Details

analyze437.0ms

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

25.0ms	256×	body	80	valid
2.0ms	24×	body	80	nan

simplify92.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (89.0ms)

Iter	Nodes	Cost
0	5536	12

prune8.0ms

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: 32.1b

Counts

2 → 2

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 re re) (.f64 im im))
0.4b	(/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base))
29.8b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite22.0ms

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:

5.0ms	(+.f64 (.f64 re re) (.f64 im im))
11.0ms	(/.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)))

series37.0ms

Counts

3 → 9

Calls

3 calls:

6.0ms	(+.f64 (.f64 re re) (.f64 im im))
24.0ms	(/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base))
7.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify57.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5208	1163

prune80.0ms

Filtered

55 candidates to 83 candidates (-50.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	72	11	83
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	73	12	85

Merged error: 7.1b

Counts

85 → 12

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 re re) (.f64 im im))
0.3b	(/.f64 1 (log.f64 base))
0.3b	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (/.f64 1 (log.f64 base)))
29.8b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt_binary64`
26×	`times-frac_binary64`
24×	`*-un-lft-identity_binary64`
23×	`add-cube-cbrt_binary64`
17×	`pow1_binary64` `add-exp-log_binary64`
16×	`associate-r_binary64`
11×	`add-cbrt-cube_binary64`
10×	`log-pow_binary64`
6×	`add-log-exp_binary64` `associate-l_binary64`
4×	`associate-/r*_binary64` `prod-exp_binary64` `div-exp_binary64`
3×	`unswap-sqr_binary64` `associate-/l*_binary64` `sqrt-prod_binary64`
2×	`flip3-+_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `rec-exp_binary64` `div-inv_binary64` `flip-+_binary64` `sqrt-div_binary64`
1×	`pow-prod-down_binary64` `associate-r/_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `un-div-inv_binary64` `+-commutative_binary64` `pow-flip_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

4 → 103

Calls

4 calls:

5.0ms	(+.f64 (.f64 re re) (.f64 im im))
4.0ms	(/.f64 1 (log.f64 base))
10.0ms	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (/.f64 1 (log.f64 base)))
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series52.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(+.f64 (.f64 re re) (.f64 im im))
12.0ms	(/.f64 1 (log.f64 base))
24.0ms	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (/.f64 1 (log.f64 base)))
6.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify48.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4964	1131
1	4964	1131

prune68.0ms

Filtered

67 candidates to 115 candidates (-71.6%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	110	5	115
Fresh	2	9	11
Picked	0	1	1
Done	0	0	0
Total	112	15	127

Merged error: 7.1b

Counts

127 → 15

localize18.0ms

Local error

Found 4 expressions with local error:

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)))
0.4b	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (log.f64 base))
0.5b	(*.f64 (log.f64 base) (log.f64 base))
29.8b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite30.0ms

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:

11.0ms	(/.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)))
6.0ms	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (log.f64 base))
5.0ms	(*.f64 (log.f64 base) (log.f64 base))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series64.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(/.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)))
21.0ms	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (log.f64 base))
12.0ms	(*.f64 (log.f64 base) (log.f64 base))
7.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify56.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5258	1536

prune95.0ms

Filtered

84 candidates to 122 candidates (-45.2%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	117	5	122
Fresh	1	12	13
Picked	1	0	1
Done	0	1	1
Total	119	18	137

Merged error: 7.1b

Counts

137 → 18

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(.f64 (/.f64 (/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) 1) (pow.f64 (log.f64 base) 3)) (-.f64 (.f64 (log.f64 base) (log.f64 base)) (*.f64 0 0)))
0.5b	(*.f64 (log.f64 base) (log.f64 base))
0.8b	(pow.f64 (log.f64 base) 3)
29.8b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

580×	`times-frac_binary64`
316×	`associate-l_binary64`
268×	`add-sqr-sqrt_binary64`
232×	`*-un-lft-identity_binary64`
226×	`add-cube-cbrt_binary64`
178×	`log-pow_binary64`
151×	`pow1_binary64`
95×	`unpow-prod-down_binary64` `cube-prod_binary64`
43×	`pow1/2_binary64` `sqrt-pow1_binary64`
36×	`add-exp-log_binary64`
26×	`sqr-pow_binary64`
23×	`unpow3_binary64` `cube-mult_binary64`
18×	`log-prod_binary64`
16×	`add-cbrt-cube_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64`
15×	`div-inv_binary64` `div-exp_binary64`
14×	`unswap-sqr_binary64`
12×	`associate--l+_binary64`
11×	`prod-exp_binary64`
8×	`associate-r_binary64`
6×	`swap-sqr_binary64`
4×	`pow-to-exp_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64` `pow-exp_binary64`
3×	`pow-unpow_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `sqrt-prod_binary64`
2×	`pow-prod-down_binary64` `sub-neg_binary64` `flip3--_binary64` `associate-r/_binary64` `flip--_binary64` `frac-times_binary64` `sqrt-div_binary64` `-commutative_binary64`
1×	`flip3-+_binary64` `pow-prod-up_binary64` `pow-pow_binary64` `pow-plus_binary64` `rem-sqrt-square_binary64` `rem-cube-cbrt_binary64` `difference-of-squares_binary64` `pow-sqr_binary64` `flip-+_binary64` `pow2_binary64` `associate-*l/_binary64`

Counts

4 → 446

Calls

4 calls:

63.0ms	(.f64 (/.f64 (/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) 1) (pow.f64 (log.f64 base) 3)) (-.f64 (.f64 (log.f64 base) (log.f64 base)) (*.f64 0 0)))
5.0ms	(*.f64 (log.f64 base) (log.f64 base))
3.0ms	(pow.f64 (log.f64 base) 3)
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series55.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(.f64 (/.f64 (/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) 1) (pow.f64 (log.f64 base) 3)) (-.f64 (.f64 (log.f64 base) (log.f64 base)) (*.f64 0 0)))
10.0ms	(*.f64 (log.f64 base) (log.f64 base))
14.0ms	(pow.f64 (log.f64 base) 3)
7.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify105.0ms

Algorithm

egg-herbie

Counts

458 → 458

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4941	6899
1	4941	6899

prune223.0ms

Filtered

247 candidates to 458 candidates (-85.4%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	454	4	458
Fresh	4	12	16
Picked	0	1	1
Done	1	0	1
Total	459	17	476

Merged error: 7.1b

Counts

476 → 17

regimes375.0ms

Accuracy

57.3% (10.5b remaining)

Error of 18.1b against oracle of 7.6b and baseline of 32.2b

bsearch76.0ms

Steps

Iters	Range		Point
9	1.1853992966883918e+79	7.581488589275615e+86	1.265749424662431e+86
7	-5.815072936701277e+136	-7.630552340071416e+134	-7.806590709529468e+134

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	46	51
1	46	51

end0.0ms

sample1.1s

Algorithm

intervals

Results

785.0ms	8000×	body	80	valid
89.0ms	990×	body	80	nan

Details

analyze437.0ms

sample37.0ms

simplify92.0ms

prune8.0ms

localize11.0ms

rewrite22.0ms

series37.0ms

simplify57.0ms

prune80.0ms

localize12.0ms

rewrite26.0ms

series52.0ms

simplify48.0ms

prune68.0ms

localize18.0ms

rewrite30.0ms

series64.0ms

simplify56.0ms

prune95.0ms

localize19.0ms

rewrite113.0ms

series55.0ms

simplify105.0ms

prune223.0ms

regimes375.0ms

bsearch76.0ms

simplify2.0ms

end0.0ms

sample1.1s

Profiling