fresh011
Picked011
Done000
Total62668
Error
3.8b
Counts
68 → 6
Alt Table
StatusErrorProgram
31.7b
(*.f64 (*.f64 x.im (sqrt.f64 (fma.f64 x.re (*.f64 x.re 3) (neg.f64 (*.f64 x.im x.im))))) (sqrt.f64 (fma.f64 x.re (*.f64 x.re 3) (neg.f64 (*.f64 x.im x.im)))))
27.8b
(*.f64 3 (*.f64 (pow.f64 x.re 2) x.im))
6.7b
(*.f64 x.im (fma.f64 x.re (*.f64 x.re 3) (neg.f64 (*.f64 x.im x.im))))
13.1b
(-.f64 (*.f64 3 (*.f64 (pow.f64 x.re 2) x.im)) (pow.f64 x.im 3))
11.1b
(+.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))
7.1b
(*.f64 (*.f64 (cbrt.f64 x.im) (cbrt.f64 x.im)) (*.f64 (cbrt.f64 x.im) (fma.f64 x.re (*.f64 x.re 3) (neg.f64 (*.f64 x.im x.im)))))
Compiler

Compiled 1290 to 621 computations (51.9% saved)

localize24.0ms (0.5%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.6b
(cbrt.f64 x.im)
1.5b
(*.f64 (*.f64 (cbrt.f64 x.im) (cbrt.f64 x.im)) (*.f64 (cbrt.f64 x.im) (fma.f64 x.re (*.f64 x.re 3) (neg.f64 (*.f64 x.im x.im)))))
2.5b
(*.f64 (cbrt.f64 x.im) (fma.f64 x.re (*.f64 x.re 3) (neg.f64 (*.f64 x.im x.im))))
2.9b
(fma.f64 x.re (*.f64 x.re 3) (neg.f64 (*.f64 x.im x.im)))

series224.0ms (4.8%)

Counts
3 → 60
Calls

3 calls:

131.0ms
(*.f64 (cbrt.f64 x.im) (fma.f64 x.re (*.f64 x.re 3) (neg.f64 (*.f64 x.im x.im))))
55.0ms
(cbrt.f64 x.im)
37.0ms
(*.f64 (*.f64 (cbrt.f64 x.im) (cbrt.f64 x.im)) (*.f64 (cbrt.f64 x.im) (fma.f64 x.re (*.f64 x.re 3) (neg.f64 (*.f64 x.im x.im)))))

rewrite19.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
17×add-exp-log_binary64
17×pow1_binary64
11×add-sqr-sqrt_binary64
10×add-cbrt-cube_binary64
cbrt-unprod_binary64
Counts
3 → 67
Calls

3 calls:

8.0ms
(*.f64 (*.f64 (cbrt.f64 x.im) (cbrt.f64 x.im)) (*.f64 (cbrt.f64 x.im) (fma.f64 x.re (*.f64 x.re 3) (neg.f64 (*.f64 x.im x.im)))))
4.0ms
(*.f64 (cbrt.f64 x.im) (fma.f64 x.re (*.f64 x.re 3) (neg.f64 (*.f64 x.im x.im))))
1.0ms
(cbrt.f64 x.im)

simplify134.0ms (2.9%)

Algorithm
egg-herbie
Rules
616×exp-prod_binary64
602×fma-def_binary64
532×unswap-sqr_binary64
369×*-commutative_binary64
230×associate-*l*_binary64
Counts
127 → 113
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01142240
12701985
29441959
323251959
448131959
553601959

prune308.0ms (6.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New1730173
Fresh044
Picked011
Done011
Total1736179
Error
3.8b
Counts
179 → 6
Alt Table
StatusErrorProgram
31.7b
(*.f64 (*.f64 x.im (sqrt.f64 (fma.f64 x.re (*.f64 x.re 3) (neg.f64 (*.f64 x.im x.im))))) (sqrt.f64 (fma.f64 x.re (*.f64 x.re 3) (neg.f64 (*.f64 x.im x.im)))))
27.8b
(*.f64 3 (*.f64 (pow.f64 x.re 2) x.im))
6.7b
(*.f64 x.im (fma.f64 x.re (*.f64 x.re 3) (neg.f64 (*.f64 x.im x.im))))
13.1b
(-.f64 (*.f64 3 (*.f64 (pow.f64 x.re 2) x.im)) (pow.f64 x.im 3))
11.1b
(+.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))
7.1b
(*.f64 (*.f64 (cbrt.f64 x.im) (cbrt.f64 x.im)) (*.f64 (cbrt.f64 x.im) (fma.f64 x.re (*.f64 x.re 3) (neg.f64 (*.f64 x.im x.im)))))
Compiler

Compiled 4174 to 1531 computations (63.3% saved)

localize24.0ms (0.5%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.re)
3.2b
(-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im))
3.9b
(*.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) x.im)
4.2b
(+.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))

series96.0ms (2.1%)

Counts
4 → 96
Calls

4 calls:

28.0ms
(*.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) x.im)
27.0ms
(+.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))
24.0ms
(*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.re)
15.0ms
(-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im))

rewrite49.0ms (1.1%)

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 → 80
Calls

4 calls:

13.0ms
(*.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) x.im)
12.0ms
(+.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))
9.0ms
(*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.re)
7.0ms
(-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im))

simplify173.0ms (3.7%)

Algorithm
egg-herbie
Rules
477×fma-neg_binary64
405×cancel-sign-sub-inv_binary64
345×unswap-sqr_binary64
229×associate-*l*_binary64
193×associate-*r*_binary64
Counts
176 → 143
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01543209
14322746
216842496
331722485
448672485

prune173.0ms (3.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New1412143
Fresh123
Picked101
Done112
Total1445149
Error
0.0b
Counts
149 → 5
Alt Table
StatusErrorProgram
31.7b
(*.f64 (*.f64 x.im (sqrt.f64 (fma.f64 x.re (*.f64 x.re 3) (neg.f64 (*.f64 x.im x.im))))) (sqrt.f64 (fma.f64 x.re (*.f64 x.re 3) (neg.f64 (*.f64 x.im x.im)))))
6.7b
(*.f64 x.im (fma.f64 x.re (*.f64 x.re 3) (neg.f64 (*.f64 x.im x.im))))
4.7b
(+.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))
11.1b
(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))
13.1b
(-.f64 (*.f64 3 (*.f64 (pow.f64 x.re 2) x.im)) (pow.f64 x.im 3))
Compiler

Compiled 4216 to 871 computations (79.3% saved)

localize17.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re))
0.1b
(*.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.im))
0.2b
(*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.re)
4.2b
(+.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))

series49.0ms (1.1%)

Counts
3 → 72
Calls

3 calls:

27.0ms
(+.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))
15.0ms
(*.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.im))
8.0ms
(+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re))

rewrite51.0ms (1.1%)

Algorithm
rewrite-expression-head
Rules
40×associate-*l/_binary64
19×flip-+_binary64
19×flip3-+_binary64
16×frac-add_binary64
12×frac-times_binary64
Counts
3 → 73
Calls

3 calls:

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

simplify261.0ms (5.6%)

Algorithm
egg-herbie
Rules
546×associate-*l*_binary64
493×associate-*r*_binary64
420×fma-neg_binary64
329×distribute-rgt-out_binary64
304×distribute-rgt-in_binary64
Counts
145 → 127
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01864479
16933630
232252562
342872562
449692562
547622562

prune249.0ms (5.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New1624166
Fresh123
Picked101
Done011
Total1647171
Error
0b
Counts
171 → 7
Alt Table
StatusErrorProgram
29.4b
(*.f64 (sqrt.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))) (sqrt.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))))
4.6b
(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))
4.9b
(+.f64 (*.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.im)) (*.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 2 (*.f64 x.im x.re))) (cbrt.f64 (*.f64 2 (*.f64 x.im x.re)))) (cbrt.f64 (*.f64 2 (*.f64 x.im x.re)))) x.re))
4.9b
(+.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))
11.1b
(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))
13.1b
(-.f64 (*.f64 3 (*.f64 (pow.f64 x.re 2) x.im)) (pow.f64 x.im 3))
6.7b
(*.f64 x.im (fma.f64 x.re (*.f64 x.re 3) (neg.f64 (*.f64 x.im x.im))))
Compiler

Compiled 5855 to 1258 computations (78.5% saved)

regimes591.0ms (12.7%)

Accuracy

Total 2.2b remaining (99.4%)

Threshold costs 0b (0%)

Counts
57 → 3
Compiler

Compiled 3981 to 2103 computations (47.2% saved)

bsearch26.0ms (0.6%)

Steps
ItersRangePoint
5
6.030015917516793e+150
1.2839763804528959e+151
1.2725287036008839e+151
7
-2.615278891903897e+144
-4.664326686153622e+142
-2.580140784623766e+144
Compiler

Compiled 3 to 2 computations (33.3% 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
02456
13856
24656
35056
45256
55256

end128.0ms (2.7%)

Compiler

Compiled 255 to 129 computations (49.4% saved)

Profiling

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