Details

Time bar (total: 8.2s)

analyze751.0ms (9.1%)

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)

sample1.2s (14.4%)

Results
1.1s8256×body128valid
59.0ms478×body128invalid
Compiler

Compiled 59 to 35 computations (40.7% saved)

simplify10.0ms (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

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
29.3b
Counts
3 → 1
Alt Table
StatusErrorProgram
29.3b
(/.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)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.2b
(fma.f64 x.re y.re (*.f64 x.im y.im))
28.7b
(/.f64 (fma.f64 x.re y.re (*.f64 x.im y.im)) (fma.f64 y.re y.re (*.f64 y.im y.im)))

series98.0ms (1.2%)

Counts
2 → 96
Calls

2 calls:

89.0ms
(/.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))

simplify157.0ms (1.9%)

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

prune75.0ms (0.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New87895
Fresh000
Picked101
Done000
Total88896
Error
2.6b
Counts
96 → 8
Alt Table
StatusErrorProgram
18.9b
(*.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)))
43.1b
(*.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)))
19.5b
(*.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)))
34.1b
(+.f64 (/.f64 (*.f64 y.im x.im) (pow.f64 y.re 2)) (/.f64 x.re y.re))
36.2b
(/.f64 x.re y.re)
36.0b
(fma.f64 y.re (/.f64 x.re (*.f64 y.im y.im)) (/.f64 x.im y.im))
36.9b
(/.f64 x.im y.im)
27.1b
(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))))
Compiler

Compiled 2282 to 488 computations (78.6% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
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)))
0.3b
(fma.f64 y.im x.im (*.f64 y.re x.re))
17.7b
(/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (hypot.f64 y.im y.re))

series236.0ms (2.9%)

Counts
3 → 144
Calls

3 calls:

117.0ms
(/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (hypot.f64 y.im y.re))
110.0ms
(*.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)))
9.0ms
(fma.f64 y.im x.im (*.f64 y.re x.re))

rewrite20.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
42×add-sqr-sqrt_binary64
34×times-frac_binary64
27×*-un-lft-identity_binary64
27×add-exp-log_binary64
25×add-cube-cbrt_binary64
Counts
3 → 97
Calls

3 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)))
4.0ms
(/.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))

simplify194.0ms (2.4%)

Algorithm
egg-herbie
Rules
735×times-frac_binary64
339×fma-neg_binary64
266×distribute-rgt-in_binary64
259×fma-def_binary64
254×distribute-lft-in_binary64
Counts
241 → 221
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01865547
14904784
216864627
346064609
449754609
549944609
649784609

prune151.0ms (1.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New2156221
Fresh527
Picked101
Done000
Total2218229
Error
0.1b
Counts
229 → 8
Alt Table
StatusErrorProgram
33.3b
(fma.f64 (/.f64 x.re y.im) (/.f64 y.re y.im) (/.f64 x.im y.im))
19.5b
(*.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)))
19.1b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (*.f64 (/.f64 1 (sqrt.f64 (hypot.f64 y.im y.re))) (/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (sqrt.f64 (hypot.f64 y.im y.re)))))
29.6b
(fma.f64 (/.f64 y.im y.re) (/.f64 x.im y.re) (/.f64 x.re y.re))
34.1b
(+.f64 (/.f64 (*.f64 y.im x.im) (pow.f64 y.re 2)) (/.f64 x.re y.re))
43.5b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (neg.f64 (fma.f64 (/.f64 y.im y.re) x.im x.re)))
46.0b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (neg.f64 (fma.f64 (/.f64 x.re y.im) y.re x.im)))
45.1b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (fma.f64 (/.f64 x.re y.im) y.re x.im))
Compiler

Compiled 5727 to 1551 computations (72.9% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (*.f64 (/.f64 1 (sqrt.f64 (hypot.f64 y.im y.re))) (/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (sqrt.f64 (hypot.f64 y.im y.re)))))
0.3b
(fma.f64 y.im x.im (*.f64 y.re x.re))
7.9b
(*.f64 (/.f64 1 (sqrt.f64 (hypot.f64 y.im y.re))) (/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (sqrt.f64 (hypot.f64 y.im y.re))))
9.9b
(/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (sqrt.f64 (hypot.f64 y.im y.re)))

series374.0ms (4.6%)

Counts
3 → 128
Calls

3 calls:

143.0ms
(/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (sqrt.f64 (hypot.f64 y.im y.re)))
122.0ms
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (*.f64 (/.f64 1 (sqrt.f64 (hypot.f64 y.im y.re))) (/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (sqrt.f64 (hypot.f64 y.im y.re)))))
108.0ms
(*.f64 (/.f64 1 (sqrt.f64 (hypot.f64 y.im y.re))) (/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (sqrt.f64 (hypot.f64 y.im y.re))))

rewrite63.0ms (0.8%)

Algorithm
rewrite-expression-head
Rules
164×add-exp-log_binary64
97×add-sqr-sqrt_binary64
85×times-frac_binary64
76×prod-exp_binary64
59×div-exp_binary64
Counts
3 → 205
Calls

3 calls:

14.0ms
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (*.f64 (/.f64 1 (sqrt.f64 (hypot.f64 y.im y.re))) (/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (sqrt.f64 (hypot.f64 y.im y.re)))))
13.0ms
(*.f64 (/.f64 1 (sqrt.f64 (hypot.f64 y.im y.re))) (/.f64 (fma.f64 y.im x.im (*.f64 y.re x.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)))

simplify325.0ms (4%)

Algorithm
egg-herbie
Rules
451×fma-def_binary64
409×cancel-sign-sub-inv_binary64
319×fma-neg_binary64
297×distribute-rgt-in_binary64
287×associate-*r*_binary64
Counts
333 → 355
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
030911159
17938213
226328063
346798063
449798063
550008063
649498063

prune258.0ms (3.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New3751376
Fresh167
Picked011
Done000
Total3768384
Error
0.1b
Counts
384 → 8
Alt Table
StatusErrorProgram
33.3b
(fma.f64 (/.f64 x.re y.im) (/.f64 y.re y.im) (/.f64 x.im y.im))
48.6b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (*.f64 (/.f64 1 (sqrt.f64 (hypot.f64 y.im y.re))) (*.f64 (sqrt.f64 y.im) x.im)))
19.5b
(*.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)))
19.1b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (*.f64 (/.f64 1 (sqrt.f64 (hypot.f64 y.im y.re))) (/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (sqrt.f64 (hypot.f64 y.im y.re)))))
29.6b
(fma.f64 (/.f64 y.im y.re) (/.f64 x.im y.re) (/.f64 x.re y.re))
34.1b
(+.f64 (/.f64 (*.f64 y.im x.im) (pow.f64 y.re 2)) (/.f64 x.re y.re))
43.5b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (neg.f64 (fma.f64 (/.f64 y.im y.re) x.im x.re)))
46.0b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (neg.f64 (fma.f64 (/.f64 x.re y.im) y.re x.im)))
Compiler

Compiled 12289 to 3569 computations (71% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(*.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)))
0.5b
(*.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))))
3.4b
(/.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))
18.3b
(cbrt.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)))

series452.0ms (5.5%)

Counts
4 → 192
Calls

4 calls:

162.0ms
(/.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))
117.0ms
(*.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)))
97.0ms
(*.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))))
75.0ms
(cbrt.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)))

rewrite38.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
54×add-sqr-sqrt_binary64
32×add-exp-log_binary64
31×times-frac_binary64
30×*-un-lft-identity_binary64
30×cbrt-prod_binary64
Counts
4 → 139
Calls

4 calls:

10.0ms
(*.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)))
5.0ms
(/.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))
4.0ms
(*.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))))
1.0ms
(cbrt.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)))

simplify316.0ms (3.8%)

Algorithm
egg-herbie
Rules
627×fma-def_binary64
367×*-commutative_binary64
279×cancel-sign-sub-inv_binary64
193×sub-neg_binary64
130×associate-*r*_binary64
Counts
331 → 505
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
092518141
1317816428
2476116156
3496816156

prune552.0ms (6.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New7110711
Fresh066
Picked011
Done011
Total7118719
Error
0.1b
Counts
719 → 8
Alt Table
StatusErrorProgram
33.3b
(fma.f64 (/.f64 x.re y.im) (/.f64 y.re y.im) (/.f64 x.im y.im))
48.6b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (*.f64 (/.f64 1 (sqrt.f64 (hypot.f64 y.im y.re))) (*.f64 (sqrt.f64 y.im) x.im)))
19.5b
(*.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)))
19.1b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (*.f64 (/.f64 1 (sqrt.f64 (hypot.f64 y.im y.re))) (/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (sqrt.f64 (hypot.f64 y.im y.re)))))
29.6b
(fma.f64 (/.f64 y.im y.re) (/.f64 x.im y.re) (/.f64 x.re y.re))
34.1b
(+.f64 (/.f64 (*.f64 y.im x.im) (pow.f64 y.re 2)) (/.f64 x.re y.re))
43.5b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (neg.f64 (fma.f64 (/.f64 y.im y.re) x.im x.re)))
46.0b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (neg.f64 (fma.f64 (/.f64 x.re y.im) y.re x.im)))
Compiler

Compiled 40827 to 14617 computations (64.2% saved)

regimes2.8s (33.6%)

Accuracy

Total 10.5b remaining (98%)

Threshold costs 0b (0%)

Counts
185 → 5
Compiler

Compiled 20908 to 11519 computations (44.9% saved)

bsearch35.0ms (0.4%)

Steps
ItersRangePoint
0
6.028664080338301e+104
6.140481187827058e+104
6.084572634082679e+104
2
1.6159942391959563e-231
5.6360165410342416e-216
7.229271600501672e-220
2
-1.335002183548449e-51
-1.2112636267372775e-51
-1.226730946338674e-51
7
-3.4252112330067093e+64
-1.150456185566696e+63
-2.971421814725982e+64
Compiler

Compiled 5 to 4 computations (20% saved)

simplify3.0ms (0%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
*-lft-identity_binary64
1-exp_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
035106
139106
236106

end117.0ms (1.4%)

Compiler

Compiled 317 to 147 computations (53.6% saved)

Profiling

Loading profile data...