Details

analyze432.0ms

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
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
23.4%	51.5%	25.1%	7
24.2%	50.7%	25.1%	8
24.6%	50.3%	25.1%	9
36.9%	25.5%	37.6%	10
37.2%	25.3%	37.6%	11
37.3%	25.1%	37.6%	12
43.5%	12.7%	43.8%	13
43.6%	12.6%	43.8%	14

sample37.0ms

Algorithm

intervals

Results

24.0ms	256×	body	80	valid
3.0ms	34×	body	80	nan

simplify127.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (118.0ms)

Iter	Nodes	Cost
0	5741	19

prune7.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 30.4b

Counts

2 → 2

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 re re) (.f64 im im))
0.3b	(/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base))
28.2b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

24×	`times-frac_binary64`
22×	`log-pow_binary64`
21×	`pow1_binary64`
17×	`add-sqr-sqrt_binary64`
16×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
6×	`pow1/2_binary64` `sqrt-pow1_binary64` `associate-/l*_binary64`
5×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`associate-/r*_binary64` `sqrt-div_binary64`
3×	`flip3-+_binary64` `sqrt-prod_binary64` `flip-+_binary64`
2×	`div-sub_binary64` `log-div_binary64`
1×	`cbrt-undiv_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

3 → 74

Calls

3 calls:

4.0ms	(+.f64 (.f64 re re) (.f64 im im))
8.0ms	(/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series136.0ms

Counts

3 → 9

Calls

3 calls:

22.0ms	(+.f64 (.f64 re re) (.f64 im im))
89.0ms	(/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base))
24.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify96.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	5289	1833

prune85.0ms

Filtered

55 candidates to 83 candidates (-50.9%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	71	12	83
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	72	13	85

Merged error: 6.2b

Counts

85 → 13

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))
28.2b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
28.2b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
28.2b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64` `sqrt-prod_binary64`
9×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
8×	`sqrt-div_binary64`
7×	`pow1_binary64`
6×	`cbrt-prod_binary64`
4×	`flip3-+_binary64` `add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip-+_binary64`
3×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`
2×	`cbrt-div_binary64`
1×	`pow1/3_binary64`

Counts

4 → 61

Calls

4 calls:

4.0ms	(cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series147.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(cbrt.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im))))
22.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
23.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
27.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify80.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4901	1087
1	4901	1087

prune83.0ms

Filtered

61 candidates to 73 candidates (-19.7%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	73	0	73
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	73	13	86

Merged error: 6.2b

Counts

86 → 13

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (log.f64 base))
0.3b	(/.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) (.f64 (atan2.f64 im re) 0)) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 0 0)))
0.5b	(*.f64 (log.f64 base) (log.f64 base))
28.2b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
25×	`*-un-lft-identity_binary64`
23×	`pow1_binary64` `add-cube-cbrt_binary64`
12×	`log-prod_binary64`
10×	`log-pow_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-l_binary64`
9×	`times-frac_binary64`
8×	`associate-r_binary64`
6×	`swap-sqr_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64`
4×	`add-log-exp_binary64`
3×	`flip3-+_binary64` `associate-/r_binary64` `associate-/l_binary64` `sqrt-prod_binary64` `flip-+_binary64`
2×	`pow-prod-down_binary64` `associate-/l/_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `associate-/r/_binary64` `sqrt-pow1_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `sqrt-div_binary64` `*-commutative_binary64`
1×	`pow-prod-up_binary64` `cbrt-undiv_binary64` `pow-plus_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `pow-sqr_binary64` `pow2_binary64`

Counts

4 → 110

Calls

4 calls:

6.0ms	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (log.f64 base))
10.0ms	(/.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) (.f64 (atan2.f64 im re) 0)) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 0 0)))
5.0ms	(*.f64 (log.f64 base) (log.f64 base))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series271.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (log.f64 base))
94.0ms	(/.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) (.f64 (atan2.f64 im re) 0)) (+.f64 (.f64 (log.f64 base) (log.f64 base)) (.f64 0 0)))
69.0ms	(*.f64 (log.f64 base) (log.f64 base))
29.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify118.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (87.0ms)

Iter	Nodes	Cost
0	4884	2437
1	4884	2437

prune114.0ms

Filtered

83 candidates to 122 candidates (-47.0%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	117	5	122
Fresh	2	9	11
Picked	1	0	1
Done	0	1	1
Total	120	15	135

Merged error: 6.2b

Counts

135 → 15

localize25.0ms

Local error

Found 4 expressions with local error:

0.4b	(*.f64 (log.f64 base) (log.f64 (cbrt.f64 base)))
0.5b	(cbrt.f64 base)
0.5b	(cbrt.f64 base)
28.2b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64`
13×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
12×	`log-prod_binary64` `cbrt-prod_binary64`
9×	`pow1_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64`
5×	`associate-r_binary64`
4×	`add-log-exp_binary64` `associate-l_binary64`
3×	`pow1/3_binary64` `log-pow_binary64` `sqrt-prod_binary64`
2×	`sqrt-div_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `sqrt-pow1_binary64` `unswap-sqr_binary64` `rem-sqrt-square_binary64` `prod-exp_binary64` `flip-+_binary64` `*-commutative_binary64`

Counts

4 → 70

Calls

4 calls:

5.0ms	(*.f64 (log.f64 base) (log.f64 (cbrt.f64 base)))
1.0ms	(cbrt.f64 base)
1.0ms	(cbrt.f64 base)
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series400.0ms

Counts

4 → 12

Calls

4 calls:

201.0ms	(*.f64 (log.f64 base) (log.f64 (cbrt.f64 base)))
84.0ms	(cbrt.f64 base)
85.0ms	(cbrt.f64 base)
29.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify90.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	5043	955

prune86.0ms

Filtered

58 candidates to 82 candidates (-41.4%)

Pruning

17 alts after pruning (15 fresh and 2 done)

	Pruned	Kept	Total
New	79	3	82
Fresh	1	12	13
Picked	0	1	1
Done	0	1	1
Total	80	17	97

Merged error: 6.2b

Counts

97 → 17

regimes319.0ms

Accuracy

56.4% (10.7b remaining)

Error of 17.9b against oracle of 7.2b and baseline of 31.8b

bsearch59.0ms

Steps

Iters	Range		Point
5	2.513276816682016e+118	5.468472039626132e+118	3.1078363892846655e+118
5	-3246224579.727251	-1003621698.3290997	-2309443542.211869

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	43	86
1	43	86

end0.0ms

sample1.1s

Algorithm

intervals

Results

771.0ms	8000×	body	80	valid
89.0ms	979×	body	80	nan

Details

analyze432.0ms

sample37.0ms

simplify127.0ms

prune7.0ms

localize10.0ms

rewrite18.0ms

series136.0ms

simplify96.0ms

prune85.0ms

localize17.0ms

rewrite18.0ms

series147.0ms

simplify80.0ms

prune83.0ms

localize19.0ms

rewrite29.0ms

series271.0ms

simplify118.0ms

prune114.0ms

localize25.0ms

rewrite14.0ms

series400.0ms

simplify90.0ms

prune86.0ms

regimes319.0ms

bsearch59.0ms

simplify4.0ms

end0.0ms

sample1.1s

Profiling