Details

Time bar (total: 8.8s)

analyze727.0ms (8.3%)

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 (12.9%)

Results
1.0s8256×body128valid
72.0ms510×body128invalid
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

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New112
Fresh011
Picked000
Done000
Total123
Error
28.1b
Counts
3 → 1
Alt Table
StatusErrorProgram
28.1b
(/.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 70 to 36 computations (48.6% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(+.f64 (*.f64 y.re y.re) (*.f64 y.im y.im))
0.9b
(+.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))
27.5b
(/.f64 (+.f64 (*.f64 x.re y.re) (*.f64 x.im y.im)) (+.f64 (*.f64 y.re y.re) (*.f64 y.im y.im)))

series96.0ms (1.1%)

Counts
3 → 120
Calls

3 calls:

79.0ms
(/.f64 (+.f64 (*.f64 x.re y.re) (*.f64 x.im y.im)) (+.f64 (*.f64 y.re y.re) (*.f64 y.im y.im)))
11.0ms
(+.f64 (*.f64 x.re y.re) (*.f64 x.im y.im))
6.0ms
(+.f64 (*.f64 y.re y.re) (*.f64 y.im y.im))

rewrite15.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
11×*-un-lft-identity_binary64
11×add-sqr-sqrt_binary64
11×add-cube-cbrt_binary64
times-frac_binary64
add-log-exp_binary64
Counts
3 → 61
Calls

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

simplify96.0ms (1.1%)

Algorithm
egg-herbie
Rules
498×associate-*l*_binary64
483×fma-def_binary64
426×associate-*r*_binary64
349×times-frac_binary64
327×fma-neg_binary64
Counts
181 → 138
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01323026
13812904
212602820
348332820
450182820

prune88.0ms (1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1317138
Fresh000
Picked101
Done000
Total1327139
Error
0.4b
Counts
139 → 7
Alt Table
StatusErrorProgram
28.3b
(/.f64 1 (/.f64 (fma.f64 y.im y.im (*.f64 y.re y.re)) (fma.f64 y.im x.im (*.f64 y.re x.re))))
32.9b
(fma.f64 (/.f64 y.im y.re) (/.f64 x.im y.re) (/.f64 x.re y.re))
31.7b
(fma.f64 (/.f64 y.re y.im) (/.f64 x.re y.im) (/.f64 x.im y.im))
19.7b
(*.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)))
20.2b
(*.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)))
26.2b
(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))))
48.3b
(*.f64 (/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (-.f64 (pow.f64 y.re 4) (pow.f64 y.im 4))) (-.f64 (*.f64 y.re y.re) (*.f64 y.im y.im)))
Compiler

Compiled 3454 to 693 computations (79.9% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(/.f64 1 (hypot.f64 y.im y.re))
0.2b
(*.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)))
0.5b
(fma.f64 y.im x.im (*.f64 y.re x.re))
18.4b
(/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (hypot.f64 y.im y.re))

series311.0ms (3.5%)

Counts
4 → 168
Calls

4 calls:

200.0ms
(*.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)))
87.0ms
(/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (hypot.f64 y.im y.re))
15.0ms
(/.f64 1 (hypot.f64 y.im y.re))
8.0ms
(fma.f64 y.im x.im (*.f64 y.re x.re))

rewrite23.0ms (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:

10.0ms
(*.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))

simplify165.0ms (1.9%)

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

prune202.0ms (2.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New2805285
Fresh246
Picked101
Done000
Total2839292
Error
0.2b
Counts
292 → 9
Alt Table
StatusErrorProgram
32.9b
(fma.f64 (/.f64 y.im y.re) (/.f64 x.im y.re) (/.f64 x.re y.re))
42.0b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (neg.f64 (fma.f64 (/.f64 x.re y.im) y.re x.im)))
31.7b
(fma.f64 (/.f64 y.re y.im) (/.f64 x.re y.im) (/.f64 x.im y.im))
46.0b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (fma.f64 (/.f64 x.re y.im) y.re x.im))
26.2b
(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))))
28.5b
(fma.f64 (/.f64 x.re (fma.f64 y.im y.im (*.f64 y.re y.re))) y.re (/.f64 (*.f64 y.im x.im) (fma.f64 y.im y.im (*.f64 y.re y.re))))
48.3b
(*.f64 (/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (-.f64 (pow.f64 y.re 4) (pow.f64 y.im 4))) (-.f64 (*.f64 y.re y.re) (*.f64 y.im y.im)))
46.6b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (fma.f64 (/.f64 y.im y.re) x.im x.re))
19.9b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (/.f64 (/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (sqrt.f64 (hypot.f64 y.im y.re))) (sqrt.f64 (hypot.f64 y.im y.re))))
Compiler

Compiled 7410 to 2233 computations (69.9% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (/.f64 (/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (sqrt.f64 (hypot.f64 y.im y.re))) (sqrt.f64 (hypot.f64 y.im y.re))))
0.5b
(fma.f64 y.im x.im (*.f64 y.re x.re))
8.1b
(/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (sqrt.f64 (hypot.f64 y.im y.re)))
10.4b
(/.f64 (/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (sqrt.f64 (hypot.f64 y.im y.re))) (sqrt.f64 (hypot.f64 y.im y.re)))

series297.0ms (3.4%)

Counts
3 → 128
Calls

3 calls:

109.0ms
(/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (sqrt.f64 (hypot.f64 y.im y.re)))
99.0ms
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (/.f64 (/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (sqrt.f64 (hypot.f64 y.im y.re))) (sqrt.f64 (hypot.f64 y.im y.re))))
89.0ms
(/.f64 (/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (sqrt.f64 (hypot.f64 y.im y.re))) (sqrt.f64 (hypot.f64 y.im y.re)))

rewrite152.0ms (1.7%)

Algorithm
rewrite-expression-head
Rules
569×times-frac_binary64
364×add-sqr-sqrt_binary64
292×*-un-lft-identity_binary64
285×add-cube-cbrt_binary64
279×sqrt-prod_binary64
Counts
3 → 420
Calls

3 calls:

46.0ms
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (/.f64 (/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (sqrt.f64 (hypot.f64 y.im y.re))) (sqrt.f64 (hypot.f64 y.im y.re))))
9.0ms
(/.f64 (/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (sqrt.f64 (hypot.f64 y.im y.re))) (sqrt.f64 (hypot.f64 y.im y.re)))
3.0ms
(/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (sqrt.f64 (hypot.f64 y.im y.re)))

simplify415.0ms (4.7%)

Algorithm
egg-herbie
Rules
791×fma-def_binary64
409×cancel-sign-sub-inv_binary64
350×associate-/l/_binary64
325×associate-/l*_binary64
315×associate-*l/_binary64
Counts
548 → 592
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
044120646
1120418191
2374317457
3483917457
4516617457

prune388.0ms (4.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New6112613
Fresh178
Picked011
Done000
Total61210622
Error
0.2b
Counts
622 → 10
Alt Table
StatusErrorProgram
31.7b
(fma.f64 (/.f64 y.re y.im) (/.f64 x.re y.im) (/.f64 x.im y.im))
23.0b
(/.f64 (/.f64 (fma.f64 x.re y.re (*.f64 y.im x.im)) (sqrt.f64 (hypot.f64 y.im y.re))) (pow.f64 (sqrt.f64 (hypot.f64 y.im y.re)) 3))
19.9b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (/.f64 (/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (sqrt.f64 (hypot.f64 y.im y.re))) (sqrt.f64 (hypot.f64 y.im y.re))))
51.1b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (/.f64 (*.f64 x.re (sqrt.f64 y.re)) (sqrt.f64 (hypot.f64 y.im y.re))))
32.9b
(fma.f64 (/.f64 y.im y.re) (/.f64 x.im y.re) (/.f64 x.re y.re))
42.0b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (neg.f64 (fma.f64 (/.f64 x.re y.im) y.re x.im)))
46.0b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (fma.f64 (/.f64 x.re y.im) y.re x.im))
26.2b
(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))))
28.5b
(fma.f64 (/.f64 x.re (fma.f64 y.im y.im (*.f64 y.re y.re))) y.re (/.f64 (*.f64 y.im x.im) (fma.f64 y.im y.im (*.f64 y.re y.re))))
46.6b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (fma.f64 (/.f64 y.im y.re) x.im x.re))
Compiler

Compiled 22845 to 4335 computations (81% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.5b
(pow.f64 (sqrt.f64 (hypot.f64 y.im y.re)) 3)
0.5b
(fma.f64 x.re y.re (*.f64 y.im x.im))
8.1b
(/.f64 (fma.f64 x.re y.re (*.f64 y.im x.im)) (sqrt.f64 (hypot.f64 y.im y.re)))
19.3b
(/.f64 (/.f64 (fma.f64 x.re y.re (*.f64 y.im x.im)) (sqrt.f64 (hypot.f64 y.im y.re))) (pow.f64 (sqrt.f64 (hypot.f64 y.im y.re)) 3))

series264.0ms (3%)

Counts
4 → 136
Calls

4 calls:

123.0ms
(/.f64 (fma.f64 x.re y.re (*.f64 y.im x.im)) (sqrt.f64 (hypot.f64 y.im y.re)))
100.0ms
(/.f64 (/.f64 (fma.f64 x.re y.re (*.f64 y.im x.im)) (sqrt.f64 (hypot.f64 y.im y.re))) (pow.f64 (sqrt.f64 (hypot.f64 y.im y.re)) 3))
29.0ms
(pow.f64 (sqrt.f64 (hypot.f64 y.im y.re)) 3)
11.0ms
(fma.f64 x.re y.re (*.f64 y.im x.im))

rewrite134.0ms (1.5%)

Algorithm
rewrite-expression-head
Rules
756×times-frac_binary64
386×*-un-lft-identity_binary64
386×add-sqr-sqrt_binary64
386×add-cube-cbrt_binary64
327×sqrt-prod_binary64
Counts
4 → 542
Calls

4 calls:

15.0ms
(/.f64 (/.f64 (fma.f64 x.re y.re (*.f64 y.im x.im)) (sqrt.f64 (hypot.f64 y.im y.re))) (pow.f64 (sqrt.f64 (hypot.f64 y.im y.re)) 3))
3.0ms
(/.f64 (fma.f64 x.re y.re (*.f64 y.im x.im)) (sqrt.f64 (hypot.f64 y.im y.re)))
2.0ms
(pow.f64 (sqrt.f64 (hypot.f64 y.im y.re)) 3)
0.0ms
(fma.f64 x.re y.re (*.f64 y.im x.im))

simplify718.0ms (8.2%)

Algorithm
egg-herbie
Rules
810×associate-/r*_binary64
665×fma-def_binary64
427×associate-/l/_binary64
363×unswap-sqr_binary64
338×log-prod_binary64
Counts
678 → 507
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
051329042
1104623151
2389522045
3390321757
4445921613
5499321613
6492021613

prune319.0ms (3.6%)

Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New5070507
Fresh088
Picked011
Done011
Total50710517
Error
0.2b
Counts
517 → 10
Alt Table
StatusErrorProgram
31.7b
(fma.f64 (/.f64 y.re y.im) (/.f64 x.re y.im) (/.f64 x.im y.im))
23.0b
(/.f64 (/.f64 (fma.f64 x.re y.re (*.f64 y.im x.im)) (sqrt.f64 (hypot.f64 y.im y.re))) (pow.f64 (sqrt.f64 (hypot.f64 y.im y.re)) 3))
19.9b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (/.f64 (/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (sqrt.f64 (hypot.f64 y.im y.re))) (sqrt.f64 (hypot.f64 y.im y.re))))
51.1b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (/.f64 (*.f64 x.re (sqrt.f64 y.re)) (sqrt.f64 (hypot.f64 y.im y.re))))
32.9b
(fma.f64 (/.f64 y.im y.re) (/.f64 x.im y.re) (/.f64 x.re y.re))
42.0b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (neg.f64 (fma.f64 (/.f64 x.re y.im) y.re x.im)))
46.0b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (fma.f64 (/.f64 x.re y.im) y.re x.im))
26.2b
(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))))
28.5b
(fma.f64 (/.f64 x.re (fma.f64 y.im y.im (*.f64 y.re y.re))) y.re (/.f64 (*.f64 y.im x.im) (fma.f64 y.im y.im (*.f64 y.re y.re))))
46.6b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (fma.f64 (/.f64 y.im y.re) x.im x.re))
Compiler

Compiled 17209 to 4063 computations (76.4% saved)

regimes3.0s (33.6%)

Accuracy

Total 9.6b remaining (98.4%)

Threshold costs 0b (0%)

Counts
159 → 5
Compiler

Compiled 16094 to 9680 computations (39.9% saved)

bsearch91.0ms (1%)

Steps
ItersRangePoint
10
1.2045822682945516e+112
3.8845504360818415e+123
6.768222319451061e+117
8
7.791125343640146e-118
4.455649642112476e-113
3.449177705343384e-117
7
-1.4026749661707206e-116
-8.973733078458052e-119
-1.2836238063303858e-118
9
-7.092206962473592e+136
-5.765799447911338e+131
-1.28353704106374e+133
Compiler

Compiled 5 to 4 computations (20% saved)

simplify7.0ms (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
039114
150114
257112
365112
468112
569112
667112

end140.0ms (1.6%)

Compiler

Compiled 356 to 178 computations (50% saved)

Profiling

Loading profile data...