Details

Time bar (total: 7.9s)

analyze718.0ms (9.1%)

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)

sample1.2s (15.1%)

Results
1.0s8256×body128valid
59.0ms471×body128invalid
Compiler

Compiled 59 to 35 computations (40.7% saved)

simplify64.0ms (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
22.2b
Counts
3 → 1
Alt Table
StatusErrorProgram
22.2b
(/.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
0.0b
(-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im))
21.8b
(/.f64 (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im)) (fma.f64 y.re y.re (*.f64 y.im y.im)))

series404.0ms (5.1%)

Counts
2 → 96
Calls

2 calls:

394.0ms
(/.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))

rewrite10.0ms (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 → 48
Calls

2 calls:

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)))
3.0ms
(-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im))

simplify128.0ms (1.6%)

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

prune96.0ms (1.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1029111
Fresh000
Picked101
Done000
Total1039112
Error
2.6b
Counts
112 → 9
Alt Table
StatusErrorProgram
22.7b
(*.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 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))) (fma.f64 y.im y.im (*.f64 y.re y.re))))
36.3b
(-.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))))
14.3b
(*.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)))) (hypot.f64 y.im y.re)) (/.f64 (cbrt.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))) (hypot.f64 y.im y.re)))
35.8b
(/.f64 x.im y.re)
40.4b
(-.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))
40.7b
(neg.f64 (/.f64 x.re y.im))
22.3b
(/.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))))
13.7b
(*.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)))
22.7b
(*.f64 (/.f64 1 (*.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 (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im)) (cbrt.f64 (fma.f64 y.re y.re (*.f64 y.im y.im)))))
Compiler

Compiled 2951 to 660 computations (77.6% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))
0.2b
(*.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)))
12.9b
(/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re))

series222.0ms (2.8%)

Counts
3 → 108
Calls

3 calls:

109.0ms
(*.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)))
103.0ms
(/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re))
9.0ms
(-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))

rewrite27.0ms (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 → 106
Calls

3 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)))
5.0ms
(/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re))
4.0ms
(-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))

simplify172.0ms (2.2%)

Algorithm
egg-herbie
Rules
747×times-frac_binary64
528×fma-neg_binary64
402×fma-def_binary64
254×cancel-sign-sub-inv_binary64
230×distribute-rgt-in_binary64
Counts
214 → 211
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02265757
16074941
220964883
347654882
451024882

prune175.0ms (2.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New2056211
Fresh358
Picked101
Done000
Total20911220
Error
2.6b
Counts
220 → 11
Alt Table
StatusErrorProgram
36.3b
(-.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))))
45.2b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (-.f64 x.re (/.f64 (*.f64 y.re x.im) y.im)))
16.0b
(*.f64 (/.f64 (/.f64 1 (sqrt.f64 (hypot.f64 y.im y.re))) (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))))
13.6b
(/.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))
42.9b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (-.f64 (/.f64 (*.f64 x.re y.im) y.re) x.im))
40.4b
(-.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))
44.2b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) x.im)
40.7b
(neg.f64 (/.f64 x.re y.im))
46.9b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (neg.f64 x.re))
22.3b
(/.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))))
22.7b
(*.f64 (/.f64 1 (*.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 (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im)) (cbrt.f64 (fma.f64 y.re y.re (*.f64 y.im y.im)))))
Compiler

Compiled 5912 to 1678 computations (71.6% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))
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))
12.9b
(/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re))

series106.0ms (1.3%)

Counts
1 → 48
Calls

1 calls:

106.0ms
(/.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))

rewrite15.0ms (0.2%)

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:

7.0ms
(/.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))

simplify130.0ms (1.6%)

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

prune186.0ms (2.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New2305235
Fresh6410
Picked101
Done000
Total2379246
Error
2.6b
Counts
246 → 9
Alt Table
StatusErrorProgram
36.3b
(-.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))))
13.8b
(/.f64 (/.f64 (/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (sqrt.f64 (hypot.f64 y.im y.re))) (sqrt.f64 (hypot.f64 y.im y.re))) (hypot.f64 y.im y.re))
40.4b
(-.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))
14.3b
(/.f64 1 (/.f64 (hypot.f64 y.im y.re) (/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re))))
42.9b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (-.f64 (/.f64 (*.f64 x.re y.im) y.re) x.im))
45.1b
(/.f64 (-.f64 x.re (/.f64 (*.f64 y.re x.im) y.im)) (hypot.f64 y.im y.re))
22.3b
(/.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))))
47.1b
(/.f64 (-.f64 (/.f64 (*.f64 y.re x.im) y.im) x.re) (hypot.f64 y.im y.re))
42.3b
(/.f64 (-.f64 x.im (/.f64 (*.f64 x.re y.im) y.re)) (hypot.f64 y.im y.re))
Compiler

Compiled 6411 to 1390 computations (78.3% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))
0.1b
(/.f64 (/.f64 (/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (sqrt.f64 (hypot.f64 y.im y.re))) (sqrt.f64 (hypot.f64 y.im y.re))) (hypot.f64 y.im y.re))
4.2b
(/.f64 (/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (sqrt.f64 (hypot.f64 y.im y.re))) (sqrt.f64 (hypot.f64 y.im y.re)))
8.7b
(/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (sqrt.f64 (hypot.f64 y.im y.re)))

series377.0ms (4.8%)

Counts
3 → 128
Calls

3 calls:

139.0ms
(/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (sqrt.f64 (hypot.f64 y.im y.re)))
128.0ms
(/.f64 (/.f64 (/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (sqrt.f64 (hypot.f64 y.im y.re))) (sqrt.f64 (hypot.f64 y.im y.re))) (hypot.f64 y.im y.re))
110.0ms
(/.f64 (/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (sqrt.f64 (hypot.f64 y.im y.re))) (sqrt.f64 (hypot.f64 y.im y.re)))

rewrite320.0ms (4%)

Algorithm
rewrite-expression-head
Rules
1644×times-frac_binary64
784×*-un-lft-identity_binary64
784×add-sqr-sqrt_binary64
784×add-cube-cbrt_binary64
624×sqrt-prod_binary64
Counts
3 → 789
Calls

3 calls:

29.0ms
(/.f64 (/.f64 (/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (sqrt.f64 (hypot.f64 y.im y.re))) (sqrt.f64 (hypot.f64 y.im y.re))) (hypot.f64 y.im y.re))
17.0ms
(/.f64 (/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (sqrt.f64 (hypot.f64 y.im y.re))) (sqrt.f64 (hypot.f64 y.im y.re)))
5.0ms
(/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (sqrt.f64 (hypot.f64 y.im y.re)))

simplify1.0s (12.7%)

Algorithm
egg-herbie
Rules
537×fma-def_binary64
519×associate-/r*_binary64
464×div-sub_binary64
445×associate-/l/_binary64
273×associate-/l*_binary64
Counts
917 → 965
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
081448063
1186844983
2400742572
3539942572

prune611.0ms (7.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New9872989
Fresh088
Picked011
Done000
Total98711998
Error
2.5b
Counts
998 → 11
Alt Table
StatusErrorProgram
36.3b
(-.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))))
13.8b
(/.f64 (/.f64 (/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (sqrt.f64 (hypot.f64 y.im y.re))) (sqrt.f64 (hypot.f64 y.im y.re))) (hypot.f64 y.im y.re))
48.2b
(/.f64 (/.f64 (*.f64 (sqrt.f64 y.re) x.im) (sqrt.f64 (hypot.f64 y.im y.re))) (hypot.f64 y.im y.re))
40.4b
(-.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))
14.3b
(/.f64 1 (/.f64 (hypot.f64 y.im y.re) (/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re))))
51.0b
(/.f64 (/.f64 (neg.f64 (*.f64 x.re (sqrt.f64 y.im))) (sqrt.f64 (hypot.f64 y.im y.re))) (hypot.f64 y.im y.re))
42.9b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (-.f64 (/.f64 (*.f64 x.re y.im) y.re) x.im))
45.1b
(/.f64 (-.f64 x.re (/.f64 (*.f64 y.re x.im) y.im)) (hypot.f64 y.im y.re))
22.3b
(/.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))))
47.1b
(/.f64 (-.f64 (/.f64 (*.f64 y.re x.im) y.im) x.re) (hypot.f64 y.im y.re))
42.3b
(/.f64 (-.f64 x.im (/.f64 (*.f64 x.re y.im) y.re)) (hypot.f64 y.im y.re))
Compiler

Compiled 41287 to 5377 computations (87% saved)

regimes1.6s (20.6%)

Accuracy

Total 12.1b remaining (85.3%)

Threshold costs 0b (0%)

Counts
181 → 5
Compiler

Compiled 19268 to 11044 computations (42.7% saved)

bsearch111.0ms (1.4%)

Steps
ItersRangePoint
9
1.2062456310266416e+30
3.152343568014545e+36
3.0970906241597073e+36
7
-1.4070828750648742e-192
-7.862765862347215e-195
-9.658402922807776e-195
10
-4.167357273759762e-132
-4.963514388699338e-144
-1.9738142544677371e-143
10
-1.5928261157303677e+235
-4.3180897455970947e+223
-5.124136587792355e+226
Compiler

Compiled 5 to 4 computations (20% saved)

simplify6.0ms (0.1%)

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

Useful iterations: 0 (0.0ms)

IterNodesCost
042129
156129
274129
384129
490129
591129
691129

end170.0ms (2.1%)

Compiler

Compiled 395 to 199 computations (49.6% saved)

Profiling

Loading profile data...