Details

Time bar (total: 11.1s)

analyze98.0ms (0.9%)

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
74.9%25%0.2%5
74.9%25%0.2%6
74.9%25%0.2%7
87.3%12.5%0.2%8
93.6%6.2%0.2%9
93.6%6.2%0.2%10
93.6%6.2%0.2%11
96.7%3.1%0.2%12
98.2%1.6%0.2%13
98.2%1.6%0.2%14
Compiler

Compiled 20 to 12 computations (40% saved)

sample1.3s (11.6%)

Results
1.2s8256×body128valid
Compiler

Compiled 59 to 35 computations (40.7% saved)

simplify14.0ms (0.1%)

Algorithm
egg-herbie
Rules
fma-def_binary64
+-commutative_binary64
*-commutative_binary64
Counts
1 → 2
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01218
11818
22218
32218

prune6.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
28.8b
Counts
3 → 1
Alt Table
StatusErrorProgram
28.8b
(/.f64 (fma.f64 x.re y.re (*.f64 x.im y.im)) (fma.f64 y.re y.re (*.f64 y.im y.im)))
Compiler

Compiled 66 to 32 computations (51.5% saved)

localize27.0ms (0.2%)

Local error

Found 2 expressions with local error:

NewErrorProgram
1.0b
(fma.f64 x.re y.re (*.f64 x.im y.im))
28.6b
(/.f64 (fma.f64 x.re y.re (*.f64 x.im y.im)) (fma.f64 y.re y.re (*.f64 y.im y.im)))

series181.0ms (1.6%)

Counts
2 → 96
Calls

2 calls:

166.0ms
(/.f64 (fma.f64 x.re y.re (*.f64 x.im y.im)) (fma.f64 y.re y.re (*.f64 y.im y.im)))
15.0ms
(fma.f64 x.re y.re (*.f64 x.im y.im))

rewrite8.0ms (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 → 39
Calls

2 calls:

4.0ms
(/.f64 (fma.f64 x.re y.re (*.f64 x.im y.im)) (fma.f64 y.re y.re (*.f64 y.im y.im)))
1.0ms
(fma.f64 x.re y.re (*.f64 x.im y.im))

simplify128.0ms (1.2%)

Algorithm
egg-herbie
Rules
687×fma-def_binary64
413×associate-/l/_binary64
364×fma-neg_binary64
246×distribute-rgt-neg-in_binary64
245×distribute-lft-neg-in_binary64
Counts
135 → 95
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0972544
12022411
26062327
321922279
451012279

prune149.0ms (1.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New851095
Fresh000
Picked101
Done000
Total861096
Error
2.0b
Counts
96 → 10
Alt Table
StatusErrorProgram
17.4b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (hypot.f64 y.im y.re)))
35.6b
(+.f64 (/.f64 x.im y.im) (*.f64 (/.f64 y.re (*.f64 y.im y.im)) (-.f64 x.re (/.f64 (*.f64 x.im y.re) y.im))))
28.7b
(/.f64 (/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (hypot.f64 y.im y.re)) (sqrt.f64 (fma.f64 y.re y.re (*.f64 y.im y.im))))
32.1b
(fma.f64 x.im (/.f64 y.im (*.f64 y.re y.re)) (/.f64 x.re y.re))
28.8b
(*.f64 (fma.f64 x.re y.re (*.f64 x.im y.im)) (/.f64 1 (fma.f64 y.re y.re (*.f64 y.im y.im))))
36.0b
(/.f64 x.re y.re)
34.4b
(fma.f64 y.re (/.f64 x.re (*.f64 y.im y.im)) (/.f64 x.im y.im))
42.2b
(*.f64 (/.f64 (sqrt.f64 (fma.f64 y.im x.im (*.f64 y.re x.re))) (hypot.f64 y.im y.re)) (/.f64 (sqrt.f64 (fma.f64 y.im x.im (*.f64 y.re x.re))) (hypot.f64 y.im y.re)))
17.9b
(*.f64 (/.f64 (*.f64 (cbrt.f64 (fma.f64 y.im x.im (*.f64 y.re x.re))) (cbrt.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)))) (hypot.f64 y.im y.re)) (/.f64 (cbrt.f64 (fma.f64 y.im x.im (*.f64 y.re x.re))) (hypot.f64 y.im y.re)))
29.2b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (fma.f64 x.re y.re (*.f64 x.im y.im)) (fma.f64 y.re y.re (*.f64 y.im y.im)))) (cbrt.f64 (/.f64 (fma.f64 x.re y.re (*.f64 x.im y.im)) (fma.f64 y.re y.re (*.f64 y.im y.im))))) (cbrt.f64 (/.f64 (fma.f64 x.re y.re (*.f64 x.im y.im)) (fma.f64 y.re y.re (*.f64 y.im y.im)))))
Compiler

Compiled 2438 to 548 computations (77.5% saved)

localize23.0ms (0.2%)

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 (fma.f64 y.im x.im (*.f64 y.re x.re)) (hypot.f64 y.im y.re)))
0.2b
(fma.f64 y.im x.im (*.f64 y.re x.re))
16.7b
(/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (hypot.f64 y.im y.re))

series400.0ms (3.6%)

Counts
4 → 168
Calls

4 calls:

188.0ms
(/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (hypot.f64 y.im y.re))
172.0ms
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (hypot.f64 y.im y.re)))
19.0ms
(fma.f64 y.im x.im (*.f64 y.re x.re))
16.0ms
(hypot.f64 y.im y.re)

rewrite21.0ms (0.2%)

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 → 107
Calls

4 calls:

9.0ms
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (hypot.f64 y.im y.re)))
3.0ms
(/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (hypot.f64 y.im y.re))
0.0ms
(fma.f64 y.im x.im (*.f64 y.re x.re))
0.0ms
(hypot.f64 y.im y.re)

simplify249.0ms (2.2%)

Algorithm
egg-herbie
Rules
868×times-frac_binary64
516×fma-neg_binary64
377×fma-def_binary64
306×cancel-sign-sub-inv_binary64
282×distribute-rgt-in_binary64
Counts
275 → 263
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02295947
16195325
220945152
348405152
451435152

prune413.0ms (3.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New2978305
Fresh819
Picked101
Done000
Total3069315
Error
0.2b
Counts
315 → 9
Alt Table
StatusErrorProgram
31.8b
(fma.f64 (/.f64 x.re y.im) (/.f64 y.re y.im) (/.f64 x.im y.im))
17.3b
(/.f64 (/.f64 (fma.f64 x.re y.re (*.f64 y.im x.im)) (hypot.f64 y.im y.re)) (hypot.f64 y.im y.re))
25.0b
(*.f64 (/.f64 (/.f64 1 (*.f64 (cbrt.f64 (hypot.f64 y.im y.re)) (cbrt.f64 (hypot.f64 y.im y.re)))) (hypot.f64 y.im y.re)) (/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (cbrt.f64 (hypot.f64 y.im y.re))))
46.5b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (neg.f64 (fma.f64 (/.f64 x.re y.im) y.re x.im)))
28.8b
(*.f64 (fma.f64 x.re y.re (*.f64 x.im y.im)) (/.f64 1 (fma.f64 y.re y.re (*.f64 y.im y.im))))
42.3b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (fma.f64 (/.f64 x.re y.im) y.re x.im))
17.6b
(*.f64 (/.f64 1 (sqrt.f64 (hypot.f64 y.im y.re))) (/.f64 (/.f64 (fma.f64 x.re y.re (*.f64 y.im x.im)) (hypot.f64 y.im y.re)) (sqrt.f64 (hypot.f64 y.im y.re))))
29.5b
(fma.f64 (/.f64 y.im y.re) (/.f64 x.im y.re) (/.f64 x.re y.re))
44.8b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (neg.f64 (fma.f64 (/.f64 y.im y.re) x.im x.re)))
Compiler

Compiled 7935 to 2482 computations (68.7% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(hypot.f64 y.im y.re)
0.1b
(/.f64 (/.f64 (fma.f64 x.re y.re (*.f64 y.im x.im)) (hypot.f64 y.im y.re)) (hypot.f64 y.im y.re))
1.0b
(fma.f64 x.re y.re (*.f64 y.im x.im))
16.7b
(/.f64 (fma.f64 x.re y.re (*.f64 y.im x.im)) (hypot.f64 y.im y.re))

series399.0ms (3.6%)

Counts
3 → 144
Calls

3 calls:

204.0ms
(/.f64 (/.f64 (fma.f64 x.re y.re (*.f64 y.im x.im)) (hypot.f64 y.im y.re)) (hypot.f64 y.im y.re))
179.0ms
(/.f64 (fma.f64 x.re y.re (*.f64 y.im x.im)) (hypot.f64 y.im y.re))
16.0ms
(fma.f64 x.re y.re (*.f64 y.im x.im))

rewrite35.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
84×times-frac_binary64
53×*-un-lft-identity_binary64
53×add-sqr-sqrt_binary64
53×add-cube-cbrt_binary64
16×associate-/l*_binary64
Counts
3 → 111
Calls

3 calls:

8.0ms
(/.f64 (/.f64 (fma.f64 x.re y.re (*.f64 y.im x.im)) (hypot.f64 y.im y.re)) (hypot.f64 y.im y.re))
4.0ms
(/.f64 (fma.f64 x.re y.re (*.f64 y.im x.im)) (hypot.f64 y.im y.re))
1.0ms
(fma.f64 x.re y.re (*.f64 y.im x.im))

simplify284.0ms (2.5%)

Algorithm
egg-herbie
Rules
701×times-frac_binary64
519×associate-/l*_binary64
443×fma-neg_binary64
384×associate-/r*_binary64
364×associate-/l/_binary64
Counts
255 → 251
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02216578
15375929
214515628
346645628
449865628

prune270.0ms (2.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New3305335
Fresh628
Picked011
Done000
Total3368344
Error
0.2b
Counts
344 → 8
Alt Table
StatusErrorProgram
31.8b
(fma.f64 (/.f64 x.re y.im) (/.f64 y.re y.im) (/.f64 x.im y.im))
17.3b
(/.f64 (/.f64 (fma.f64 x.re y.re (*.f64 y.im x.im)) (hypot.f64 y.im y.re)) (hypot.f64 y.im y.re))
17.5b
(/.f64 (/.f64 (/.f64 (fma.f64 x.re y.re (*.f64 y.im x.im)) (sqrt.f64 (hypot.f64 y.im y.re))) (sqrt.f64 (hypot.f64 y.im y.re))) (hypot.f64 y.im y.re))
42.3b
(/.f64 (fma.f64 (/.f64 x.re y.im) y.re x.im) (hypot.f64 y.im y.re))
46.4b
(/.f64 (neg.f64 (fma.f64 (/.f64 x.re y.im) y.re x.im)) (hypot.f64 y.im y.re))
44.7b
(/.f64 (neg.f64 (fma.f64 (/.f64 y.im y.re) x.im x.re)) (hypot.f64 y.im y.re))
29.5b
(fma.f64 (/.f64 y.im y.re) (/.f64 x.im y.re) (/.f64 x.re y.re))
27.9b
(*.f64 (/.f64 (fma.f64 x.re y.re (*.f64 y.im x.im)) 1) (/.f64 (/.f64 1 (hypot.f64 y.im y.re)) (hypot.f64 y.im y.re)))
Compiler

Compiled 8507 to 1947 computations (77.1% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(/.f64 (/.f64 (/.f64 (fma.f64 x.re y.re (*.f64 y.im x.im)) (sqrt.f64 (hypot.f64 y.im y.re))) (sqrt.f64 (hypot.f64 y.im y.re))) (hypot.f64 y.im y.re))
1.0b
(fma.f64 x.re y.re (*.f64 y.im x.im))
7.9b
(/.f64 (/.f64 (fma.f64 x.re y.re (*.f64 y.im x.im)) (sqrt.f64 (hypot.f64 y.im y.re))) (sqrt.f64 (hypot.f64 y.im y.re)))
9.0b
(/.f64 (fma.f64 x.re y.re (*.f64 y.im x.im)) (sqrt.f64 (hypot.f64 y.im y.re)))

series653.0ms (5.9%)

Counts
3 → 128
Calls

3 calls:

286.0ms
(/.f64 (/.f64 (fma.f64 x.re y.re (*.f64 y.im x.im)) (sqrt.f64 (hypot.f64 y.im y.re))) (sqrt.f64 (hypot.f64 y.im y.re)))
236.0ms
(/.f64 (fma.f64 x.re y.re (*.f64 y.im x.im)) (sqrt.f64 (hypot.f64 y.im y.re)))
131.0ms
(/.f64 (/.f64 (/.f64 (fma.f64 x.re y.re (*.f64 y.im x.im)) (sqrt.f64 (hypot.f64 y.im y.re))) (sqrt.f64 (hypot.f64 y.im y.re))) (hypot.f64 y.im y.re))

rewrite503.0ms (4.5%)

Algorithm
rewrite-expression-head
Rules
1644×times-frac_binary64
784×*-un-lft-identity_binary64
784×add-sqr-sqrt_binary64
784×add-cube-cbrt_binary64
624×sqrt-prod_binary64
Counts
3 → 784
Calls

3 calls:

48.0ms
(/.f64 (/.f64 (/.f64 (fma.f64 x.re y.re (*.f64 y.im x.im)) (sqrt.f64 (hypot.f64 y.im y.re))) (sqrt.f64 (hypot.f64 y.im y.re))) (hypot.f64 y.im y.re))
16.0ms
(/.f64 (/.f64 (fma.f64 x.re y.re (*.f64 y.im x.im)) (sqrt.f64 (hypot.f64 y.im y.re))) (sqrt.f64 (hypot.f64 y.im y.re)))
6.0ms
(/.f64 (fma.f64 x.re y.re (*.f64 y.im x.im)) (sqrt.f64 (hypot.f64 y.im y.re)))

simplify2.2s (20.1%)

Algorithm
egg-herbie
Rules
596×fma-def_binary64
512×associate-/r*_binary64
441×associate-/l/_binary64
406×cancel-sign-sub-inv_binary64
280×fma-neg_binary64
Counts
912 → 1003
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
077545265
1176642279
2345039665
3454239014
4498639014
5495339014

prune1.0s (9.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New102511026
Fresh156
Picked011
Done011
Total102681034
Error
0.2b
Counts
1034 → 8
Alt Table
StatusErrorProgram
31.8b
(fma.f64 (/.f64 x.re y.im) (/.f64 y.re y.im) (/.f64 x.im y.im))
17.3b
(/.f64 (/.f64 (fma.f64 x.re y.re (*.f64 y.im x.im)) (hypot.f64 y.im y.re)) (hypot.f64 y.im y.re))
17.5b
(/.f64 (/.f64 (/.f64 (fma.f64 x.re y.re (*.f64 y.im x.im)) (sqrt.f64 (hypot.f64 y.im y.re))) (sqrt.f64 (hypot.f64 y.im y.re))) (hypot.f64 y.im y.re))
42.3b
(/.f64 (fma.f64 (/.f64 x.re y.im) y.re x.im) (hypot.f64 y.im y.re))
46.4b
(/.f64 (neg.f64 (fma.f64 (/.f64 x.re y.im) y.re x.im)) (hypot.f64 y.im y.re))
44.7b
(/.f64 (neg.f64 (fma.f64 (/.f64 y.im y.re) x.im x.re)) (hypot.f64 y.im y.re))
27.9b
(*.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (/.f64 (/.f64 1 (hypot.f64 y.im y.re)) (hypot.f64 y.im y.re)))
29.5b
(fma.f64 (/.f64 y.im y.re) (/.f64 x.im y.re) (/.f64 x.re y.re))
Compiler

Compiled 41019 to 5437 computations (86.7% saved)

regimes2.3s (20.4%)

Accuracy

Total 9.5b remaining (97.8%)

Threshold costs 0b (0%)

Counts
123 → 5
Compiler

Compiled 12098 to 6584 computations (45.6% saved)

bsearch121.0ms (1.1%)

Steps
ItersRangePoint
9
2.3747717619077724e+92
7.865607200093191e+99
1.7908903707439708e+98
7
9.514026573838576e-131
2.6717172040399705e-129
8.272481472784187e-130
10
-6.075455576341602e-127
-8.581049049977316e-142
-3.6283479029046922e-140
9
-2.4807475401011038e+103
-7.293119437331218e+94
-2.1840157650846506e+101
Compiler

Compiled 5 to 4 computations (20% saved)

simplify6.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
038116
145116
249116
352116
453116
553116

end291.0ms (2.6%)

Compiler

Compiled 304 to 145 computations (52.3% saved)

Profiling

Loading profile data...