Details

Time bar (total: 7.3s)

analyze850.0ms (11.6%)

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)

sample1.3s (17.2%)

Results
1.2s8256×body128valid
74.0ms535×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

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
23.7b
Counts
3 → 1
Alt Table
StatusErrorProgram
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)))
Compiler

Compiled 66 to 32 computations (51.5% saved)

localize13.0ms (0.2%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.3b
(fma.f64 x.re y.re (*.f64 x.im y.im))
23.3b
(/.f64 (fma.f64 x.re y.re (*.f64 x.im y.im)) (fma.f64 y.re y.re (*.f64 y.im y.im)))

series93.0ms (1.3%)

Counts
2 → 96
Calls

2 calls:

85.0ms
(/.f64 (fma.f64 x.re y.re (*.f64 x.im y.im)) (fma.f64 y.re y.re (*.f64 y.im y.im)))
8.0ms
(fma.f64 x.re y.re (*.f64 x.im y.im))

rewrite20.0ms (0.3%)

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:

17.0ms
(/.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))

simplify73.0ms (1%)

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

prune77.0ms (1.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New87895
Fresh000
Picked101
Done000
Total88896
Error
3.1b
Counts
96 → 8
Alt Table
StatusErrorProgram
34.3b
(fma.f64 x.im (/.f64 y.im (*.f64 y.re y.re)) (/.f64 x.re y.re))
36.9b
(/.f64 x.re y.re)
17.1b
(*.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)))
23.7b
(/.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))))
38.4b
(/.f64 x.im y.im)
24.2b
(/.f64 (/.f64 (fma.f64 x.re y.re (*.f64 x.im y.im)) (*.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))))) (cbrt.f64 (fma.f64 y.re y.re (*.f64 y.im y.im))))
16.6b
(*.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)))
23.7b
(/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (fma.f64 y.re y.re (*.f64 y.im y.im)))
Compiler

Compiled 2296 to 494 computations (78.5% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(hypot.f64 y.im y.re)
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)))
15.5b
(/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (hypot.f64 y.im y.re))

series315.0ms (4.3%)

Counts
4 → 144
Calls

4 calls:

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)))
108.0ms
(/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (hypot.f64 y.im y.re))
85.0ms
(/.f64 1 (hypot.f64 y.im y.re))
12.0ms
(hypot.f64 y.im y.re)

rewrite25.0ms (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:

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
(hypot.f64 y.im y.re)

simplify185.0ms (2.5%)

Algorithm
egg-herbie
Rules
476×fma-def_binary64
412×cancel-sign-sub-inv_binary64
393×fma-neg_binary64
207×sub-neg_binary64
191×distribute-rgt-in_binary64
Counts
274 → 306
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02686451
17375818
224565629
346825621
449885621
549665621

prune252.0ms (3.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New3399348
Fresh617
Picked101
Done000
Total34610356
Error
0.4b
Counts
356 → 10
Alt Table
StatusErrorProgram
16.6b
(*.f64 (/.f64 (fma.f64 x.re y.re (*.f64 y.im x.im)) (hypot.f64 y.im y.re)) (/.f64 1 (hypot.f64 y.im y.re)))
44.2b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (neg.f64 (fma.f64 (/.f64 y.im y.re) x.im x.re)))
44.1b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (neg.f64 x.im))
44.3b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (fma.f64 (/.f64 x.re y.im) y.re x.im))
16.8b
(*.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))))
41.7b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (fma.f64 (/.f64 y.im y.re) x.im x.re))
33.1b
(fma.f64 (/.f64 x.re y.im) (/.f64 y.re y.im) (/.f64 x.im y.im))
31.3b
(fma.f64 (/.f64 y.im y.re) (/.f64 x.im y.re) (/.f64 x.re y.re))
20.0b
(*.f64 (/.f64 (/.f64 1 (sqrt.f64 (hypot.f64 y.im y.re))) (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))))
23.7b
(/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (fma.f64 y.re y.re (*.f64 y.im y.im)))
Compiler

Compiled 9158 to 3033 computations (66.9% 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 (fma.f64 x.re y.re (*.f64 y.im x.im)) (hypot.f64 y.im y.re)) (/.f64 1 (hypot.f64 y.im y.re)))
0.3b
(fma.f64 x.re y.re (*.f64 y.im x.im))
15.5b
(/.f64 (fma.f64 x.re y.re (*.f64 y.im x.im)) (hypot.f64 y.im y.re))

series211.0ms (2.9%)

Counts
3 → 144
Calls

3 calls:

107.0ms
(*.f64 (/.f64 (fma.f64 x.re y.re (*.f64 y.im x.im)) (hypot.f64 y.im y.re)) (/.f64 1 (hypot.f64 y.im y.re)))
95.0ms
(/.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))

rewrite22.0ms (0.3%)

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 → 98
Calls

3 calls:

10.0ms
(*.f64 (/.f64 (fma.f64 x.re y.re (*.f64 y.im x.im)) (hypot.f64 y.im y.re)) (/.f64 1 (hypot.f64 y.im y.re)))
3.0ms
(/.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))

simplify147.0ms (2%)

Algorithm
egg-herbie
Rules
646×times-frac_binary64
645×associate-/l*_binary64
455×fma-neg_binary64
241×fma-def_binary64
224×cancel-sign-sub-inv_binary64
Counts
242 → 224
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01845531
14944762
215964605
349414605
452624605

prune188.0ms (2.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New2871288
Fresh189
Picked101
Done000
Total2899298
Error
0.4b
Counts
298 → 9
Alt Table
StatusErrorProgram
44.1b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (neg.f64 x.im))
44.3b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (fma.f64 (/.f64 x.re y.im) y.re x.im))
16.8b
(*.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))))
41.7b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (fma.f64 (/.f64 y.im y.re) x.im x.re))
23.7b
(/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (*.f64 (hypot.f64 y.im y.re) (hypot.f64 y.im y.re)))
33.1b
(fma.f64 (/.f64 x.re y.im) (/.f64 y.re y.im) (/.f64 x.im y.im))
31.3b
(fma.f64 (/.f64 y.im y.re) (/.f64 x.im y.re) (/.f64 x.re y.re))
44.2b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (neg.f64 (fma.f64 (/.f64 y.im y.re) x.im x.re)))
20.0b
(*.f64 (/.f64 (/.f64 1 (sqrt.f64 (hypot.f64 y.im y.re))) (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))))
Compiler

Compiled 7409 to 2227 computations (69.9% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(fma.f64 x.re y.re (*.f64 y.im x.im))
0.3b
(/.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)))
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))))
15.5b
(/.f64 (fma.f64 x.re y.re (*.f64 y.im x.im)) (hypot.f64 y.im y.re))

series375.0ms (5.1%)

Counts
2 → 80
Calls

2 calls:

241.0ms
(/.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)))
134.0ms
(*.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))))

rewrite96.0ms (1.3%)

Algorithm
rewrite-expression-head
Rules
341×times-frac_binary64
251×add-sqr-sqrt_binary64
171×*-un-lft-identity_binary64
161×add-cube-cbrt_binary64
110×sqrt-prod_binary64
Counts
2 → 275
Calls

2 calls:

35.0ms
(*.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))))
6.0ms
(/.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)))

simplify319.0ms (4.4%)

Algorithm
egg-herbie
Rules
736×fma-def_binary64
303×cancel-sign-sub-inv_binary64
289×associate-*l/_binary64
273×associate-/l*_binary64
270×associate-/l/_binary64
Counts
355 → 404
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
037415294
1101412775
2319812653
3454012653
4506312653

prune302.0ms (4.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New5122514
Fresh268
Picked011
Done000
Total5149523
Error
0.4b
Counts
523 → 9
Alt Table
StatusErrorProgram
44.3b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (fma.f64 (/.f64 x.re y.im) y.re x.im))
16.8b
(*.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))))
23.7b
(/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (*.f64 (hypot.f64 y.im y.re) (hypot.f64 y.im y.re)))
41.8b
(*.f64 (/.f64 1 (sqrt.f64 (hypot.f64 y.im y.re))) (/.f64 (fma.f64 (/.f64 y.im y.re) x.im x.re) (sqrt.f64 (hypot.f64 y.im y.re))))
44.1b
(*.f64 (/.f64 1 (sqrt.f64 (hypot.f64 y.im y.re))) (/.f64 (neg.f64 x.im) (sqrt.f64 (hypot.f64 y.im y.re))))
33.1b
(fma.f64 (/.f64 x.re y.im) (/.f64 y.re y.im) (/.f64 x.im y.im))
31.3b
(fma.f64 (/.f64 y.im y.re) (/.f64 x.im y.re) (/.f64 x.re y.re))
44.2b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (neg.f64 (fma.f64 (/.f64 y.im y.re) x.im x.re)))
20.0b
(*.f64 (/.f64 (/.f64 1 (sqrt.f64 (hypot.f64 y.im y.re))) (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))))
Compiler

Compiled 18534 to 3877 computations (79.1% saved)

regimes2.2s (29.9%)

Accuracy

Total 10.6b remaining (98.3%)

Threshold costs 0b (0%)

Counts
143 → 5
Compiler

Compiled 15793 to 8509 computations (46.1% saved)

bsearch68.0ms (0.9%)

Steps
ItersRangePoint
6
4.736540780035276e+114
4.989109541383205e+115
3.6928906212212155e+115
7
3.559551160767353e-66
1.2488211763571394e-64
3.893486015778443e-66
8
-1.0592995119089323e-122
-1.0521748428297923e-125
-1.1787479681689879e-125
4
-9.235502145661662e+148
-5.0843124959565825e+148
-7.798094340522651e+148
Compiler

Compiled 5 to 4 computations (20% saved)

simplify3.0ms (0%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
042117
148117
247117

end185.0ms (2.5%)

Compiler

Compiled 343 to 173 computations (49.6% saved)

Profiling

Loading profile data...