Details

Time bar (total: 5.8s)

analyze751.0ms (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)

sample1.3s (22.6%)

Results
1.1s8256×body128valid
62.0ms511×body128invalid
Compiler

Compiled 59 to 35 computations (40.7% saved)

simplify69.0ms (1.2%)

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

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)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(fma.f64 y.re y.re (*.f64 y.im y.im))
0.0b
(-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im))
27.1b
(/.f64 (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im)) (fma.f64 y.re y.re (*.f64 y.im y.im)))

series99.0ms (1.7%)

Counts
3 → 120
Calls

3 calls:

84.0ms
(/.f64 (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im)) (fma.f64 y.re y.re (*.f64 y.im y.im)))
9.0ms
(-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im))
6.0ms
(fma.f64 y.re y.re (*.f64 y.im y.im))

rewrite12.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
11×*-un-lft-identity_binary64
11×add-sqr-sqrt_binary64
11×add-cube-cbrt_binary64
times-frac_binary64
add-cbrt-cube_binary64
Counts
3 → 58
Calls

3 calls:

6.0ms
(/.f64 (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im)) (fma.f64 y.re y.re (*.f64 y.im y.im)))
3.0ms
(-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im))
0.0ms
(fma.f64 y.re y.re (*.f64 y.im y.im))

simplify115.0ms (2%)

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
178 → 135
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01363054
13262877
210952830
344072830
449952830
549462830

prune138.0ms (2.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New12510135
Fresh000
Picked101
Done000
Total12610136
Error
1.9b
Counts
136 → 10
Alt Table
StatusErrorProgram
27.6b
(/.f64 (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im)) (*.f64 (hypot.f64 y.im y.re) (hypot.f64 y.im y.re)))
39.7b
(-.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))
27.5b
(/.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))))
40.0b
(cbrt.f64 (*.f64 (*.f64 (/.f64 (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im)) (fma.f64 y.re y.re (*.f64 y.im y.im))) (/.f64 (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im)) (fma.f64 y.re y.re (*.f64 y.im y.im)))) (/.f64 (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im)) (fma.f64 y.re y.re (*.f64 y.im y.im)))))
40.2b
(neg.f64 (/.f64 x.re y.im))
27.6b
(*.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))))
44.5b
(/.f64 (cbrt.f64 (pow.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) 3)) (fma.f64 y.re y.re (*.f64 y.im y.im)))
17.5b
(*.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)))
36.1b
(-.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))))
36.8b
(/.f64 x.im y.re)
Compiler

Compiled 3360 to 742 computations (77.9% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(/.f64 1 (hypot.f64 y.im y.re))
0.0b
(-.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)))
16.3b
(/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re))

series227.0ms (3.9%)

Counts
4 → 132
Calls

4 calls:

104.0ms
(*.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)))
96.0ms
(/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re))
18.0ms
(/.f64 1 (hypot.f64 y.im y.re))
9.0ms
(-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))

rewrite32.0ms (0.6%)

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)))
6.0ms
(/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re))
3.0ms
(-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))
2.0ms
(/.f64 1 (hypot.f64 y.im y.re))

simplify124.0ms (2.1%)

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

prune250.0ms (4.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New2687275
Fresh459
Picked101
Done000
Total27312285
Error
1.8b
Counts
285 → 12
Alt Table
StatusErrorProgram
17.3b
(/.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))
33.9b
(-.f64 (/.f64 x.im y.re) (/.f64 (*.f64 x.re y.im) (*.f64 y.re y.re)))
27.6b
(/.f64 (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im)) (*.f64 (hypot.f64 y.im y.re) (hypot.f64 y.im y.re)))
39.7b
(-.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))
17.6b
(*.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))))
40.2b
(neg.f64 (/.f64 x.re y.im))
17.4b
(/.f64 (*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))) (hypot.f64 y.im y.re))
27.6b
(*.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))))
46.5b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) x.re)
44.1b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (neg.f64 x.im))
36.1b
(-.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))))
46.3b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (neg.f64 x.re))
Compiler

Compiled 7610 to 2331 computations (69.4% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))
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))
16.3b
(/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re))

series99.0ms (1.7%)

Counts
1 → 48
Calls

1 calls:

99.0ms
(/.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))

rewrite17.0ms (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:

6.0ms
(/.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))

simplify117.0ms (2%)

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

prune161.0ms (2.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New2323235
Fresh4711
Picked011
Done000
Total23611247
Error
1.8b
Counts
247 → 11
Alt Table
StatusErrorProgram
17.3b
(/.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))
33.9b
(-.f64 (/.f64 x.im y.re) (/.f64 (*.f64 x.re y.im) (*.f64 y.re y.re)))
27.6b
(/.f64 (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im)) (*.f64 (hypot.f64 y.im y.re) (hypot.f64 y.im y.re)))
39.7b
(-.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))
43.3b
(/.f64 (-.f64 (/.f64 (*.f64 x.re y.im) y.re) x.im) (hypot.f64 y.im y.re))
17.6b
(*.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))))
46.4b
(/.f64 x.re (hypot.f64 y.im y.re))
17.4b
(/.f64 (*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))) (hypot.f64 y.im y.re))
27.6b
(*.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))))
46.2b
(/.f64 (neg.f64 x.re) (hypot.f64 y.im y.re))
36.1b
(-.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))))
Compiler

Compiled 6449 to 1411 computations (78.1% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(/.f64 1 (hypot.f64 y.im y.re))
0.0b
(-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))
0.1b
(/.f64 (*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))) (hypot.f64 y.im y.re))
16.5b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)))

series195.0ms (3.4%)

Counts
2 → 96
Calls

2 calls:

98.0ms
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)))
97.0ms
(/.f64 (*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))) (hypot.f64 y.im y.re))

rewrite23.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
26×add-exp-log_binary64
19×add-sqr-sqrt_binary64
16×add-cbrt-cube_binary64
14×times-frac_binary64
13×associate-*l*_binary64
Counts
2 → 79
Calls

2 calls:

9.0ms
(/.f64 (*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))) (hypot.f64 y.im y.re))
8.0ms
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)))

simplify160.0ms (2.8%)

Algorithm
egg-herbie
Rules
508×fma-def_binary64
434×associate-/l/_binary64
342×fma-neg_binary64
251×cancel-sign-sub-inv_binary64
228×distribute-rgt-in_binary64
Counts
175 → 187
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02124849
15744060
221243988
347633986
449833986
549423986

prune201.0ms (3.5%)

Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New2750275
Fresh099
Picked011
Done011
Total27511286
Error
1.8b
Counts
286 → 11
Alt Table
StatusErrorProgram
17.3b
(/.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))
33.9b
(-.f64 (/.f64 x.im y.re) (/.f64 (*.f64 x.re y.im) (*.f64 y.re y.re)))
27.6b
(/.f64 (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im)) (*.f64 (hypot.f64 y.im y.re) (hypot.f64 y.im y.re)))
39.7b
(-.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))
43.3b
(/.f64 (-.f64 (/.f64 (*.f64 x.re y.im) y.re) x.im) (hypot.f64 y.im y.re))
17.6b
(*.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))))
46.4b
(/.f64 x.re (hypot.f64 y.im y.re))
17.4b
(/.f64 (*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))) (hypot.f64 y.im y.re))
27.6b
(*.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))))
46.2b
(/.f64 (neg.f64 x.re) (hypot.f64 y.im y.re))
36.1b
(-.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))))
Compiler

Compiled 7041 to 2305 computations (67.3% saved)

regimes1.4s (24.5%)

Accuracy

Total 9.3b remaining (83.7%)

Threshold costs 0b (0%)

Counts
138 → 5
Compiler

Compiled 14238 to 8029 computations (43.6% saved)

bsearch81.0ms (1.4%)

Steps
ItersRangePoint
6
8.814912888856409e+114
1.0956645416915016e+116
9.404920977360152e+115
7
5.4178372222264666e-148
3.4505738353189185e-146
7.65422322254339e-148
9
-2.5297655491628054e-100
-1.4597024894819825e-106
-1.4818093018118505e-106
7
-3.2411715011111546e+146
-2.9608330447315637e+144
-5.506291912962585e+144
Compiler

Compiled 5 to 4 computations (20% saved)

simplify7.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
038122
152122
277122
391122
499122
5100122
6100122

end138.0ms (2.4%)

Compiler

Compiled 377 to 187 computations (50.4% saved)

Profiling

Loading profile data...