Details

Time bar (total: 8.3s)

analyze1.1s (13.7%)

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)

sample3.8s (45.7%)

Results
2.5s3319×body8192exit
1.1s8256×body128valid
57.0ms313×body128invalid
Compiler

Compiled 43 to 23 computations (46.5% saved)

simplify132.0ms (1.6%)

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

prune3.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
6.6b
Counts
3 → 2
Alt Table
StatusErrorProgram
6.7b
(*.f64 x.im (fma.f64 x.re (*.f64 x.re 3) (neg.f64 (*.f64 x.im x.im))))
6.6b
(+.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)

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))
0.1b
(+.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))
0.2b
(*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.re)
6.2b
(*.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) x.im)

series47.0ms (0.6%)

Counts
4 → 96
Calls

4 calls:

16.0ms
(+.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))
15.0ms
(*.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) x.im)
11.0ms
(*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.re)
5.0ms
(+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re))

rewrite28.0ms (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:

10.0ms
(*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.re)
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)
3.0ms
(+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re))

simplify84.0ms (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
01462758
14272398
216752360
348222360

prune188.0ms (2.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New1336139
Fresh011
Picked101
Done000
Total1347141
Error
0.0b
Counts
141 → 7
Alt Table
StatusErrorProgram
6.6b
(fma.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))
6.7b
(*.f64 x.im (fma.f64 x.re (*.f64 x.re 3) (neg.f64 (*.f64 x.im x.im))))
26.8b
(+.f64 (*.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im 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))))))
23.9b
(+.f64 (*.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) x.im) (*.f64 (sqrt.f64 (*.f64 x.re (*.f64 2 (*.f64 x.im x.re)))) (sqrt.f64 (*.f64 x.re (*.f64 2 (*.f64 x.im x.re))))))
6.6b
(+.f64 (-.f64 (*.f64 (pow.f64 x.re 2) x.im) (pow.f64 x.im 3)) (*.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))
33.4b
(+.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))
Compiler

Compiled 4321 to 977 computations (77.4% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series40.0ms (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))
16.0ms
(*.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.im))
6.0ms
(*.f64 (-.f64 x.re x.im) x.im)

rewrite39.0ms (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:

12.0ms
(*.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.im))
11.0ms
(+.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))
7.0ms
(*.f64 (-.f64 x.re x.im) x.im)

simplify131.0ms (1.6%)

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

prune175.0ms (2.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1794183
Fresh246
Picked101
Done000
Total1828190
Error
0.0b
Counts
190 → 8
Alt Table
StatusErrorProgram
0.8b
(+.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))
26.8b
(+.f64 (*.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im 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))))))
0.5b
(+.f64 (*.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.im)) (*.f64 (*.f64 (cbrt.f64 (*.f64 x.re (*.f64 2 (*.f64 x.im x.re)))) (cbrt.f64 (*.f64 x.re (*.f64 2 (*.f64 x.im x.re))))) (cbrt.f64 (*.f64 x.re (*.f64 2 (*.f64 x.im x.re))))))
6.6b
(+.f64 (-.f64 (*.f64 (pow.f64 x.re 2) x.im) (pow.f64 x.im 3)) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.re))
6.7b
(*.f64 x.im (fma.f64 x.re (*.f64 x.re 3) (neg.f64 (*.f64 x.im x.im))))
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))
21.9b
(+.f64 (*.f64 (sqrt.f64 (*.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.im))) (sqrt.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))
23.9b
(+.f64 (*.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) x.im) (*.f64 (sqrt.f64 (*.f64 x.re (*.f64 2 (*.f64 x.im x.re)))) (sqrt.f64 (*.f64 x.re (*.f64 2 (*.f64 x.im x.re))))))
Compiler

Compiled 6537 to 1447 computations (77.9% 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))
0.0b
(*.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 (0.2%)

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:

1.0ms
(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))

simplify71.0ms (0.9%)

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

prune140.0ms (1.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1235128
Fresh527
Picked011
Done000
Total1288136
Error
0b
Counts
136 → 8
Alt Table
StatusErrorProgram
0.8b
(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))
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))
6.7b
(*.f64 x.im (fma.f64 x.re (*.f64 x.re 3) (neg.f64 (*.f64 x.im x.im))))
17.8b
(fma.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.im) (cbrt.f64 (pow.f64 (*.f64 x.re (*.f64 2 (*.f64 x.im x.re))) 3)))
0.5b
(fma.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.im) (*.f64 (*.f64 (cbrt.f64 (*.f64 x.re (*.f64 2 (*.f64 x.im x.re)))) (cbrt.f64 (*.f64 x.re (*.f64 2 (*.f64 x.im x.re))))) (cbrt.f64 (*.f64 x.re (*.f64 2 (*.f64 x.im x.re))))))
20.4b
(fma.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.im) (*.f64 (sqrt.f64 (*.f64 x.re (*.f64 2 (*.f64 x.im x.re)))) (sqrt.f64 (*.f64 x.re (*.f64 2 (*.f64 x.im x.re))))))
23.9b
(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))))))
6.6b
(+.f64 (-.f64 (*.f64 (pow.f64 x.re 2) x.im) (pow.f64 x.im 3)) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.re))
Compiler

Compiled 3397 to 777 computations (77.1% saved)

localize15.0ms (0.2%)

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.im) (*.f64 (*.f64 (cbrt.f64 (*.f64 x.re (*.f64 2 (*.f64 x.im x.re)))) (cbrt.f64 (*.f64 x.re (*.f64 2 (*.f64 x.im x.re))))) (cbrt.f64 (*.f64 x.re (*.f64 2 (*.f64 x.im x.re))))))
0.2b
(*.f64 (*.f64 (cbrt.f64 (*.f64 x.re (*.f64 2 (*.f64 x.im x.re)))) (cbrt.f64 (*.f64 x.re (*.f64 2 (*.f64 x.im x.re))))) (cbrt.f64 (*.f64 x.re (*.f64 2 (*.f64 x.im x.re)))))
0.4b
(*.f64 (cbrt.f64 (*.f64 x.re (*.f64 2 (*.f64 x.im x.re)))) (cbrt.f64 (*.f64 x.re (*.f64 2 (*.f64 x.im x.re)))))
23.7b
(cbrt.f64 (*.f64 x.re (*.f64 2 (*.f64 x.im x.re))))

series1.3s (15.4%)

Counts
4 → 96
Calls

4 calls:

664.0ms
(*.f64 (cbrt.f64 (*.f64 x.re (*.f64 2 (*.f64 x.im x.re)))) (cbrt.f64 (*.f64 x.re (*.f64 2 (*.f64 x.im x.re)))))
516.0ms
(cbrt.f64 (*.f64 x.re (*.f64 2 (*.f64 x.im x.re))))
52.0ms
(*.f64 (*.f64 (cbrt.f64 (*.f64 x.re (*.f64 2 (*.f64 x.im x.re)))) (cbrt.f64 (*.f64 x.re (*.f64 2 (*.f64 x.im x.re))))) (cbrt.f64 (*.f64 x.re (*.f64 2 (*.f64 x.im x.re)))))
51.0ms
(fma.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.im) (*.f64 (*.f64 (cbrt.f64 (*.f64 x.re (*.f64 2 (*.f64 x.im x.re)))) (cbrt.f64 (*.f64 x.re (*.f64 2 (*.f64 x.im x.re))))) (cbrt.f64 (*.f64 x.re (*.f64 2 (*.f64 x.im x.re))))))

rewrite28.0ms (0.3%)

Algorithm
rewrite-expression-head
Rules
30×pow1_binary64
16×pow1/3_binary64
12×add-sqr-sqrt_binary64
11×pow-prod-up_binary64
11×add-exp-log_binary64
Counts
4 → 89
Calls

4 calls:

9.0ms
(*.f64 (*.f64 (cbrt.f64 (*.f64 x.re (*.f64 2 (*.f64 x.im x.re)))) (cbrt.f64 (*.f64 x.re (*.f64 2 (*.f64 x.im x.re))))) (cbrt.f64 (*.f64 x.re (*.f64 2 (*.f64 x.im x.re)))))
8.0ms
(*.f64 (cbrt.f64 (*.f64 x.re (*.f64 2 (*.f64 x.im x.re)))) (cbrt.f64 (*.f64 x.re (*.f64 2 (*.f64 x.im x.re)))))
5.0ms
(cbrt.f64 (*.f64 x.re (*.f64 2 (*.f64 x.im x.re))))
0.0ms
(fma.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.im) (*.f64 (*.f64 (cbrt.f64 (*.f64 x.re (*.f64 2 (*.f64 x.im x.re)))) (cbrt.f64 (*.f64 x.re (*.f64 2 (*.f64 x.im x.re))))) (cbrt.f64 (*.f64 x.re (*.f64 2 (*.f64 x.im x.re))))))

simplify128.0ms (1.5%)

Algorithm
egg-herbie
Rules
636×fma-def_binary64
359×distribute-rgt-in_binary64
346×unswap-sqr_binary64
300×fma-neg_binary64
260×*-commutative_binary64
Counts
185 → 152
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
01693554
13453189
28572805
319282618
448342618
549512618

prune268.0ms (3.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New2060206
Fresh066
Picked011
Done011
Total2068214
Error
0b
Counts
214 → 8
Alt Table
StatusErrorProgram
0.8b
(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))
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))
6.7b
(*.f64 x.im (fma.f64 x.re (*.f64 x.re 3) (neg.f64 (*.f64 x.im x.im))))
17.8b
(fma.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.im) (cbrt.f64 (pow.f64 (*.f64 x.re (*.f64 2 (*.f64 x.im x.re))) 3)))
0.5b
(fma.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.im) (*.f64 (*.f64 (cbrt.f64 (*.f64 x.re (*.f64 2 (*.f64 x.im x.re)))) (cbrt.f64 (*.f64 x.re (*.f64 2 (*.f64 x.im x.re))))) (cbrt.f64 (*.f64 x.re (*.f64 2 (*.f64 x.im x.re))))))
20.4b
(fma.f64 (+.f64 x.re x.im) (*.f64 (-.f64 x.re x.im) x.im) (*.f64 (sqrt.f64 (*.f64 x.re (*.f64 2 (*.f64 x.im x.re)))) (sqrt.f64 (*.f64 x.re (*.f64 2 (*.f64 x.im x.re))))))
23.9b
(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))))))
6.6b
(+.f64 (-.f64 (*.f64 (pow.f64 x.re 2) x.im) (pow.f64 x.im 3)) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.re))
Compiler

Compiled 7962 to 3737 computations (53.1% saved)

regimes380.0ms (4.6%)

Accuracy

Total 0.2b remaining (88.9%)

Threshold costs 0.2b (88.9%)

Counts
110 → 1
Compiler

Compiled 7578 to 4113 computations (45.7% 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
01123
11823
22323
32523
42623
52623

end133.0ms (1.6%)

Compiler

Compiled 231 to 129 computations (44.2% saved)

Profiling

Loading profile data...