Details

Time bar (total: 6.8s)

analyze54.0ms (0.8%)

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)

sample845.0ms (12.4%)

Infinites
5.6% of outputs are infinite.
Results
799.0ms8256×body128valid
Compiler

Compiled 59 to 35 computations (40.7% saved)

simplify8.0ms (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

prune3.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
25.9b
Counts
3 → 2
Alt Table
StatusErrorProgram
25.9b
(/.f64 (fma.f64 x.re y.re (*.f64 x.im y.im)) (fma.f64 y.re y.re (*.f64 y.im y.im)))
25.9b
(/.f64 (+.f64 (*.f64 x.re y.re) (*.f64 x.im y.im)) (+.f64 (*.f64 y.re y.re) (*.f64 y.im y.im)))
Compiler

Compiled 104 to 54 computations (48.1% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.0b
(+.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))
25.6b
(/.f64 (+.f64 (*.f64 x.re y.re) (*.f64 x.im y.im)) (+.f64 (*.f64 y.re y.re) (*.f64 y.im y.im)))

series91.0ms (1.3%)

Counts
2 → 96
Calls

2 calls:

81.0ms
(/.f64 (+.f64 (*.f64 x.re y.re) (*.f64 x.im y.im)) (+.f64 (*.f64 y.re y.re) (*.f64 y.im y.im)))
10.0ms
(+.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))

rewrite12.0ms (0.2%)

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 → 47
Calls

2 calls:

6.0ms
(/.f64 (+.f64 (*.f64 x.re y.re) (*.f64 x.im y.im)) (+.f64 (*.f64 y.re y.re) (*.f64 y.im y.im)))
3.0ms
(+.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))

simplify109.0ms (1.6%)

Algorithm
egg-herbie
Rules
472×associate-*l*_binary64
412×fma-def_binary64
396×associate-*r*_binary64
349×times-frac_binary64
329×fma-neg_binary64
Counts
143 → 108
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01212682
13412585
211682501
345422489
449472489
549822489

prune76.0ms (1.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New1035108
Fresh101
Picked101
Done000
Total1055110
Error
0.2b
Counts
110 → 5
Alt Table
StatusErrorProgram
33.8b
(fma.f64 (/.f64 y.im y.re) (/.f64 x.im y.re) (/.f64 x.re y.re))
26.4b
(*.f64 (/.f64 (*.f64 (cbrt.f64 (+.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))) (cbrt.f64 (+.f64 (*.f64 x.re y.re) (*.f64 x.im y.im)))) (*.f64 (cbrt.f64 (+.f64 (*.f64 y.re y.re) (*.f64 y.im y.im))) (cbrt.f64 (+.f64 (*.f64 y.re y.re) (*.f64 y.im y.im))))) (/.f64 (cbrt.f64 (+.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))) (cbrt.f64 (+.f64 (*.f64 y.re y.re) (*.f64 y.im y.im)))))
28.2b
(fma.f64 (/.f64 y.re y.im) (/.f64 x.re y.im) (/.f64 x.im y.im))
25.7b
(fma.f64 (/.f64 y.im (fma.f64 y.im y.im (*.f64 y.re y.re))) x.im (/.f64 (*.f64 y.re x.re) (fma.f64 y.im y.im (*.f64 y.re y.re))))
17.9b
(*.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)))
Compiler

Compiled 2822 to 541 computations (80.8% 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)))
17.3b
(/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (hypot.f64 y.im y.re))

series235.0ms (3.5%)

Counts
4 → 168
Calls

4 calls:

104.0ms
(*.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)))
103.0ms
(/.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))
8.0ms
(fma.f64 y.im x.im (*.f64 y.re x.re))

rewrite24.0ms (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 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))

simplify154.0ms (2.3%)

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

prune349.0ms (5.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New2823285
Fresh134
Picked011
Done000
Total2837290
Error
0.2b
Counts
290 → 7
Alt Table
StatusErrorProgram
33.8b
(fma.f64 (/.f64 y.im y.re) (/.f64 x.im y.re) (/.f64 x.re y.re))
46.7b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (neg.f64 (fma.f64 (/.f64 y.im y.re) x.im x.re)))
28.2b
(fma.f64 (/.f64 y.re y.im) (/.f64 x.re y.im) (/.f64 x.im y.im))
18.0b
(*.f64 (*.f64 (sqrt.f64 (/.f64 1 (hypot.f64 y.im y.re))) (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)))
25.7b
(fma.f64 (/.f64 y.im (fma.f64 y.im y.im (*.f64 y.re y.re))) x.im (/.f64 (*.f64 y.re x.re) (fma.f64 y.im y.im (*.f64 y.re y.re))))
17.8b
(/.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))
17.9b
(*.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)))
Compiler

Compiled 7306 to 2176 computations (70.2% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(fma.f64 x.re y.re (*.f64 y.im x.im))
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))
17.3b
(/.f64 (fma.f64 x.re y.re (*.f64 y.im x.im)) (hypot.f64 y.im y.re))

series204.0ms (3%)

Counts
3 → 144
Calls

3 calls:

99.0ms
(/.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))
96.0ms
(/.f64 (fma.f64 x.re y.re (*.f64 y.im x.im)) (hypot.f64 y.im y.re))
9.0ms
(fma.f64 x.re y.re (*.f64 y.im x.im))

rewrite18.0ms (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:

4.0ms
(/.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))

simplify162.0ms (2.4%)

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

prune152.0ms (2.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New2501251
Fresh145
Picked011
Done011
Total2517258
Error
0.2b
Counts
258 → 7
Alt Table
StatusErrorProgram
33.8b
(fma.f64 (/.f64 y.im y.re) (/.f64 x.im y.re) (/.f64 x.re y.re))
46.7b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (neg.f64 (fma.f64 (/.f64 y.im y.re) x.im x.re)))
28.2b
(fma.f64 (/.f64 y.re y.im) (/.f64 x.re y.im) (/.f64 x.im y.im))
18.1b
(/.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)))))
18.0b
(*.f64 (*.f64 (sqrt.f64 (/.f64 1 (hypot.f64 y.im y.re))) (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)))
17.8b
(/.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))
17.9b
(*.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)))
Compiler

Compiled 6477 to 1201 computations (81.5% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(sqrt.f64 (/.f64 1 (hypot.f64 y.im y.re)))
0.3b
(*.f64 (*.f64 (sqrt.f64 (/.f64 1 (hypot.f64 y.im y.re))) (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)))
0.4b
(*.f64 (sqrt.f64 (/.f64 1 (hypot.f64 y.im y.re))) (sqrt.f64 (/.f64 1 (hypot.f64 y.im y.re))))
17.3b
(/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (hypot.f64 y.im y.re))

series149.0ms (2.2%)

Counts
3 → 80
Calls

3 calls:

103.0ms
(*.f64 (*.f64 (sqrt.f64 (/.f64 1 (hypot.f64 y.im y.re))) (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)))
24.0ms
(*.f64 (sqrt.f64 (/.f64 1 (hypot.f64 y.im y.re))) (sqrt.f64 (/.f64 1 (hypot.f64 y.im y.re))))
22.0ms
(sqrt.f64 (/.f64 1 (hypot.f64 y.im y.re)))

rewrite56.0ms (0.8%)

Algorithm
rewrite-expression-head
Rules
132×add-sqr-sqrt_binary64
95×sqrt-prod_binary64
89×times-frac_binary64
68×*-un-lft-identity_binary64
49×add-cube-cbrt_binary64
Counts
3 → 191
Calls

3 calls:

18.0ms
(*.f64 (*.f64 (sqrt.f64 (/.f64 1 (hypot.f64 y.im y.re))) (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)))
12.0ms
(*.f64 (sqrt.f64 (/.f64 1 (hypot.f64 y.im y.re))) (sqrt.f64 (/.f64 1 (hypot.f64 y.im y.re))))
2.0ms
(sqrt.f64 (/.f64 1 (hypot.f64 y.im y.re)))

simplify178.0ms (2.6%)

Algorithm
egg-herbie
Rules
958×times-frac_binary64
358×cancel-sign-sub-inv_binary64
358×fma-def_binary64
245×associate-*l*_binary64
199×fma-neg_binary64
Counts
271 → 298
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02745744
16395237
222625055
348145055
449745055

prune322.0ms (4.7%)

Pruning

7 alts after pruning (4 fresh and 3 done)

PrunedKeptTotal
New4310431
Fresh044
Picked011
Done022
Total4317438
Error
0.2b
Counts
438 → 7
Alt Table
StatusErrorProgram
33.8b
(fma.f64 (/.f64 y.im y.re) (/.f64 x.im y.re) (/.f64 x.re y.re))
46.7b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (neg.f64 (fma.f64 (/.f64 y.im y.re) x.im x.re)))
28.2b
(fma.f64 (/.f64 y.re y.im) (/.f64 x.re y.im) (/.f64 x.im y.im))
18.1b
(/.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)))))
18.0b
(*.f64 (*.f64 (sqrt.f64 (/.f64 1 (hypot.f64 y.im y.re))) (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)))
17.8b
(/.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))
17.9b
(*.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)))
Compiler

Compiled 13717 to 5491 computations (60% saved)

regimes3.4s (49.7%)

Accuracy

Total 10.0b remaining (98.1%)

Threshold costs 0b (0%)

Counts
205 → 5
Compiler

Compiled 24779 to 13237 computations (46.6% saved)

bsearch66.0ms (1%)

Steps
ItersRangePoint
6
3.049032678034964e+76
2.748169300587671e+77
2.050130680515523e+77
9
-4.677684765432969e-302
-2.772761058196398e-307
-3.6480508373439315e-304
7
-2.5814516884498723e-28
-8.631760532516668e-30
-4.650358285454888e-29
9
-2.296980759982771e+136
-2.377027144023158e+131
-2.6364804888683188e+131
Compiler

Compiled 5 to 4 computations (20% 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: 0 (0.0ms)

IterNodesCost
032108
138108
242108
345108
446108
546108

end102.0ms (1.5%)

Compiler

Compiled 289 to 134 computations (53.6% saved)

Profiling

Loading profile data...