Details

Time bar (total: 3.4s)

analyze296.0ms (8.8%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
25%74.9%0.1%5
25%62.4%12.6%6
31.2%50%18.8%7
40.6%37.5%22%8
45.3%26.5%28.2%9
46.8%19.5%33.7%10
48.8%14%37.2%11
51.7%10.1%38.1%12
52.8%7.1%40.1%13
53.3%5.1%41.6%14
Compiler

Compiled 22 to 12 computations (45.5% saved)

sample23.0ms (0.7%)

Algorithm
intervals
Results
14.0ms256×body128valid
1.0ms12×body128invalid
Compiler

Compiled 45 to 25 computations (44.4% saved)

simplify137.0ms (4.1%)

Algorithm
egg-herbie
Rules
680×unsub-neg_binary64
594×fma-neg_binary64
560×sub-neg_binary64
520×fma-def_binary64
399×cancel-sign-sub-inv_binary64
Counts
1 → 2
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01436
13233
27331
319620
457518
5178118
6305018
7413918
8461718
9475118
10478618
11490918
12500018

prune4.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
7.8b
Counts
3 → 2
Alt Table
StatusErrorProgram
8.1b
(fma.f64 x.re (*.f64 (*.f64 x.im x.im) -3) (pow.f64 x.re 3))
8.0b
(-.f64 (*.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) x.re) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.im))
Compiler

Compiled 97 to 54 computations (44.3% saved)

localize10.0ms (0.3%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.1b
(*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.im)
0.2b
(-.f64 (*.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) x.re) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.im))
7.4b
(*.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) x.re)

rewrite21.0ms (0.6%)

Algorithm
rewrite-expression-head
Rules
12×associate-*l/_binary64
11×add-sqr-sqrt_binary64
associate-*l*_binary64
*-un-lft-identity_binary64
add-cube-cbrt_binary64
Counts
3 → 65
Calls

3 calls:

7.0ms
(-.f64 (*.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) x.re) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.im))
5.0ms
(*.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) x.re)
5.0ms
(*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.im)

series97.0ms (2.9%)

Counts
3 → 72
Calls

3 calls:

36.0ms
(-.f64 (*.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) x.re) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.im))
32.0ms
(*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.im)
28.0ms
(*.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) x.re)

simplify124.0ms (3.7%)

Algorithm
egg-herbie
Rules
585×distribute-rgt-neg-in_binary64
221×associate-*l*_binary64
211×distribute-rgt-out_binary64
205×fma-neg_binary64
199×cancel-sign-sub-inv_binary64
Counts
137 → 218
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01503219
14352693
217412521
335032483
449502483

prune119.0ms (3.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New2117218
Fresh011
Picked101
Done000
Total2128220
Error
0.0b
Counts
220 → 8
Alt Table
StatusErrorProgram
7.9b
(fma.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) x.re (neg.f64 (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.im)))
25.1b
(*.f64 -3 (*.f64 x.re (pow.f64 x.im 2)))
8.3b
(-.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) x.re)) (cbrt.f64 (*.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) x.re))) (cbrt.f64 (*.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) x.re))) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.im))
8.2b
(fma.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) x.re (*.f64 x.re (*.f64 (pow.f64 x.im 2) -2)))
8.1b
(fma.f64 x.re (*.f64 (*.f64 x.im x.im) -3) (pow.f64 x.re 3))
8.4b
(-.f64 (*.f64 (*.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) (*.f64 (cbrt.f64 x.re) (cbrt.f64 x.re))) (cbrt.f64 x.re)) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.im))
0.2b
(-.f64 (*.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.re)) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.im))
31.0b
(-.f64 (/.f64 (*.f64 x.re (-.f64 (pow.f64 x.re 4) (pow.f64 x.im 4))) (+.f64 (*.f64 x.re x.re) (*.f64 x.im x.im))) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.im))
Compiler

Compiled 3892 to 1129 computations (71% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(*.f64 (-.f64 x.re x.im) x.re)
0.1b
(*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.im)
0.1b
(*.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.re))
0.2b
(-.f64 (*.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.re)) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.im))

rewrite31.0ms (0.9%)

Algorithm
rewrite-expression-head
Rules
42×associate-*l/_binary64
17×flip-+_binary64
17×flip3-+_binary64
16×frac-sub_binary64
12×frac-times_binary64
Counts
3 → 85
Calls

3 calls:

10.0ms
(-.f64 (*.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.re)) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.im))
8.0ms
(*.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.re))
6.0ms
(*.f64 (-.f64 x.re x.im) x.re)

series77.0ms (2.3%)

Counts
3 → 72
Calls

3 calls:

35.0ms
(-.f64 (*.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.re)) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.im))
28.0ms
(*.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.re))
13.0ms
(*.f64 (-.f64 x.re x.im) x.re)

simplify165.0ms (4.9%)

Algorithm
egg-herbie
Rules
600×fma-neg_binary64
595×associate-*l*_binary64
550×associate-*r*_binary64
324×cancel-sign-sub-inv_binary64
307×distribute-rgt-in_binary64
Counts
157 → 273
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02094733
17773662
236483402
343603402
446973402

prune199.0ms (5.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New3335338
Fresh257
Picked101
Done000
Total33610346
Error
0b
Counts
346 → 10
Alt Table
StatusErrorProgram
0.6b
(-.f64 (*.f64 (*.f64 (cbrt.f64 (+.f64 x.re x.im)) (cbrt.f64 (+.f64 x.re x.im))) (*.f64 (cbrt.f64 (+.f64 x.re x.im)) (*.f64 (-.f64 x.re x.im) x.re))) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.im))
25.1b
(*.f64 -3 (*.f64 x.re (pow.f64 x.im 2)))
8.3b
(-.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) x.re)) (cbrt.f64 (*.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) x.re))) (cbrt.f64 (*.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) x.re))) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.im))
8.2b
(fma.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) x.re (*.f64 x.re (*.f64 (pow.f64 x.im 2) -2)))
8.1b
(fma.f64 x.re (*.f64 (*.f64 x.im x.im) -3) (pow.f64 x.re 3))
43.3b
(-.f64 (*.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.re)) (*.f64 (*.f64 (sqrt.f64 (*.f64 2 (*.f64 x.re x.im))) (sqrt.f64 x.im)) (*.f64 (sqrt.f64 (*.f64 2 (*.f64 x.re x.im))) (sqrt.f64 x.im))))
0.2b
(fma.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.re) (*.f64 x.im (*.f64 (*.f64 x.re x.im) -2)))
29.3b
(-.f64 (*.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.re)) (*.f64 (*.f64 (*.f64 2 (*.f64 x.re x.im)) (sqrt.f64 x.im)) (sqrt.f64 x.im)))
0.7b
(-.f64 (*.f64 (+.f64 x.re x.im) (*.f64 (*.f64 (cbrt.f64 (*.f64 (-.f64 x.re x.im) x.re)) (cbrt.f64 (*.f64 (-.f64 x.re x.im) x.re))) (cbrt.f64 (*.f64 (-.f64 x.re x.im) x.re)))) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.im))
31.0b
(-.f64 (/.f64 (*.f64 x.re (-.f64 (pow.f64 x.re 4) (pow.f64 x.im 4))) (+.f64 (*.f64 x.re x.re) (*.f64 x.im x.im))) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.im))
Compiler

Compiled 6680 to 1826 computations (72.7% saved)

localize12.0ms (0.4%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(*.f64 (-.f64 x.re x.im) x.re)
0.1b
(*.f64 x.im (*.f64 (*.f64 x.re x.im) -2))
0.2b
(fma.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.re) (*.f64 x.im (*.f64 (*.f64 x.re x.im) -2)))

rewrite7.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
11×add-cbrt-cube_binary64
11×add-exp-log_binary64
11×pow1_binary64
cbrt-unprod_binary64
prod-exp_binary64
Counts
2 → 33
Calls

2 calls:

5.0ms
(*.f64 x.im (*.f64 (*.f64 x.re x.im) -2))
0.0ms
(fma.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.re) (*.f64 x.im (*.f64 (*.f64 x.re x.im) -2)))

series80.0ms (2.4%)

Counts
2 → 48
Calls

2 calls:

48.0ms
(fma.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.re) (*.f64 x.im (*.f64 (*.f64 x.re x.im) -2)))
32.0ms
(*.f64 x.im (*.f64 (*.f64 x.re x.im) -2))

simplify100.0ms (3%)

Algorithm
egg-herbie
Rules
441×unswap-sqr_binary64
398×fma-neg_binary64
334×*-commutative_binary64
250×exp-prod_binary64
235×fma-def_binary64
Counts
81 → 151
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
0761517
11771339
25801283
310841260
422311260
541591260
649381260

prune115.0ms (3.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New2362238
Fresh369
Picked011
Done000
Total2399248
Error
0b
Counts
248 → 9
Alt Table
StatusErrorProgram
29.3b
(fma.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.re) (*.f64 (sqrt.f64 x.im) (*.f64 (sqrt.f64 x.im) (*.f64 (*.f64 x.re x.im) -2))))
8.3b
(-.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) x.re)) (cbrt.f64 (*.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) x.re))) (cbrt.f64 (*.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) x.re))) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.im))
8.2b
(fma.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) x.re (*.f64 x.re (*.f64 (pow.f64 x.im 2) -2)))
8.1b
(fma.f64 x.re (*.f64 (*.f64 x.im x.im) -3) (pow.f64 x.re 3))
43.3b
(-.f64 (*.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.re)) (*.f64 (*.f64 (sqrt.f64 (*.f64 2 (*.f64 x.re x.im))) (sqrt.f64 x.im)) (*.f64 (sqrt.f64 (*.f64 2 (*.f64 x.re x.im))) (sqrt.f64 x.im))))
0.6b
(fma.f64 (+.f64 x.re x.im) (*.f64 (*.f64 (cbrt.f64 (-.f64 x.re x.im)) (cbrt.f64 (-.f64 x.re x.im))) (*.f64 x.re (cbrt.f64 (-.f64 x.re x.im)))) (*.f64 x.im (*.f64 (*.f64 x.re x.im) -2)))
0.2b
(fma.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.re) (*.f64 x.im (*.f64 (*.f64 x.re x.im) -2)))
0.7b
(-.f64 (*.f64 (+.f64 x.re x.im) (*.f64 (*.f64 (cbrt.f64 (*.f64 (-.f64 x.re x.im) x.re)) (cbrt.f64 (*.f64 (-.f64 x.re x.im) x.re))) (cbrt.f64 (*.f64 (-.f64 x.re x.im) x.re)))) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.im))
31.0b
(-.f64 (/.f64 (*.f64 x.re (-.f64 (pow.f64 x.re 4) (pow.f64 x.im 4))) (+.f64 (*.f64 x.re x.re) (*.f64 x.im x.im))) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.im))
Compiler

Compiled 2493 to 952 computations (61.8% saved)

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.5b
(*.f64 (cbrt.f64 (-.f64 x.re x.im)) (cbrt.f64 (-.f64 x.re x.im)))
0.6b
(cbrt.f64 (-.f64 x.re x.im))
0.6b
(cbrt.f64 (-.f64 x.re x.im))
0.6b
(cbrt.f64 (-.f64 x.re x.im))

rewrite17.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
33×cbrt-prod_binary64
29×add-sqr-sqrt_binary64
27×*-un-lft-identity_binary64
14×cbrt-div_binary64
11×add-cube-cbrt_binary64
Counts
2 → 75
Calls

2 calls:

11.0ms
(*.f64 (cbrt.f64 (-.f64 x.re x.im)) (cbrt.f64 (-.f64 x.re x.im)))
2.0ms
(cbrt.f64 (-.f64 x.re x.im))

series57.0ms (1.7%)

Counts
2 → 48
Calls

2 calls:

31.0ms
(*.f64 (cbrt.f64 (-.f64 x.re x.im)) (cbrt.f64 (-.f64 x.re x.im)))
26.0ms
(cbrt.f64 (-.f64 x.re x.im))

simplify173.0ms (5.1%)

Algorithm
egg-herbie
Rules
702×fma-def_binary64
469×fma-neg_binary64
461×cancel-sign-sub-inv_binary64
283×distribute-rgt-neg-in_binary64
268×distribute-lft-neg-in_binary64
Counts
123 → 224
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02463519
16433400
220313210
345783123
449863123
549543123

prune262.0ms (7.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New4370437
Fresh077
Picked011
Done011
Total4379446
Error
0b
Counts
446 → 9
Alt Table
StatusErrorProgram
29.3b
(fma.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.re) (*.f64 (sqrt.f64 x.im) (*.f64 (sqrt.f64 x.im) (*.f64 (*.f64 x.re x.im) -2))))
8.3b
(-.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) x.re)) (cbrt.f64 (*.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) x.re))) (cbrt.f64 (*.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) x.re))) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.im))
8.2b
(fma.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) x.re (*.f64 x.re (*.f64 (pow.f64 x.im 2) -2)))
8.1b
(fma.f64 x.re (*.f64 (*.f64 x.im x.im) -3) (pow.f64 x.re 3))
43.3b
(-.f64 (*.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.re)) (*.f64 (*.f64 (sqrt.f64 (*.f64 2 (*.f64 x.re x.im))) (sqrt.f64 x.im)) (*.f64 (sqrt.f64 (*.f64 2 (*.f64 x.re x.im))) (sqrt.f64 x.im))))
0.6b
(fma.f64 (+.f64 x.re x.im) (*.f64 (*.f64 (cbrt.f64 (-.f64 x.re x.im)) (cbrt.f64 (-.f64 x.re x.im))) (*.f64 x.re (cbrt.f64 (-.f64 x.re x.im)))) (*.f64 x.im (*.f64 (*.f64 x.re x.im) -2)))
0.2b
(fma.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.re) (*.f64 x.im (*.f64 (*.f64 x.re x.im) -2)))
0.7b
(-.f64 (*.f64 (+.f64 x.re x.im) (*.f64 (*.f64 (cbrt.f64 (*.f64 (-.f64 x.re x.im) x.re)) (cbrt.f64 (*.f64 (-.f64 x.re x.im) x.re))) (cbrt.f64 (*.f64 (-.f64 x.re x.im) x.re)))) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.im))
31.0b
(-.f64 (/.f64 (*.f64 x.re (-.f64 (pow.f64 x.re 4) (pow.f64 x.im 4))) (+.f64 (*.f64 x.re x.re) (*.f64 x.im x.im))) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.im))
Compiler

Compiled 10349 to 4316 computations (58.3% saved)

regimes375.0ms (11.1%)

Accuracy

Total 0.2b remaining (91.3%)

Threshold costs 0.2b (91.3%)

Compiler

Compiled 8674 to 4445 computations (48.8% saved)

simplify5.0ms (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
01331
12031
22531
32731
42831
52831

end1.0ms (0%)

Compiler

Compiled 18 to 10 computations (44.4% saved)

sample847.0ms (25.1%)

Algorithm
intervals
Results
465.0ms8000×body128valid
27.0ms448×body128invalid
Compiler

Compiled 281 to 141 computations (49.8% saved)

Profiling

Loading profile data...