Details

analyze436.0ms

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

sample39.0ms

Algorithm

intervals

Results

26.0ms	256×	body	80	valid
3.0ms	36×	body	80	nan

simplify129.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (119.0ms)

Iter	Nodes	Cost
0	5741	19

prune5.0ms

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: 29.1b

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))
27.0b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite19.0ms

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)))

series141.0ms

Counts

3 → 9

Calls

3 calls:

20.0ms	(+.f64 (.f64 re re) (.f64 im im))
97.0ms	(/.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

prune81.0ms

Filtered

55 candidates to 83 candidates (-50.9%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	70	13	83
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	71	14	85

Merged error: 6.2b

Counts

85 → 14

localize13.0ms

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)))
27.0b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite25.0ms

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:

4.0ms	(+.f64 (.f64 re re) (.f64 im im))
3.0ms	(/.f64 1 (log.f64 base))
10.0ms	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (/.f64 1 (log.f64 base)))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series215.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(+.f64 (.f64 re re) (.f64 im im))
74.0ms	(/.f64 1 (log.f64 base))
94.0ms	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (/.f64 1 (log.f64 base)))
26.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify84.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4961	1782
1	4961	1782

prune76.0ms

Filtered

67 candidates to 115 candidates (-71.6%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	109	6	115
Fresh	2	11	13
Picked	1	0	1
Done	0	0	0
Total	112	17	129

Merged error: 6.2b

Counts

129 → 17

localize20.0ms

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)))
0.6b	(*.f64 (log.f64 base) (log.f64 base))
27.0b	(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))
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)))
5.0ms	(*.f64 (log.f64 base) (log.f64 base))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series279.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (log.f64 base))
104.0ms	(/.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))
25.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify120.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (89.0ms)

Iter	Nodes	Cost
0	4884	2437
1	4884	2437

prune113.0ms

Filtered

84 candidates to 122 candidates (-45.2%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	118	4	122
Fresh	2	14	16
Picked	0	1	1
Done	0	0	0
Total	120	19	139

Merged error: 6.1b

Counts

139 → 19

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 re re) (.f64 im im))
0.3b	(/.f64 1/2 (/.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))))
0.4b	(/.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (.f64 im im))))
28.1b	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

140×	`times-frac_binary64`
72×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
47×	`pow1_binary64`
43×	`log-pow_binary64`
24×	`associate-/r*_binary64`
12×	`add-exp-log_binary64`
11×	`add-cbrt-cube_binary64`
7×	`associate-/l*_binary64`
6×	`add-log-exp_binary64` `div-inv_binary64`
4×	`cbrt-undiv_binary64` `div-exp_binary64`
3×	`log-prod_binary64`
2×	`flip3-+_binary64` `clear-num_binary64` `frac-2neg_binary64` `log-div_binary64` `flip-+_binary64`
1×	`rem-log-exp_binary64` `associate-/r/_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 159

Calls

4 calls:

4.0ms	(+.f64 (.f64 re re) (.f64 im im))
7.0ms	(/.f64 1/2 (/.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))))
4.0ms	(/.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (.f64 im im))))
4.0ms	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))

series293.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(+.f64 (.f64 re re) (.f64 im im))
111.0ms	(/.f64 1/2 (/.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (.f64 im im)))))
126.0ms	(/.f64 (log.f64 base) (log.f64 (+.f64 (.f64 re re) (.f64 im im))))
36.0ms	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify117.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	5464	4862

prune101.0ms

Filtered

109 candidates to 171 candidates (-56.9%)

Pruning

21 alts after pruning (20 fresh and 1 done)

	Pruned	Kept	Total
New	166	5	171
Fresh	2	15	17
Picked	1	0	1
Done	0	1	1
Total	169	21	190

Merged error: 6.1b

Counts

190 → 21

regimes261.0ms

Accuracy

58.2% (10.3b remaining)

Error of 17.6b against oracle of 7.3b and baseline of 31.9b

bsearch105.0ms

Steps

Iters	Range		Point
8	2.0391040634918283e+105	1.8070324512864223e+109	8.305432065725839e+108
10	-1.0173633528385462e+163	-2.400530483774655e+149	-2.445723404147339e+149

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	41	75
1	41	75

end0.0ms

sample1.1s

Algorithm

intervals

Results

770.0ms	8000×	body	80	valid
95.0ms	1028×	body	80	nan

Details

analyze436.0ms

sample39.0ms

simplify129.0ms

prune5.0ms

localize11.0ms

rewrite19.0ms

series141.0ms

simplify96.0ms

prune81.0ms

localize13.0ms

rewrite25.0ms

series215.0ms

simplify84.0ms

prune76.0ms

localize20.0ms

rewrite29.0ms

series279.0ms

simplify120.0ms

prune113.0ms

localize11.0ms

rewrite26.0ms

series293.0ms

simplify117.0ms

prune101.0ms

regimes261.0ms

bsearch105.0ms

simplify3.0ms

end0.0ms

sample1.1s

Profiling