Details

Time bar (total: 7.4s)

analyze1.3s (16.9%)

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
0%99.9%0.1%5
0%99.9%0.1%6
6.2%84.3%9.5%7
6.2%82.7%11%8
7.8%78%14.1%9
8.6%76.5%14.9%10
11.3%70%18.6%11
11.7%69.2%19.1%12
12.2%67.7%20.1%13
12.4%67.2%20.3%14
Compiler

Compiled 22 to 12 computations (45.5% saved)

sample3.7s (49.4%)

Results
2.4s3306×body8192exit
1.1s8256×body128valid
42.0ms271×body128invalid
Compiler

Compiled 43 to 23 computations (46.5% saved)

simplify134.0ms (1.8%)

Algorithm
egg-herbie
Rules
613×sub-neg_binary64
578×fma-neg_binary64
529×neg-mul-1_binary64
501×neg-sub0_binary64
455×unsub-neg_binary64
Counts
1 → 2
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01224
12623
26023
313016
433516
588116
6149616
7351116
8406116
9397716
10461416
11477116
12491816
13491416

prune4.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
6.9b
Counts
3 → 2
Alt Table
StatusErrorProgram
7.0b
(*.f64 x.im (fma.f64 x.re (*.f64 x.re 3) (neg.f64 (*.f64 x.im x.im))))
6.9b
(+.f64 (*.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) x.im) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.re))
Compiler

Compiled 100 to 54 computations (46% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.0b
(+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re))
0.2b
(*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.re)
0.2b
(+.f64 (*.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) x.im) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.re))
6.5b
(*.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) x.im)

series48.0ms (0.6%)

Counts
4 → 96
Calls

4 calls:

16.0ms
(*.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) x.im)
15.0ms
(+.f64 (*.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) x.im) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.re))
11.0ms
(*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.re)
7.0ms
(+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re))

rewrite24.0ms (0.3%)

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 → 77
Calls

4 calls:

6.0ms
(+.f64 (*.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) x.im) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.re))
5.0ms
(*.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) x.im)
5.0ms
(*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.re)
3.0ms
(+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re))

simplify82.0ms (1.1%)

Algorithm
egg-herbie
Rules
727×distribute-rgt-in_binary64
685×distribute-lft-in_binary64
245×associate-*l*_binary64
206×associate-*r*_binary64
181×distribute-rgt-out_binary64
Counts
173 → 139
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01463157
14242650
216742360
348222360

prune113.0ms (1.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New1345139
Fresh011
Picked011
Done000
Total1347141
Error
0.0b
Counts
141 → 7
Alt Table
StatusErrorProgram
0.3b
(+.f64 (*.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.im)) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.re))
30.9b
(+.f64 (/.f64 (*.f64 x.im (-.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.re))
7.2b
(+.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) x.im)) (cbrt.f64 (*.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) x.im))) (cbrt.f64 (*.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) x.im))) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.re))
7.0b
(*.f64 x.im (fma.f64 x.re (*.f64 x.re 3) (neg.f64 (*.f64 x.im x.im))))
6.9b
(+.f64 (*.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) x.im) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.re))
25.9b
(*.f64 (sqrt.f64 (+.f64 (*.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) x.im) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.re))) (sqrt.f64 (+.f64 (*.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) x.im) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.re))))
25.4b
(+.f64 (neg.f64 (pow.f64 x.im 3)) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.re))
Compiler

Compiled 4350 to 950 computations (78.2% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series35.0ms (0.5%)

Counts
3 → 72
Calls

3 calls:

17.0ms
(+.f64 (*.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.im)) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.re))
12.0ms
(*.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.im))
6.0ms
(*.f64 (-.f64 x.re x.im) x.im)

rewrite34.0ms (0.5%)

Algorithm
rewrite-expression-head
Rules
42×associate-*l/_binary64
18×flip-+_binary64
18×flip3-+_binary64
16×frac-add_binary64
12×frac-times_binary64
Counts
3 → 83
Calls

3 calls:

13.0ms
(+.f64 (*.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.im)) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.re))
8.0ms
(*.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.im))
5.0ms
(*.f64 (-.f64 x.re x.im) x.im)

simplify128.0ms (1.7%)

Algorithm
egg-herbie
Rules
602×associate-*l*_binary64
526×associate-*r*_binary64
306×distribute-rgt-out_binary64
303×distribute-rgt-in_binary64
291×distribute-lft-in_binary64
Counts
155 → 144
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
01974461
17103616
233932663
343792663
446442663

prune155.0ms (2.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1794183
Fresh235
Picked101
Done101
Total1837190
Error
0.0b
Counts
190 → 7
Alt Table
StatusErrorProgram
7.0b
(*.f64 x.im (fma.f64 x.re (*.f64 x.re 3) (neg.f64 (*.f64 x.im x.im))))
0.7b
(+.f64 (*.f64 (+.f64 x.re x.im) (*.f64 (*.f64 (-.f64 x.re x.im) (*.f64 (cbrt.f64 x.im) (cbrt.f64 x.im))) (cbrt.f64 x.im))) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.re))
25.9b
(*.f64 (sqrt.f64 (+.f64 (*.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) x.im) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.re))) (sqrt.f64 (+.f64 (*.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) x.im) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.re))))
0.3b
(fma.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.im) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.re))
0.7b
(+.f64 (*.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.im)) (*.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.re (cbrt.f64 (*.f64 2 (*.f64 x.im x.re))))))
0.6b
(+.f64 (*.f64 (+.f64 x.re x.im) (*.f64 (*.f64 (cbrt.f64 (-.f64 x.re x.im)) (cbrt.f64 (-.f64 x.re x.im))) (*.f64 (cbrt.f64 (-.f64 x.re x.im)) x.im))) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.re))
25.4b
(+.f64 (neg.f64 (pow.f64 x.im 3)) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.re))
Compiler

Compiled 6495 to 1393 computations (78.6% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series20.0ms (0.3%)

Counts
1 → 24
Calls

1 calls:

20.0ms
(fma.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.im) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.re))

rewrite1.0ms (0%)

Algorithm
rewrite-expression-head
Rules
*-un-lft-identity_binary64
add-sqr-sqrt_binary64
add-cube-cbrt_binary64
add-cbrt-cube_binary64
add-exp-log_binary64
Counts
1 → 10
Calls

1 calls:

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

simplify72.0ms (1%)

Algorithm
egg-herbie
Rules
444×distribute-rgt-out_binary64
423×associate-*l*_binary64
406×distribute-rgt-in_binary64
398×distribute-lft-in_binary64
364×associate-*r*_binary64
Counts
34 → 24
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
030661
161602
2159602
3501592
42769592
54897592
65076592

prune146.0ms (2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1226128
Fresh426
Picked011
Done000
Total1269135
Error
0.0b
Counts
135 → 9
Alt Table
StatusErrorProgram
0.6b
(fma.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.im) (*.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 2 (*.f64 x.im x.re))) (cbrt.f64 (*.f64 2 (*.f64 x.im x.re)))) (cbrt.f64 (*.f64 2 (*.f64 x.im x.re)))) x.re))
0.7b
(fma.f64 (+.f64 x.re x.im) (*.f64 (*.f64 (-.f64 x.re x.im) (*.f64 (cbrt.f64 x.im) (cbrt.f64 x.im))) (cbrt.f64 x.im)) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.re))
7.0b
(*.f64 x.im (fma.f64 x.re (*.f64 x.re 3) (neg.f64 (*.f64 x.im x.im))))
30.6b
(neg.f64 (pow.f64 x.im 3))
0.6b
(fma.f64 (+.f64 x.re x.im) (*.f64 (*.f64 (cbrt.f64 (*.f64 x.im (-.f64 x.re x.im))) (cbrt.f64 (*.f64 x.im (-.f64 x.re x.im)))) (cbrt.f64 (*.f64 x.im (-.f64 x.re x.im)))) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.re))
0.6b
(+.f64 (*.f64 (+.f64 x.re x.im) (*.f64 (*.f64 (cbrt.f64 (-.f64 x.re x.im)) (cbrt.f64 (-.f64 x.re x.im))) (*.f64 (cbrt.f64 (-.f64 x.re x.im)) x.im))) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.re))
23.4b
(fma.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.im) (*.f64 (sqrt.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re))) (*.f64 x.re (sqrt.f64 (*.f64 2 (*.f64 x.im x.re))))))
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.im (cbrt.f64 (-.f64 x.re x.im)))) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.re))
0.3b
(fma.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.im) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.re))
Compiler

Compiled 3457 to 779 computations (77.5% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 x.im (cbrt.f64 (-.f64 x.re x.im)))
0.3b
(*.f64 (*.f64 (cbrt.f64 (-.f64 x.re x.im)) (cbrt.f64 (-.f64 x.re x.im))) (*.f64 x.im (cbrt.f64 (-.f64 x.re x.im))))
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))

series130.0ms (1.7%)

Counts
4 → 96
Calls

4 calls:

41.0ms
(*.f64 x.im (cbrt.f64 (-.f64 x.re x.im)))
39.0ms
(*.f64 (cbrt.f64 (-.f64 x.re x.im)) (cbrt.f64 (-.f64 x.re x.im)))
32.0ms
(cbrt.f64 (-.f64 x.re x.im))
17.0ms
(*.f64 (*.f64 (cbrt.f64 (-.f64 x.re x.im)) (cbrt.f64 (-.f64 x.re x.im))) (*.f64 x.im (cbrt.f64 (-.f64 x.re x.im))))

rewrite53.0ms (0.7%)

Algorithm
rewrite-expression-head
Rules
70×cbrt-div_binary64
40×add-sqr-sqrt_binary64
39×cbrt-prod_binary64
35×flip--_binary64
35×flip3--_binary64
Counts
4 → 153
Calls

4 calls:

17.0ms
(*.f64 (*.f64 (cbrt.f64 (-.f64 x.re x.im)) (cbrt.f64 (-.f64 x.re x.im))) (*.f64 x.im (cbrt.f64 (-.f64 x.re x.im))))
9.0ms
(*.f64 (cbrt.f64 (-.f64 x.re x.im)) (cbrt.f64 (-.f64 x.re x.im)))
7.0ms
(*.f64 x.im (cbrt.f64 (-.f64 x.re x.im)))
2.0ms
(cbrt.f64 (-.f64 x.re x.im))

simplify180.0ms (2.4%)

Algorithm
egg-herbie
Rules
560×associate-*r*_binary64
522×times-frac_binary64
508×fma-neg_binary64
462×associate-*l*_binary64
233×*-commutative_binary64
Counts
249 → 284
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03796612
110345902
234575712
349265712
450355712

prune396.0ms (5.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New3871388
Fresh077
Picked011
Done011
Total38710397
Error
0b
Counts
397 → 10
Alt Table
StatusErrorProgram
19.5b
(fma.f64 (+.f64 x.re x.im) (*.f64 (/.f64 (*.f64 (cbrt.f64 (-.f64 (pow.f64 x.re 3) (pow.f64 x.im 3))) (cbrt.f64 (-.f64 (pow.f64 x.re 3) (pow.f64 x.im 3)))) (*.f64 (cbrt.f64 (fma.f64 x.im (+.f64 x.im x.re) (*.f64 x.re x.re))) (cbrt.f64 (fma.f64 x.im (+.f64 x.im x.re) (*.f64 x.re x.re))))) (*.f64 x.im (cbrt.f64 (-.f64 x.re x.im)))) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.re))
0.6b
(fma.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.im) (*.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 2 (*.f64 x.im x.re))) (cbrt.f64 (*.f64 2 (*.f64 x.im x.re)))) (cbrt.f64 (*.f64 2 (*.f64 x.im x.re)))) x.re))
0.7b
(fma.f64 (+.f64 x.re x.im) (*.f64 (*.f64 (-.f64 x.re x.im) (*.f64 (cbrt.f64 x.im) (cbrt.f64 x.im))) (cbrt.f64 x.im)) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.re))
7.0b
(*.f64 x.im (fma.f64 x.re (*.f64 x.re 3) (neg.f64 (*.f64 x.im x.im))))
30.6b
(neg.f64 (pow.f64 x.im 3))
0.6b
(fma.f64 (+.f64 x.re x.im) (*.f64 (*.f64 (cbrt.f64 (*.f64 x.im (-.f64 x.re x.im))) (cbrt.f64 (*.f64 x.im (-.f64 x.re x.im)))) (cbrt.f64 (*.f64 x.im (-.f64 x.re x.im)))) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.re))
0.6b
(+.f64 (*.f64 (+.f64 x.re x.im) (*.f64 (*.f64 (cbrt.f64 (-.f64 x.re x.im)) (cbrt.f64 (-.f64 x.re x.im))) (*.f64 (cbrt.f64 (-.f64 x.re x.im)) x.im))) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.re))
23.4b
(fma.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.im) (*.f64 (sqrt.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re))) (*.f64 x.re (sqrt.f64 (*.f64 2 (*.f64 x.im x.re))))))
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.im (cbrt.f64 (-.f64 x.re x.im)))) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.re))
0.3b
(fma.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.im) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.re))
Compiler

Compiled 17031 to 4970 computations (70.8% saved)

regimes542.0ms (7.3%)

Accuracy

Total 0.2b remaining (93.6%)

Threshold costs 0.2b (93.6%)

Counts
148 → 1
Compiler

Compiled 11944 to 5947 computations (50.2% saved)

simplify3.0ms (0%)

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
01024
11624
22124
32324
42424
52424

end152.0ms (2%)

Compiler

Compiled 322 to 159 computations (50.6% saved)

Profiling

Loading profile data...