Details

Time bar (total: 8.4s)

analyze750.0ms (9%)

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)

sample1.5s (18.4%)

Results
1.4s8256×body128valid
62.0ms493×body128invalid
Compiler

Compiled 59 to 35 computations (40.7% saved)

simplify67.0ms (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

prune3.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
26.1b
Counts
3 → 2
Alt Table
StatusErrorProgram
26.1b
(/.f64 (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im)) (fma.f64 y.re y.re (*.f64 y.im y.im)))
26.1b
(/.f64 (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im)) (+.f64 (*.f64 y.re y.re) (*.f64 y.im y.im)))
Compiler

Compiled 107 to 55 computations (48.6% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(+.f64 (*.f64 y.re y.re) (*.f64 y.im y.im))
0.7b
(-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im))
25.6b
(/.f64 (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im)) (+.f64 (*.f64 y.re y.re) (*.f64 y.im y.im)))

series112.0ms (1.3%)

Counts
3 → 120
Calls

3 calls:

95.0ms
(/.f64 (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im)) (+.f64 (*.f64 y.re y.re) (*.f64 y.im y.im)))
11.0ms
(-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im))
6.0ms
(+.f64 (*.f64 y.re y.re) (*.f64 y.im y.im))

rewrite37.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
11×*-un-lft-identity_binary64
11×add-sqr-sqrt_binary64
11×add-cube-cbrt_binary64
times-frac_binary64
add-log-exp_binary64
Counts
3 → 64
Calls

3 calls:

6.0ms
(/.f64 (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im)) (+.f64 (*.f64 y.re y.re) (*.f64 y.im y.im)))
3.0ms
(+.f64 (*.f64 y.re y.re) (*.f64 y.im y.im))
3.0ms
(-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im))

simplify102.0ms (1.2%)

Algorithm
egg-herbie
Rules
514×fma-def_binary64
396×fma-neg_binary64
392×times-frac_binary64
348×associate-/l*_binary64
235×associate-*l/_binary64
Counts
184 → 145
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01513114
14132977
213922931
348372930
450472930

prune148.0ms (1.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1378145
Fresh101
Picked101
Done000
Total1398147
Error
2.1b
Counts
147 → 8
Alt Table
StatusErrorProgram
39.6b
(-.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))))
44.5b
(/.f64 (/.f64 (-.f64 (pow.f64 (*.f64 x.im y.re) 3) (pow.f64 (*.f64 x.re y.im) 3)) (+.f64 (*.f64 (*.f64 x.im y.re) (*.f64 x.im y.re)) (+.f64 (*.f64 (*.f64 x.re y.im) (*.f64 x.re y.im)) (*.f64 (*.f64 x.im y.re) (*.f64 x.re y.im))))) (+.f64 (*.f64 y.re y.re) (*.f64 y.im y.im)))
26.4b
(/.f64 (*.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)))) (cbrt.f64 (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im)))) (+.f64 (*.f64 y.re y.re) (*.f64 y.im y.im)))
38.7b
(/.f64 x.im y.re)
36.9b
(-.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))
35.9b
(neg.f64 (/.f64 x.re y.im))
26.1b
(-.f64 (/.f64 (*.f64 y.re x.im) (fma.f64 y.im y.im (*.f64 y.re y.re))) (/.f64 (*.f64 x.re y.im) (fma.f64 y.im y.im (*.f64 y.re y.re))))
16.0b
(*.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)))
Compiler

Compiled 3709 to 781 computations (78.9% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(/.f64 1 (hypot.f64 y.im y.re))
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)))
0.7b
(-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))
15.0b
(/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re))

series272.0ms (3.3%)

Counts
4 → 132
Calls

4 calls:

127.0ms
(/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re))
115.0ms
(*.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)))
20.0ms
(/.f64 1 (hypot.f64 y.im y.re))
9.0ms
(-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))

rewrite32.0ms (0.4%)

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))
4.0ms
(-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))
3.0ms
(/.f64 1 (hypot.f64 y.im y.re))

simplify133.0ms (1.6%)

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 → 275
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02756721
17485877
225565818
350795818

prune246.0ms (2.9%)

Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New2705275
Fresh257
Picked011
Done000
Total27211283
Error
2.0b
Counts
283 → 11
Alt Table
StatusErrorProgram
35.9b
(neg.f64 (/.f64 x.re y.im))
26.1b
(*.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))))
39.6b
(-.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))))
44.6b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (-.f64 x.im (/.f64 (*.f64 x.re y.im) y.re)))
26.4b
(/.f64 (*.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)))) (cbrt.f64 (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im)))) (+.f64 (*.f64 y.re y.re) (*.f64 y.im y.im)))
38.7b
(/.f64 x.im y.re)
46.1b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (neg.f64 x.re))
36.9b
(-.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))
16.1b
(*.f64 (/.f64 1 (sqrt.f64 (hypot.f64 y.im y.re))) (/.f64 (/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re)) (sqrt.f64 (hypot.f64 y.im y.re))))
16.0b
(*.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)))
46.7b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (neg.f64 x.im))
Compiler

Compiled 7587 to 2305 computations (69.6% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(/.f64 (/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re)) (sqrt.f64 (hypot.f64 y.im y.re)))
0.3b
(*.f64 (/.f64 1 (sqrt.f64 (hypot.f64 y.im y.re))) (/.f64 (/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re)) (sqrt.f64 (hypot.f64 y.im y.re))))
0.7b
(-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))
15.0b
(/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re))

series394.0ms (4.7%)

Counts
2 → 80
Calls

2 calls:

274.0ms
(/.f64 (/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re)) (sqrt.f64 (hypot.f64 y.im y.re)))
119.0ms
(*.f64 (/.f64 1 (sqrt.f64 (hypot.f64 y.im y.re))) (/.f64 (/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re)) (sqrt.f64 (hypot.f64 y.im y.re))))

rewrite110.0ms (1.3%)

Algorithm
rewrite-expression-head
Rules
341×times-frac_binary64
251×add-sqr-sqrt_binary64
171×*-un-lft-identity_binary64
161×add-cube-cbrt_binary64
110×sqrt-prod_binary64
Counts
2 → 276
Calls

2 calls:

44.0ms
(*.f64 (/.f64 1 (sqrt.f64 (hypot.f64 y.im y.re))) (/.f64 (/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re)) (sqrt.f64 (hypot.f64 y.im y.re))))
7.0ms
(/.f64 (/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re)) (sqrt.f64 (hypot.f64 y.im y.re)))

simplify353.0ms (4.2%)

Algorithm
egg-herbie
Rules
849×fma-def_binary64
311×associate-/l*_binary64
292×associate-*l/_binary64
287×cancel-sign-sub-inv_binary64
279×associate-*r*_binary64
Counts
356 → 433
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
039715848
1108313619
2348613546
3473613545
4520313545

prune350.0ms (4.2%)

Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New5281529
Fresh099
Picked011
Done011
Total52812540
Error
2.0b
Counts
540 → 12
Alt Table
StatusErrorProgram
35.9b
(neg.f64 (/.f64 x.re y.im))
26.1b
(*.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))))
39.6b
(-.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))))
44.6b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (-.f64 x.im (/.f64 (*.f64 x.re y.im) y.re)))
26.4b
(/.f64 (*.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)))) (cbrt.f64 (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im)))) (+.f64 (*.f64 y.re y.re) (*.f64 y.im y.im)))
38.7b
(/.f64 x.im y.re)
46.1b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (neg.f64 x.re))
36.9b
(-.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))
45.2b
(*.f64 (/.f64 1 (sqrt.f64 (hypot.f64 y.im y.re))) (/.f64 x.im (sqrt.f64 (hypot.f64 y.im y.re))))
16.1b
(*.f64 (/.f64 1 (sqrt.f64 (hypot.f64 y.im y.re))) (/.f64 (/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re)) (sqrt.f64 (hypot.f64 y.im y.re))))
16.0b
(*.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)))
46.7b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (neg.f64 x.im))
Compiler

Compiled 20383 to 4279 computations (79% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(hypot.f64 y.im y.re)
0.0b
(*.f64 (hypot.f64 y.im y.re) (hypot.f64 y.im y.re))
0.7b
(-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))
25.6b
(/.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)))

series191.0ms (2.3%)

Counts
3 → 96
Calls

3 calls:

119.0ms
(/.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)))
59.0ms
(*.f64 (hypot.f64 y.im y.re) (hypot.f64 y.im y.re))
13.0ms
(hypot.f64 y.im y.re)

rewrite12.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt_binary64
10×add-cbrt-cube_binary64
10×add-exp-log_binary64
10×pow1_binary64
*-un-lft-identity_binary64
Counts
3 → 65
Calls

3 calls:

5.0ms
(/.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)))
3.0ms
(*.f64 (hypot.f64 y.im y.re) (hypot.f64 y.im y.re))
0.0ms
(hypot.f64 y.im y.re)

simplify104.0ms (1.2%)

Algorithm
egg-herbie
Rules
920×times-frac_binary64
546×associate-/l*_binary64
455×fma-neg_binary64
406×fma-def_binary64
194×cancel-sign-sub-inv_binary64
Counts
161 → 151
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01653141
14522881
215302762
349732761
452502761

prune176.0ms (2.1%)

Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New2161217
Fresh189
Picked101
Done022
Total21811229
Error
2.0b
Counts
229 → 11
Alt Table
StatusErrorProgram
34.8b
(*.f64 1 (-.f64 (/.f64 x.im y.re) (/.f64 (*.f64 x.re y.im) (pow.f64 y.re 2))))
16.0b
(*.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)))
39.6b
(-.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))))
44.6b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (-.f64 x.im (/.f64 (*.f64 x.re y.im) y.re)))
26.4b
(/.f64 (*.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)))) (cbrt.f64 (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im)))) (+.f64 (*.f64 y.re y.re) (*.f64 y.im y.im)))
46.1b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (neg.f64 x.re))
36.9b
(-.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))
45.2b
(*.f64 (/.f64 1 (sqrt.f64 (hypot.f64 y.im y.re))) (/.f64 x.im (sqrt.f64 (hypot.f64 y.im y.re))))
35.9b
(neg.f64 (/.f64 x.re y.im))
16.1b
(*.f64 (/.f64 1 (sqrt.f64 (hypot.f64 y.im y.re))) (/.f64 (/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re)) (sqrt.f64 (hypot.f64 y.im y.re))))
46.7b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (neg.f64 x.im))
Compiler

Compiled 5531 to 1932 computations (65.1% saved)

regimes2.9s (35.1%)

Accuracy

Total 10.6b remaining (86.5%)

Threshold costs 0b (0%)

Counts
247 → 5
Compiler

Compiled 28568 to 16564 computations (42% saved)

bsearch98.0ms (1.2%)

Steps
ItersRangePoint
9
1.0083278595207532e+123
4.83136891467237e+129
2.4176762365015643e+126
7
1.874380745687011e-130
6.95001546492247e-129
1.184468592590644e-129
9
-2.313504356654372e-120
-2.58924084504863e-127
-4.650305513891855e-126
7
-4.5622314456646637e+170
-3.5916675293233e+168
-3.6431575460204783e+168
Compiler

Compiled 5 to 4 computations (20% saved)

simplify6.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
037122
156122
276122
388122
495122
596122
695122

end146.0ms (1.7%)

Compiler

Compiled 391 to 195 computations (50.1% saved)

Profiling

Loading profile data...