Details

analyze5.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
74.9%	25%	0.1%	3
87.4%	12.5%	0.1%	4
93.7%	6.2%	0.1%	5
96.8%	3.1%	0.1%	6
98.3%	1.6%	0.1%	7
99.1%	0.8%	0.1%	8
99.5%	0.4%	0.1%	9
99.7%	0.2%	0.1%	10
99.8%	0.1%	0.1%	11
99.9%	0%	0.1%	12
99.9%	0%	0.1%	13
99.9%	0%	0.1%	14

sample20.0ms

Algorithm

intervals

Results

14.0ms

256×

body

valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	12	19
1	12	19

prune1.0ms

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: 33.2b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 re re) (.f64 im im))
0.6b	(/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 10))
30.7b	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite23.0ms

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:

9.0ms	(+.f64 (.f64 re re) (.f64 im im))
8.0ms	(/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 10))
4.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

series114.0ms

Counts

3 → 9

Calls

3 calls:

20.0ms	(+.f64 (.f64 re re) (.f64 im im))
70.0ms	(/.f64 (log.f64 (sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))) (log.f64 10))
23.0ms	(sqrt.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify99.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	5034	1833

prune88.0ms

Filtered

55 candidates to 83 candidates (-50.9%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	70	13	83
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	71	13	84

Merged error: 7.8b

Counts

84 → 13

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 re re) (.f64 im im))
0.3b	(.f64 (/.f64 1/2 (sqrt.f64 (log.f64 10))) (/.f64 (log.f64 (+.f64 (.f64 re re) (*.f64 im im))) (sqrt.f64 (log.f64 10))))
0.4b	(/.f64 (log.f64 (+.f64 (.f64 re re) (.f64 im im))) (sqrt.f64 (log.f64 10)))
31.9b	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

89×	`times-frac_binary64`
83×	`add-sqr-sqrt_binary64`
54×	`sqrt-prod_binary64`
53×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
34×	`pow1_binary64`
32×	`associate-r_binary64`
28×	`log-pow_binary64`
25×	`associate-l_binary64`
19×	`add-exp-log_binary64`
18×	`add-cbrt-cube_binary64`
9×	`unswap-sqr_binary64`
7×	`associate-/r*_binary64`
6×	`add-log-exp_binary64`
5×	`cbrt-undiv_binary64` `div-exp_binary64`
4×	`cbrt-unprod_binary64` `prod-exp_binary64` `associate-/l*_binary64` `log-div_binary64`
3×	`flip3-+_binary64` `log-prod_binary64` `div-inv_binary64` `flip-+_binary64`
2×	`div-sub_binary64`
1×	`pow-prod-down_binary64` `rem-log-exp_binary64` `associate-r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `+-commutative_binary64` `frac-times_binary64` `associate-l/_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 164

Calls

4 calls:

4.0ms	(+.f64 (.f64 re re) (.f64 im im))
26.0ms	(.f64 (/.f64 1/2 (sqrt.f64 (log.f64 10))) (/.f64 (log.f64 (+.f64 (.f64 re re) (*.f64 im im))) (sqrt.f64 (log.f64 10))))
8.0ms	(/.f64 (log.f64 (+.f64 (.f64 re re) (.f64 im im))) (sqrt.f64 (log.f64 10)))
4.0ms	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))

series228.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(+.f64 (.f64 re re) (.f64 im im))
79.0ms	(.f64 (/.f64 1/2 (sqrt.f64 (log.f64 10))) (/.f64 (log.f64 (+.f64 (.f64 re re) (*.f64 im im))) (sqrt.f64 (log.f64 10))))
91.0ms	(/.f64 (log.f64 (+.f64 (.f64 re re) (.f64 im im))) (sqrt.f64 (log.f64 10)))
36.0ms	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify154.0ms

Algorithm

egg-herbie

Counts

176 → 176

Iterations

Useful iterations: 0 (107.0ms)

Iter	Nodes	Cost
0	4932	4675
1	4932	4675

prune154.0ms

Filtered

104 candidates to 176 candidates (-69.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	169	7	176
Fresh	8	4	12
Picked	1	0	1
Done	0	0	0
Total	178	11	189

Merged error: 7.7b

Counts

189 → 11

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 re re) (.f64 im im))
0.3b	(.f64 (/.f64 1/2 (sqrt.f64 (log.f64 10))) (log.f64 (pow.f64 (+.f64 (.f64 re re) (*.f64 im im)) (/.f64 1 (sqrt.f64 (log.f64 10))))))
15.1b	(log.f64 (pow.f64 (+.f64 (.f64 re re) (.f64 im im)) (/.f64 1 (sqrt.f64 (log.f64 10)))))
17.9b	(pow.f64 (+.f64 (.f64 re re) (.f64 im im)) (/.f64 1 (sqrt.f64 (log.f64 10))))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-sqr-sqrt_binary64`
44×	`times-frac_binary64`
40×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
25×	`pow-unpow_binary64` `associate-l_binary64` `sqrt-prod_binary64`
21×	`log-prod_binary64`
13×	`pow1_binary64`
12×	`add-exp-log_binary64` `unpow-prod-down_binary64`
9×	`add-cbrt-cube_binary64`
8×	`log-pow_binary64`
7×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64`
6×	`add-log-exp_binary64`
4×	`associate-r_binary64` `sqr-pow_binary64`
3×	`rem-log-exp_binary64` `unswap-sqr_binary64`
2×	`pow-to-exp_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `div-inv_binary64` `pow-exp_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `cbrt-undiv_binary64` `pow-pow_binary64` `div-exp_binary64` `+-commutative_binary64` `flip-+_binary64` `associate-l/_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

4 → 128

Calls

4 calls:

4.0ms	(+.f64 (.f64 re re) (.f64 im im))
16.0ms	(.f64 (/.f64 1/2 (sqrt.f64 (log.f64 10))) (log.f64 (pow.f64 (+.f64 (.f64 re re) (*.f64 im im)) (/.f64 1 (sqrt.f64 (log.f64 10))))))
5.0ms	(log.f64 (pow.f64 (+.f64 (.f64 re re) (.f64 im im)) (/.f64 1 (sqrt.f64 (log.f64 10)))))
8.0ms	(pow.f64 (+.f64 (.f64 re re) (.f64 im im)) (/.f64 1 (sqrt.f64 (log.f64 10))))

series465.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(+.f64 (.f64 re re) (.f64 im im))
170.0ms	(.f64 (/.f64 1/2 (sqrt.f64 (log.f64 10))) (log.f64 (pow.f64 (+.f64 (.f64 re re) (*.f64 im im)) (/.f64 1 (sqrt.f64 (log.f64 10))))))
135.0ms	(log.f64 (pow.f64 (+.f64 (.f64 re re) (.f64 im im)) (/.f64 1 (sqrt.f64 (log.f64 10)))))
137.0ms	(pow.f64 (+.f64 (.f64 re re) (.f64 im im)) (/.f64 1 (sqrt.f64 (log.f64 10))))

simplify135.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (97.0ms)

Iter	Nodes	Cost
0	4925	3493
1	4925	3493

prune134.0ms

Filtered

85 candidates to 140 candidates (-64.7%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	139	1	140
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	139	12	151

Merged error: 7.7b

Counts

151 → 12

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(.f64 (/.f64 (log.f64 (+.f64 (.f64 re re) (*.f64 im im))) (sqrt.f64 (log.f64 10))) (sqrt.f64 (/.f64 1/2 (sqrt.f64 (log.f64 10)))))
0.4b	(.f64 (sqrt.f64 (/.f64 1/2 (sqrt.f64 (log.f64 10)))) (.f64 (/.f64 (log.f64 (+.f64 (.f64 re re) (.f64 im im))) (sqrt.f64 (log.f64 10))) (sqrt.f64 (/.f64 1/2 (sqrt.f64 (log.f64 10))))))
0.4b	(/.f64 (log.f64 (+.f64 (.f64 re re) (.f64 im im))) (sqrt.f64 (log.f64 10)))
31.9b	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

126×	`sqrt-prod_binary64`
112×	`times-frac_binary64`
107×	`add-sqr-sqrt_binary64`
69×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
60×	`associate-l_binary64`
42×	`pow1_binary64`
31×	`log-pow_binary64`
29×	`associate-r_binary64`
21×	`add-exp-log_binary64`
20×	`add-cbrt-cube_binary64`
12×	`unswap-sqr_binary64`
10×	`sqrt-div_binary64`
7×	`associate-/r*_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
6×	`associate-*r/_binary64` `frac-times_binary64`
4×	`pow-prod-down_binary64` `add-log-exp_binary64` `associate-/l_binary64` `div-inv_binary64` `log-div_binary64` `associate-l/_binary64`
3×	`log-prod_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
2×	`flip3-+_binary64` `div-sub_binary64` `flip-+_binary64` `*-commutative_binary64`
1×	`rem-log-exp_binary64` `clear-num_binary64` `frac-2neg_binary64`

Counts

4 → 207

Calls

4 calls:

30.0ms	(.f64 (/.f64 (log.f64 (+.f64 (.f64 re re) (*.f64 im im))) (sqrt.f64 (log.f64 10))) (sqrt.f64 (/.f64 1/2 (sqrt.f64 (log.f64 10)))))
21.0ms	(.f64 (sqrt.f64 (/.f64 1/2 (sqrt.f64 (log.f64 10)))) (.f64 (/.f64 (log.f64 (+.f64 (.f64 re re) (.f64 im im))) (sqrt.f64 (log.f64 10))) (sqrt.f64 (/.f64 1/2 (sqrt.f64 (log.f64 10))))))
8.0ms	(/.f64 (log.f64 (+.f64 (.f64 re re) (.f64 im im))) (sqrt.f64 (log.f64 10)))
4.0ms	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))

series467.0ms

Counts

4 → 12

Calls

4 calls:

214.0ms	(.f64 (/.f64 (log.f64 (+.f64 (.f64 re re) (*.f64 im im))) (sqrt.f64 (log.f64 10))) (sqrt.f64 (/.f64 1/2 (sqrt.f64 (log.f64 10)))))
121.0ms	(.f64 (sqrt.f64 (/.f64 1/2 (sqrt.f64 (log.f64 10)))) (.f64 (/.f64 (log.f64 (+.f64 (.f64 re re) (.f64 im im))) (sqrt.f64 (log.f64 10))) (sqrt.f64 (/.f64 1/2 (sqrt.f64 (log.f64 10))))))
95.0ms	(/.f64 (log.f64 (+.f64 (.f64 re re) (.f64 im im))) (sqrt.f64 (log.f64 10)))
37.0ms	(log.f64 (+.f64 (.f64 re re) (.f64 im im)))

simplify133.0ms

Algorithm

egg-herbie

Counts

219 → 219

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4965	7134
1	4965	7134

prune245.0ms

Filtered

132 candidates to 219 candidates (-65.9%)

Pruning

17 alts after pruning (15 fresh and 2 done)

	Pruned	Kept	Total
New	213	6	219
Fresh	1	9	10
Picked	0	1	1
Done	0	1	1
Total	214	17	231

Merged error: 7.6b

Counts

231 → 17

regimes429.0ms

Accuracy

57% (10.5b remaining)

Error of 17.5b against oracle of 7.1b and baseline of 31.4b

bsearch79.0ms

Steps

Iters	Range		Point
9	1.5085485656691157e+84	1.2331806014381182e+89	2.7773647014065815e+88
7	3.463726408844937e-297	1.5453723785233492e-295	6.406642900144384e-297
9	-3.3614708406870103e-174	-1.9276552853043914e-180	-6.923684505821139e-180
5	-2.60978388630145e+133	-9.115767021670006e+132	-1.810553704526183e+133

simplify5.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	70	191
1	70	191

end0.0ms

sample612.0ms

Algorithm

intervals

Results

470.0ms

8000×

body

valid

Details

analyze5.0ms

sample20.0ms

simplify11.0ms

prune1.0ms

localize10.0ms

rewrite23.0ms

series114.0ms

simplify99.0ms

prune88.0ms

localize13.0ms

rewrite50.0ms

series228.0ms

simplify154.0ms

prune154.0ms

localize18.0ms

rewrite38.0ms

series465.0ms

simplify135.0ms

prune134.0ms

localize15.0ms

rewrite73.0ms

series467.0ms

simplify133.0ms

prune245.0ms

regimes429.0ms

bsearch79.0ms

simplify5.0ms

end0.0ms

sample612.0ms

Profiling