Details

Time bar (total: 6.2s)

analyze51.0ms (0.8%)

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
74.9%25%0.2%5
74.9%25%0.2%6
74.9%25%0.2%7
87.3%12.5%0.2%8
93.6%6.2%0.2%9
93.6%6.2%0.2%10
93.6%6.2%0.2%11
96.7%3.1%0.2%12
98.2%1.6%0.2%13
98.2%1.6%0.2%14
Compiler

Compiled 20 to 12 computations (40% saved)

sample971.0ms (15.5%)

Results
838.0ms8256×body128valid
Compiler

Compiled 59 to 35 computations (40.7% saved)

simplify68.0ms (1.1%)

Algorithm
egg-herbie
Rules
1070×fma-neg_binary64
881×fma-def_binary64
768×times-frac_binary64
551×cancel-sign-sub-inv_binary64
514×unsub-neg_binary64
Counts
1 → 2
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01220
12520
24720
37820
414920
522820
632420
750020
869420
986720
1099920
11242220
12392020
13495020

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New112
Fresh101
Picked000
Done000
Total213
Error
22.9b
Counts
3 → 1
Alt Table
StatusErrorProgram
22.9b
(/.f64 (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im)) (fma.f64 y.re y.re (*.f64 y.im y.im)))
Compiler

Compiled 69 to 33 computations (52.2% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.2b
(-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im))
22.6b
(/.f64 (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im)) (fma.f64 y.re y.re (*.f64 y.im y.im)))

series133.0ms (2.1%)

Counts
2 → 96
Calls

2 calls:

123.0ms
(/.f64 (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im)) (fma.f64 y.re y.re (*.f64 y.im y.im)))
9.0ms
(-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im))

rewrite12.0ms (0.2%)

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 → 48
Calls

2 calls:

5.0ms
(-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im))
4.0ms
(/.f64 (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im)) (fma.f64 y.re y.re (*.f64 y.im y.im)))

simplify91.0ms (1.5%)

Algorithm
egg-herbie
Rules
523×fma-neg_binary64
383×associate-*l*_binary64
348×fma-def_binary64
319×associate-*r*_binary64
252×associate-/l*_binary64
Counts
144 → 111
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01322762
13232614
210882567
343982567
449522567

prune90.0ms (1.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New10110111
Fresh000
Picked101
Done000
Total10210112
Error
0.8b
Counts
112 → 10
Alt Table
StatusErrorProgram
40.0b
(/.f64 x.im y.re)
36.8b
(-.f64 (fma.f64 (/.f64 y.re y.im) (/.f64 x.im y.im) (/.f64 (*.f64 x.re (*.f64 y.re y.re)) (pow.f64 y.im 3))) (/.f64 x.re y.im))
34.1b
(neg.f64 (/.f64 x.re y.im))
23.4b
(/.f64 (*.f64 (cbrt.f64 (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im))) (cbrt.f64 (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im)))) (/.f64 (fma.f64 y.re y.re (*.f64 y.im y.im)) (cbrt.f64 (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im)))))
38.5b
(/.f64 (-.f64 (*.f64 (*.f64 x.im y.re) (*.f64 x.im y.re)) (*.f64 (*.f64 x.re y.im) (*.f64 x.re y.im))) (*.f64 (fma.f64 y.im y.im (*.f64 y.re y.re)) (fma.f64 x.re y.im (*.f64 y.re x.im))))
29.3b
(expm1.f64 (log1p.f64 (/.f64 (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im)) (fma.f64 y.re y.re (*.f64 y.im y.im)))))
23.0b
(/.f64 1 (/.f64 (fma.f64 y.re y.re (*.f64 y.im y.im)) (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im))))
16.5b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re)))
22.9b
(/.f64 (+.f64 (fma.f64 x.im y.re (neg.f64 (*.f64 y.im x.re))) (fma.f64 (neg.f64 y.im) x.re (*.f64 y.im x.re))) (fma.f64 y.re y.re (*.f64 y.im y.im)))
39.7b
(-.f64 (/.f64 x.im y.re) (fma.f64 (/.f64 x.re y.re) (/.f64 y.im y.re) (/.f64 (*.f64 (*.f64 y.im y.im) x.im) (pow.f64 y.re 3))))
Compiler

Compiled 2959 to 684 computations (76.9% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(/.f64 1 (hypot.f64 y.im y.re))
0.2b
(-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))
0.3b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re)))
15.9b
(/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re))

series254.0ms (4.1%)

Counts
4 → 132
Calls

4 calls:

122.0ms
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re)))
102.0ms
(/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re))
21.0ms
(/.f64 1 (hypot.f64 y.im y.re))
9.0ms
(-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))

rewrite33.0ms (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 → 139
Calls

4 calls:

10.0ms
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re)))
4.0ms
(/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re))
3.0ms
(-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))
2.0ms
(/.f64 1 (hypot.f64 y.im y.re))

simplify128.0ms (2%)

Algorithm
egg-herbie
Rules
884×times-frac_binary64
524×fma-def_binary64
365×cancel-sign-sub-inv_binary64
204×fma-neg_binary64
186×sub-neg_binary64
Counts
271 → 275
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02756721
17485877
225565818
350795818

prune258.0ms (4.1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New2687275
Fresh369
Picked101
Done000
Total27213285
Error
0.8b
Counts
285 → 13
Alt Table
StatusErrorProgram
16.5b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (/.f64 1 (/.f64 (hypot.f64 y.im y.re) (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)))))
44.7b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) x.re)
45.4b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (-.f64 (/.f64 (*.f64 x.re y.im) y.re) x.im))
22.9b
(/.f64 (+.f64 (fma.f64 x.im y.re (neg.f64 (*.f64 y.im x.re))) (fma.f64 (neg.f64 y.im) x.re (*.f64 y.im x.re))) (fma.f64 y.re y.re (*.f64 y.im y.im)))
40.0b
(/.f64 x.im y.re)
36.8b
(-.f64 (fma.f64 (/.f64 y.re y.im) (/.f64 x.im y.im) (/.f64 (*.f64 x.re (*.f64 y.re y.re)) (pow.f64 y.im 3))) (/.f64 x.re y.im))
42.5b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (neg.f64 x.re))
34.1b
(neg.f64 (/.f64 x.re y.im))
16.4b
(/.f64 (/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re)) (hypot.f64 y.im y.re))
38.5b
(/.f64 (-.f64 (*.f64 (*.f64 x.im y.re) (*.f64 x.im y.re)) (*.f64 (*.f64 x.re y.im) (*.f64 x.re y.im))) (*.f64 (fma.f64 y.im y.im (*.f64 y.re y.re)) (fma.f64 x.re y.im (*.f64 y.re x.im))))
17.0b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (/.f64 (/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (*.f64 (cbrt.f64 (hypot.f64 y.im y.re)) (cbrt.f64 (hypot.f64 y.im y.re)))) (cbrt.f64 (hypot.f64 y.im y.re))))
39.7b
(-.f64 (/.f64 x.im y.re) (fma.f64 (/.f64 x.re y.re) (/.f64 y.im y.re) (/.f64 (*.f64 (*.f64 y.im y.im) x.im) (pow.f64 y.re 3))))
19.0b
(*.f64 (*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (/.f64 1 (sqrt.f64 (hypot.f64 y.im y.re)))) (/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (sqrt.f64 (hypot.f64 y.im y.re))))
Compiler

Compiled 7716 to 2377 computations (69.2% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(hypot.f64 y.im y.re)
0.1b
(/.f64 (/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re)) (hypot.f64 y.im y.re))
0.2b
(-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))
15.9b
(/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re))

series127.0ms (2%)

Counts
2 → 72
Calls

2 calls:

114.0ms
(/.f64 (/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re)) (hypot.f64 y.im y.re))
12.0ms
(hypot.f64 y.im y.re)

rewrite20.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
75×times-frac_binary64
44×*-un-lft-identity_binary64
44×add-sqr-sqrt_binary64
44×add-cube-cbrt_binary64
13×associate-/l*_binary64
Counts
2 → 83
Calls

2 calls:

6.0ms
(/.f64 (/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re)) (hypot.f64 y.im y.re))
0.0ms
(hypot.f64 y.im y.re)

simplify150.0ms (2.4%)

Algorithm
egg-herbie
Rules
698×times-frac_binary64
572×associate-/l*_binary64
471×associate-/l/_binary64
465×fma-neg_binary64
224×fma-def_binary64
Counts
155 → 170
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02334852
15704607
215054399
345574352
449884352
549604352

prune249.0ms (4%)

Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New3044308
Fresh4812
Picked011
Done000
Total30813321
Error
0.8b
Counts
321 → 13
Alt Table
StatusErrorProgram
42.5b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (neg.f64 x.re))
33.3b
(/.f64 (/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re)) (cbrt.f64 (*.f64 (*.f64 (hypot.f64 y.im y.re) (hypot.f64 y.im y.re)) (hypot.f64 y.im y.re))))
45.4b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (-.f64 (/.f64 (*.f64 x.re y.im) y.re) x.im))
22.9b
(/.f64 (+.f64 (fma.f64 x.im y.re (neg.f64 (*.f64 y.im x.re))) (fma.f64 (neg.f64 y.im) x.re (*.f64 y.im x.re))) (fma.f64 y.re y.re (*.f64 y.im y.im)))
40.0b
(/.f64 x.im y.re)
36.8b
(-.f64 (fma.f64 (/.f64 y.re y.im) (/.f64 x.im y.im) (/.f64 (*.f64 x.re (*.f64 y.re y.re)) (pow.f64 y.im 3))) (/.f64 x.re y.im))
34.1b
(neg.f64 (/.f64 x.re y.im))
16.6b
(/.f64 (/.f64 (/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re)) (sqrt.f64 (hypot.f64 y.im y.re))) (sqrt.f64 (hypot.f64 y.im y.re)))
16.4b
(/.f64 (/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re)) (hypot.f64 y.im y.re))
44.7b
(/.f64 x.re (hypot.f64 y.im y.re))
16.5b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (/.f64 1 (/.f64 (hypot.f64 y.im y.re) (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)))))
39.7b
(-.f64 (/.f64 x.im y.re) (fma.f64 (/.f64 x.re y.re) (/.f64 y.im y.re) (/.f64 (*.f64 (*.f64 y.im y.im) x.im) (pow.f64 y.re 3))))
16.6b
(/.f64 (/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re)) (*.f64 (sqrt.f64 (hypot.f64 y.im y.re)) (sqrt.f64 (hypot.f64 y.im y.re))))
Compiler

Compiled 8375 to 2108 computations (74.8% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))
0.2b
(/.f64 1 (/.f64 (hypot.f64 y.im y.re) (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))))
0.3b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (/.f64 1 (/.f64 (hypot.f64 y.im y.re) (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)))))
15.9b
(/.f64 (hypot.f64 y.im y.re) (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)))

series295.0ms (4.7%)

Counts
3 → 144
Calls

3 calls:

115.0ms
(/.f64 1 (/.f64 (hypot.f64 y.im y.re) (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))))
108.0ms
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (/.f64 1 (/.f64 (hypot.f64 y.im y.re) (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)))))
71.0ms
(/.f64 (hypot.f64 y.im y.re) (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)))

rewrite77.0ms (1.2%)

Algorithm
rewrite-expression-head
Rules
199×times-frac_binary64
146×add-sqr-sqrt_binary64
110×*-un-lft-identity_binary64
99×add-cube-cbrt_binary64
99×add-exp-log_binary64
Counts
3 → 246
Calls

3 calls:

23.0ms
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (/.f64 1 (/.f64 (hypot.f64 y.im y.re) (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)))))
7.0ms
(/.f64 (hypot.f64 y.im y.re) (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)))
7.0ms
(/.f64 1 (/.f64 (hypot.f64 y.im y.re) (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))))

simplify251.0ms (4%)

Algorithm
egg-herbie
Rules
455×times-frac_binary64
363×associate-/l*_binary64
263×associate-/r*_binary64
231×associate-*l*_binary64
214×associate-*r*_binary64
Counts
390 → 485
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
037813351
1106411363
2438411257
3514611257

prune431.0ms (6.9%)

Pruning

13 alts after pruning (11 fresh and 2 done)

PrunedKeptTotal
New5081509
Fresh11011
Picked011
Done011
Total50913522
Error
0.8b
Counts
522 → 13
Alt Table
StatusErrorProgram
16.6b
(/.f64 (/.f64 (/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re)) (sqrt.f64 (hypot.f64 y.im y.re))) (sqrt.f64 (hypot.f64 y.im y.re)))
16.5b
(/.f64 (/.f64 1 (hypot.f64 y.im y.re)) (/.f64 (hypot.f64 y.im y.re) (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))))
45.4b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (-.f64 (/.f64 (*.f64 x.re y.im) y.re) x.im))
22.9b
(/.f64 (+.f64 (fma.f64 x.im y.re (neg.f64 (*.f64 y.im x.re))) (fma.f64 (neg.f64 y.im) x.re (*.f64 y.im x.re))) (fma.f64 y.re y.re (*.f64 y.im y.im)))
40.0b
(/.f64 x.im y.re)
36.8b
(-.f64 (fma.f64 (/.f64 y.re y.im) (/.f64 x.im y.im) (/.f64 (*.f64 x.re (*.f64 y.re y.re)) (pow.f64 y.im 3))) (/.f64 x.re y.im))
42.5b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (neg.f64 x.re))
34.1b
(neg.f64 (/.f64 x.re y.im))
16.4b
(/.f64 (/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re)) (hypot.f64 y.im y.re))
44.7b
(/.f64 x.re (hypot.f64 y.im y.re))
16.5b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (/.f64 1 (/.f64 (hypot.f64 y.im y.re) (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)))))
39.7b
(-.f64 (/.f64 x.im y.re) (fma.f64 (/.f64 x.re y.re) (/.f64 y.im y.re) (/.f64 (*.f64 (*.f64 y.im y.im) x.im) (pow.f64 y.re 3))))
16.6b
(/.f64 (/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re)) (*.f64 (sqrt.f64 (hypot.f64 y.im y.re)) (sqrt.f64 (hypot.f64 y.im y.re))))
Compiler

Compiled 16675 to 5279 computations (68.3% saved)

regimes2.2s (35.8%)

Accuracy

Total 10.4b remaining (88.3%)

Threshold costs 0b (0%)

Counts
165 → 5
Compiler

Compiled 18298 to 10094 computations (44.8% saved)

bsearch70.0ms (1.1%)

Steps
ItersRangePoint
10
1.7497877100692573e+140
1.3072218755024796e+152
2.5508280192928966e+145
7
1.2346372475500144e-70
5.528107228473118e-69
1.2501679329591383e-70
7
-2.1955358366336685e-192
-1.9595475588495853e-194
-4.902684341493697e-194
9
-1.2824711495316275e+90
-4.524004925957706e+83
-3.9892431633599146e+89
Compiler

Compiled 5 to 4 computations (20% saved)

simplify7.0ms (0.1%)

Algorithm
egg-herbie
Rules
14×*-commutative_binary64
13×+-commutative_binary64
13×sub-neg_binary64
10×neg-sub0_binary64
10×neg-mul-1_binary64
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
035112
153112
275110
399110
4113110
5120110
6122110
7120110

end204.0ms (3.3%)

Compiler

Compiled 398 to 202 computations (49.2% saved)

Profiling

Loading profile data...