Details

Time bar (total: 8.4s)

analyze738.0ms (8.7%)

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)

sample1.5s (17.9%)

Results
1.3s8256×body128valid
90.0ms521×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
24.6b
Counts
3 → 1
Alt Table
StatusErrorProgram
24.6b
(/.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 2 expressions with local error:

NewErrorProgram
0.9b
(-.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)))

series95.0ms (1.1%)

Counts
2 → 96
Calls

2 calls:

86.0ms
(/.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:

5.0ms
(/.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))

simplify94.0ms (1.1%)

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

prune89.0ms (1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1029111
Fresh000
Picked101
Done000
Total1039112
Error
2.3b
Counts
112 → 9
Alt Table
StatusErrorProgram
25.1b
(*.f64 (*.f64 (cbrt.f64 (/.f64 (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im)) (fma.f64 y.re y.re (*.f64 y.im y.im)))) (cbrt.f64 (/.f64 (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im)) (fma.f64 y.re y.re (*.f64 y.im y.im))))) (cbrt.f64 (/.f64 (-.f64 (*.f64 x.im y.re) (*.f64 x.re y.im)) (fma.f64 y.re y.re (*.f64 y.im y.im)))))
24.9b
(/.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))))
18.0b
(*.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)))
41.9b
(-.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))))
40.6b
(/.f64 x.im y.re)
37.0b
(-.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))
18.5b
(*.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)))
35.7b
(neg.f64 (/.f64 x.re 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)))))
Compiler

Compiled 3013 to 662 computations (78% saved)

localize9.0ms (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)))
0.9b
(-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))
16.9b
(/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re))

series381.0ms (4.5%)

Counts
4 → 132
Calls

4 calls:

202.0ms
(*.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)))
146.0ms
(/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re))
23.0ms
(/.f64 1 (hypot.f64 y.im y.re))
9.0ms
(-.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:

11.0ms
(*.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))

simplify166.0ms (2%)

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

prune273.0ms (3.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New2696275
Fresh358
Picked101
Done000
Total27311284
Error
2.3b
Counts
284 → 11
Alt Table
StatusErrorProgram
41.9b
(-.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))))
46.4b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) x.im)
40.6b
(/.f64 x.im y.re)
24.6b
(*.f64 1 (/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (*.f64 (hypot.f64 y.im y.re) (hypot.f64 y.im y.re))))
18.1b
(*.f64 (sqrt.f64 (/.f64 1 (hypot.f64 y.im y.re))) (*.f64 (sqrt.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))))
37.0b
(-.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))
44.5b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) x.re)
21.4b
(*.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))))
42.2b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (neg.f64 x.re))
18.5b
(*.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)))
35.7b
(neg.f64 (/.f64 x.re y.im))
Compiler

Compiled 7610 to 2317 computations (69.6% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.3b
(*.f64 (sqrt.f64 (/.f64 1 (hypot.f64 y.im y.re))) (*.f64 (sqrt.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))))
0.3b
(*.f64 (sqrt.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)))
0.9b
(-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))
16.9b
(/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (hypot.f64 y.im y.re))

series397.0ms (4.7%)

Counts
2 → 80
Calls

2 calls:

279.0ms
(*.f64 (sqrt.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)))
117.0ms
(*.f64 (sqrt.f64 (/.f64 1 (hypot.f64 y.im y.re))) (*.f64 (sqrt.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))))

rewrite39.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
47×add-sqr-sqrt_binary64
35×times-frac_binary64
32×associate-*l*_binary64
32×sqrt-prod_binary64
27×*-un-lft-identity_binary64
Counts
2 → 97
Calls

2 calls:

15.0ms
(*.f64 (sqrt.f64 (/.f64 1 (hypot.f64 y.im y.re))) (*.f64 (sqrt.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))))
12.0ms
(*.f64 (sqrt.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)))

simplify115.0ms (1.4%)

Algorithm
egg-herbie
Rules
726×times-frac_binary64
384×fma-def_binary64
264×cancel-sign-sub-inv_binary64
248×associate-*r*_binary64
248×distribute-rgt-in_binary64
Counts
177 → 180
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02316347
15855453
220095383
350475383

prune247.0ms (2.9%)

Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New2751276
Fresh01010
Picked011
Done000
Total27512287
Error
2.3b
Counts
287 → 12
Alt Table
StatusErrorProgram
41.9b
(-.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))))
46.4b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) x.im)
40.6b
(/.f64 x.im y.re)
24.6b
(*.f64 1 (/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (*.f64 (hypot.f64 y.im y.re) (hypot.f64 y.im y.re))))
18.1b
(*.f64 (sqrt.f64 (/.f64 1 (hypot.f64 y.im y.re))) (*.f64 (sqrt.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))))
42.2b
(*.f64 (sqrt.f64 (/.f64 1 (hypot.f64 y.im y.re))) (*.f64 (sqrt.f64 (/.f64 1 (hypot.f64 y.im y.re))) (neg.f64 x.re)))
37.0b
(-.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))
44.5b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) x.re)
21.4b
(*.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))))
42.2b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (neg.f64 x.re))
18.5b
(*.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)))
35.7b
(neg.f64 (/.f64 x.re y.im))
Compiler

Compiled 9626 to 3844 computations (60.1% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.5b
(*.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))))
0.9b
(-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im))
4.6b
(/.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))
17.4b
(cbrt.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)))

series417.0ms (4.9%)

Counts
3 → 144
Calls

3 calls:

202.0ms
(/.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)))) (hypot.f64 y.im y.re))
122.0ms
(*.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))))
92.0ms
(cbrt.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)))

rewrite32.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
26×cbrt-div_binary64
22×add-sqr-sqrt_binary64
19×cbrt-prod_binary64
14×*-un-lft-identity_binary64
14×add-cube-cbrt_binary64
Counts
3 → 96
Calls

3 calls:

11.0ms
(/.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)))) (hypot.f64 y.im y.re))
8.0ms
(*.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))))
2.0ms
(cbrt.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)))

simplify265.0ms (3.1%)

Algorithm
egg-herbie
Rules
531×fma-def_binary64
363×*-commutative_binary64
237×cancel-sign-sub-inv_binary64
231×sub-neg_binary64
198×fma-neg_binary64
Counts
240 → 373
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
090515365
1318314588
2499614588
3501514588

prune586.0ms (6.9%)

Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New6330633
Fresh01010
Picked011
Done011
Total63312645
Error
2.3b
Counts
645 → 12
Alt Table
StatusErrorProgram
41.9b
(-.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))))
46.4b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) x.im)
40.6b
(/.f64 x.im y.re)
24.6b
(*.f64 1 (/.f64 (-.f64 (*.f64 y.re x.im) (*.f64 x.re y.im)) (*.f64 (hypot.f64 y.im y.re) (hypot.f64 y.im y.re))))
18.1b
(*.f64 (sqrt.f64 (/.f64 1 (hypot.f64 y.im y.re))) (*.f64 (sqrt.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))))
42.2b
(*.f64 (sqrt.f64 (/.f64 1 (hypot.f64 y.im y.re))) (*.f64 (sqrt.f64 (/.f64 1 (hypot.f64 y.im y.re))) (neg.f64 x.re)))
37.0b
(-.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))
44.5b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) x.re)
21.4b
(*.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))))
42.2b
(*.f64 (/.f64 1 (hypot.f64 y.im y.re)) (neg.f64 x.re))
18.5b
(*.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)))
35.7b
(neg.f64 (/.f64 x.re y.im))
Compiler

Compiled 41112 to 16268 computations (60.4% saved)

regimes2.7s (31.7%)

Accuracy

Total 9.0b remaining (86.6%)

Threshold costs 0b (0%)

Counts
208 → 3
Compiler

Compiled 27613 to 14819 computations (46.3% saved)

bsearch8.0ms (0.1%)

Compiler

Compiled 19 to 11 computations (42.1% saved)

simplify4.0ms (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
02986
14286
25286
35986
46386
56486
66386

end151.0ms (1.8%)

Compiler

Compiled 356 to 180 computations (49.4% saved)

Profiling

Loading profile data...