Details

Time bar (total: 12.2s)

analyze1.4s (11.8%)

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)

sample51.0ms (0.4%)

Algorithm
intervals
Results
29.0ms256×body128valid
2.0ms18×body128invalid
Compiler

Compiled 43 to 27 computations (37.2% saved)

simplify96.0ms (0.8%)

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
01220
12520
24720
37820
414920
522820
632420
750020
869420
986720
1099920
11242220
12392020
13495020

prune6.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
25.3b
Counts
3 → 1
Alt Table
StatusErrorProgram
25.3b
(/.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)

localize22.0ms (0.2%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.2b
(-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im))
24.8b
(/.f64 (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im)) (fma.f64 y.re y.re (*.f64 y.im y.im)))

series183.0ms (1.5%)

Counts
2 → 96
Calls

2 calls:

165.0ms
(/.f64 (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im)) (fma.f64 y.re y.re (*.f64 y.im y.im)))
18.0ms
(-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im))

rewrite19.0ms (0.2%)

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:

9.0ms
(/.f64 (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im)) (fma.f64 y.re y.re (*.f64 y.im y.im)))
5.0ms
(-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im))

simplify159.0ms (1.3%)

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 → 111
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01322762
13232614
210882567
343982567
449522567

prune160.0ms (1.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1047111
Fresh000
Picked011
Done000
Total1048112
Error
1.1b
Counts
112 → 8
Alt Table
StatusErrorProgram
38.9b
(-.f64 (/.f64 x.im y.re) (fma.f64 (/.f64 x.re y.re) (/.f64 y.im y.re) (/.f64 (*.f64 (*.f64 y.im y.im) x.im) (pow.f64 y.re 3))))
25.3b
(/.f64 (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im)) (fma.f64 y.re y.re (*.f64 y.im y.im)))
36.8b
(neg.f64 (/.f64 x.re y.im))
25.7b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im)) (fma.f64 y.re y.re (*.f64 y.im y.im)))) (cbrt.f64 (/.f64 (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im)) (fma.f64 y.re y.re (*.f64 y.im y.im))))) (cbrt.f64 (/.f64 (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im)) (fma.f64 y.re y.re (*.f64 y.im y.im)))))
25.2b
(/.f64 (/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re)) (sqrt.f64 (fma.f64 y.re y.re (*.f64 y.im y.im))))
16.7b
(*.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)))
37.7b
(/.f64 x.im y.re)
38.9b
(-.f64 (fma.f64 (/.f64 y.re y.im) (/.f64 x.im y.im) (/.f64 (*.f64 x.re (*.f64 y.re y.re)) (pow.f64 y.im 3))) (/.f64 x.re y.im))
Compiler

Compiled 2853 to 616 computations (78.4% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(/.f64 1 (hypot.f64 y.im y.re))
0.2b
(-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))
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)))
15.6b
(/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re))

series462.0ms (3.8%)

Counts
4 → 132
Calls

4 calls:

215.0ms
(*.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)))
190.0ms
(/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re))
33.0ms
(/.f64 1 (hypot.f64 y.im y.re))
23.0ms
(-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))

rewrite62.0ms (0.5%)

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:

19.0ms
(*.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)))
13.0ms
(/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re))
5.0ms
(-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))
4.0ms
(/.f64 1 (hypot.f64 y.im y.re))

simplify263.0ms (2.2%)

Algorithm
egg-herbie
Rules
884×times-frac_binary64
524×fma-def_binary64
365×cancel-sign-sub-inv_binary64
204×fma-neg_binary64
186×sub-neg_binary64
Counts
271 → 275
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02756721
17485877
225565818
350795818

prune406.0ms (3.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New2705275
Fresh156
Picked101
Done101
Total27310283
Error
1.0b
Counts
283 → 10
Alt Table
StatusErrorProgram
25.7b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im)) (fma.f64 y.re y.re (*.f64 y.im y.im)))) (cbrt.f64 (/.f64 (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im)) (fma.f64 y.re y.re (*.f64 y.im y.im))))) (cbrt.f64 (/.f64 (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im)) (fma.f64 y.re y.re (*.f64 y.im y.im)))))
16.7b
(*.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)))))
38.9b
(-.f64 (fma.f64 (/.f64 y.re y.im) (/.f64 x.im y.im) (/.f64 (*.f64 x.re (*.f64 y.re y.re)) (pow.f64 y.im 3))) (/.f64 x.re y.im))
43.6b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (-.f64 (/.f64 (*.f64 y.re x.im) y.im) x.re))
36.8b
(neg.f64 (/.f64 x.re y.im))
16.6b
(/.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))
38.9b
(-.f64 (/.f64 x.im y.re) (fma.f64 (/.f64 x.re y.re) (/.f64 y.im y.re) (/.f64 (*.f64 (*.f64 y.im y.im) x.im) (pow.f64 y.re 3))))
42.3b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (-.f64 x.re (/.f64 (*.f64 y.re x.im) y.im)))
37.7b
(/.f64 x.im y.re)
25.3b
(*.f64 1 (/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (*.f64 (hypot.f64 y.im y.re) (hypot.f64 y.im y.re))))
Compiler

Compiled 7608 to 2297 computations (69.8% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(hypot.f64 y.im y.re)
0.1b
(/.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))
0.2b
(-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))
15.6b
(/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re))

series230.0ms (1.9%)

Counts
2 → 72
Calls

2 calls:

201.0ms
(/.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))
28.0ms
(hypot.f64 y.im y.re)

rewrite33.0ms (0.3%)

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:

12.0ms
(/.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))
1.0ms
(hypot.f64 y.im y.re)

simplify473.0ms (3.9%)

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 → 170
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02334852
15704607
215054399
345574352
449884352
549604352

prune487.0ms (4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New3044308
Fresh459
Picked101
Done000
Total3099318
Error
1.0b
Counts
318 → 9
Alt Table
StatusErrorProgram
17.4b
(/.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))))
42.2b
(/.f64 (-.f64 x.re (/.f64 (*.f64 y.re x.im) y.im)) (hypot.f64 y.im y.re))
36.8b
(neg.f64 (/.f64 x.re y.im))
16.7b
(*.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)))))
20.9b
(/.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)))) (sqrt.f64 (hypot.f64 y.im y.re))) (/.f64 (pow.f64 (sqrt.f64 (hypot.f64 y.im y.re)) 3) (cbrt.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)))))
43.6b
(/.f64 (-.f64 (/.f64 (*.f64 y.re x.im) y.im) x.re) (hypot.f64 y.im y.re))
38.9b
(-.f64 (/.f64 x.im y.re) (fma.f64 (/.f64 x.re y.re) (/.f64 y.im y.re) (/.f64 (*.f64 (*.f64 y.im y.im) x.im) (pow.f64 y.re 3))))
37.7b
(/.f64 x.im y.re)
38.9b
(-.f64 (fma.f64 (/.f64 y.re y.im) (/.f64 x.im y.im) (/.f64 (*.f64 x.re (*.f64 y.re y.re)) (pow.f64 y.im 3))) (/.f64 x.re y.im))
Compiler

Compiled 8258 to 2038 computations (75.3% saved)

localize23.0ms (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 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)))))
15.7b
(/.f64 (hypot.f64 y.im y.re) (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)))

series546.0ms (4.5%)

Counts
3 → 144
Calls

3 calls:

213.0ms
(*.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)))))
199.0ms
(/.f64 1 (/.f64 (hypot.f64 y.im y.re) (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))))
132.0ms
(/.f64 (hypot.f64 y.im y.re) (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)))

rewrite158.0ms (1.3%)

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:

44.0ms
(*.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)))))
12.0ms
(/.f64 1 (/.f64 (hypot.f64 y.im y.re) (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))))
8.0ms
(/.f64 (hypot.f64 y.im y.re) (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)))

simplify468.0ms (3.8%)

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 → 485
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
037813351
1106411363
2438411257
3514611257

prune672.0ms (5.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New5090509
Fresh088
Picked011
Done000
Total5099518
Error
1.0b
Counts
518 → 9
Alt Table
StatusErrorProgram
17.4b
(/.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))))
42.2b
(/.f64 (-.f64 x.re (/.f64 (*.f64 y.re x.im) y.im)) (hypot.f64 y.im y.re))
36.8b
(neg.f64 (/.f64 x.re y.im))
16.7b
(*.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)))))
20.9b
(/.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)))) (sqrt.f64 (hypot.f64 y.im y.re))) (/.f64 (pow.f64 (sqrt.f64 (hypot.f64 y.im y.re)) 3) (cbrt.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)))))
43.6b
(/.f64 (-.f64 (/.f64 (*.f64 y.re x.im) y.im) x.re) (hypot.f64 y.im y.re))
38.9b
(-.f64 (/.f64 x.im y.re) (fma.f64 (/.f64 x.re y.re) (/.f64 y.im y.re) (/.f64 (*.f64 (*.f64 y.im y.im) x.im) (pow.f64 y.re 3))))
37.7b
(/.f64 x.im y.re)
38.9b
(-.f64 (fma.f64 (/.f64 y.re y.im) (/.f64 x.im y.im) (/.f64 (*.f64 x.re (*.f64 y.re y.re)) (pow.f64 y.im 3))) (/.f64 x.re y.im))
Compiler

Compiled 16614 to 5240 computations (68.5% saved)

regimes3.6s (29.3%)

Accuracy

Total 10.5b remaining (86.7%)

Threshold costs 0b (0%)

Counts
156 → 5
Compiler

Compiled 16998 to 9504 computations (44.1% saved)

bsearch132.0ms (1.1%)

Steps
ItersRangePoint
5
9.863307307441638e+148
3.8313112010895703e+149
2.5261196808138677e+149
5
1.2064014089437035e-167
4.4921205841424985e-167
1.2315960820976547e-167
9
-3.532725507415324e-226
-6.386343516206783e-232
-1.851745546982872e-226
8
-8.356676410479414e+108
-1.2828768107206344e+105
-4.988426382296112e+108
Compiler

Compiled 5 to 4 computations (20% saved)

simplify12.0ms (0.1%)

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

Useful iterations: 1 (0.0ms)

IterNodesCost
032101
14297
25697
37497
48697
59397
69597
79597

end2.0ms (0%)

Compiler

Compiled 70 to 28 computations (60% saved)

sample2.0s (16.6%)

Algorithm
intervals
Results
1.0s8000×body128valid
53.0ms484×body128invalid
Compiler

Compiled 273 to 143 computations (47.6% saved)

Profiling

Loading profile data...