Details

Time bar (total: 3.2s)

analyze193.0ms (6%)

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)

sample1.1s (35.5%)

Results
991.0ms8256×body128valid
46.0ms413×body128invalid
Compiler

Compiled 65 to 35 computations (46.2% saved)

simplify127.0ms (3.9%)

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
8.1b
Counts
3 → 2
Alt Table
StatusErrorProgram
8.2b
(*.f64 x.re (fma.f64 x.re x.re (*.f64 (*.f64 x.im x.im) -3)))
8.2b
(-.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))
Compiler

Compiled 97 to 51 computations (47.4% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.0b
(fma.f64 x.re x.re (*.f64 (*.f64 x.im x.im) -3))
0.2b
(*.f64 (*.f64 x.im x.im) -3)
7.6b
(*.f64 x.re (fma.f64 x.re x.re (*.f64 (*.f64 x.im x.im) -3)))

series28.0ms (0.9%)

Counts
3 → 60
Calls

3 calls:

16.0ms
(*.f64 x.re (fma.f64 x.re x.re (*.f64 (*.f64 x.im x.im) -3)))
9.0ms
(fma.f64 x.re x.re (*.f64 (*.f64 x.im x.im) -3))
2.0ms
(*.f64 (*.f64 x.im x.im) -3)

rewrite12.0ms (0.4%)

Algorithm
rewrite-expression-head
Rules
10×add-cbrt-cube_binary64
10×add-exp-log_binary64
10×pow1_binary64
add-sqr-sqrt_binary64
associate-*r*_binary64
Counts
3 → 53
Calls

3 calls:

6.0ms
(*.f64 (*.f64 x.im x.im) -3)
3.0ms
(*.f64 x.re (fma.f64 x.re x.re (*.f64 (*.f64 x.im x.im) -3)))
0.0ms
(fma.f64 x.re x.re (*.f64 (*.f64 x.im x.im) -3))

simplify54.0ms (1.7%)

Algorithm
egg-herbie
Rules
652×distribute-rgt-in_binary64
645×distribute-lft-in_binary64
429×fma-def_binary64
175×*-commutative_binary64
160×associate-+l+_binary64
Counts
113 → 93
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
0881459
11811302
25251293
311351293
449531293

prune79.0ms (2.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New86793
Fresh101
Picked011
Done000
Total87895
Error
7.8b
Counts
95 → 8
Alt Table
StatusErrorProgram
31.3b
(cbrt.f64 (*.f64 (*.f64 (*.f64 x.re (fma.f64 x.re x.re (*.f64 (*.f64 x.im x.im) -3))) (*.f64 x.re (fma.f64 x.re x.re (*.f64 (*.f64 x.im x.im) -3)))) (*.f64 x.re (fma.f64 x.re x.re (*.f64 (*.f64 x.im x.im) -3)))))
8.2b
(*.f64 x.re (fma.f64 x.re x.re (*.f64 (*.f64 x.im x.im) -3)))
28.4b
(pow.f64 x.re 3)
8.3b
(*.f64 x.re (fma.f64 x.re x.re (*.f64 (*.f64 (*.f64 x.im x.im) (*.f64 (cbrt.f64 -3) (cbrt.f64 -3))) (cbrt.f64 -3))))
8.1b
(fma.f64 -3 (*.f64 x.re (*.f64 x.im x.im)) (pow.f64 x.re 3))
8.2b
(*.f64 x.re (fma.f64 x.re x.re (*.f64 x.im (*.f64 x.im -3))))
8.5b
(*.f64 x.re (fma.f64 x.re x.re (*.f64 (*.f64 (cbrt.f64 (*.f64 (*.f64 x.im x.im) -3)) (cbrt.f64 (*.f64 (*.f64 x.im x.im) -3))) (cbrt.f64 (*.f64 (*.f64 x.im x.im) -3)))))
22.3b
(*.f64 x.re (fma.f64 x.re x.re (cbrt.f64 (*.f64 (*.f64 (*.f64 (*.f64 x.im x.im) -3) (*.f64 (*.f64 x.im x.im) -3)) (*.f64 (*.f64 x.im x.im) -3)))))
Compiler

Compiled 1713 to 852 computations (50.3% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.1b
(fma.f64 -3 (*.f64 x.re (*.f64 x.im x.im)) (pow.f64 x.re 3))
7.6b
(*.f64 x.re (*.f64 x.im x.im))

series24.0ms (0.8%)

Counts
2 → 48
Calls

2 calls:

16.0ms
(fma.f64 -3 (*.f64 x.re (*.f64 x.im x.im)) (pow.f64 x.re 3))
8.0ms
(*.f64 x.re (*.f64 x.im x.im))

rewrite6.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
add-cbrt-cube_binary64
add-exp-log_binary64
pow1_binary64
add-sqr-sqrt_binary64
associate-*l*_binary64
Counts
2 → 31
Calls

2 calls:

4.0ms
(*.f64 x.re (*.f64 x.im x.im))
0.0ms
(fma.f64 -3 (*.f64 x.re (*.f64 x.im x.im)) (pow.f64 x.re 3))

simplify80.0ms (2.5%)

Algorithm
egg-herbie
Rules
854×unswap-sqr_binary64
731×fma-def_binary64
327×*-commutative_binary64
294×associate-*l*_binary64
221×associate-*r*_binary64
Counts
79 → 47
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
054931
1109821
2295821
3890821
42027821
54878821
64993821
74950821

prune51.0ms (1.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New45247
Fresh246
Picked101
Done011
Total48755
Error
0.1b
Counts
55 → 7
Alt Table
StatusErrorProgram
31.3b
(cbrt.f64 (*.f64 (*.f64 (*.f64 x.re (fma.f64 x.re x.re (*.f64 (*.f64 x.im x.im) -3))) (*.f64 x.re (fma.f64 x.re x.re (*.f64 (*.f64 x.im x.im) -3)))) (*.f64 x.re (fma.f64 x.re x.re (*.f64 (*.f64 x.im x.im) -3)))))
8.2b
(*.f64 x.re (fma.f64 x.re x.re (*.f64 (*.f64 x.im x.im) -3)))
0.2b
(fma.f64 -3 (*.f64 (*.f64 x.re x.im) x.im) (pow.f64 x.re 3))
8.2b
(*.f64 x.re (fma.f64 x.re x.re (*.f64 x.im (*.f64 x.im -3))))
30.9b
(fma.f64 -3 (*.f64 (*.f64 (sqrt.f64 x.re) x.im) (*.f64 (sqrt.f64 x.re) x.im)) (pow.f64 x.re 3))
8.5b
(*.f64 x.re (fma.f64 x.re x.re (*.f64 (*.f64 (cbrt.f64 (*.f64 (*.f64 x.im x.im) -3)) (cbrt.f64 (*.f64 (*.f64 x.im x.im) -3))) (cbrt.f64 (*.f64 (*.f64 x.im x.im) -3)))))
22.3b
(*.f64 x.re (fma.f64 x.re x.re (cbrt.f64 (*.f64 (*.f64 (*.f64 (*.f64 x.im x.im) -3) (*.f64 (*.f64 x.im x.im) -3)) (*.f64 (*.f64 x.im x.im) -3)))))
Compiler

Compiled 964 to 482 computations (50% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.1b
(fma.f64 -3 (*.f64 (*.f64 x.re x.im) x.im) (pow.f64 x.re 3))
0.2b
(*.f64 (*.f64 x.re x.im) x.im)

series25.0ms (0.8%)

Counts
2 → 48
Calls

2 calls:

15.0ms
(fma.f64 -3 (*.f64 (*.f64 x.re x.im) x.im) (pow.f64 x.re 3))
10.0ms
(*.f64 (*.f64 x.re x.im) x.im)

rewrite5.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
add-cbrt-cube_binary64
add-exp-log_binary64
pow1_binary64
associate-*r*_binary64
*-un-lft-identity_binary64
Counts
2 → 30
Calls

2 calls:

4.0ms
(*.f64 (*.f64 x.re x.im) x.im)
0.0ms
(fma.f64 -3 (*.f64 (*.f64 x.re x.im) x.im) (pow.f64 x.re 3))

simplify110.0ms (3.4%)

Algorithm
egg-herbie
Rules
453×unswap-sqr_binary64
447×times-frac_binary64
350×fma-def_binary64
237×*-commutative_binary64
230×distribute-rgt-in_binary64
Counts
78 → 52
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
056921
1129811
2411811
3703809
41377809
53652809
64974809
75000809
85000809
94870809

prune54.0ms (1.7%)

Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New48452
Fresh145
Picked011
Done011
Total491059
Error
0.0b
Counts
59 → 10
Alt Table
StatusErrorProgram
0.6b
(fma.f64 -3 (*.f64 (*.f64 (*.f64 x.re x.im) (*.f64 (cbrt.f64 x.im) (cbrt.f64 x.im))) (cbrt.f64 x.im)) (pow.f64 x.re 3))
31.3b
(cbrt.f64 (*.f64 (*.f64 (*.f64 x.re (fma.f64 x.re x.re (*.f64 (*.f64 x.im x.im) -3))) (*.f64 x.re (fma.f64 x.re x.re (*.f64 (*.f64 x.im x.im) -3)))) (*.f64 x.re (fma.f64 x.re x.re (*.f64 (*.f64 x.im x.im) -3)))))
8.2b
(*.f64 x.re (fma.f64 x.re x.re (*.f64 (*.f64 x.im x.im) -3)))
0.2b
(fma.f64 -3 (*.f64 (*.f64 x.re x.im) x.im) (pow.f64 x.re 3))
8.2b
(*.f64 x.re (fma.f64 x.re x.re (*.f64 x.im (*.f64 x.im -3))))
0.7b
(fma.f64 -3 (*.f64 (*.f64 (cbrt.f64 (*.f64 (*.f64 x.re x.im) x.im)) (cbrt.f64 (*.f64 (*.f64 x.re x.im) x.im))) (cbrt.f64 (*.f64 (*.f64 x.re x.im) x.im))) (pow.f64 x.re 3))
30.9b
(fma.f64 -3 (*.f64 (*.f64 (sqrt.f64 x.re) x.im) (*.f64 (sqrt.f64 x.re) x.im)) (pow.f64 x.re 3))
8.5b
(*.f64 x.re (fma.f64 x.re x.re (*.f64 (*.f64 (cbrt.f64 (*.f64 (*.f64 x.im x.im) -3)) (cbrt.f64 (*.f64 (*.f64 x.im x.im) -3))) (cbrt.f64 (*.f64 (*.f64 x.im x.im) -3)))))
23.5b
(*.f64 (sqrt.f64 (fma.f64 -3 (*.f64 (*.f64 x.re x.im) x.im) (pow.f64 x.re 3))) (sqrt.f64 (fma.f64 -3 (*.f64 (*.f64 x.re x.im) x.im) (pow.f64 x.re 3))))
32.4b
(fma.f64 -3 (*.f64 (*.f64 x.re (pow.f64 x.im 3/2)) (sqrt.f64 x.im)) (pow.f64 x.re 3))
Compiler

Compiled 1143 to 576 computations (49.6% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 (*.f64 (*.f64 x.re x.im) (*.f64 (cbrt.f64 x.im) (cbrt.f64 x.im))) (cbrt.f64 x.im))
0.2b
(*.f64 (*.f64 x.re x.im) (*.f64 (cbrt.f64 x.im) (cbrt.f64 x.im)))
0.5b
(*.f64 (cbrt.f64 x.im) (cbrt.f64 x.im))
0.6b
(cbrt.f64 x.im)

series476.0ms (14.8%)

Counts
4 → 72
Calls

4 calls:

379.0ms
(*.f64 (*.f64 x.re x.im) (*.f64 (cbrt.f64 x.im) (cbrt.f64 x.im)))
38.0ms
(*.f64 (cbrt.f64 x.im) (cbrt.f64 x.im))
36.0ms
(cbrt.f64 x.im)
22.0ms
(*.f64 (*.f64 (*.f64 x.re x.im) (*.f64 (cbrt.f64 x.im) (cbrt.f64 x.im))) (cbrt.f64 x.im))

rewrite29.0ms (0.9%)

Algorithm
rewrite-expression-head
Rules
41×pow1_binary64
36×add-exp-log_binary64
23×pow-prod-down_binary64
23×add-sqr-sqrt_binary64
22×cbrt-unprod_binary64
Counts
4 → 111
Calls

4 calls:

11.0ms
(*.f64 (*.f64 (*.f64 x.re x.im) (*.f64 (cbrt.f64 x.im) (cbrt.f64 x.im))) (cbrt.f64 x.im))
7.0ms
(*.f64 (*.f64 x.re x.im) (*.f64 (cbrt.f64 x.im) (cbrt.f64 x.im)))
5.0ms
(*.f64 (cbrt.f64 x.im) (cbrt.f64 x.im))
1.0ms
(cbrt.f64 x.im)

simplify131.0ms (4.1%)

Algorithm
egg-herbie
Rules
501×*-commutative_binary64
399×sqr-pow_binary64
371×log-prod_binary64
354×exp-prod_binary64
292×associate-*l*_binary64
Counts
183 → 149
Iterations

Useful iterations: 5 (0.0ms)

IterNodesCost
01251908
12661583
210441476
318871448
437781300
545221296
647971296
748561296

prune203.0ms (6.3%)

Pruning

11 alts after pruning (8 fresh and 3 done)

PrunedKeptTotal
New1841185
Fresh077
Picked011
Done022
Total18411195
Error
0.0b
Counts
195 → 11
Alt Table
StatusErrorProgram
0.6b
(fma.f64 -3 (*.f64 (*.f64 (*.f64 x.re x.im) (*.f64 (cbrt.f64 x.im) (cbrt.f64 x.im))) (cbrt.f64 x.im)) (pow.f64 x.re 3))
31.3b
(cbrt.f64 (*.f64 (*.f64 (*.f64 x.re (fma.f64 x.re x.re (*.f64 (*.f64 x.im x.im) -3))) (*.f64 x.re (fma.f64 x.re x.re (*.f64 (*.f64 x.im x.im) -3)))) (*.f64 x.re (fma.f64 x.re x.re (*.f64 (*.f64 x.im x.im) -3)))))
8.2b
(*.f64 x.re (fma.f64 x.re x.re (*.f64 (*.f64 x.im x.im) -3)))
0.7b
(fma.f64 -3 (*.f64 (*.f64 (*.f64 x.re x.im) (*.f64 (cbrt.f64 (*.f64 (cbrt.f64 x.im) (cbrt.f64 x.im))) (*.f64 (cbrt.f64 (cbrt.f64 x.im)) (cbrt.f64 x.im)))) (cbrt.f64 x.im)) (pow.f64 x.re 3))
0.2b
(fma.f64 -3 (*.f64 (*.f64 x.re x.im) x.im) (pow.f64 x.re 3))
8.2b
(*.f64 x.re (fma.f64 x.re x.re (*.f64 x.im (*.f64 x.im -3))))
0.7b
(fma.f64 -3 (*.f64 (*.f64 (cbrt.f64 (*.f64 (*.f64 x.re x.im) x.im)) (cbrt.f64 (*.f64 (*.f64 x.re x.im) x.im))) (cbrt.f64 (*.f64 (*.f64 x.re x.im) x.im))) (pow.f64 x.re 3))
30.9b
(fma.f64 -3 (*.f64 (*.f64 (sqrt.f64 x.re) x.im) (*.f64 (sqrt.f64 x.re) x.im)) (pow.f64 x.re 3))
8.5b
(*.f64 x.re (fma.f64 x.re x.re (*.f64 (*.f64 (cbrt.f64 (*.f64 (*.f64 x.im x.im) -3)) (cbrt.f64 (*.f64 (*.f64 x.im x.im) -3))) (cbrt.f64 (*.f64 (*.f64 x.im x.im) -3)))))
23.5b
(*.f64 (sqrt.f64 (fma.f64 -3 (*.f64 (*.f64 x.re x.im) x.im) (pow.f64 x.re 3))) (sqrt.f64 (fma.f64 -3 (*.f64 (*.f64 x.re x.im) x.im) (pow.f64 x.re 3))))
32.4b
(fma.f64 -3 (*.f64 (*.f64 x.re (pow.f64 x.im 3/2)) (sqrt.f64 x.im)) (pow.f64 x.re 3))
Compiler

Compiled 4131 to 1642 computations (60.3% saved)

regimes201.0ms (6.3%)

Accuracy

Total 0.1b remaining (78.2%)

Threshold costs 0.1b (78.2%)

Counts
68 → 1
Compiler

Compiled 3813 to 2346 computations (38.5% saved)

simplify2.0ms (0.1%)

Algorithm
egg-herbie
Rules
*-commutative_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0914
11114
21114

end147.0ms (4.6%)

Compiler

Compiled 251 to 144 computations (42.6% saved)

Profiling

Loading profile data...