Details

Time bar (total: 8.7s)

analyze664.0ms (7.7%)

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)

sample138.0ms (1.6%)

Algorithm
intervals
Results
16.0ms256×body128valid
0.0msbody128invalid
Compiler

Compiled 43 to 27 computations (37.2% saved)

simplify66.0ms (0.8%)

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
24.7b
Counts
3 → 1
Alt Table
StatusErrorProgram
24.7b
(/.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)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(fma.f64 y.re y.re (*.f64 y.im y.im))
0.7b
(-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im))
24.2b
(/.f64 (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im)) (fma.f64 y.re y.re (*.f64 y.im y.im)))

series124.0ms (1.4%)

Counts
3 → 120
Calls

3 calls:

108.0ms
(/.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))
6.0ms
(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 → 58
Calls

3 calls:

6.0ms
(/.f64 (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im)) (fma.f64 y.re y.re (*.f64 y.im y.im)))
3.0ms
(-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im))
0.0ms
(fma.f64 y.re y.re (*.f64 y.im y.im))

simplify118.0ms (1.4%)

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
178 → 135
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01363054
13262877
210952830
344072830
449952830
549462830

prune96.0ms (1.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1269135
Fresh000
Picked101
Done000
Total1279136
Error
1.3b
Counts
136 → 9
Alt Table
StatusErrorProgram
24.6b
(/.f64 (/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re)) (sqrt.f64 (fma.f64 y.re y.re (*.f64 y.im y.im))))
25.3b
(*.f64 (/.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 (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))))) (/.f64 (cbrt.f64 (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im))) (cbrt.f64 (fma.f64 y.re y.re (*.f64 y.im y.im)))))
35.2b
(-.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))))
32.3b
(-.f64 (/.f64 x.im y.re) (/.f64 (*.f64 x.re y.im) (pow.f64 y.re 2)))
33.6b
(/.f64 x.im y.re)
24.7b
(*.f64 (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im)) (/.f64 1 (fma.f64 y.re y.re (*.f64 y.im y.im))))
40.1b
(-.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))
39.2b
(neg.f64 (/.f64 x.re y.im))
14.8b
(*.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)))
Compiler

Compiled 3320 to 722 computations (78.3% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(/.f64 1 (hypot.f64 y.im y.re))
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)))
0.7b
(-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))
13.8b
(/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re))

series585.0ms (6.7%)

Counts
4 → 132
Calls

4 calls:

412.0ms
(/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re))
106.0ms
(*.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)))
18.0ms
(/.f64 1 (hypot.f64 y.im y.re))
10.0ms
(-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))

rewrite31.0ms (0.4%)

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))

simplify141.0ms (1.6%)

Algorithm
egg-herbie
Rules
884×times-frac_binary64
524×fma-def_binary64
372×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

prune217.0ms (2.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New2705275
Fresh178
Picked101
Done000
Total27212284
Error
1.3b
Counts
284 → 12
Alt Table
StatusErrorProgram
35.3b
(-.f64 (/.f64 x.im y.re) (fma.f64 (/.f64 (*.f64 y.im y.im) (pow.f64 y.re 3)) x.im (/.f64 (*.f64 x.re y.im) (*.f64 y.re y.re))))
39.2b
(neg.f64 (/.f64 x.re y.im))
46.4b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) x.re)
25.3b
(*.f64 (/.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 (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))))) (/.f64 (cbrt.f64 (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im))) (cbrt.f64 (fma.f64 y.re y.re (*.f64 y.im y.im)))))
35.2b
(-.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))))
32.3b
(-.f64 (/.f64 x.im y.re) (/.f64 (*.f64 x.re y.im) (pow.f64 y.re 2)))
33.6b
(/.f64 x.im y.re)
43.2b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (-.f64 x.im (/.f64 (*.f64 x.re y.im) y.re)))
24.7b
(*.f64 (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im)) (/.f64 1 (fma.f64 y.re y.re (*.f64 y.im y.im))))
40.1b
(-.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))
46.0b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (neg.f64 x.re))
14.7b
(/.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))
Compiler

Compiled 7656 to 2335 computations (69.5% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(/.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))
0.7b
(-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))
13.8b
(/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re))

series111.0ms (1.3%)

Counts
1 → 48
Calls

1 calls:

111.0ms
(/.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))

rewrite24.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
75×times-frac_binary64
43×*-un-lft-identity_binary64
43×add-sqr-sqrt_binary64
43×add-cube-cbrt_binary64
13×associate-/l*_binary64
Counts
1 → 73
Calls

1 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))

simplify120.0ms (1.4%)

Algorithm
egg-herbie
Rules
566×times-frac_binary64
497×fma-neg_binary64
471×associate-/l*_binary64
471×associate-/l/_binary64
359×div-sub_binary64
Counts
121 → 139
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01894368
14404066
210933872
341043805
453093805

prune192.0ms (2.2%)

Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New2314235
Fresh4711
Picked011
Done000
Total23512247
Error
1.3b
Counts
247 → 12
Alt Table
StatusErrorProgram
24.5b
(*.f64 (/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) 1) (/.f64 (/.f64 1 (hypot.f64 y.im y.re)) (hypot.f64 y.im y.re)))
24.7b
(*.f64 (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im)) (/.f64 1 (fma.f64 y.re y.re (*.f64 y.im y.im))))
15.9b
(*.f64 (/.f64 (/.f64 (*.f64 (cbrt.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))) (cbrt.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)))) (*.f64 (cbrt.f64 (hypot.f64 y.im y.re)) (cbrt.f64 (hypot.f64 y.im y.re)))) (/.f64 (/.f64 (cbrt.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))) (cbrt.f64 (hypot.f64 y.im y.re))) (cbrt.f64 (hypot.f64 y.im y.re))))
14.7b
(/.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))
46.0b
(/.f64 (neg.f64 x.re) (hypot.f64 y.im y.re))
46.4b
(/.f64 x.re (hypot.f64 y.im y.re))
35.2b
(-.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))))
32.3b
(-.f64 (/.f64 x.im y.re) (/.f64 (*.f64 x.re y.im) (pow.f64 y.re 2)))
33.6b
(/.f64 x.im y.re)
43.2b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (-.f64 x.im (/.f64 (*.f64 x.re y.im) y.re)))
40.1b
(-.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))
35.3b
(-.f64 (/.f64 x.im y.re) (fma.f64 (/.f64 (*.f64 y.im y.im) (pow.f64 y.re 3)) x.im (/.f64 (*.f64 x.re y.im) (*.f64 y.re y.re))))
Compiler

Compiled 6547 to 1445 computations (77.9% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.5b
(cbrt.f64 (hypot.f64 y.im y.re))
0.7b
(-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))
3.9b
(/.f64 (*.f64 (cbrt.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))) (cbrt.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))))
14.3b
(cbrt.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)))

series336.0ms (3.9%)

Counts
3 → 120
Calls

3 calls:

200.0ms
(/.f64 (*.f64 (cbrt.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))) (cbrt.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))))
94.0ms
(cbrt.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)))
40.0ms
(cbrt.f64 (hypot.f64 y.im y.re))

rewrite26.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
15×add-exp-log_binary64
14×cbrt-div_binary64
associate-/l/_binary64
flip--_binary64
flip3--_binary64
Counts
3 → 59
Calls

3 calls:

14.0ms
(/.f64 (*.f64 (cbrt.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))) (cbrt.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))))
3.0ms
(cbrt.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)))
1.0ms
(cbrt.f64 (hypot.f64 y.im y.re))

simplify152.0ms (1.8%)

Algorithm
egg-herbie
Rules
767×associate-/l*_binary64
401×fma-def_binary64
276×*-commutative_binary64
182×cancel-sign-sub-inv_binary64
164×sub-neg_binary64
Counts
179 → 256
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
07439788
125489378
254349378

prune842.0ms (9.7%)

Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New7451746
Fresh01010
Picked101
Done011
Total74612758
Error
1.3b
Counts
758 → 12
Alt Table
StatusErrorProgram
24.5b
(*.f64 (/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) 1) (/.f64 (/.f64 1 (hypot.f64 y.im y.re)) (hypot.f64 y.im y.re)))
24.7b
(*.f64 (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im)) (/.f64 1 (fma.f64 y.re y.re (*.f64 y.im y.im))))
46.0b
(/.f64 (neg.f64 x.re) (hypot.f64 y.im y.re))
46.4b
(/.f64 x.re (hypot.f64 y.im y.re))
35.2b
(-.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))))
32.3b
(-.f64 (/.f64 x.im y.re) (/.f64 (*.f64 x.re y.im) (pow.f64 y.re 2)))
33.6b
(/.f64 x.im y.re)
43.2b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (-.f64 x.im (/.f64 (*.f64 x.re y.im) y.re)))
40.1b
(-.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))
55.9b
(*.f64 (/.f64 (/.f64 (*.f64 (cbrt.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))) (cbrt.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)))) (*.f64 (cbrt.f64 (hypot.f64 y.im y.re)) (cbrt.f64 (hypot.f64 y.im y.re)))) (/.f64 (/.f64 (*.f64 (exp.f64 (*.f64 1/3 (-.f64 (log.f64 x.im) (log.f64 (/.f64 -1 y.re))))) (cbrt.f64 -1)) (cbrt.f64 (hypot.f64 y.im y.re))) (cbrt.f64 (hypot.f64 y.im y.re))))
35.3b
(-.f64 (/.f64 x.im y.re) (fma.f64 (/.f64 (*.f64 y.im y.im) (pow.f64 y.re 3)) x.im (/.f64 (*.f64 x.re y.im) (*.f64 y.re y.re))))
14.7b
(/.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))
Compiler

Compiled 59253 to 15496 computations (73.8% saved)

regimes3.0s (34.1%)

Accuracy

Total 10.8b remaining (86.8%)

Threshold costs 0b (0%)

Counts
123 → 5
Compiler

Compiled 15043 to 7864 computations (47.7% saved)

bsearch128.0ms (1.5%)

Steps
ItersRangePoint
7
7.048308635377611e+166
2.7531313403615044e+168
7.169555933218119e+166
8
6.580886305226325e-222
2.294655182412034e-217
3.354325968273711e-221
8
1.2811088663525464e-307
4.7254027422535434e-303
1.8848197063060136e-306
8
-2.2493101471643397e+108
-1.0693850308112913e+105
-1.8184599620892983e+108
Compiler

Compiled 5 to 4 computations (20% saved)

simplify9.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
03195
14295
25295
35895
46295
56395
66295

end1.0ms (0%)

Compiler

Compiled 69 to 27 computations (60.9% saved)

sample1.5s (17.7%)

Algorithm
intervals
Results
733.0ms8000×body128valid
46.0ms495×body128invalid
Compiler

Compiled 350 to 188 computations (46.3% saved)

Profiling

Loading profile data...