Details

Time bar (total: 11.5s)

analyze1.5s (13%)

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)

sample47.0ms (0.4%)

Algorithm
intervals
Results
25.0ms256×body128valid
2.0ms26×body128invalid
Compiler

Compiled 43 to 27 computations (37.2% saved)

simplify78.0ms (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

prune5.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
23.3b
Counts
3 → 1
Alt Table
StatusErrorProgram
23.3b
(/.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)

localize17.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.2b
(-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im))
23.0b
(/.f64 (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im)) (fma.f64 y.re y.re (*.f64 y.im y.im)))

series174.0ms (1.5%)

Counts
2 → 96
Calls

2 calls:

155.0ms
(/.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))

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:

8.0ms
(/.f64 (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im)) (fma.f64 y.re y.re (*.f64 y.im y.im)))
7.0ms
(-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im))

simplify160.0ms (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

prune170.0ms (1.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1038111
Fresh000
Picked101
Done000
Total1048112
Error
0.9b
Counts
112 → 8
Alt Table
StatusErrorProgram
23.7b
(/.f64 (*.f64 (cbrt.f64 (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im))) (cbrt.f64 (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im)))) (/.f64 (fma.f64 y.re y.re (*.f64 y.im y.im)) (cbrt.f64 (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im)))))
33.8b
(neg.f64 (/.f64 x.re y.im))
14.2b
(*.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)))
23.7b
(*.f64 (/.f64 1 (*.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))))) (/.f64 (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im)) (cbrt.f64 (fma.f64 y.re y.re (*.f64 y.im y.im)))))
37.8b
(/.f64 x.im y.re)
39.4b
(*.f64 (/.f64 (sqrt.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))) (hypot.f64 y.im y.re)) (/.f64 (sqrt.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))) (hypot.f64 y.im y.re)))
32.1b
(-.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))
23.4b
(/.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))))
Compiler

Compiled 2885 to 628 computations (78.2% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(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)))
13.2b
(/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re))

series473.0ms (4.1%)

Counts
4 → 132
Calls

4 calls:

223.0ms
(*.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)))
200.0ms
(/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re))
25.0ms
(hypot.f64 y.im y.re)
24.0ms
(-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))

rewrite61.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
43×add-sqr-sqrt_binary64
34×times-frac_binary64
28×*-un-lft-identity_binary64
28×add-exp-log_binary64
26×add-cube-cbrt_binary64
Counts
4 → 116
Calls

4 calls:

23.0ms
(*.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)))
10.0ms
(/.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))
1.0ms
(hypot.f64 y.im y.re)

simplify240.0ms (2.1%)

Algorithm
egg-herbie
Rules
880×times-frac_binary64
525×fma-def_binary64
334×cancel-sign-sub-inv_binary64
217×fma-neg_binary64
176×sub-neg_binary64
Counts
248 → 253
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02696157
17355482
225025423
349855423

prune417.0ms (3.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New2896295
Fresh347
Picked101
Done000
Total29310303
Error
0.9b
Counts
303 → 10
Alt Table
StatusErrorProgram
14.1b
(/.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))
39.4b
(*.f64 (/.f64 (sqrt.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))) (hypot.f64 y.im y.re)) (/.f64 (sqrt.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))) (hypot.f64 y.im y.re)))
42.7b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (-.f64 (/.f64 (*.f64 y.re x.im) y.im) x.re))
37.8b
(/.f64 x.im y.re)
32.1b
(-.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))
23.3b
(/.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)))
33.8b
(neg.f64 (/.f64 x.re y.im))
14.4b
(*.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))))
14.3b
(*.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)))))
44.3b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) x.im)
Compiler

Compiled 8105 to 2533 computations (68.7% saved)

localize16.0ms (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))
0.2b
(-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))
13.2b
(/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re))

series194.0ms (1.7%)

Counts
1 → 48
Calls

1 calls:

194.0ms
(/.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))

rewrite31.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
75×times-frac_binary64
43×*-un-lft-identity_binary64
43×add-sqr-sqrt_binary64
43×add-cube-cbrt_binary64
13×associate-/l*_binary64
Counts
1 → 73
Calls

1 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))

simplify237.0ms (2.1%)

Algorithm
egg-herbie
Rules
566×times-frac_binary64
497×fma-neg_binary64
471×associate-/l*_binary64
471×associate-/l/_binary64
359×div-sub_binary64
Counts
121 → 139
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01894368
14404066
210933872
341043805
453093805

prune416.0ms (3.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New3172319
Fresh279
Picked011
Done000
Total31910329
Error
0.9b
Counts
329 → 10
Alt Table
StatusErrorProgram
43.2b
(/.f64 (neg.f64 x.re) (hypot.f64 y.im y.re))
37.8b
(/.f64 x.im y.re)
14.1b
(/.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))
39.4b
(*.f64 (/.f64 (sqrt.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))) (hypot.f64 y.im y.re)) (/.f64 (sqrt.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))) (hypot.f64 y.im y.re)))
14.4b
(/.f64 (/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re)) (*.f64 (sqrt.f64 (hypot.f64 y.im y.re)) (sqrt.f64 (hypot.f64 y.im y.re))))
32.1b
(-.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))
23.3b
(/.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)))
33.8b
(neg.f64 (/.f64 x.re y.im))
14.3b
(*.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)))))
44.3b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) x.im)
Compiler

Compiled 8477 to 2103 computations (75.2% saved)

localize21.0ms (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)))))
13.3b
(/.f64 (hypot.f64 y.im y.re) (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)))

series749.0ms (6.5%)

Counts
3 → 144
Calls

3 calls:

393.0ms
(*.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)))))
224.0ms
(/.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)))

rewrite151.0ms (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:

47.0ms
(*.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)))))
14.0ms
(/.f64 1 (/.f64 (hypot.f64 y.im y.re) (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))))
10.0ms
(/.f64 (hypot.f64 y.im y.re) (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)))

simplify475.0ms (4.1%)

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

prune696.0ms (6%)

Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New5081509
Fresh178
Picked011
Done011
Total50910519
Error
0.9b
Counts
519 → 10
Alt Table
StatusErrorProgram
43.2b
(/.f64 (neg.f64 x.re) (hypot.f64 y.im y.re))
37.8b
(/.f64 x.im y.re)
28.3b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (/.f64 1 (cbrt.f64 (pow.f64 (/.f64 (hypot.f64 y.im y.re) (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im))) 3))))
14.4b
(/.f64 (/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re)) (*.f64 (sqrt.f64 (hypot.f64 y.im y.re)) (sqrt.f64 (hypot.f64 y.im y.re))))
14.1b
(/.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))
32.1b
(-.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))
23.3b
(/.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)))
33.8b
(neg.f64 (/.f64 x.re y.im))
14.3b
(*.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)))))
44.3b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) x.im)
Compiler

Compiled 16607 to 5244 computations (68.4% saved)

regimes3.2s (28%)

Accuracy

Total 9.2b remaining (82.2%)

Threshold costs 0b (0%)

Counts
163 → 5
Compiler

Compiled 17943 to 10024 computations (44.1% saved)

bsearch141.0ms (1.2%)

Steps
ItersRangePoint
7
5.13890299102147e+127
1.0795096187577246e+129
1.0637981004967216e+128
6
1.2555717542346906e-143
1.3706639873012685e-142
2.3930967509278203e-143
10
-1.3278658839979282e-133
-1.3471659000824467e-146
-2.263639590356727e-145
9
-4.2043555668513834e+140
-8.58439819502743e+134
-2.4390351264177468e+135
Compiler

Compiled 5 to 4 computations (20% saved)

simplify13.0ms (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
033116
145116
265116
383116
495116
5101116
6103116
7103116

end2.0ms (0%)

Compiler

Compiled 83 to 31 computations (62.7% saved)

sample1.8s (15.4%)

Algorithm
intervals
Results
951.0ms8000×body128valid
49.0ms472×body128invalid
Compiler

Compiled 279 to 150 computations (46.2% saved)

Profiling

Loading profile data...