Details

Time bar (total: 7.3s)

analyze719.0ms (9.9%)

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)

sample142.0ms (2%)

Algorithm
intervals
Results
18.0ms256×body128valid
1.0ms11×body128invalid
Compiler

Compiled 43 to 27 computations (37.2% saved)

simplify67.0ms (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
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)

localize12.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(fma.f64 y.re y.re (*.f64 y.im y.im))
0.5b
(-.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)))

series114.0ms (1.6%)

Counts
3 → 120
Calls

3 calls:

98.0ms
(/.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))

rewrite36.0ms (0.5%)

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:

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)))
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))

simplify118.0ms (1.6%)

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

prune95.0ms (1.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1278135
Fresh000
Picked011
Done000
Total1279136
Error
2.0b
Counts
136 → 9
Alt Table
StatusErrorProgram
42.9b
(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)))))
40.7b
(-.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))))
39.6b
(/.f64 x.im y.re)
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)))
17.8b
(*.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)))
28.4b
(/.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))))
37.0b
(-.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))
18.4b
(*.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)))
34.7b
(neg.f64 (/.f64 x.re y.im))
Compiler

Compiled 3358 to 708 computations (78.9% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(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)))
0.5b
(-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))
16.6b
(/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re))

series269.0ms (3.7%)

Counts
4 → 132
Calls

4 calls:

143.0ms
(*.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)))
103.0ms
(/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re))
12.0ms
(hypot.f64 y.im y.re)
11.0ms
(-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))

rewrite28.0ms (0.4%)

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:

12.0ms
(*.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))
3.0ms
(-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))
0.0ms
(hypot.f64 y.im y.re)

simplify123.0ms (1.7%)

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

prune229.0ms (3.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New2896295
Fresh347
Picked101
Done011
Total29311304
Error
2.0b
Counts
304 → 11
Alt Table
StatusErrorProgram
46.0b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) x.im)
17.9b
(*.f64 (sqrt.f64 (/.f64 1 (hypot.f64 y.im y.re))) (*.f64 (sqrt.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))))
17.9b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (*.f64 (/.f64 1 (sqrt.f64 (hypot.f64 y.im y.re))) (/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (sqrt.f64 (hypot.f64 y.im y.re)))))
39.6b
(/.f64 x.im y.re)
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)))
43.2b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (neg.f64 x.re))
37.0b
(-.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))
40.7b
(-.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))))
17.7b
(/.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))
47.2b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (neg.f64 x.im))
34.7b
(neg.f64 (/.f64 x.re y.im))
Compiler

Compiled 8109 to 2557 computations (68.5% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(hypot.f64 y.im y.re)
0.1b
(/.f64 (*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))) (hypot.f64 y.im y.re))
0.5b
(-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))
16.7b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)))

series216.0ms (3%)

Counts
2 → 96
Calls

2 calls:

110.0ms
(/.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))
105.0ms
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)))

rewrite24.0ms (0.3%)

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:

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

simplify154.0ms (2.1%)

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

prune220.0ms (3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New2914295
Fresh549
Picked011
Done101
Total2979306
Error
2.0b
Counts
306 → 9
Alt Table
StatusErrorProgram
47.2b
(/.f64 (neg.f64 x.im) (hypot.f64 y.im y.re))
17.9b
(*.f64 (sqrt.f64 (/.f64 1 (hypot.f64 y.im y.re))) (*.f64 (sqrt.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))))
46.0b
(/.f64 x.im (hypot.f64 y.im y.re))
17.7b
(/.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))
17.8b
(/.f64 (/.f64 (*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (-.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)))
40.7b
(-.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))))
43.1b
(/.f64 (neg.f64 x.re) (hypot.f64 y.im y.re))
37.0b
(-.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))
34.7b
(neg.f64 (/.f64 x.re y.im))
Compiler

Compiled 7692 to 2597 computations (66.2% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(/.f64 (*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))) (sqrt.f64 (hypot.f64 y.im y.re)))
0.2b
(/.f64 (/.f64 (*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (-.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)))
0.5b
(-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))
16.7b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)))

series381.0ms (5.2%)

Counts
2 → 80
Calls

2 calls:

265.0ms
(/.f64 (*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))) (sqrt.f64 (hypot.f64 y.im y.re)))
116.0ms
(/.f64 (/.f64 (*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (-.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)))

rewrite39.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
108×times-frac_binary64
60×sqrt-prod_binary64
49×*-un-lft-identity_binary64
49×add-sqr-sqrt_binary64
49×add-cube-cbrt_binary64
Counts
2 → 137
Calls

2 calls:

11.0ms
(/.f64 (/.f64 (*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (-.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)))
8.0ms
(/.f64 (*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))) (sqrt.f64 (hypot.f64 y.im y.re)))

simplify212.0ms (2.9%)

Algorithm
egg-herbie
Rules
538×fma-def_binary64
296×fma-neg_binary64
278×cancel-sign-sub-inv_binary64
218×distribute-rgt-in_binary64
211×associate-/l/_binary64
Counts
217 → 235
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02929117
17757488
225087282
348577274
449527274

prune243.0ms (3.3%)

Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New3692371
Fresh077
Picked011
Done011
Total36911380
Error
2.0b
Counts
380 → 11
Alt Table
StatusErrorProgram
47.2b
(/.f64 (neg.f64 x.im) (hypot.f64 y.im y.re))
17.9b
(*.f64 (sqrt.f64 (/.f64 1 (hypot.f64 y.im y.re))) (*.f64 (sqrt.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))))
46.0b
(/.f64 x.im (hypot.f64 y.im y.re))
17.7b
(/.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))
17.8b
(/.f64 (/.f64 (*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (-.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)))
40.7b
(-.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 x.im (sqrt.f64 (hypot.f64 y.im y.re))) (sqrt.f64 (hypot.f64 y.im y.re)))
43.1b
(/.f64 (neg.f64 x.re) (hypot.f64 y.im y.re))
37.0b
(-.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))
46.5b
(/.f64 (/.f64 (-.f64 (/.f64 (*.f64 x.re y.im) y.re) x.im) (sqrt.f64 (hypot.f64 y.im y.re))) (sqrt.f64 (hypot.f64 y.im y.re)))
34.7b
(neg.f64 (/.f64 x.re y.im))
Compiler

Compiled 12199 to 3440 computations (71.8% saved)

regimes2.8s (38.9%)

Accuracy

Total 9.2b remaining (85.6%)

Threshold costs 0b (0%)

Counts
192 → 3
Compiler

Compiled 20528 to 11794 computations (42.5% saved)

bsearch8.0ms (0.1%)

Compiler

Compiled 19 to 11 computations (42.1% saved)

simplify5.0ms (0.1%)

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

Useful iterations: 2 (0.0ms)

IterNodesCost
02994
14394
25592
36492
46992
57192
67192

end1.0ms (0%)

Compiler

Compiled 66 to 25 computations (62.1% saved)

sample965.0ms (13.2%)

Algorithm
intervals
Results
468.0ms8000×body128valid
28.0ms462×body128invalid
Compiler

Compiled 288 to 157 computations (45.5% saved)

Profiling

Loading profile data...