Details

Time bar (total: 4.9s)

analyze742.0ms (15.1%)

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)

sample27.0ms (0.5%)

Algorithm
intervals
Results
15.0ms256×body128valid
1.0ms16×body128invalid
Compiler

Compiled 43 to 27 computations (37.2% 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 (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
21.9b
Counts
3 → 1
Alt Table
StatusErrorProgram
21.9b
(/.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)

localize10.0ms (0.2%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.5b
(fma.f64 x.re y.re (*.f64 x.im y.im))
21.5b
(/.f64 (fma.f64 x.re y.re (*.f64 x.im y.im)) (fma.f64 y.re y.re (*.f64 y.im y.im)))

series97.0ms (2%)

Counts
2 → 96
Calls

2 calls:

88.0ms
(/.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))

rewrite6.0ms (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))

simplify93.0ms (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

prune66.0ms (1.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New86995
Fresh000
Picked101
Done000
Total87996
Error
1.2b
Counts
96 → 9
Alt Table
StatusErrorProgram
13.7b
(*.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)))
34.8b
(+.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))))
39.3b
(*.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)))
36.4b
(/.f64 x.im y.im)
21.9b
(/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (fma.f64 y.re y.re (*.f64 y.im y.im)))
39.1b
(/.f64 x.re y.re)
35.8b
(fma.f64 y.re (/.f64 x.re (*.f64 y.im y.im)) (/.f64 x.im y.im))
14.4b
(*.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)))
21.2b
(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 2328 to 510 computations (78.1% saved)

localize10.0ms (0.2%)

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))
0.2b
(*.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)))
12.8b
(/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (hypot.f64 y.im y.re))

series253.0ms (5.1%)

Counts
4 → 168
Calls

4 calls:

114.0ms
(*.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))
21.0ms
(/.f64 1 (hypot.f64 y.im y.re))
9.0ms
(fma.f64 y.im x.im (*.f64 y.re x.re))

rewrite24.0ms (0.5%)

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
(fma.f64 y.im x.im (*.f64 y.re x.re))

simplify166.0ms (3.4%)

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

prune185.0ms (3.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New2796285
Fresh718
Picked101
Done000
Total2877294
Error
0.0b
Counts
294 → 7
Alt Table
StatusErrorProgram
13.7b
(/.f64 (*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (fma.f64 y.im x.im (*.f64 y.re x.re))) (hypot.f64 y.im y.re))
32.4b
(fma.f64 (/.f64 y.im y.re) (/.f64 x.im y.re) (/.f64 x.re y.re))
32.7b
(fma.f64 (/.f64 x.re y.im) (/.f64 y.re y.im) (/.f64 x.im y.im))
13.6b
(/.f64 (*.f64 1 (/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (hypot.f64 y.im y.re))) (hypot.f64 y.im y.re))
14.0b
(*.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))))
13.7b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (/.f64 (fma.f64 x.re y.re (*.f64 y.im x.im)) (hypot.f64 y.im y.re)))
21.2b
(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 7332 to 2185 computations (70.2% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(fma.f64 y.im x.im (*.f64 y.re x.re))
0.0b
(/.f64 (*.f64 1 (/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (hypot.f64 y.im y.re))) (hypot.f64 y.im y.re))
12.8b
(/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (hypot.f64 y.im y.re))

series113.0ms (2.3%)

Counts
1 → 48
Calls

1 calls:

113.0ms
(/.f64 (*.f64 1 (/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (hypot.f64 y.im y.re))) (hypot.f64 y.im y.re))

rewrite8.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
15×add-exp-log_binary64
10×add-cbrt-cube_binary64
div-exp_binary64
cbrt-undiv_binary64
prod-exp_binary64
Counts
1 → 28
Calls

1 calls:

6.0ms
(/.f64 (*.f64 1 (/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (hypot.f64 y.im y.re))) (hypot.f64 y.im y.re))

simplify85.0ms (1.7%)

Algorithm
egg-herbie
Rules
659×fma-def_binary64
559×fma-neg_binary64
468×times-frac_binary64
356×associate-/l*_binary64
257×distribute-rgt-neg-in_binary64
Counts
76 → 64
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01002092
12421844
27851742
329391724
447291688
551371688

prune116.0ms (2.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1702172
Fresh066
Picked011
Done000
Total1709179
Error
0b
Counts
179 → 9
Alt Table
StatusErrorProgram
13.7b
(/.f64 (*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (fma.f64 y.im x.im (*.f64 y.re x.re))) (hypot.f64 y.im y.re))
32.4b
(fma.f64 (/.f64 y.im y.re) (/.f64 x.im y.re) (/.f64 x.re y.re))
32.7b
(fma.f64 (/.f64 x.re y.im) (/.f64 y.re y.im) (/.f64 x.im y.im))
13.6b
(/.f64 (*.f64 1 (/.f64 (fma.f64 y.im x.im (*.f64 y.re x.re)) (hypot.f64 y.im y.re))) (hypot.f64 y.im y.re))
14.0b
(*.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))))
47.3b
(/.f64 (*.f64 1 (neg.f64 (fma.f64 (/.f64 y.im y.re) x.im x.re))) (hypot.f64 y.im y.re))
42.6b
(/.f64 (*.f64 1 (fma.f64 (/.f64 y.im y.re) x.im x.re)) (hypot.f64 y.im y.re))
13.7b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (/.f64 (fma.f64 x.re y.re (*.f64 y.im x.im)) (hypot.f64 y.im y.re)))
21.2b
(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 4202 to 1302 computations (69% saved)

localize10.0ms (0.2%)

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))
0.0b
(/.f64 (*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (fma.f64 y.im x.im (*.f64 y.re x.re))) (hypot.f64 y.im y.re))
12.9b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (fma.f64 y.im x.im (*.f64 y.re x.re)))

series218.0ms (4.4%)

Counts
2 → 96
Calls

2 calls:

115.0ms
(/.f64 (*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (fma.f64 y.im x.im (*.f64 y.re x.re))) (hypot.f64 y.im y.re))
103.0ms
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (fma.f64 y.im x.im (*.f64 y.re x.re)))

rewrite18.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
26×add-exp-log_binary64
19×add-sqr-sqrt_binary64
16×add-cbrt-cube_binary64
14×times-frac_binary64
13×associate-*l*_binary64
Counts
2 → 67
Calls

2 calls:

8.0ms
(/.f64 (*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (fma.f64 y.im x.im (*.f64 y.re x.re))) (hypot.f64 y.im y.re))
5.0ms
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (fma.f64 y.im x.im (*.f64 y.re x.re)))

simplify212.0ms (4.3%)

Algorithm
egg-herbie
Rules
452×associate-/r*_binary64
413×fma-neg_binary64
396×associate-/l/_binary64
377×associate-*l/_binary64
272×associate-/r/_binary64
Counts
163 → 163
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01654277
14473558
215813392
343133392
447873380
549753380

prune199.0ms (4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New2453248
Fresh437
Picked011
Done101
Total2507257
Error
0b
Counts
257 → 7
Alt Table
StatusErrorProgram
42.6b
(/.f64 (fma.f64 (/.f64 y.im y.re) x.im x.re) (hypot.f64 y.im y.re))
21.2b
(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))))
32.7b
(fma.f64 (/.f64 x.re y.im) (/.f64 y.re y.im) (/.f64 x.im y.im))
13.7b
(/.f64 (*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (fma.f64 y.im x.im (*.f64 y.re x.re))) (hypot.f64 y.im y.re))
47.3b
(/.f64 (neg.f64 (fma.f64 (/.f64 y.im y.re) x.im x.re)) (hypot.f64 y.im y.re))
14.0b
(*.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))))
13.8b
(/.f64 (/.f64 1 (hypot.f64 y.im y.re)) (/.f64 (hypot.f64 y.im y.re) (fma.f64 y.im x.im (*.f64 y.re x.re))))
Compiler

Compiled 5814 to 1986 computations (65.8% saved)

regimes1.2s (23.9%)

Accuracy

Total 9.9b remaining (98.5%)

Threshold costs 0b (0%)

Counts
123 → 5
Compiler

Compiled 11483 to 6704 computations (41.6% saved)

bsearch128.0ms (2.6%)

Steps
ItersRangePoint
9
4.2571927394273145e+43
3.0349045419026963e+52
2.9662526794780484e+52
7
6.146168223893681e-215
5.373071921704079e-213
1.7823166624850088e-214
8
-2.1040684640661418e-256
-2.4887846950895897e-259
-1.9783308039270236e-256
9
-5.2877111965278726e+160
-1.4463384618016356e+152
-4.471960695254782e+155
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
034111
143111
250109
358109
461109
562109
660109

end1.0ms (0%)

Compiler

Compiled 80 to 31 computations (61.3% saved)

sample934.0ms (19%)

Algorithm
intervals
Results
452.0ms8000×body128valid
26.0ms473×body128invalid
Compiler

Compiled 237 to 117 computations (50.6% saved)

Profiling

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