Details

Time bar (total: 7.4s)

analyze743.0ms (10.1%)

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 (17%)

Results
1.1s8256×body128valid
61.0ms510×body128invalid
Compiler

Compiled 59 to 35 computations (40.7% saved)

simplify69.0ms (0.9%)

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
25.8b
Counts
3 → 1
Alt Table
StatusErrorProgram
25.8b
(/.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 2 expressions with local error:

NewErrorProgram
0.9b
(-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im))
25.2b
(/.f64 (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im)) (fma.f64 y.re y.re (*.f64 y.im y.im)))

series104.0ms (1.4%)

Counts
2 → 96
Calls

2 calls:

95.0ms
(/.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))

rewrite9.0ms (0.1%)

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:

4.0ms
(/.f64 (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im)) (fma.f64 y.re y.re (*.f64 y.im y.im)))
2.0ms
(-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im))

simplify90.0ms (1.2%)

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
144 → 111
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01322762
13232614
210882567
343982567
449522567

prune85.0ms (1.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New10011111
Fresh000
Picked101
Done000
Total10111112
Error
1.7b
Counts
112 → 11
Alt Table
StatusErrorProgram
25.8b
(*.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))))
37.5b
(-.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))
18.3b
(*.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)))
43.5b
(*.f64 (sqrt.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))) (/.f64 (sqrt.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))) (fma.f64 y.im y.im (*.f64 y.re y.re))))
38.4b
(-.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))))
18.8b
(*.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)))
39.3b
(/.f64 x.im y.re)
39.9b
(fma.f64 (/.f64 x.re (pow.f64 y.im 3)) (*.f64 y.re y.re) (fma.f64 x.im (-.f64 (/.f64 y.re (*.f64 y.im y.im)) (/.f64 (pow.f64 y.re 3) (pow.f64 y.im 4))) (neg.f64 (/.f64 x.re y.im))))
25.8b
(/.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))))
25.7b
(-.f64 (/.f64 (*.f64 x.im y.re) (fma.f64 y.re y.re (*.f64 y.im y.im))) (/.f64 (*.f64 x.re y.im) (fma.f64 y.re y.re (*.f64 y.im y.im))))
38.4b
(neg.f64 (/.f64 x.re y.im))
Compiler

Compiled 3013 to 714 computations (76.3% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(hypot.f64 y.im y.re)
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)))
0.9b
(-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))
17.1b
(/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re))

series241.0ms (3.3%)

Counts
4 → 132
Calls

4 calls:

112.0ms
(*.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)))
105.0ms
(/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re))
14.0ms
(hypot.f64 y.im y.re)
9.0ms
(-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))

rewrite60.0ms (0.8%)

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:

45.0ms
(*.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))
2.0ms
(-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))
0.0ms
(hypot.f64 y.im y.re)

simplify118.0ms (1.6%)

Algorithm
egg-herbie
Rules
880×times-frac_binary64
525×fma-def_binary64
343×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

prune222.0ms (3%)

Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New2878295
Fresh3710
Picked101
Done000
Total29115306
Error
1.7b
Counts
306 → 15
Alt Table
StatusErrorProgram
47.2b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) x.im)
43.5b
(*.f64 (sqrt.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))) (/.f64 (sqrt.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))) (fma.f64 y.im y.im (*.f64 y.re y.re))))
47.5b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (neg.f64 x.re))
39.3b
(/.f64 x.im y.re)
18.3b
(*.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)))))
39.9b
(fma.f64 (/.f64 x.re (pow.f64 y.im 3)) (*.f64 y.re y.re) (fma.f64 x.im (-.f64 (/.f64 y.re (*.f64 y.im y.im)) (/.f64 (pow.f64 y.re 3) (pow.f64 y.im 4))) (neg.f64 (/.f64 x.re y.im))))
34.0b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (cbrt.f64 (pow.f64 (/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re)) 3)))
25.8b
(*.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))))
37.5b
(-.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))
46.4b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (-.f64 (/.f64 (*.f64 x.re y.im) y.re) x.im))
38.4b
(neg.f64 (/.f64 x.re y.im))
18.1b
(/.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))
18.5b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (*.f64 (sqrt.f64 (hypot.f64 y.im y.re)) (sqrt.f64 (hypot.f64 y.im y.re)))))
38.4b
(-.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))))
46.0b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (-.f64 x.re (/.f64 (*.f64 y.re x.im) y.im)))
Compiler

Compiled 8323 to 2677 computations (67.8% saved)

localize12.0ms (0.2%)

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))
0.9b
(-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))
17.1b
(/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re))

series113.0ms (1.5%)

Counts
1 → 48
Calls

1 calls:

113.0ms
(/.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))

rewrite16.0ms (0.2%)

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))

simplify118.0ms (1.6%)

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

prune240.0ms (3.3%)

Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New3154319
Fresh41014
Picked101
Done000
Total32014334
Error
1.7b
Counts
334 → 14
Alt Table
StatusErrorProgram
43.5b
(*.f64 (sqrt.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))) (/.f64 (sqrt.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))) (fma.f64 y.im y.im (*.f64 y.re y.re))))
45.9b
(/.f64 (-.f64 x.re (/.f64 (*.f64 y.re x.im) y.im)) (hypot.f64 y.im y.re))
47.2b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) x.im)
18.4b
(/.f64 (/.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))) (sqrt.f64 (hypot.f64 y.im y.re)))
39.3b
(/.f64 x.im y.re)
18.3b
(*.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)))))
39.9b
(fma.f64 (/.f64 x.re (pow.f64 y.im 3)) (*.f64 y.re y.re) (fma.f64 x.im (-.f64 (/.f64 y.re (*.f64 y.im y.im)) (/.f64 (pow.f64 y.re 3) (pow.f64 y.im 4))) (neg.f64 (/.f64 x.re y.im))))
46.4b
(/.f64 (-.f64 (/.f64 (*.f64 y.re x.im) y.im) x.re) (hypot.f64 y.im y.re))
18.3b
(/.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))))
25.8b
(*.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))))
37.5b
(-.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))
46.4b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (-.f64 (/.f64 (*.f64 x.re y.im) y.re) x.im))
38.4b
(neg.f64 (/.f64 x.re y.im))
38.4b
(-.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))))
Compiler

Compiled 8686 to 2235 computations (74.3% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(/.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)))
0.3b
(/.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))))
0.9b
(-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))
17.1b
(/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re))

series193.0ms (2.6%)

Counts
2 → 96
Calls

2 calls:

114.0ms
(/.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))))
79.0ms
(/.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)))

rewrite73.0ms (1%)

Algorithm
rewrite-expression-head
Rules
471×times-frac_binary64
229×*-un-lft-identity_binary64
229×add-sqr-sqrt_binary64
229×add-cube-cbrt_binary64
57×associate-/r*_binary64
Counts
2 → 278
Calls

2 calls:

10.0ms
(/.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))))
10.0ms
(/.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)))

simplify346.0ms (4.7%)

Algorithm
egg-herbie
Rules
817×fma-def_binary64
319×associate-/r/_binary64
273×associate-/l*_binary64
270×times-frac_binary64
219×associate-/r*_binary64
Counts
374 → 466
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
038217043
193715411
2356414607
3483114501
4497214501

prune387.0ms (5.3%)

Pruning

15 alts after pruning (14 fresh and 1 done)

PrunedKeptTotal
New5593562
Fresh21113
Picked011
Done000
Total56115576
Error
1.6b
Counts
576 → 15
Alt Table
StatusErrorProgram
43.5b
(*.f64 (sqrt.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))) (/.f64 (sqrt.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))) (fma.f64 y.im y.im (*.f64 y.re y.re))))
45.9b
(/.f64 (-.f64 x.re (/.f64 (*.f64 y.re x.im) y.im)) (hypot.f64 y.im y.re))
47.2b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) x.im)
18.4b
(/.f64 (/.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))) (sqrt.f64 (hypot.f64 y.im y.re)))
39.3b
(/.f64 x.im y.re)
18.3b
(*.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)))))
39.9b
(fma.f64 (/.f64 x.re (pow.f64 y.im 3)) (*.f64 y.re y.re) (fma.f64 x.im (-.f64 (/.f64 y.re (*.f64 y.im y.im)) (/.f64 (pow.f64 y.re 3) (pow.f64 y.im 4))) (neg.f64 (/.f64 x.re y.im))))
46.4b
(/.f64 (-.f64 (/.f64 (*.f64 y.re x.im) y.im) x.re) (hypot.f64 y.im y.re))
18.3b
(/.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))))
35.6b
(-.f64 (/.f64 (*.f64 x.im y.re) (*.f64 y.im y.im)) (/.f64 x.re y.im))
46.4b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (-.f64 (/.f64 (*.f64 x.re y.im) y.re) x.im))
39.9b
(-.f64 (/.f64 x.im y.re) (fma.f64 (/.f64 x.re (*.f64 y.re y.re)) y.im (/.f64 (*.f64 x.im (*.f64 y.im y.im)) (pow.f64 y.re 3))))
38.4b
(-.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))))
37.5b
(-.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))
38.1b
(/.f64 1 (neg.f64 (fma.f64 (/.f64 x.im x.re) (/.f64 y.re x.re) (/.f64 y.im x.re))))
Compiler

Compiled 19013 to 4252 computations (77.6% saved)

regimes2.4s (32.8%)

Accuracy

Total 11.1b remaining (87.2%)

Threshold costs 0b (0%)

Counts
179 → 5
Compiler

Compiled 17768 to 10449 computations (41.2% saved)

bsearch109.0ms (1.5%)

Steps
ItersRangePoint
7
1.3156119714767684e+121
1.0106600787707174e+123
5.693440792837767e+122
7
8.465462286151301e-215
1.8151499656883771e-212
1.7078829799238133e-212
10
-4.7073043862324776e-119
-3.742493218619098e-129
-7.250896876502094e-122
10
-2.1913658306618039e+36
-1.1300136073051258e+26
-2.169176490284663e+36
Compiler

Compiled 5 to 4 computations (20% saved)

simplify6.0ms (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
032104
143104
260104
370104
476104
577104
677104

end307.0ms (4.2%)

Compiler

Compiled 448 to 234 computations (47.8% saved)

Profiling

Loading profile data...