Details

Time bar (total: 3.7s)

analyze197.0ms (5.3%)

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)

sample1.3s (34.4%)

Results
1.1s8256×body128valid
52.0ms453×body128invalid
Compiler

Compiled 65 to 35 computations (46.2% saved)

simplify131.0ms (3.5%)

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
01226
13025
27123
319416
457314
5177914
6304814
7413714
8461514
9474914
10478414
11490714
12499814

prune3.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
6.4b
Counts
3 → 2
Alt Table
StatusErrorProgram
6.4b
(*.f64 x.re (fma.f64 x.re x.re (*.f64 (*.f64 x.im x.im) -3)))
6.4b
(-.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 51 computations (47.4% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re))
0.1b
(-.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))
0.2b
(*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.im)
6.0b
(*.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) x.re)

series55.0ms (1.5%)

Counts
4 → 96
Calls

4 calls:

17.0ms
(*.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) x.re)
14.0ms
(-.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))
12.0ms
(*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.im)
5.0ms
(+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re))

rewrite29.0ms (0.8%)

Algorithm
rewrite-expression-head
Rules
12×associate-*l/_binary64
12×add-sqr-sqrt_binary64
*-un-lft-identity_binary64
add-cube-cbrt_binary64
add-cbrt-cube_binary64
Counts
4 → 79
Calls

4 calls:

6.0ms
(-.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)
3.0ms
(+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re))

simplify118.0ms (3.2%)

Algorithm
egg-herbie
Rules
245×times-frac_binary64
240×associate-*l*_binary64
214×associate-*r*_binary64
204×fma-neg_binary64
200×distribute-rgt-out_binary64
Counts
175 → 142
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01562858
14472479
217562377
335392365
447752365
550892365

prune123.0ms (3.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1366142
Fresh011
Picked101
Done000
Total1377144
Error
0.1b
Counts
144 → 7
Alt Table
StatusErrorProgram
6.4b
(*.f64 x.re (fma.f64 x.re x.re (*.f64 (*.f64 x.im x.im) -3)))
0.3b
(-.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))
6.4b
(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)))
6.4b
(-.f64 (pow.f64 x.re 3) (*.f64 3 (*.f64 x.re (pow.f64 x.im 2))))
31.3b
(-.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))
6.7b
(-.f64 (*.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) x.re) (*.f64 (*.f64 (*.f64 2 (*.f64 x.re x.im)) (*.f64 (cbrt.f64 x.im) (cbrt.f64 x.im))) (cbrt.f64 x.im)))
23.1b
(-.f64 (*.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) x.re) (*.f64 (sqrt.f64 (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.im)) (sqrt.f64 (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.im))))
Compiler

Compiled 4356 to 909 computations (79.1% saved)

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

series28.0ms (0.8%)

Counts
2 → 48
Calls

2 calls:

17.0ms
(-.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))
12.0ms
(*.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.re))

rewrite29.0ms (0.8%)

Algorithm
rewrite-expression-head
Rules
40×associate-*l/_binary64
17×flip-+_binary64
17×flip3-+_binary64
16×frac-sub_binary64
12×frac-times_binary64
Counts
2 → 61
Calls

2 calls:

13.0ms
(-.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))

simplify112.0ms (3%)

Algorithm
egg-herbie
Rules
567×fma-neg_binary64
525×associate-*l*_binary64
507×associate-*r*_binary64
326×neg-sub0_binary64
325×neg-mul-1_binary64
Counts
109 → 107
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01833168
17322601
234242376
340952376
447022376

prune215.0ms (5.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1618169
Fresh426
Picked101
Done000
Total16610176
Error
0.0b
Counts
176 → 10
Alt Table
StatusErrorProgram
19.4b
(-.f64 (*.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.re)) (*.f64 (sqrt.f64 (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.im)) (sqrt.f64 (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.im))))
0.2b
(fma.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.re) (neg.f64 (*.f64 x.im (*.f64 2 (*.f64 x.re x.im)))))
25.2b
(*.f64 (sqrt.f64 (-.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))) (sqrt.f64 (-.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))))
6.4b
(*.f64 x.re (fma.f64 x.re x.re (*.f64 (*.f64 x.im x.im) -3)))
0.5b
(-.f64 (*.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.re)) (*.f64 (*.f64 (cbrt.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re))) (cbrt.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)))) (*.f64 x.im (cbrt.f64 (*.f64 2 (*.f64 x.re x.im))))))
0.6b
(-.f64 (*.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.re)) (*.f64 (*.f64 (*.f64 2 (*.f64 x.re x.im)) (*.f64 (cbrt.f64 x.im) (cbrt.f64 x.im))) (cbrt.f64 x.im)))
6.4b
(-.f64 (pow.f64 x.re 3) (*.f64 3 (*.f64 x.re (pow.f64 x.im 2))))
31.6b
(-.f64 (*.f64 (sqrt.f64 (+.f64 x.re x.im)) (*.f64 (sqrt.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))
14.4b
(-.f64 (/.f64 (*.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) (*.f64 (-.f64 x.re x.im) x.re)) (-.f64 x.re x.im)) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.im))
0.6b
(-.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.re))) (cbrt.f64 (*.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.re)))) (cbrt.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))
Compiler

Compiled 6382 to 1456 computations (77.2% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series51.0ms (1.4%)

Counts
4 → 72
Calls

4 calls:

18.0ms
(*.f64 x.im (*.f64 2 (*.f64 x.re x.im)))
16.0ms
(fma.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.re) (neg.f64 (*.f64 x.im (*.f64 2 (*.f64 x.re x.im)))))
10.0ms
(*.f64 2 (*.f64 x.re x.im))
5.0ms
(*.f64 (-.f64 x.re x.im) x.re)

rewrite21.0ms (0.6%)

Algorithm
rewrite-expression-head
Rules
20×add-cbrt-cube_binary64
20×add-exp-log_binary64
20×pow1_binary64
12×add-sqr-sqrt_binary64
11×associate-*l*_binary64
Counts
4 → 77
Calls

4 calls:

8.0ms
(*.f64 (-.f64 x.re x.im) x.re)
5.0ms
(*.f64 x.im (*.f64 2 (*.f64 x.re x.im)))
4.0ms
(*.f64 2 (*.f64 x.re x.im))
0.0ms
(fma.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.re) (neg.f64 (*.f64 x.im (*.f64 2 (*.f64 x.re x.im)))))

simplify96.0ms (2.6%)

Algorithm
egg-herbie
Rules
798×fma-def_binary64
590×fma-neg_binary64
401×*-commutative_binary64
288×unswap-sqr_binary64
263×associate-+l+_binary64
Counts
149 → 117
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01221941
12841669
29441623
319581541
447861541
552511541

prune159.0ms (4.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1125117
Fresh639
Picked011
Done000
Total1189127
Error
0b
Counts
127 → 9
Alt Table
StatusErrorProgram
19.4b
(fma.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.re) (neg.f64 (*.f64 (sqrt.f64 (*.f64 x.im (*.f64 2 (*.f64 x.re x.im)))) (sqrt.f64 (*.f64 x.im (*.f64 2 (*.f64 x.re x.im)))))))
0.2b
(fma.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.re) (neg.f64 (*.f64 x.im (*.f64 2 (*.f64 x.re x.im)))))
6.4b
(*.f64 x.re (fma.f64 x.re x.re (*.f64 (*.f64 x.im x.im) -3)))
0.5b
(fma.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.re) (neg.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 x.im (*.f64 2 (*.f64 x.re x.im)))) (cbrt.f64 (*.f64 x.im (*.f64 2 (*.f64 x.re x.im))))) (cbrt.f64 (*.f64 x.im (*.f64 2 (*.f64 x.re x.im)))))))
6.4b
(fma.f64 (*.f64 x.re (*.f64 x.im x.im)) -3 (pow.f64 x.re 3))
0.4b
(fma.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.re) (neg.f64 (*.f64 x.im (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (*.f64 x.re x.im))))))
12.2b
(fma.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.re) (neg.f64 (*.f64 x.im (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 x.re x.im)) 3)))))
14.4b
(-.f64 (/.f64 (*.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) (*.f64 (-.f64 x.re x.im) x.re)) (-.f64 x.re x.im)) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.im))
0.6b
(-.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.re))) (cbrt.f64 (*.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.re)))) (cbrt.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))
Compiler

Compiled 3003 to 1181 computations (60.7% saved)

localize18.0ms (0.5%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(fma.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.re) (neg.f64 (*.f64 x.im (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (*.f64 x.re x.im))))))
0.2b
(*.f64 x.im (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (*.f64 x.re x.im))))
0.3b
(*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (*.f64 x.re x.im)))
0.4b
(*.f64 (sqrt.f64 2) (*.f64 x.re x.im))

series108.0ms (2.9%)

Counts
4 → 96
Calls

4 calls:

37.0ms
(fma.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.re) (neg.f64 (*.f64 x.im (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (*.f64 x.re x.im))))))
33.0ms
(*.f64 x.im (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (*.f64 x.re x.im))))
26.0ms
(*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (*.f64 x.re x.im)))
12.0ms
(*.f64 (sqrt.f64 2) (*.f64 x.re x.im))

rewrite31.0ms (0.8%)

Algorithm
rewrite-expression-head
Rules
32×add-cbrt-cube_binary64
32×add-exp-log_binary64
32×pow1_binary64
19×cbrt-unprod_binary64
19×prod-exp_binary64
Counts
4 → 85
Calls

4 calls:

13.0ms
(*.f64 x.im (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (*.f64 x.re x.im))))
7.0ms
(*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (*.f64 x.re x.im)))
5.0ms
(*.f64 (sqrt.f64 2) (*.f64 x.re x.im))
0.0ms
(fma.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.re) (neg.f64 (*.f64 x.im (*.f64 (sqrt.f64 2) (*.f64 (sqrt.f64 2) (*.f64 x.re x.im))))))

simplify111.0ms (3%)

Algorithm
egg-herbie
Rules
544×fma-neg_binary64
541×fma-def_binary64
502×*-commutative_binary64
302×distribute-rgt-in_binary64
284×associate-*r*_binary64
Counts
181 → 130
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01202296
12942018
210471972
320261884
448251884
552081884

prune190.0ms (5.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1282130
Fresh257
Picked101
Done011
Total1318139
Error
0b
Counts
139 → 8
Alt Table
StatusErrorProgram
0.5b
(fma.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.re) (neg.f64 (*.f64 (*.f64 (cbrt.f64 x.im) (cbrt.f64 x.im)) (*.f64 (*.f64 x.re (*.f64 2 x.im)) (cbrt.f64 x.im)))))
14.4b
(-.f64 (/.f64 (*.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) (*.f64 (-.f64 x.re x.im) x.re)) (-.f64 x.re x.im)) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.im))
6.4b
(*.f64 x.re (fma.f64 x.re x.re (*.f64 (*.f64 x.im x.im) -3)))
0.2b
(fma.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.re) (neg.f64 (*.f64 x.im (*.f64 2 (*.f64 x.re x.im)))))
0.5b
(fma.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.re) (neg.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 x.im (*.f64 2 (*.f64 x.re x.im)))) (cbrt.f64 (*.f64 x.im (*.f64 2 (*.f64 x.re x.im))))) (cbrt.f64 (*.f64 x.im (*.f64 2 (*.f64 x.re x.im)))))))
6.4b
(fma.f64 (*.f64 x.re (*.f64 x.im x.im)) -3 (pow.f64 x.re 3))
0.2b
(fma.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.re) (neg.f64 (*.f64 x.im (*.f64 (sqrt.f64 (sqrt.f64 2)) (*.f64 x.re (*.f64 x.im (pow.f64 (sqrt.f64 2) 3/2)))))))
12.2b
(fma.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.re) (neg.f64 (*.f64 x.im (cbrt.f64 (pow.f64 (*.f64 2 (*.f64 x.re x.im)) 3)))))
Compiler

Compiled 3536 to 1778 computations (49.7% saved)

regimes434.0ms (11.8%)

Accuracy

Total 0.2b remaining (90.5%)

Threshold costs 0.2b (90.5%)

Counts
123 → 1
Compiler

Compiled 9108 to 5112 computations (43.9% saved)

simplify3.0ms (0.1%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
+-commutative_binary64
distribute-lft-neg-in_binary64
distribute-rgt-neg-in_binary64
sub-neg_binary64
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
01225
12623
24223
35423
46023
56323
66423
76323

end127.0ms (3.4%)

Compiler

Compiled 220 to 128 computations (41.8% saved)

Profiling

Loading profile data...