Details

analyze430.0ms

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	35×	body	80	nan

simplify91.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (88.0ms)

Iter	Nodes	Cost
0	5536	12

prune10.0ms

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: 32.2b

Counts

2 → 2

localize13.0ms

Local error

Found 2 expressions with local error:

0.3b	(/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base))
30.0b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 63

Calls

2 calls:

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)))

series36.0ms

Counts

2 → 6

Calls

2 calls:

28.0ms	(/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base))
8.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify49.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5798	1032

prune108.0ms

Filtered

45 candidates to 69 candidates (-53.3%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	57	12	69
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	57	14	71

Merged error: 7.3b

Counts

71 → 14

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)))
0.3b	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (log.f64 base))
0.5b	(*.f64 (log.f64 base) (log.f64 base))
30.0b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite33.0ms

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:

13.0ms	(/.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))
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series74.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(/.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)))
24.0ms	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (log.f64 base))
13.0ms	(*.f64 (log.f64 base) (log.f64 base))
8.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify58.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5258	1536

prune157.0ms

Filtered

84 candidates to 122 candidates (-45.2%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	113	9	122
Fresh	2	10	12
Picked	1	0	1
Done	1	0	1
Total	117	19	136

Merged error: 7.3b

Counts

136 → 19

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))
0.4b	(.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) (*.f64 (atan2.f64 im re) 0)) (/.f64 1 (pow.f64 (log.f64 base) 2)))
0.5b	(pow.f64 (log.f64 base) 2)
30.0b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-sqr-sqrt_binary64`
35×	`associate-r_binary64` `times-frac_binary64`
32×	`*-un-lft-identity_binary64`
28×	`add-cube-cbrt_binary64`
27×	`add-exp-log_binary64`
18×	`unpow-prod-down_binary64`
17×	`pow1_binary64`
11×	`add-cbrt-cube_binary64` `prod-exp_binary64`
10×	`unswap-sqr_binary64`
9×	`associate-l_binary64`
8×	`log-pow_binary64`
6×	`log-prod_binary64` `unpow2_binary64` `sqr-pow_binary64` `div-exp_binary64`
4×	`pow-to-exp_binary64` `add-log-exp_binary64` `pow-exp_binary64`
3×	`flip3-+_binary64` `pow-unpow_binary64` `cbrt-unprod_binary64` `1-exp_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `rec-exp_binary64` `sqrt-prod_binary64` `flip-+_binary64`
2×	`pow-prod-down_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `frac-times_binary64` `sqrt-div_binary64` `associate-l/_binary64` `-commutative_binary64`
1×	`cbrt-undiv_binary64` `associate-*r/_binary64` `pow-pow_binary64` `rem-sqrt-square_binary64` `un-div-inv_binary64` `div-inv_binary64`

Counts

4 → 132

Calls

4 calls:

6.0ms	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (log.f64 base))
18.0ms	(.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) (*.f64 (atan2.f64 im re) 0)) (/.f64 1 (pow.f64 (log.f64 base) 2)))
2.0ms	(pow.f64 (log.f64 base) 2)
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series76.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))) (log.f64 base))
31.0ms	(.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 base)) (*.f64 (atan2.f64 im re) 0)) (/.f64 1 (pow.f64 (log.f64 base) 2)))
13.0ms	(pow.f64 (log.f64 base) 2)
8.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify49.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	4955	2035
1	4955	2035

prune159.0ms

Filtered

93 candidates to 144 candidates (-54.8%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	137	7	144
Fresh	9	9	18
Picked	1	0	1
Done	0	0	0
Total	147	16	163

Merged error: 7.3b

Counts

163 → 16

localize18.0ms

Local error

Found 4 expressions with local error:

0.5b	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
30.0b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
30.0b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
30.0b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

24×	`pow1_binary64`
20×	`add-sqr-sqrt_binary64`
17×	`*-un-lft-identity_binary64`
15×	`add-cube-cbrt_binary64` `sqrt-prod_binary64`
14×	`log-pow_binary64`
12×	`log-prod_binary64`
8×	`swap-sqr_binary64`
7×	`pow1/2_binary64` `sqrt-pow1_binary64`
6×	`associate-r_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `distribute-lft-in_binary64` `associate-l_binary64` `distribute-rgt-in_binary64` `sqrt-div_binary64`
4×	`add-log-exp_binary64`
3×	`flip3-+_binary64` `rem-sqrt-square_binary64` `flip-+_binary64`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `pow-prod-up_binary64` `pow-plus_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `pow-sqr_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 93

Calls

4 calls:

11.0ms	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.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)))
5.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series42.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (*.f64 im im)))))
7.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
10.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))
8.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify63.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4902	1300
1	4902	1300

prune79.0ms

Filtered

70 candidates to 105 candidates (-50.0%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	103	2	105
Fresh	0	15	15
Picked	0	1	1
Done	0	0	0
Total	103	18	121

Merged error: 7.2b

Counts

121 → 18

regimes458.0ms

Accuracy

57.1% (10.4b remaining)

Error of 18.0b against oracle of 7.6b and baseline of 31.9b

bsearch155.0ms

Steps

Iters	Range		Point
9	2.742846384821079e+28	2.573805552041366e+35	2.5362193761446767e+35
9	9.317771181504113e-281	5.196805194780243e-272	8.950330598317258e-276
6	-5.093211122374936e-261	-3.65607763076758e-262	-4.337372021152796e-262
8	-2.1915322657080793e+63	-2.1090434721521167e+59	-1.8073559612423165e+63

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	116	108
1	116	108

end0.0ms

sample1.0s

Algorithm

intervals

Results

755.0ms	8000×	body	80	valid
84.0ms	975×	body	80	nan

Details

analyze430.0ms

sample37.0ms

simplify91.0ms

prune10.0ms

localize13.0ms

rewrite15.0ms

series36.0ms

simplify49.0ms

prune108.0ms

localize18.0ms

rewrite33.0ms

series74.0ms

simplify58.0ms

prune157.0ms

localize20.0ms

rewrite36.0ms

series76.0ms

simplify49.0ms

prune159.0ms

localize18.0ms

rewrite27.0ms

series42.0ms

simplify63.0ms

prune79.0ms

regimes458.0ms

bsearch155.0ms

simplify4.0ms

end0.0ms

sample1.0s

Profiling