Details

Time bar (total: 7.7s)

analyze756.0ms (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)

sample1.1s (14.4%)

Results
1.0s8256×body128valid
52.0ms456×body128invalid
Compiler

Compiled 59 to 35 computations (40.7% saved)

simplify16.0ms (0.2%)

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

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
24.2b
Counts
3 → 1
Alt Table
StatusErrorProgram
24.2b
(/.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)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.3b
(fma.f64 x.re y.re (*.f64 x.im y.im))
23.7b
(/.f64 (fma.f64 x.re y.re (*.f64 x.im y.im)) (fma.f64 y.re y.re (*.f64 y.im y.im)))

series100.0ms (1.3%)

Counts
2 → 96
Calls

2 calls:

91.0ms
(/.f64 (fma.f64 x.re y.re (*.f64 x.im y.im)) (fma.f64 y.re y.re (*.f64 y.im y.im)))
9.0ms
(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:

2.0ms
(/.f64 (fma.f64 x.re y.re (*.f64 x.im y.im)) (fma.f64 y.re y.re (*.f64 y.im y.im)))
0.0ms
(fma.f64 x.re y.re (*.f64 x.im y.im))

simplify72.0ms (0.9%)

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

prune69.0ms (0.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New88795
Fresh000
Picked011
Done000
Total88896
Error
0.6b
Counts
96 → 8
Alt Table
StatusErrorProgram
24.2b
(/.f64 (fma.f64 x.re y.re (*.f64 x.im y.im)) (fma.f64 y.re y.re (*.f64 y.im y.im)))
39.3b
(/.f64 x.re y.re)
14.5b
(*.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)))
33.9b
(/.f64 x.im y.im)
13.9b
(*.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)))
22.7b
(fma.f64 x.im (/.f64 y.im (fma.f64 y.im y.im (*.f64 y.re y.re))) (/.f64 (*.f64 y.re x.re) (fma.f64 y.im y.im (*.f64 y.re y.re))))
24.7b
(*.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)))))
24.1b
(/.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))))
Compiler

Compiled 2327 to 489 computations (79% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(/.f64 1 (hypot.f64 y.im y.re))
0.0b
(fma.f64 y.im x.im (*.f64 y.re x.re))
0.3b
(*.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)))
12.9b
(/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (hypot.f64 y.im y.re))

series228.0ms (3%)

Counts
4 → 168
Calls

4 calls:

98.0ms
(*.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)))
89.0ms
(/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (hypot.f64 y.im y.re))
32.0ms
(/.f64 1 (hypot.f64 y.im y.re))
9.0ms
(fma.f64 y.im x.im (*.f64 y.re x.re))

rewrite22.0ms (0.3%)

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 → 130
Calls

4 calls:

8.0ms
(*.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)))
2.0ms
(/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (hypot.f64 y.im y.re))
2.0ms
(/.f64 1 (hypot.f64 y.im y.re))
0.0ms
(fma.f64 y.im x.im (*.f64 y.re x.re))

simplify162.0ms (2.1%)

Algorithm
egg-herbie
Rules
872×times-frac_binary64
508×fma-neg_binary64
381×fma-def_binary64
335×cancel-sign-sub-inv_binary64
274×distribute-rgt-in_binary64
Counts
298 → 285
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02356511
16295720
221355547
348795539
451835539

prune212.0ms (2.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New2796285
Fresh516
Picked101
Done011
Total2858293
Error
0b
Counts
293 → 8
Alt Table
StatusErrorProgram
14.0b
(*.f64 (/.f64 (/.f64 1 (sqrt.f64 (hypot.f64 y.im y.re))) (sqrt.f64 (hypot.f64 y.im y.re))) (/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (hypot.f64 y.im y.re)))
29.4b
(fma.f64 (/.f64 x.re y.im) (/.f64 y.re y.im) (/.f64 x.im y.im))
14.5b
(*.f64 (/.f64 1 (*.f64 (cbrt.f64 (hypot.f64 y.im y.re)) (cbrt.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)) (cbrt.f64 (hypot.f64 y.im y.re))))
14.5b
(*.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)))
35.9b
(fma.f64 (/.f64 y.im y.re) (/.f64 x.im y.re) (/.f64 x.re y.re))
24.2b
(/.f64 (fma.f64 x.re y.re (*.f64 x.im y.im)) (fma.f64 y.re y.re (*.f64 y.im y.im)))
14.0b
(*.f64 (sqrt.f64 (/.f64 1 (hypot.f64 y.im y.re))) (*.f64 (sqrt.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))))
13.7b
(/.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))
Compiler

Compiled 7405 to 2210 computations (70.2% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
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))
0.3b
(fma.f64 x.re y.re (*.f64 y.im x.im))
12.9b
(/.f64 (fma.f64 x.re y.re (*.f64 y.im x.im)) (hypot.f64 y.im y.re))

series204.0ms (2.7%)

Counts
3 → 144
Calls

3 calls:

102.0ms
(/.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))
93.0ms
(/.f64 (fma.f64 x.re y.re (*.f64 y.im x.im)) (hypot.f64 y.im y.re))
8.0ms
(fma.f64 x.re y.re (*.f64 y.im x.im))

rewrite17.0ms (0.2%)

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:

6.0ms
(/.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))
2.0ms
(/.f64 (fma.f64 x.re y.re (*.f64 y.im x.im)) (hypot.f64 y.im y.re))
0.0ms
(fma.f64 x.re y.re (*.f64 y.im x.im))

simplify144.0ms (1.9%)

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

prune166.0ms (2.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New2483251
Fresh336
Picked101
Done011
Total2527259
Error
0b
Counts
259 → 7
Alt Table
StatusErrorProgram
14.0b
(/.f64 1 (*.f64 (hypot.f64 y.im y.re) (/.f64 (hypot.f64 y.im y.re) (fma.f64 y.im x.im (*.f64 y.re x.re)))))
29.4b
(fma.f64 (/.f64 x.re y.im) (/.f64 y.re y.im) (/.f64 x.im y.im))
35.9b
(fma.f64 (/.f64 y.im y.re) (/.f64 x.im y.re) (/.f64 x.re y.re))
24.3b
(*.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (/.f64 1 (*.f64 (hypot.f64 y.im y.re) (hypot.f64 y.im y.re))))
24.2b
(/.f64 (fma.f64 x.re y.re (*.f64 x.im y.im)) (fma.f64 y.re y.re (*.f64 y.im y.im)))
14.5b
(*.f64 (/.f64 1 (*.f64 (cbrt.f64 (hypot.f64 y.im y.re)) (cbrt.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)) (cbrt.f64 (hypot.f64 y.im y.re))))
14.0b
(/.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))
Compiler

Compiled 6516 to 1208 computations (81.5% saved)

localize10.0ms (0.1%)

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))
0.3b
(fma.f64 x.re y.re (*.f64 y.im x.im))
5.7b
(/.f64 (fma.f64 x.re y.re (*.f64 y.im x.im)) (sqrt.f64 (hypot.f64 y.im y.re)))
7.4b
(/.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)))

series317.0ms (4.1%)

Counts
3 → 128
Calls

3 calls:

124.0ms
(/.f64 (fma.f64 x.re y.re (*.f64 y.im x.im)) (sqrt.f64 (hypot.f64 y.im y.re)))
99.0ms
(/.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))
95.0ms
(/.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)))

rewrite247.0ms (3.2%)

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:

28.0ms
(/.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))
7.0ms
(/.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)))
3.0ms
(/.f64 (fma.f64 x.re y.re (*.f64 y.im x.im)) (sqrt.f64 (hypot.f64 y.im y.re)))

simplify1.1s (13.8%)

Algorithm
egg-herbie
Rules
589×fma-def_binary64
512×associate-/r*_binary64
441×associate-/l/_binary64
406×cancel-sign-sub-inv_binary64
280×fma-neg_binary64
Counts
912 → 1006
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
077546029
1176642251
2345239665
3455239014
4499639014
5494339014

prune669.0ms (8.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New102811029
Fresh235
Picked011
Done011
Total103061036
Error
0b
Counts
1036 → 6
Alt Table
StatusErrorProgram
14.0b
(/.f64 1 (*.f64 (hypot.f64 y.im y.re) (/.f64 (hypot.f64 y.im y.re) (fma.f64 y.im x.im (*.f64 y.re x.re)))))
29.4b
(fma.f64 (/.f64 x.re y.im) (/.f64 y.re y.im) (/.f64 x.im y.im))
35.9b
(fma.f64 (/.f64 y.im y.re) (/.f64 x.im y.re) (/.f64 x.re y.re))
24.2b
(/.f64 (fma.f64 x.re y.re (*.f64 x.im y.im)) (fma.f64 y.re y.re (*.f64 y.im y.im)))
14.2b
(/.f64 (/.f64 (/.f64 (/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (sqrt.f64 (hypot.f64 y.im y.re))) (cbrt.f64 (hypot.f64 y.im y.re))) (sqrt.f64 (cbrt.f64 (hypot.f64 y.im y.re)))) (hypot.f64 y.im y.re))
14.0b
(/.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))
Compiler

Compiled 41092 to 5449 computations (86.7% saved)

regimes1.8s (23.9%)

Accuracy

Total 11.1b remaining (98.2%)

Threshold costs 0b (0%)

Counts
139 → 5
Compiler

Compiled 14683 to 8004 computations (45.5% saved)

bsearch102.0ms (1.3%)

Steps
ItersRangePoint
9
9.47909946656105e+110
5.605060041271639e+116
5.563402658894378e+112
4
2.8148372276966703e-255
5.585239231986436e-255
5.453427998098388e-255
8
-2.6626641483518966e-84
-1.627013727558533e-87
-4.082695455232209e-87
8
-2.278630121051136e+137
-1.3022486668961583e+134
-8.374813608163854e+134
Compiler

Compiled 5 to 4 computations (20% saved)

simplify12.0ms (0.2%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
044120
155120
261120
371120
478120
583120
685120
784120

end107.0ms (1.4%)

Compiler

Compiled 293 to 143 computations (51.2% saved)

Profiling

Loading profile data...