Details

Time bar (total: 10.8s)

analyze1.8s (16.2%)

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)

sample70.0ms (0.7%)

Algorithm
intervals
Results
24.0ms256×body128valid
2.0ms19×body128invalid
Compiler

Compiled 43 to 27 computations (37.2% saved)

simplify77.0ms (0.7%)

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 (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
27.9b
Counts
3 → 1
Alt Table
StatusErrorProgram
27.9b
(/.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)

localize66.0ms (0.6%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.2b
(-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im))
27.4b
(/.f64 (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im)) (fma.f64 y.re y.re (*.f64 y.im y.im)))

series191.0ms (1.8%)

Counts
2 → 96
Calls

2 calls:

168.0ms
(/.f64 (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im)) (fma.f64 y.re y.re (*.f64 y.im y.im)))
22.0ms
(-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im))

rewrite20.0ms (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)))
6.0ms
(-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im))

simplify151.0ms (1.4%)

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

prune219.0ms (2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New10110111
Fresh000
Picked101
Done000
Total10210112
Error
0.3b
Counts
112 → 10
Alt Table
StatusErrorProgram
28.3b
(/.f64 (/.f64 (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im)) (*.f64 (cbrt.f64 (fma.f64 y.re y.re (*.f64 y.im y.im))) (cbrt.f64 (fma.f64 y.re y.re (*.f64 y.im y.im))))) (cbrt.f64 (fma.f64 y.re y.re (*.f64 y.im y.im))))
37.4b
(-.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))))
27.9b
(/.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))))
36.2b
(/.f64 x.im y.re)
28.1b
(*.f64 (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im)) (/.f64 1 (fma.f64 y.re y.re (*.f64 y.im y.im))))
38.5b
(-.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))
17.3b
(*.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)))
37.0b
(neg.f64 (/.f64 x.re y.im))
17.8b
(*.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)))
27.9b
(/.f64 (+.f64 (fma.f64 x.im y.re (neg.f64 (*.f64 y.im x.re))) (fma.f64 (neg.f64 y.im) x.re (*.f64 y.im x.re))) (fma.f64 y.re y.re (*.f64 y.im y.im)))
Compiler

Compiled 2965 to 680 computations (77.1% saved)

localize26.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.2b
(-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))
0.3b
(*.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)))
16.1b
(/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re))

series460.0ms (4.3%)

Counts
3 → 108
Calls

3 calls:

233.0ms
(/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re))
207.0ms
(*.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)))
19.0ms
(-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))

rewrite130.0ms (1.2%)

Algorithm
rewrite-expression-head
Rules
42×add-sqr-sqrt_binary64
34×times-frac_binary64
27×*-un-lft-identity_binary64
27×add-exp-log_binary64
25×add-cube-cbrt_binary64
Counts
3 → 106
Calls

3 calls:

20.0ms
(*.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)))
9.0ms
(/.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))

simplify257.0ms (2.4%)

Algorithm
egg-herbie
Rules
747×times-frac_binary64
528×fma-neg_binary64
402×fma-def_binary64
254×cancel-sign-sub-inv_binary64
230×distribute-rgt-in_binary64
Counts
214 → 211
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02265757
16074941
220964883
347654882
451024882

prune325.0ms (3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New2074211
Fresh459
Picked101
Done000
Total2129221
Error
0.3b
Counts
221 → 9
Alt Table
StatusErrorProgram
17.3b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (/.f64 (fma.f64 y.re x.im (neg.f64 (*.f64 x.re y.im))) (hypot.f64 y.im y.re)))
27.9b
(/.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))))
36.2b
(/.f64 x.im y.re)
38.5b
(-.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))
37.0b
(neg.f64 (/.f64 x.re y.im))
17.3b
(*.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)))))
17.5b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (/.f64 (/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (sqrt.f64 (hypot.f64 y.im y.re))) (sqrt.f64 (hypot.f64 y.im y.re))))
43.8b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (-.f64 (/.f64 (*.f64 x.re y.im) y.re) x.im))
27.9b
(/.f64 (+.f64 (fma.f64 x.im y.re (neg.f64 (*.f64 y.im x.re))) (fma.f64 (neg.f64 y.im) x.re (*.f64 y.im x.re))) (fma.f64 y.re y.re (*.f64 y.im y.im)))
Compiler

Compiled 5826 to 1632 computations (72% saved)

localize22.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(fma.f64 y.re x.im (neg.f64 (*.f64 x.re y.im)))
0.3b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (/.f64 (fma.f64 y.re x.im (neg.f64 (*.f64 x.re y.im))) (hypot.f64 y.im y.re)))
16.1b
(/.f64 (fma.f64 y.re x.im (neg.f64 (*.f64 x.re y.im))) (hypot.f64 y.im y.re))

series520.0ms (4.8%)

Counts
3 → 144
Calls

3 calls:

291.0ms
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (/.f64 (fma.f64 y.re x.im (neg.f64 (*.f64 x.re y.im))) (hypot.f64 y.im y.re)))
207.0ms
(/.f64 (fma.f64 y.re x.im (neg.f64 (*.f64 x.re y.im))) (hypot.f64 y.im y.re))
21.0ms
(fma.f64 y.re x.im (neg.f64 (*.f64 x.re y.im)))

rewrite48.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
42×add-sqr-sqrt_binary64
34×times-frac_binary64
27×*-un-lft-identity_binary64
27×add-exp-log_binary64
25×add-cube-cbrt_binary64
Counts
3 → 97
Calls

3 calls:

22.0ms
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (/.f64 (fma.f64 y.re x.im (neg.f64 (*.f64 x.re y.im))) (hypot.f64 y.im y.re)))
5.0ms
(/.f64 (fma.f64 y.re x.im (neg.f64 (*.f64 x.re y.im))) (hypot.f64 y.im y.re))
1.0ms
(fma.f64 y.re x.im (neg.f64 (*.f64 x.re y.im)))

simplify322.0ms (3%)

Algorithm
egg-herbie
Rules
746×times-frac_binary64
497×fma-neg_binary64
251×associate-/l/_binary64
227×fma-def_binary64
212×cancel-sign-sub-inv_binary64
Counts
241 → 218
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01955939
14995126
216785074
345555073
449785073
549785073

prune238.0ms (2.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New2180218
Fresh088
Picked011
Done000
Total2189227
Error
0.3b
Counts
227 → 9
Alt Table
StatusErrorProgram
17.3b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (/.f64 (fma.f64 y.re x.im (neg.f64 (*.f64 x.re y.im))) (hypot.f64 y.im y.re)))
27.9b
(/.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))))
36.2b
(/.f64 x.im y.re)
38.5b
(-.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))
37.0b
(neg.f64 (/.f64 x.re y.im))
17.3b
(*.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)))))
17.5b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (/.f64 (/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (sqrt.f64 (hypot.f64 y.im y.re))) (sqrt.f64 (hypot.f64 y.im y.re))))
43.8b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (-.f64 (/.f64 (*.f64 x.re y.im) y.re) x.im))
27.9b
(/.f64 (+.f64 (fma.f64 x.im y.re (neg.f64 (*.f64 y.im x.re))) (fma.f64 (neg.f64 y.im) x.re (*.f64 y.im x.re))) (fma.f64 y.re y.re (*.f64 y.im y.im)))
Compiler

Compiled 5973 to 1596 computations (73.3% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))
0.2b
(/.f64 1 (/.f64 (hypot.f64 y.im y.re) (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))))
0.3b
(*.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)))))
16.1b
(/.f64 (hypot.f64 y.im y.re) (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)))

series631.0ms (5.8%)

Counts
3 → 144
Calls

3 calls:

235.0ms
(*.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)))))
209.0ms
(/.f64 1 (/.f64 (hypot.f64 y.im y.re) (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))))
187.0ms
(/.f64 (hypot.f64 y.im y.re) (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)))

rewrite164.0ms (1.5%)

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:

56.0ms
(*.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)))))
18.0ms
(/.f64 1 (/.f64 (hypot.f64 y.im y.re) (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))))
9.0ms
(/.f64 (hypot.f64 y.im y.re) (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)))

simplify480.0ms (4.4%)

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

prune674.0ms (6.2%)

Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New5072509
Fresh167
Picked011
Done011
Total50810518
Error
0.2b
Counts
518 → 10
Alt Table
StatusErrorProgram
17.3b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (/.f64 (fma.f64 y.re x.im (neg.f64 (*.f64 x.re y.im))) (hypot.f64 y.im y.re)))
36.2b
(/.f64 x.im y.re)
17.4b
(pow.f64 (*.f64 (hypot.f64 y.im y.re) (/.f64 (hypot.f64 y.im y.re) (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)))) -1)
37.0b
(neg.f64 (/.f64 x.re y.im))
47.8b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (/.f64 1 (fma.f64 (/.f64 x.re y.re) (/.f64 y.im (*.f64 x.im x.im)) (/.f64 1 x.im))))
38.5b
(-.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))
17.3b
(*.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)))))
17.5b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (/.f64 (/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (sqrt.f64 (hypot.f64 y.im y.re))) (sqrt.f64 (hypot.f64 y.im y.re))))
43.8b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (-.f64 (/.f64 (*.f64 x.re y.im) y.re) x.im))
27.9b
(/.f64 (+.f64 (fma.f64 x.im y.re (neg.f64 (*.f64 y.im x.re))) (fma.f64 (neg.f64 y.im) x.re (*.f64 y.im x.re))) (fma.f64 y.re y.re (*.f64 y.im y.im)))
Compiler

Compiled 16633 to 5259 computations (68.4% saved)

regimes2.1s (19.8%)

Accuracy

Total 10.6b remaining (83.6%)

Threshold costs 0b (0%)

Counts
119 → 5
Compiler

Compiled 13013 to 7449 computations (42.8% saved)

bsearch141.0ms (1.3%)

Steps
ItersRangePoint
10
4.220492607566289e+123
1.2539043013395607e+136
1.846500094027842e+129
8
3.107488801263146e-88
1.1196052952513972e-85
6.614960636702775e-88
8
-1.6749620616680856e-277
-3.3867836777268165e-282
-7.25891010860212e-279
7
-1.1574424551914318e+180
-4.53562149755061e+178
-6.768602245328106e+178
Compiler

Compiled 5 to 4 computations (20% saved)

simplify10.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
043107
155107
267107
375107
480107
581107
679107

end2.0ms (0%)

Compiler

Compiled 77 to 38 computations (50.6% saved)

sample1.6s (15.2%)

Algorithm
intervals
Results
814.0ms8000×body128valid
41.0ms444×body128invalid
Compiler

Compiled 299 to 171 computations (42.8% saved)

Profiling

Loading profile data...