Details

analyze368.0ms

Algorithm

Search

True	Other	False	Iter
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
50%	50%	0.1%	5
50%	50%	0.1%	6
50%	37.5%	12.6%	7
50%	37.5%	12.6%	8
50%	31.2%	18.8%	9
50%	31.2%	18.8%	10
50%	28.1%	22%	11
50%	28.1%	22%	12
50%	26.5%	23.5%	13
50%	26.5%	23.5%	14

sample147.0ms

Algorithm

intervals

Results

71.0ms	137×	body	1280	valid
23.0ms	75×	body	640	valid
14.0ms	45×	body	1280	invalid
13.0ms	58×	body	640	invalid
6.0ms	31×	body	320	valid
3.0ms	17×	body	320	invalid
1.0ms	10×	body	160	valid
1.0ms	10×	body	160	invalid
1.0ms	13×	body	80	invalid
0.0ms	3×	body	80	valid

simplify71.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	5348	12

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 58.3b

Counts

2 → 1

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(.f64 (.f64 0.5 (cos.f64 re)) (-.f64 (exp.f64 (-.f64 0.0 im)) (exp.f64 im)))
5.7b	(-.f64 (exp.f64 (-.f64 0.0 im)) (exp.f64 im))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

7×	`*-un-lft-identity_binary64` `pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-sqr-sqrt_binary64`
5×	`associate-r_binary64`
4×	`add-log-exp_binary64`
3×	`pow-prod-down_binary64` `sub-neg_binary64` `cbrt-unprod_binary64` `add-cube-cbrt_binary64` `prod-exp_binary64`
2×	`flip3--_binary64` `associate-*r/_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `flip--_binary64`
1×	`diff-log_binary64` `distribute-lft-in_binary64` `associate-l_binary64` `distribute-rgt-in_binary64` `*-commutative_binary64`

Counts

2 → 37

Calls

2 calls:

13.0ms	(.f64 (.f64 0.5 (cos.f64 re)) (-.f64 (exp.f64 (-.f64 0.0 im)) (exp.f64 im)))
8.0ms	(-.f64 (exp.f64 (-.f64 0.0 im)) (exp.f64 im))

series26.0ms

Counts

2 → 6

Calls

2 calls:

21.0ms	(.f64 (.f64 0.5 (cos.f64 re)) (-.f64 (exp.f64 (-.f64 0.0 im)) (exp.f64 im)))
5.0ms	(-.f64 (exp.f64 (-.f64 0.0 im)) (exp.f64 im))

simplify60.0ms

Algorithm

egg-herbie

Counts

43 → 43

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5332	526

prune67.0ms

Filtered

31 candidates to 43 candidates (-38.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	40	3	43
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	41	3	44

Merged error: 0.1b

Counts

44 → 3

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (-.f64 (.f64 (pow.f64 im 3) -1/3) (.f64 1/60 (pow.f64 im 5))) (*.f64 im -2))
0.0b	(*.f64 1/60 (pow.f64 im 5))
0.1b	(.f64 (.f64 0.5 (cos.f64 re)) (+.f64 (-.f64 (.f64 (pow.f64 im 3) -1/3) (.f64 1/60 (pow.f64 im 5))) (*.f64 im -2)))
0.1b	(*.f64 (pow.f64 im 3) -1/3)

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64`
19×	`add-exp-log_binary64`
16×	`associate-l_binary64`
13×	`associate-r_binary64` `add-cbrt-cube_binary64`
12×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
9×	`add-log-exp_binary64` `pow1_binary64` `prod-exp_binary64`
8×	`unpow-prod-down_binary64`
7×	`unswap-sqr_binary64`
5×	`cbrt-unprod_binary64`
4×	`sqr-pow_binary64` `cube-prod_binary64`
3×	`pow-prod-down_binary64` `*-commutative_binary64`
2×	`pow-to-exp_binary64` `flip3-+_binary64` `associate-*r/_binary64` `flip-+_binary64` `pow-exp_binary64` `sum-log_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `associate-+l+_binary64` `distribute-lft-in_binary64` `associate-+l-_binary64` `distribute-rgt-in_binary64` `+-commutative_binary64` `unpow3_binary64` `cube-mult_binary64`

Counts

4 → 92

Calls

4 calls:

9.0ms	(+.f64 (-.f64 (.f64 (pow.f64 im 3) -1/3) (.f64 1/60 (pow.f64 im 5))) (*.f64 im -2))
5.0ms	(*.f64 1/60 (pow.f64 im 5))
12.0ms	(.f64 (.f64 0.5 (cos.f64 re)) (+.f64 (-.f64 (.f64 (pow.f64 im 3) -1/3) (.f64 1/60 (pow.f64 im 5))) (*.f64 im -2)))
6.0ms	(*.f64 (pow.f64 im 3) -1/3)

series69.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(+.f64 (-.f64 (.f64 (pow.f64 im 3) -1/3) (.f64 1/60 (pow.f64 im 5))) (*.f64 im -2))
7.0ms	(*.f64 1/60 (pow.f64 im 5))
46.0ms	(.f64 (.f64 0.5 (cos.f64 re)) (+.f64 (-.f64 (.f64 (pow.f64 im 3) -1/3) (.f64 1/60 (pow.f64 im 5))) (*.f64 im -2)))
8.0ms	(*.f64 (pow.f64 im 3) -1/3)

simplify32.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5469	1284

prune145.0ms

Filtered

69 candidates to 104 candidates (-50.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	98	6	104
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	98	9	107

Merged error: 0.0b

Counts

107 → 9

localize21.0ms

Local error

Found 4 expressions with local error:

0.5b	(.f64 (cbrt.f64 (.f64 (.f64 0.5 (cos.f64 re)) (+.f64 (-.f64 (.f64 -1/3 (pow.f64 im 3)) (.f64 1/60 (pow.f64 im 5))) (.f64 im -2)))) (cbrt.f64 (.f64 (.f64 0.5 (cos.f64 re)) (+.f64 (-.f64 (.f64 -1/3 (pow.f64 im 3)) (.f64 1/60 (pow.f64 im 5))) (*.f64 im -2)))))
0.6b	(cbrt.f64 (.f64 (.f64 0.5 (cos.f64 re)) (+.f64 (-.f64 (.f64 -1/3 (pow.f64 im 3)) (.f64 1/60 (pow.f64 im 5))) (*.f64 im -2))))
0.6b	(cbrt.f64 (.f64 (.f64 0.5 (cos.f64 re)) (+.f64 (-.f64 (.f64 -1/3 (pow.f64 im 3)) (.f64 1/60 (pow.f64 im 5))) (*.f64 im -2))))
0.6b	(cbrt.f64 (.f64 (.f64 0.5 (cos.f64 re)) (+.f64 (-.f64 (.f64 -1/3 (pow.f64 im 3)) (.f64 1/60 (pow.f64 im 5))) (*.f64 im -2))))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

20×	`associate-*r/_binary64`
18×	`cbrt-div_binary64`
11×	`pow1_binary64`
10×	`add-sqr-sqrt_binary64`
9×	`flip3-+_binary64` `pow1/3_binary64` `flip-+_binary64`
8×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
7×	`cbrt-prod_binary64`
6×	`add-exp-log_binary64`
4×	`add-log-exp_binary64` `swap-sqr_binary64` `associate-r_binary64` `add-cbrt-cube_binary64` `associate-l_binary64` `frac-times_binary64`
2×	`pow-prod-down_binary64` `pow-prod-up_binary64` `pow-sqr_binary64` `associate-*l/_binary64`
1×	`cbrt-unprod_binary64` `pow-plus_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 72

Calls

4 calls:

11.0ms	(.f64 (cbrt.f64 (.f64 (.f64 0.5 (cos.f64 re)) (+.f64 (-.f64 (.f64 -1/3 (pow.f64 im 3)) (.f64 1/60 (pow.f64 im 5))) (.f64 im -2)))) (cbrt.f64 (.f64 (.f64 0.5 (cos.f64 re)) (+.f64 (-.f64 (.f64 -1/3 (pow.f64 im 3)) (.f64 1/60 (pow.f64 im 5))) (*.f64 im -2)))))
12.0ms	(cbrt.f64 (.f64 (.f64 0.5 (cos.f64 re)) (+.f64 (-.f64 (.f64 -1/3 (pow.f64 im 3)) (.f64 1/60 (pow.f64 im 5))) (*.f64 im -2))))
11.0ms	(cbrt.f64 (.f64 (.f64 0.5 (cos.f64 re)) (+.f64 (-.f64 (.f64 -1/3 (pow.f64 im 3)) (.f64 1/60 (pow.f64 im 5))) (*.f64 im -2))))
11.0ms	(cbrt.f64 (.f64 (.f64 0.5 (cos.f64 re)) (+.f64 (-.f64 (.f64 -1/3 (pow.f64 im 3)) (.f64 1/60 (pow.f64 im 5))) (*.f64 im -2))))

series596.0ms

Counts

4 → 12

Calls

4 calls:

279.0ms	(.f64 (cbrt.f64 (.f64 (.f64 0.5 (cos.f64 re)) (+.f64 (-.f64 (.f64 -1/3 (pow.f64 im 3)) (.f64 1/60 (pow.f64 im 5))) (.f64 im -2)))) (cbrt.f64 (.f64 (.f64 0.5 (cos.f64 re)) (+.f64 (-.f64 (.f64 -1/3 (pow.f64 im 3)) (.f64 1/60 (pow.f64 im 5))) (*.f64 im -2)))))
105.0ms	(cbrt.f64 (.f64 (.f64 0.5 (cos.f64 re)) (+.f64 (-.f64 (.f64 -1/3 (pow.f64 im 3)) (.f64 1/60 (pow.f64 im 5))) (*.f64 im -2))))
105.0ms	(cbrt.f64 (.f64 (.f64 0.5 (cos.f64 re)) (+.f64 (-.f64 (.f64 -1/3 (pow.f64 im 3)) (.f64 1/60 (pow.f64 im 5))) (*.f64 im -2))))
107.0ms	(cbrt.f64 (.f64 (.f64 0.5 (cos.f64 re)) (+.f64 (-.f64 (.f64 -1/3 (pow.f64 im 3)) (.f64 1/60 (pow.f64 im 5))) (*.f64 im -2))))

simplify75.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4950	2709
1	4950	2709

prune279.0ms

Filtered

67 candidates to 84 candidates (-25.4%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	82	2	84
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	83	10	93

Merged error: 0.0b

Counts

93 → 10

localize28.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (.f64 (.f64 0.5 (cos.f64 re)) (+.f64 (-.f64 (.f64 -1/3 (pow.f64 im 3)) (.f64 1/60 (pow.f64 im 5))) (*.f64 im -2))))
0.7b	(cbrt.f64 (+.f64 (-.f64 (.f64 -1/3 (pow.f64 im 3)) (.f64 1/60 (pow.f64 im 5))) (*.f64 im -2)))
0.7b	(cbrt.f64 (+.f64 (-.f64 (.f64 -1/3 (pow.f64 im 3)) (.f64 1/60 (pow.f64 im 5))) (*.f64 im -2)))
0.7b	(.f64 (cbrt.f64 (.f64 0.5 (cos.f64 re))) (cbrt.f64 (*.f64 0.5 (cos.f64 re))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64`
11×	`pow1_binary64` `cbrt-prod_binary64`
10×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
9×	`pow1/3_binary64`
6×	`cbrt-div_binary64` `add-exp-log_binary64`
4×	`add-log-exp_binary64` `swap-sqr_binary64` `associate-r_binary64` `add-cbrt-cube_binary64` `associate-l_binary64`
3×	`flip3-+_binary64` `flip-+_binary64`
2×	`pow-prod-down_binary64` `pow-prod-up_binary64` `associate-*r/_binary64` `pow-sqr_binary64`
1×	`cbrt-unprod_binary64` `pow-plus_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 68

Calls

4 calls:

10.0ms	(cbrt.f64 (.f64 (.f64 0.5 (cos.f64 re)) (+.f64 (-.f64 (.f64 -1/3 (pow.f64 im 3)) (.f64 1/60 (pow.f64 im 5))) (*.f64 im -2))))
8.0ms	(cbrt.f64 (+.f64 (-.f64 (.f64 -1/3 (pow.f64 im 3)) (.f64 1/60 (pow.f64 im 5))) (*.f64 im -2)))
8.0ms	(cbrt.f64 (+.f64 (-.f64 (.f64 -1/3 (pow.f64 im 3)) (.f64 1/60 (pow.f64 im 5))) (*.f64 im -2)))
6.0ms	(.f64 (cbrt.f64 (.f64 0.5 (cos.f64 re))) (cbrt.f64 (*.f64 0.5 (cos.f64 re))))

series195.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(cbrt.f64 (.f64 (.f64 0.5 (cos.f64 re)) (+.f64 (-.f64 (.f64 -1/3 (pow.f64 im 3)) (.f64 1/60 (pow.f64 im 5))) (*.f64 im -2))))
24.0ms	(cbrt.f64 (+.f64 (-.f64 (.f64 -1/3 (pow.f64 im 3)) (.f64 1/60 (pow.f64 im 5))) (*.f64 im -2)))
25.0ms	(cbrt.f64 (+.f64 (-.f64 (.f64 -1/3 (pow.f64 im 3)) (.f64 1/60 (pow.f64 im 5))) (*.f64 im -2)))
41.0ms	(.f64 (cbrt.f64 (.f64 0.5 (cos.f64 re))) (cbrt.f64 (*.f64 0.5 (cos.f64 re))))

simplify41.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5168	1519

prune253.0ms

Filtered

65 candidates to 80 candidates (-23.1%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	79	1	80
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	79	11	90

Merged error: 0.0b

Counts

90 → 11

regimes365.0ms

Accuracy

0% (0.7b remaining)

Error of 0.7b against oracle of 0.1b and baseline of 0.7b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	50	20
1	50	20

end0.0ms

sample4.6s

Algorithm

intervals

Results

2.4s	4291×	body	1280	valid
724.0ms	2322×	body	640	valid
502.0ms	1493×	body	1280	invalid
273.0ms	1198×	body	640	invalid
177.0ms	882×	body	320	valid
109.0ms	658×	body	320	invalid
48.0ms	359×	body	160	valid
33.0ms	299×	body	160	invalid
31.0ms	496×	body	80	invalid
10.0ms	146×	body	80	valid

Details

analyze368.0ms

sample147.0ms

simplify71.0ms

prune3.0ms

localize10.0ms

rewrite22.0ms

series26.0ms

simplify60.0ms

prune67.0ms

localize15.0ms

rewrite35.0ms

series69.0ms

simplify32.0ms

prune145.0ms

localize21.0ms

rewrite47.0ms

series596.0ms

simplify75.0ms

prune279.0ms

localize28.0ms

rewrite33.0ms

series195.0ms

simplify41.0ms

prune253.0ms

regimes365.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample4.6s

Profiling