Details

Time bar (total: 8.3s)

analyze1.7s (20.2%)

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)

sample49.0ms (0.6%)

Algorithm
intervals
Results
27.0ms256×body128valid
1.0ms13×body128invalid
Compiler

Compiled 43 to 27 computations (37.2% saved)

simplify15.0ms (0.2%)

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

prune5.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
24.8b
Counts
3 → 1
Alt Table
StatusErrorProgram
24.8b
(/.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)

localize18.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(fma.f64 y.re y.re (*.f64 y.im y.im))
0.3b
(fma.f64 x.re y.re (*.f64 x.im y.im))
24.3b
(/.f64 (fma.f64 x.re y.re (*.f64 x.im y.im)) (fma.f64 y.re y.re (*.f64 y.im y.im)))

series198.0ms (2.4%)

Counts
3 → 120
Calls

3 calls:

167.0ms
(/.f64 (fma.f64 x.re y.re (*.f64 x.im y.im)) (fma.f64 y.re y.re (*.f64 y.im y.im)))
19.0ms
(fma.f64 x.re y.re (*.f64 x.im y.im))
12.0ms
(fma.f64 y.re y.re (*.f64 y.im y.im))

rewrite12.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
11×*-un-lft-identity_binary64
11×add-sqr-sqrt_binary64
11×add-cube-cbrt_binary64
times-frac_binary64
add-cbrt-cube_binary64
Counts
3 → 49
Calls

3 calls:

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

simplify139.0ms (1.7%)

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
169 → 119
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01022836
12052674
26132590
322012542
451232542

prune243.0ms (2.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1109119
Fresh000
Picked101
Done000
Total1119120
Error
1.0b
Counts
120 → 9
Alt Table
StatusErrorProgram
38.0b
(/.f64 x.re y.re)
24.8b
(/.f64 (+.f64 (*.f64 x.re y.re) (*.f64 x.im y.im)) (fma.f64 y.re y.re (*.f64 y.im y.im)))
43.1b
(*.f64 (sqrt.f64 (fma.f64 y.im x.im (*.f64 y.re x.re))) (/.f64 (sqrt.f64 (fma.f64 y.im x.im (*.f64 y.re x.re))) (fma.f64 y.im y.im (*.f64 y.re y.re))))
34.1b
(fma.f64 x.im (/.f64 y.im (*.f64 y.re y.re)) (/.f64 x.re y.re))
38.6b
(/.f64 (*.f64 y.im x.im) (fma.f64 y.im y.im (*.f64 y.re y.re)))
15.5b
(*.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)))
36.7b
(+.f64 (/.f64 x.im y.im) (*.f64 (/.f64 y.re (*.f64 y.im y.im)) (-.f64 x.re (/.f64 (*.f64 x.im y.re) y.im))))
36.5b
(/.f64 x.im y.im)
16.2b
(*.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)))
Compiler

Compiled 2693 to 576 computations (78.6% saved)

localize67.0ms (0.8%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(/.f64 1 (hypot.f64 y.im y.re))
0.0b
(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)))
14.5b
(/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (hypot.f64 y.im y.re))

series330.0ms (4%)

Counts
4 → 144
Calls

4 calls:

151.0ms
(/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (hypot.f64 y.im y.re))
143.0ms
(*.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)))
21.0ms
(/.f64 1 (hypot.f64 y.im y.re))
14.0ms
(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)))
3.0ms
(/.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)

simplify235.0ms (2.8%)

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

prune241.0ms (2.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New3417348
Fresh628
Picked011
Done000
Total34710357
Error
0b
Counts
357 → 10
Alt Table
StatusErrorProgram
32.8b
(fma.f64 (/.f64 y.im y.re) (/.f64 x.im y.re) (/.f64 x.re y.re))
24.8b
(/.f64 (+.f64 (*.f64 x.re y.re) (*.f64 x.im y.im)) (fma.f64 y.re y.re (*.f64 y.im y.im)))
22.2b
(*.f64 (/.f64 (/.f64 1 (*.f64 (cbrt.f64 (hypot.f64 y.im y.re)) (cbrt.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)) (cbrt.f64 (hypot.f64 y.im y.re))))
43.8b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (neg.f64 (fma.f64 (/.f64 x.re y.im) y.re x.im)))
15.7b
(*.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))))
36.5b
(/.f64 x.im y.im)
45.6b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (fma.f64 (/.f64 x.re y.im) y.re x.im))
46.4b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (fma.f64 (/.f64 y.im y.re) x.im x.re))
15.5b
(*.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)))
31.9b
(fma.f64 (/.f64 x.re y.im) (/.f64 y.re y.im) (/.f64 x.im y.im))
Compiler

Compiled 9140 to 3018 computations (67% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(hypot.f64 y.im y.re)
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))))
6.5b
(/.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)))
8.1b
(/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (sqrt.f64 (hypot.f64 y.im y.re)))

series484.0ms (5.9%)

Counts
3 → 128
Calls

3 calls:

191.0ms
(/.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)))
152.0ms
(/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (sqrt.f64 (hypot.f64 y.im y.re)))
141.0ms
(*.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))))

rewrite156.0ms (1.9%)

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))))
10.0ms
(/.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)))

simplify465.0ms (5.6%)

Algorithm
egg-herbie
Rules
791×fma-def_binary64
409×cancel-sign-sub-inv_binary64
350×associate-/l/_binary64
325×associate-/l*_binary64
313×associate-*l/_binary64
Counts
548 → 590
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
044120184
1120418209
2373417457
3483917457
4516617457

prune518.0ms (6.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New7160716
Fresh088
Picked011
Done011
Total71610726
Error
0b
Counts
726 → 10
Alt Table
StatusErrorProgram
32.8b
(fma.f64 (/.f64 y.im y.re) (/.f64 x.im y.re) (/.f64 x.re y.re))
24.8b
(/.f64 (+.f64 (*.f64 x.re y.re) (*.f64 x.im y.im)) (fma.f64 y.re y.re (*.f64 y.im y.im)))
22.2b
(*.f64 (/.f64 (/.f64 1 (*.f64 (cbrt.f64 (hypot.f64 y.im y.re)) (cbrt.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)) (cbrt.f64 (hypot.f64 y.im y.re))))
43.8b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (neg.f64 (fma.f64 (/.f64 x.re y.im) y.re x.im)))
15.7b
(*.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))))
36.5b
(/.f64 x.im y.im)
45.6b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (fma.f64 (/.f64 x.re y.im) y.re x.im))
46.4b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (fma.f64 (/.f64 y.im y.re) x.im x.re))
15.5b
(*.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)))
31.9b
(fma.f64 (/.f64 x.re y.im) (/.f64 y.re y.im) (/.f64 x.im y.im))
Compiler

Compiled 26210 to 5644 computations (78.5% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.5b
(*.f64 (cbrt.f64 (hypot.f64 y.im y.re)) (cbrt.f64 (hypot.f64 y.im y.re)))
0.5b
(cbrt.f64 (hypot.f64 y.im y.re))
5.0b
(/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (cbrt.f64 (hypot.f64 y.im y.re)))
19.9b
(*.f64 (/.f64 (/.f64 1 (*.f64 (cbrt.f64 (hypot.f64 y.im y.re)) (cbrt.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)) (cbrt.f64 (hypot.f64 y.im y.re))))

series709.0ms (8.6%)

Counts
4 → 144
Calls

4 calls:

504.0ms
(/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (cbrt.f64 (hypot.f64 y.im y.re)))
115.0ms
(*.f64 (/.f64 (/.f64 1 (*.f64 (cbrt.f64 (hypot.f64 y.im y.re)) (cbrt.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)) (cbrt.f64 (hypot.f64 y.im y.re))))
47.0ms
(*.f64 (cbrt.f64 (hypot.f64 y.im y.re)) (cbrt.f64 (hypot.f64 y.im y.re)))
43.0ms
(cbrt.f64 (hypot.f64 y.im y.re))

rewrite60.0ms (0.7%)

Algorithm
rewrite-expression-head
Rules
101×add-sqr-sqrt_binary64
89×times-frac_binary64
72×add-exp-log_binary64
58×*-un-lft-identity_binary64
55×add-cube-cbrt_binary64
Counts
4 → 193
Calls

4 calls:

24.0ms
(*.f64 (/.f64 (/.f64 1 (*.f64 (cbrt.f64 (hypot.f64 y.im y.re)) (cbrt.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)) (cbrt.f64 (hypot.f64 y.im y.re))))
5.0ms
(*.f64 (cbrt.f64 (hypot.f64 y.im y.re)) (cbrt.f64 (hypot.f64 y.im y.re)))
3.0ms
(/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (cbrt.f64 (hypot.f64 y.im y.re)))
1.0ms
(cbrt.f64 (hypot.f64 y.im y.re))

simplify221.0ms (2.7%)

Algorithm
egg-herbie
Rules
378×associate-*r*_binary64
298×associate-*l*_binary64
274×fma-neg_binary64
240×associate-*l/_binary64
223×associate-/r*_binary64
Counts
337 → 390
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
046011884
112769707
246189707
349529707

prune298.0ms (3.6%)

Pruning

10 alts after pruning (7 fresh and 3 done)

PrunedKeptTotal
New4811482
Fresh167
Picked011
Done022
Total48210492
Error
0b
Counts
492 → 10
Alt Table
StatusErrorProgram
32.8b
(fma.f64 (/.f64 y.im y.re) (/.f64 x.im y.re) (/.f64 x.re y.re))
24.8b
(/.f64 (+.f64 (*.f64 x.re y.re) (*.f64 x.im y.im)) (fma.f64 y.re y.re (*.f64 y.im y.im)))
22.2b
(*.f64 (/.f64 (/.f64 1 (*.f64 (cbrt.f64 (hypot.f64 y.im y.re)) (cbrt.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)) (cbrt.f64 (hypot.f64 y.im y.re))))
43.8b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (neg.f64 (fma.f64 (/.f64 x.re y.im) y.re x.im)))
46.4b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (fma.f64 (/.f64 y.im y.re) x.im x.re))
34.3b
(+.f64 (/.f64 x.im y.im) (/.f64 (*.f64 x.re y.re) (*.f64 y.im y.im)))
15.7b
(*.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))))
45.6b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (fma.f64 (/.f64 x.re y.im) y.re x.im))
15.5b
(*.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)))
31.9b
(fma.f64 (/.f64 x.re y.im) (/.f64 y.re y.im) (/.f64 x.im y.im))
Compiler

Compiled 19299 to 5637 computations (70.8% saved)

regimes1.1s (13.1%)

Accuracy

Total 10.6b remaining (97.9%)

Threshold costs 0b (0%)

Counts
92 → 5
Compiler

Compiled 9703 to 5099 computations (47.4% saved)

bsearch58.0ms (0.7%)

Steps
ItersRangePoint
6
9.219356996474029e+48
4.016497292863998e+49
3.9773913574442064e+49
3
9.329350544994407e-148
1.2084989454288694e-147
9.846032840487084e-148
9
-4.796388480558233e-281
-4.027873907953459e-287
-4.7420300655524546e-281
6
-1.1126465326004964e+158
-2.2679240854442382e+157
-2.2932503563534942e+157
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
036111
145111
252109
360109
463109
564109
662109

end1.0ms (0%)

Compiler

Compiled 80 to 33 computations (58.8% saved)

sample935.0ms (11.3%)

Algorithm
intervals
Results
463.0ms8000×body128valid
24.0ms460×body128invalid
Compiler

Compiled 291 to 153 computations (47.4% saved)

Profiling

Loading profile data...