Details

Time bar (total: 5.7s)

analyze51.0ms (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)

sample1.0s (17.6%)

Results
967.0ms8256×body128valid
Compiler

Compiled 59 to 35 computations (40.7% saved)

simplify6.0ms (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
24.0b
Counts
3 → 1
Alt Table
StatusErrorProgram
24.0b
(/.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 (0.2%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.2b
(fma.f64 x.re y.re (*.f64 x.im y.im))
23.9b
(/.f64 (fma.f64 x.re y.re (*.f64 x.im y.im)) (fma.f64 y.re y.re (*.f64 y.im y.im)))

series95.0ms (1.7%)

Counts
2 → 96
Calls

2 calls:

86.0ms
(/.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))

rewrite5.0ms (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))

simplify75.0ms (1.3%)

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

prune78.0ms (1.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New86995
Fresh000
Picked101
Done000
Total87996
Error
2.3b
Counts
96 → 9
Alt Table
StatusErrorProgram
24.5b
(*.f64 (/.f64 1 (*.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))))) (/.f64 (fma.f64 x.re y.re (*.f64 x.im y.im)) (cbrt.f64 (fma.f64 y.re y.re (*.f64 y.im y.im)))))
39.1b
(/.f64 x.re y.re)
37.1b
(/.f64 (expm1.f64 (log1p.f64 (fma.f64 x.re y.re (*.f64 x.im y.im)))) (fma.f64 y.re y.re (*.f64 y.im y.im)))
38.7b
(*.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)))
35.0b
(/.f64 x.im y.im)
23.3b
(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))))
24.1b
(/.f64 1 (/.f64 (fma.f64 y.re y.re (*.f64 y.im y.im)) (fma.f64 x.re y.re (*.f64 x.im y.im))))
14.5b
(*.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)))
33.4b
(fma.f64 y.re (/.f64 x.re (*.f64 y.im y.im)) (/.f64 x.im y.im))
Compiler

Compiled 2330 to 516 computations (77.9% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(/.f64 1 (hypot.f64 y.im y.re))
0.2b
(*.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))
13.9b
(/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (hypot.f64 y.im y.re))

series368.0ms (6.5%)

Counts
4 → 168
Calls

4 calls:

241.0ms
(*.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)))
97.0ms
(/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (hypot.f64 y.im y.re))
20.0ms
(/.f64 1 (hypot.f64 y.im y.re))
9.0ms
(fma.f64 y.im x.im (*.f64 y.re x.re))

rewrite26.0ms (0.5%)

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:

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

simplify175.0ms (3.1%)

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

prune183.0ms (3.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New2796285
Fresh718
Picked011
Done000
Total2868294
Error
0.0b
Counts
294 → 8
Alt Table
StatusErrorProgram
32.4b
(fma.f64 (/.f64 y.im y.re) (/.f64 x.im y.re) (/.f64 x.re y.re))
14.6b
(*.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))))
45.3b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (fma.f64 (/.f64 y.im y.re) x.im x.re))
24.1b
(/.f64 1 (/.f64 (fma.f64 y.re y.re (*.f64 y.im y.im)) (fma.f64 x.re y.re (*.f64 x.im y.im))))
14.5b
(*.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)))
14.6b
(*.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))))
30.1b
(fma.f64 (/.f64 x.re y.im) (/.f64 y.re y.im) (/.f64 x.im y.im))
44.2b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (fma.f64 (/.f64 x.re y.im) y.re x.im))
Compiler

Compiled 7342 to 2204 computations (70% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(fma.f64 y.im x.im (*.f64 y.re x.re))
0.3b
(*.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)))
0.3b
(*.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))))
13.9b
(/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (hypot.f64 y.im y.re))

series366.0ms (6.4%)

Counts
2 → 80
Calls

2 calls:

249.0ms
(*.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)))
117.0ms
(*.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))))

rewrite46.0ms (0.8%)

Algorithm
rewrite-expression-head
Rules
47×add-sqr-sqrt_binary64
35×times-frac_binary64
32×sqrt-prod_binary64
32×associate-*l*_binary64
27×*-un-lft-identity_binary64
Counts
2 → 97
Calls

2 calls:

19.0ms
(*.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))))
15.0ms
(*.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)))

simplify150.0ms (2.6%)

Algorithm
egg-herbie
Rules
711×times-frac_binary64
313×fma-def_binary64
291×cancel-sign-sub-inv_binary64
236×associate-*r*_binary64
208×distribute-rgt-in_binary64
Counts
177 → 198
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02136085
15345171
218935061
345635061
450015061

prune254.0ms (4.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New3033306
Fresh246
Picked011
Done011
Total3059314
Error
0.0b
Counts
314 → 9
Alt Table
StatusErrorProgram
45.3b
(*.f64 (sqrt.f64 (/.f64 1 (hypot.f64 y.im y.re))) (*.f64 (sqrt.f64 (/.f64 1 (hypot.f64 y.im y.re))) (fma.f64 (/.f64 y.im y.re) x.im x.re)))
30.1b
(fma.f64 (/.f64 x.re y.im) (/.f64 y.re y.im) (/.f64 x.im y.im))
32.4b
(fma.f64 (/.f64 y.im y.re) (/.f64 x.im y.re) (/.f64 x.re y.re))
14.6b
(*.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))))
45.3b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (fma.f64 (/.f64 y.im y.re) x.im x.re))
24.7b
(fma.f64 (/.f64 x.re (fma.f64 y.re y.re (*.f64 y.im y.im))) y.re (/.f64 (*.f64 y.im x.im) (fma.f64 y.re y.re (*.f64 y.im y.im))))
14.5b
(*.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)))
14.6b
(*.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))))
44.2b
(*.f64 (sqrt.f64 (/.f64 1 (hypot.f64 y.im y.re))) (*.f64 (sqrt.f64 (/.f64 1 (hypot.f64 y.im y.re))) (fma.f64 (/.f64 x.re y.im) y.re x.im)))
Compiler

Compiled 10210 to 3990 computations (60.9% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(fma.f64 x.re y.re (*.f64 y.im x.im))
0.3b
(/.f64 1 (sqrt.f64 (hypot.f64 y.im y.re)))
0.3b
(*.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))))
13.9b
(/.f64 (fma.f64 x.re y.re (*.f64 y.im x.im)) (hypot.f64 y.im y.re))

series258.0ms (4.5%)

Counts
4 → 152
Calls

4 calls:

114.0ms
(*.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))))
107.0ms
(/.f64 (fma.f64 x.re y.re (*.f64 y.im x.im)) (hypot.f64 y.im y.re))
25.0ms
(/.f64 1 (sqrt.f64 (hypot.f64 y.im y.re)))
11.0ms
(fma.f64 x.re y.re (*.f64 y.im x.im))

rewrite88.0ms (1.5%)

Algorithm
rewrite-expression-head
Rules
227×times-frac_binary64
199×add-sqr-sqrt_binary64
119×*-un-lft-identity_binary64
109×add-cube-cbrt_binary64
82×associate-*r*_binary64
Counts
4 → 247
Calls

4 calls:

38.0ms
(*.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))))
3.0ms
(/.f64 1 (sqrt.f64 (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))

simplify260.0ms (4.6%)

Algorithm
egg-herbie
Rules
650×fma-def_binary64
362×cancel-sign-sub-inv_binary64
291×associate-/l*_binary64
288×associate-*l/_binary64
280×fma-neg_binary64
Counts
399 → 404
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
036111748
110119946
233149753
347169753
450719753

prune261.0ms (4.6%)

Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New4040404
Fresh066
Picked011
Done022
Total4049413
Error
0.0b
Counts
413 → 9
Alt Table
StatusErrorProgram
45.3b
(*.f64 (sqrt.f64 (/.f64 1 (hypot.f64 y.im y.re))) (*.f64 (sqrt.f64 (/.f64 1 (hypot.f64 y.im y.re))) (fma.f64 (/.f64 y.im y.re) x.im x.re)))
30.1b
(fma.f64 (/.f64 x.re y.im) (/.f64 y.re y.im) (/.f64 x.im y.im))
32.4b
(fma.f64 (/.f64 y.im y.re) (/.f64 x.im y.re) (/.f64 x.re y.re))
14.6b
(*.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))))
45.3b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (fma.f64 (/.f64 y.im y.re) x.im x.re))
24.7b
(fma.f64 (/.f64 x.re (fma.f64 y.re y.re (*.f64 y.im y.im))) y.re (/.f64 (*.f64 y.im x.im) (fma.f64 y.re y.re (*.f64 y.im y.im))))
14.5b
(*.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)))
14.6b
(*.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))))
44.2b
(*.f64 (sqrt.f64 (/.f64 1 (hypot.f64 y.im y.re))) (*.f64 (sqrt.f64 (/.f64 1 (hypot.f64 y.im y.re))) (fma.f64 (/.f64 x.re y.im) y.re x.im)))
Compiler

Compiled 13896 to 3093 computations (77.7% saved)

regimes1.7s (29.4%)

Accuracy

Total 9.1b remaining (98.6%)

Threshold costs 0b (0%)

Counts
151 → 5
Compiler

Compiled 16728 to 9269 computations (44.6% saved)

bsearch68.0ms (1.2%)

Steps
ItersRangePoint
8
1.5725879929461688e+68
2.434578705664003e+71
2.388664514967102e+71
9
3.818831401519012e-191
1.0960849953009115e-183
1.4084867377569056e-189
5
-1.0698237858781123e-201
-3.2095992332259823e-202
-7.547060237033231e-202
11
-4.201354386931583e+114
-4.416294379701873e+92
-6.262881876053762e+112
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: 2 (0.0ms)

IterNodesCost
034114
143114
250112
357112
460112
561112
659112

end146.0ms (2.6%)

Compiler

Compiled 354 to 172 computations (51.4% saved)

Profiling

Loading profile data...