Details

Time bar (total: 3.7s)

analyze1.0ms (0%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
99.9%0%0.1%1
Compiler

Compiled 22 to 12 computations (45.5% saved)

sample876.0ms (23.7%)

Infinites
44.7% of outputs are infinite.
Results
764.0ms8256×body128valid
Compiler

Compiled 65 to 35 computations (46.2% saved)

simplify128.0ms (3.4%)

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 (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New022
Fresh011
Picked000
Done000
Total033
Error
5.2b
Counts
3 → 2
Alt Table
StatusErrorProgram
5.3b
(*.f64 x.im (fma.f64 x.re (*.f64 x.re 3) (neg.f64 (*.f64 x.im x.im))))
10.8b
(+.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)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

NewErrorProgram
0.6b
(fma.f64 x.re (*.f64 x.re 3) (neg.f64 (*.f64 x.im x.im)))
4.8b
(*.f64 x.im (fma.f64 x.re (*.f64 x.re 3) (neg.f64 (*.f64 x.im x.im))))

series22.0ms (0.6%)

Counts
2 → 48
Calls

2 calls:

14.0ms
(*.f64 x.im (fma.f64 x.re (*.f64 x.re 3) (neg.f64 (*.f64 x.im x.im))))
8.0ms
(fma.f64 x.re (*.f64 x.re 3) (neg.f64 (*.f64 x.im x.im)))

rewrite5.0ms (0.1%)

Algorithm
rewrite-expression-head
Rules
add-sqr-sqrt_binary64
*-un-lft-identity_binary64
add-cube-cbrt_binary64
add-cbrt-cube_binary64
add-exp-log_binary64
Counts
2 → 32
Calls

2 calls:

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

simplify102.0ms (2.8%)

Algorithm
egg-herbie
Rules
435×exp-prod_binary64
356×unswap-sqr_binary64
355×fma-def_binary64
319×*-commutative_binary64
271×associate-*l*_binary64
Counts
80 → 66
Iterations

Useful iterations: 1 (0.0ms)

IterNodesCost
0571276
11161183
23361183
311361183
421051183
544651183
649491183
749161183

prune68.0ms (1.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New60666
Fresh101
Picked101
Done000
Total62668
Error
4.7b
Counts
68 → 6
Alt Table
StatusErrorProgram
11.7b
(-.f64 (*.f64 3 (*.f64 (pow.f64 x.re 2) x.im)) (pow.f64 x.im 3))
32.3b
(*.f64 3 (*.f64 (pow.f64 x.re 2) x.im))
11.8b
(+.f64 (*.f64 (*.f64 x.re (*.f64 x.re 3)) x.im) (*.f64 (neg.f64 (*.f64 x.im x.im)) x.im))
5.6b
(*.f64 (*.f64 (cbrt.f64 (*.f64 x.im (fma.f64 x.re (*.f64 x.re 3) (neg.f64 (*.f64 x.im x.im))))) (cbrt.f64 (*.f64 x.im (fma.f64 x.re (*.f64 x.re 3) (neg.f64 (*.f64 x.im x.im)))))) (cbrt.f64 (*.f64 x.im (fma.f64 x.re (*.f64 x.re 3) (neg.f64 (*.f64 x.im x.im))))))
18.4b
(cbrt.f64 (*.f64 (*.f64 (*.f64 x.im (fma.f64 x.re (*.f64 x.re 3) (neg.f64 (*.f64 x.im x.im)))) (*.f64 x.im (fma.f64 x.re (*.f64 x.re 3) (neg.f64 (*.f64 x.im x.im))))) (*.f64 x.im (fma.f64 x.re (*.f64 x.re 3) (neg.f64 (*.f64 x.im x.im))))))
8.5b
(*.f64 x.im (-.f64 (*.f64 3 (pow.f64 x.re 2)) (pow.f64 x.im 2)))
Compiler

Compiled 1359 to 661 computations (51.4% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.2b
(*.f64 (cbrt.f64 (*.f64 x.im (fma.f64 x.re (*.f64 x.re 3) (neg.f64 (*.f64 x.im x.im))))) (cbrt.f64 (*.f64 x.im (fma.f64 x.re (*.f64 x.re 3) (neg.f64 (*.f64 x.im x.im))))))
0.6b
(fma.f64 x.re (*.f64 x.re 3) (neg.f64 (*.f64 x.im x.im)))
4.8b
(*.f64 x.im (fma.f64 x.re (*.f64 x.re 3) (neg.f64 (*.f64 x.im x.im))))
36.0b
(cbrt.f64 (*.f64 x.im (fma.f64 x.re (*.f64 x.re 3) (neg.f64 (*.f64 x.im x.im)))))

series123.0ms (3.3%)

Counts
2 → 48
Calls

2 calls:

71.0ms
(*.f64 (cbrt.f64 (*.f64 x.im (fma.f64 x.re (*.f64 x.re 3) (neg.f64 (*.f64 x.im x.im))))) (cbrt.f64 (*.f64 x.im (fma.f64 x.re (*.f64 x.re 3) (neg.f64 (*.f64 x.im x.im))))))
52.0ms
(cbrt.f64 (*.f64 x.im (fma.f64 x.re (*.f64 x.re 3) (neg.f64 (*.f64 x.im x.im)))))

rewrite8.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
pow1_binary64
add-sqr-sqrt_binary64
pow1/3_binary64
*-un-lft-identity_binary64
add-cube-cbrt_binary64
Counts
2 → 44
Calls

2 calls:

4.0ms
(*.f64 (cbrt.f64 (*.f64 x.im (fma.f64 x.re (*.f64 x.re 3) (neg.f64 (*.f64 x.im x.im))))) (cbrt.f64 (*.f64 x.im (fma.f64 x.re (*.f64 x.re 3) (neg.f64 (*.f64 x.im x.im))))))
2.0ms
(cbrt.f64 (*.f64 x.im (fma.f64 x.re (*.f64 x.re 3) (neg.f64 (*.f64 x.im x.im)))))

simplify118.0ms (3.2%)

Algorithm
egg-herbie
Rules
622×fma-def_binary64
428×fma-neg_binary64
391×cancel-sign-sub-inv_binary64
230×unswap-sqr_binary64
203×sub-neg_binary64
Counts
92 → 148
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02874147
18043953
226573440
346583330
447883330

prune590.0ms (15.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New4720472
Fresh055
Picked011
Done000
Total4726478
Error
4.7b
Counts
478 → 6
Alt Table
StatusErrorProgram
11.7b
(-.f64 (*.f64 3 (*.f64 (pow.f64 x.re 2) x.im)) (pow.f64 x.im 3))
32.3b
(*.f64 3 (*.f64 (pow.f64 x.re 2) x.im))
11.8b
(+.f64 (*.f64 (*.f64 x.re (*.f64 x.re 3)) x.im) (*.f64 (neg.f64 (*.f64 x.im x.im)) x.im))
5.6b
(*.f64 (*.f64 (cbrt.f64 (*.f64 x.im (fma.f64 x.re (*.f64 x.re 3) (neg.f64 (*.f64 x.im x.im))))) (cbrt.f64 (*.f64 x.im (fma.f64 x.re (*.f64 x.re 3) (neg.f64 (*.f64 x.im x.im)))))) (cbrt.f64 (*.f64 x.im (fma.f64 x.re (*.f64 x.re 3) (neg.f64 (*.f64 x.im x.im))))))
18.4b
(cbrt.f64 (*.f64 (*.f64 (*.f64 x.im (fma.f64 x.re (*.f64 x.re 3) (neg.f64 (*.f64 x.im x.im)))) (*.f64 x.im (fma.f64 x.re (*.f64 x.re 3) (neg.f64 (*.f64 x.im x.im))))) (*.f64 x.im (fma.f64 x.re (*.f64 x.re 3) (neg.f64 (*.f64 x.im x.im))))))
8.5b
(*.f64 x.im (-.f64 (*.f64 3 (pow.f64 x.re 2)) (pow.f64 x.im 2)))
Compiler

Compiled 24190 to 13485 computations (44.3% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.1b
(*.f64 3 (pow.f64 x.re 2))
3.7b
(-.f64 (*.f64 3 (pow.f64 x.re 2)) (pow.f64 x.im 2))
4.8b
(*.f64 x.im (-.f64 (*.f64 3 (pow.f64 x.re 2)) (pow.f64 x.im 2)))

series31.0ms (0.8%)

Counts
3 → 30
Calls

3 calls:

17.0ms
(*.f64 x.im (-.f64 (*.f64 3 (pow.f64 x.re 2)) (pow.f64 x.im 2)))
12.0ms
(-.f64 (*.f64 3 (pow.f64 x.re 2)) (pow.f64 x.im 2))
2.0ms
(*.f64 3 (pow.f64 x.re 2))

rewrite30.0ms (0.8%)

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt_binary64
24×cancel-sign-sub-inv_binary64
24×prod-diff_binary64
22×unpow-prod-down_binary64
20×*-un-lft-identity_binary64
Counts
3 → 115
Calls

3 calls:

8.0ms
(-.f64 (*.f64 3 (pow.f64 x.re 2)) (pow.f64 x.im 2))
8.0ms
(*.f64 x.im (-.f64 (*.f64 3 (pow.f64 x.re 2)) (pow.f64 x.im 2)))
4.0ms
(*.f64 3 (pow.f64 x.re 2))

simplify149.0ms (4%)

Algorithm
egg-herbie
Rules
541×exp-prod_binary64
503×fma-neg_binary64
387×fma-def_binary64
375×*-commutative_binary64
251×neg-mul-1_binary64
Counts
145 → 169
Iterations

Useful iterations: 3 (0.0ms)

IterNodesCost
02073182
13512387
211532055
324261983
438201983
544161983
649881983
747151983

prune188.0ms (5.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New1690169
Fresh044
Picked011
Done011
Total1696175
Error
4.7b
Counts
175 → 6
Alt Table
StatusErrorProgram
11.7b
(-.f64 (*.f64 3 (*.f64 (pow.f64 x.re 2) x.im)) (pow.f64 x.im 3))
32.3b
(*.f64 3 (*.f64 (pow.f64 x.re 2) x.im))
11.8b
(+.f64 (*.f64 (*.f64 x.re (*.f64 x.re 3)) x.im) (*.f64 (neg.f64 (*.f64 x.im x.im)) x.im))
5.6b
(*.f64 (*.f64 (cbrt.f64 (*.f64 x.im (fma.f64 x.re (*.f64 x.re 3) (neg.f64 (*.f64 x.im x.im))))) (cbrt.f64 (*.f64 x.im (fma.f64 x.re (*.f64 x.re 3) (neg.f64 (*.f64 x.im x.im)))))) (cbrt.f64 (*.f64 x.im (fma.f64 x.re (*.f64 x.re 3) (neg.f64 (*.f64 x.im x.im))))))
18.4b
(cbrt.f64 (*.f64 (*.f64 (*.f64 x.im (fma.f64 x.re (*.f64 x.re 3) (neg.f64 (*.f64 x.im x.im)))) (*.f64 x.im (fma.f64 x.re (*.f64 x.re 3) (neg.f64 (*.f64 x.im x.im))))) (*.f64 x.im (fma.f64 x.re (*.f64 x.re 3) (neg.f64 (*.f64 x.im x.im))))))
8.5b
(*.f64 x.im (-.f64 (*.f64 3 (pow.f64 x.re 2)) (pow.f64 x.im 2)))
Compiler

Compiled 3687 to 2522 computations (31.6% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.2b
(*.f64 3 (*.f64 (pow.f64 x.re 2) x.im))
6.3b
(-.f64 (*.f64 3 (*.f64 (pow.f64 x.re 2) x.im)) (pow.f64 x.im 3))
8.3b
(*.f64 (pow.f64 x.re 2) x.im)

series34.0ms (0.9%)

Counts
3 → 6
Calls

3 calls:

16.0ms
(-.f64 (*.f64 3 (*.f64 (pow.f64 x.re 2) x.im)) (pow.f64 x.im 3))
10.0ms
(*.f64 3 (*.f64 (pow.f64 x.re 2) x.im))
8.0ms
(*.f64 (pow.f64 x.re 2) x.im)

rewrite20.0ms (0.6%)

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt_binary64
18×add-exp-log_binary64
13×*-un-lft-identity_binary64
13×add-cube-cbrt_binary64
12×cancel-sign-sub-inv_binary64
Counts
3 → 88
Calls

3 calls:

7.0ms
(-.f64 (*.f64 3 (*.f64 (pow.f64 x.re 2) x.im)) (pow.f64 x.im 3))
5.0ms
(*.f64 3 (*.f64 (pow.f64 x.re 2) x.im))
5.0ms
(*.f64 (pow.f64 x.re 2) x.im)

simplify100.0ms (2.7%)

Algorithm
egg-herbie
Rules
648×fma-neg_binary64
481×exp-prod_binary64
468×*-commutative_binary64
413×fma-def_binary64
317×unswap-sqr_binary64
Counts
94 → 121
Iterations

Useful iterations: 4 (0.0ms)

IterNodesCost
01601355
12891222
211841137
329921109
444131106
549581106
646371106

prune149.0ms (4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New1183121
Fresh033
Picked101
Done022
Total1198127
Error
0.0b
Counts
127 → 8
Alt Table
StatusErrorProgram
32.3b
(*.f64 3 (*.f64 (pow.f64 x.re 2) x.im))
7.1b
(-.f64 (*.f64 3 (*.f64 x.re (*.f64 x.re x.im))) (pow.f64 x.im 3))
11.8b
(+.f64 (*.f64 (*.f64 x.re (*.f64 x.re 3)) x.im) (*.f64 (neg.f64 (*.f64 x.im x.im)) x.im))
5.6b
(*.f64 (*.f64 (cbrt.f64 (*.f64 x.im (fma.f64 x.re (*.f64 x.re 3) (neg.f64 (*.f64 x.im x.im))))) (cbrt.f64 (*.f64 x.im (fma.f64 x.re (*.f64 x.re 3) (neg.f64 (*.f64 x.im x.im)))))) (cbrt.f64 (*.f64 x.im (fma.f64 x.re (*.f64 x.re 3) (neg.f64 (*.f64 x.im x.im))))))
18.4b
(cbrt.f64 (*.f64 (*.f64 (*.f64 x.im (fma.f64 x.re (*.f64 x.re 3) (neg.f64 (*.f64 x.im x.im)))) (*.f64 x.im (fma.f64 x.re (*.f64 x.re 3) (neg.f64 (*.f64 x.im x.im))))) (*.f64 x.im (fma.f64 x.re (*.f64 x.re 3) (neg.f64 (*.f64 x.im x.im))))))
37.3b
(-.f64 (*.f64 3 (*.f64 (*.f64 x.re (sqrt.f64 x.im)) (*.f64 x.re (sqrt.f64 x.im)))) (pow.f64 x.im 3))
8.5b
(*.f64 x.im (-.f64 (*.f64 3 (pow.f64 x.re 2)) (pow.f64 x.im 2)))
11.9b
(-.f64 (*.f64 3 (*.f64 (*.f64 (cbrt.f64 (*.f64 (pow.f64 x.re 2) x.im)) (cbrt.f64 (*.f64 (pow.f64 x.re 2) x.im))) (cbrt.f64 (*.f64 (pow.f64 x.re 2) x.im)))) (pow.f64 x.im 3))
Compiler

Compiled 2408 to 1598 computations (33.6% saved)

regimes722.0ms (19.5%)

Accuracy

Total 1.9b remaining (98.3%)

Threshold costs 0b (0%)

Counts
130 → 3
Compiler

Compiled 9978 to 6480 computations (35.1% saved)

bsearch27.0ms (0.7%)

Steps
ItersRangePoint
3
6.719964527794328e+96
1.8244211033834235e+102
3.841500425837586e+101
9
-1.6275496711336678e+115
-5.0777551191229645e+106
-5.179057929550085e+106
Compiler

Compiled 3 to 2 computations (33.3% saved)

simplify5.0ms (0.1%)

Algorithm
egg-herbie
Rules
11×*-commutative_binary64
+-commutative_binary64
sub-neg_binary64
neg-sub0_binary64
neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
029136
146136
253136
358136
460136
560136

end166.0ms (4.5%)

Compiler

Compiled 358 to 203 computations (43.3% saved)

Profiling

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