Details

Time bar (total: 8.0s)

analyze836.0ms (10.4%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.8%0.2%0
0%99.8%0.2%1
0%99.8%0.2%2
0%99.8%0.2%3
0%99.8%0.2%4
0%99.8%0.2%5
0%99.8%0.2%6
0%99.8%0.2%7
6.2%93.6%0.2%8
25%74.9%0.2%9
28.1%71.7%0.2%10
29.6%70.2%0.2%11
53%46.8%0.2%12
71.3%28.5%0.2%13
71.7%28.1%0.2%14
Compiler

Compiled 20 to 12 computations (40% saved)

sample27.0ms (0.3%)

Algorithm
intervals
Results
15.0ms256×body128valid
1.0ms15×body128invalid
Compiler

Compiled 43 to 27 computations (37.2% saved)

simplify72.0ms (0.9%)

Algorithm
egg-herbie
Rules
1070×fma-neg_binary64
881×fma-def_binary64
768×times-frac_binary64
551×cancel-sign-sub-inv_binary64
514×unsub-neg_binary64
Counts
1 → 2
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01428
12728
24928
38028
415128
523028
632628
750228
869628
986928
10100128
11242428
12392228
13495228

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
27.6b
Counts
3 → 1
Alt Table
StatusErrorProgram
27.6b
(/.f64 (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im)) (fma.f64 y.re y.re (*.f64 y.im y.im)))
Compiler

Compiled 69 to 33 computations (52.2% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.8b
(-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im))
27.0b
(/.f64 (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im)) (fma.f64 y.re y.re (*.f64 y.im y.im)))

rewrite11.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity_binary64
10×add-sqr-sqrt_binary64
10×add-cube-cbrt_binary64
times-frac_binary64
add-cbrt-cube_binary64
Counts
2 → 48
Calls

2 calls:

4.0ms
(/.f64 (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im)) (fma.f64 y.re y.re (*.f64 y.im y.im)))
4.0ms
(-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im))

series113.0ms (1.4%)

Counts
2 → 96
Calls

2 calls:

85.0ms
(/.f64 (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im)) (fma.f64 y.re y.re (*.f64 y.im y.im)))
27.0ms
(-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im))

simplify138.0ms (1.7%)

Algorithm
egg-herbie
Rules
523×fma-neg_binary64
383×associate-*l*_binary64
348×fma-def_binary64
319×associate-*r*_binary64
252×associate-/l*_binary64
Counts
144 → 231
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01343661
13253466
210903411
344003411
449543411

prune88.0ms (1.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New2229231
Fresh000
Picked101
Done000
Total2239232
Error
3.7b
Counts
232 → 9
Alt Table
StatusErrorProgram
19.3b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re)))
37.2b
(fma.f64 (/.f64 y.re (pow.f64 y.im 2)) x.im (*.f64 (/.f64 x.re y.im) (+.f64 (/.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)) -1)))
27.8b
(/.f64 1 (/.f64 (fma.f64 y.re y.re (*.f64 y.im y.im)) (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im))))
35.5b
(-.f64 (/.f64 x.im y.re) (/.f64 (*.f64 x.re y.im) (pow.f64 y.re 2)))
37.7b
(/.f64 x.im y.re)
36.2b
(neg.f64 (/.f64 x.re y.im))
38.9b
(/.f64 (*.f64 y.re x.im) (fma.f64 y.im y.im (pow.f64 y.re 2)))
27.9b
(*.f64 (*.f64 (cbrt.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))) (cbrt.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)))) (/.f64 (cbrt.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))) (fma.f64 y.im y.im (pow.f64 y.re 2))))
19.8b
(*.f64 (/.f64 (*.f64 (cbrt.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))) (cbrt.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)))) (hypot.f64 y.im y.re)) (/.f64 (cbrt.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))) (hypot.f64 y.im y.re)))
Compiler

Compiled 2851 to 802 computations (71.9% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(/.f64 1 (hypot.f64 y.im y.re))
0.2b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re)))
0.8b
(-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))
18.0b
(/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re))

rewrite28.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
51×add-sqr-sqrt_binary64
43×times-frac_binary64
36×*-un-lft-identity_binary64
34×add-cube-cbrt_binary64
32×add-exp-log_binary64
Counts
4 → 139
Calls

4 calls:

10.0ms
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re)))
4.0ms
(/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re))
2.0ms
(-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))
2.0ms
(/.f64 1 (hypot.f64 y.im y.re))

series550.0ms (6.8%)

Counts
4 → 132
Calls

4 calls:

328.0ms
(/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re))
107.0ms
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re)))
88.0ms
(/.f64 1 (hypot.f64 y.im y.re))
27.0ms
(-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))

simplify284.0ms (3.5%)

Algorithm
egg-herbie
Rules
884×times-frac_binary64
524×fma-def_binary64
372×cancel-sign-sub-inv_binary64
204×fma-neg_binary64
186×sub-neg_binary64
Counts
271 → 464
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02778513
17507575
225587514
350817514

prune265.0ms (3.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New4559464
Fresh538
Picked101
Done000
Total46112473
Error
3.6b
Counts
473 → 12
Alt Table
StatusErrorProgram
27.8b
(/.f64 1 (/.f64 (fma.f64 y.re y.re (*.f64 y.im y.im)) (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im))))
19.2b
(/.f64 (/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re)) (hypot.f64 y.im y.re))
19.3b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (/.f64 1 (/.f64 (hypot.f64 y.im y.re) (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)))))
38.3b
(-.f64 (/.f64 x.im y.re) (fma.f64 (/.f64 (pow.f64 y.im 2) (pow.f64 y.re 3)) x.im (/.f64 (*.f64 x.re y.im) (pow.f64 y.re 2))))
19.4b
(*.f64 (/.f64 (/.f64 1 (sqrt.f64 (hypot.f64 y.im y.re))) (sqrt.f64 (hypot.f64 y.im y.re))) (/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re)))
37.2b
(fma.f64 (/.f64 y.re (pow.f64 y.im 2)) x.im (*.f64 (/.f64 x.re y.im) (+.f64 (/.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)) -1)))
44.5b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) x.re)
44.7b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (neg.f64 x.im))
27.9b
(*.f64 (*.f64 (cbrt.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))) (cbrt.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)))) (/.f64 (cbrt.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))) (fma.f64 y.im y.im (pow.f64 y.re 2))))
20.0b
(*.f64 (*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (/.f64 (*.f64 (cbrt.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))) (cbrt.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)))) (*.f64 (cbrt.f64 (hypot.f64 y.im y.re)) (cbrt.f64 (hypot.f64 y.im y.re))))) (/.f64 (cbrt.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))) (cbrt.f64 (hypot.f64 y.im y.re))))
46.8b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) x.im)
42.9b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (neg.f64 x.re))
Compiler

Compiled 7672 to 2481 computations (67.7% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(hypot.f64 y.im y.re)
0.0b
(/.f64 (/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re)) (hypot.f64 y.im y.re))
0.8b
(-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))
18.0b
(/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re))

rewrite14.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
75×times-frac_binary64
44×*-un-lft-identity_binary64
44×add-sqr-sqrt_binary64
44×add-cube-cbrt_binary64
13×associate-/l*_binary64
Counts
2 → 83
Calls

2 calls:

7.0ms
(/.f64 (/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re)) (hypot.f64 y.im y.re))
0.0ms
(hypot.f64 y.im y.re)

series127.0ms (1.6%)

Counts
2 → 72
Calls

2 calls:

114.0ms
(/.f64 (/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re)) (hypot.f64 y.im y.re))
13.0ms
(hypot.f64 y.im y.re)

simplify234.0ms (2.9%)

Algorithm
egg-herbie
Rules
698×times-frac_binary64
572×associate-/l*_binary64
471×associate-/l/_binary64
465×fma-neg_binary64
224×fma-def_binary64
Counts
155 → 267
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02356281
15725962
215075694
345595617
449905617
549625617

prune215.0ms (2.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New4316437
Fresh5611
Picked101
Done000
Total43712449
Error
3.6b
Counts
449 → 12
Alt Table
StatusErrorProgram
19.3b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (/.f64 1 (/.f64 (hypot.f64 y.im y.re) (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)))))
38.3b
(-.f64 (/.f64 x.im y.re) (fma.f64 (/.f64 (pow.f64 y.im 2) (pow.f64 y.re 3)) x.im (/.f64 (*.f64 x.re y.im) (pow.f64 y.re 2))))
27.9b
(*.f64 (*.f64 (cbrt.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))) (cbrt.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)))) (/.f64 (cbrt.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))) (fma.f64 y.im y.im (pow.f64 y.re 2))))
44.7b
(/.f64 (neg.f64 x.im) (hypot.f64 y.im y.re))
46.8b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) x.im)
19.9b
(/.f64 1 (/.f64 (hypot.f64 y.im y.re) (/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re))))
42.9b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (neg.f64 x.re))
38.9b
(/.f64 (*.f64 (*.f64 y.re x.im) (sqrt.f64 (/.f64 1 (fma.f64 y.re y.re (pow.f64 y.im 2))))) (hypot.f64 y.im y.re))
20.2b
(*.f64 (/.f64 (/.f64 (*.f64 (cbrt.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))) (cbrt.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)))) (*.f64 (cbrt.f64 (hypot.f64 y.im y.re)) (cbrt.f64 (hypot.f64 y.im y.re)))) (*.f64 (cbrt.f64 (hypot.f64 y.im y.re)) (cbrt.f64 (hypot.f64 y.im y.re)))) (/.f64 (/.f64 (cbrt.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))) (cbrt.f64 (hypot.f64 y.im y.re))) (cbrt.f64 (hypot.f64 y.im y.re))))
19.4b
(/.f64 (/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (*.f64 (sqrt.f64 (hypot.f64 y.im y.re)) (sqrt.f64 (hypot.f64 y.im y.re)))) (hypot.f64 y.im y.re))
37.2b
(fma.f64 (/.f64 y.re (pow.f64 y.im 2)) x.im (*.f64 (/.f64 x.re y.im) (+.f64 (/.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)) -1)))
44.5b
(/.f64 x.re (hypot.f64 y.im y.re))
Compiler

Compiled 7375 to 1921 computations (74% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(/.f64 1 (/.f64 (hypot.f64 y.im y.re) (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))))
0.2b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (/.f64 1 (/.f64 (hypot.f64 y.im y.re) (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)))))
0.8b
(-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))
18.1b
(/.f64 (hypot.f64 y.im y.re) (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)))

rewrite57.0ms (0.7%)

Algorithm
rewrite-expression-head
Rules
199×times-frac_binary64
146×add-sqr-sqrt_binary64
110×*-un-lft-identity_binary64
99×add-cube-cbrt_binary64
99×add-exp-log_binary64
Counts
3 → 246
Calls

3 calls:

23.0ms
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (/.f64 1 (/.f64 (hypot.f64 y.im y.re) (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)))))
7.0ms
(/.f64 1 (/.f64 (hypot.f64 y.im y.re) (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))))
4.0ms
(/.f64 (hypot.f64 y.im y.re) (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)))

series319.0ms (4%)

Counts
3 → 144
Calls

3 calls:

111.0ms
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (/.f64 1 (/.f64 (hypot.f64 y.im y.re) (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)))))
110.0ms
(/.f64 1 (/.f64 (hypot.f64 y.im y.re) (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))))
97.0ms
(/.f64 (hypot.f64 y.im y.re) (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)))

simplify370.0ms (4.6%)

Algorithm
egg-herbie
Rules
455×times-frac_binary64
363×associate-/l*_binary64
263×associate-/r*_binary64
231×associate-*l*_binary64
214×associate-*r*_binary64
Counts
390 → 751
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
038016809
1106614631
2438614475
3514814475

prune429.0ms (5.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New8312833
Fresh11011
Picked101
Done000
Total83312845
Error
3.6b
Counts
845 → 12
Alt Table
StatusErrorProgram
38.3b
(-.f64 (/.f64 x.im y.re) (fma.f64 (/.f64 (pow.f64 y.im 2) (pow.f64 y.re 3)) x.im (/.f64 (*.f64 x.re y.im) (pow.f64 y.re 2))))
19.3b
(/.f64 (/.f64 1 (hypot.f64 y.im y.re)) (/.f64 (hypot.f64 y.im y.re) (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))))
27.9b
(*.f64 (*.f64 (cbrt.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))) (cbrt.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)))) (/.f64 (cbrt.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))) (fma.f64 y.im y.im (pow.f64 y.re 2))))
44.7b
(/.f64 (neg.f64 x.im) (hypot.f64 y.im y.re))
46.8b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) x.im)
19.9b
(/.f64 1 (/.f64 (hypot.f64 y.im y.re) (/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re))))
42.9b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (neg.f64 x.re))
20.2b
(*.f64 (/.f64 (/.f64 (*.f64 (cbrt.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))) (cbrt.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)))) (*.f64 (cbrt.f64 (hypot.f64 y.im y.re)) (cbrt.f64 (hypot.f64 y.im y.re)))) (*.f64 (cbrt.f64 (hypot.f64 y.im y.re)) (cbrt.f64 (hypot.f64 y.im y.re)))) (/.f64 (/.f64 (cbrt.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))) (cbrt.f64 (hypot.f64 y.im y.re))) (cbrt.f64 (hypot.f64 y.im y.re))))
19.4b
(/.f64 (/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (*.f64 (sqrt.f64 (hypot.f64 y.im y.re)) (sqrt.f64 (hypot.f64 y.im y.re)))) (hypot.f64 y.im y.re))
44.5b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (/.f64 1 (/.f64 1 x.re)))
37.2b
(fma.f64 (/.f64 y.re (pow.f64 y.im 2)) x.im (*.f64 (/.f64 x.re y.im) (+.f64 (/.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)) -1)))
44.5b
(/.f64 x.re (hypot.f64 y.im y.re))
Compiler

Compiled 16680 to 5768 computations (65.4% saved)

regimes2.8s (34.9%)

Accuracy

Total 10.1b remaining (81.8%)

Threshold costs 0b (0%)

Compiler

Compiled 24263 to 14144 computations (41.7% saved)

bsearch76.0ms (0.9%)

Steps
ItersRangePoint
8
7.127700921146194e+33
8.623278281317811e+36
8.516845405596207e+36
9
6.31364442710301e-98
9.42955567804823e-91
4.677589763324624e-96
3
-2.6189660293828616e-200
-8.144088214795402e-206
-5.572939327178327e-201
9
-1.2403730767656807e+122
-1.4104146971456398e+115
-2.0042077319869305e+119
Compiler

Compiled 5 to 4 computations (20% saved)

simplify9.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
037153
148153
269153
387153
499153
5105153
6107153
7106153

end1.0ms (0%)

Compiler

Compiled 83 to 32 computations (61.4% saved)

sample929.0ms (11.6%)

Algorithm
intervals
Results
432.0ms8000×body128valid
23.0ms432×body128invalid
Compiler

Compiled 376 to 190 computations (49.5% saved)

Profiling

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