Details

analyze1.8s

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
0%	99.9%	0.1%	7
0%	93.6%	6.4%	8
9.4%	84.3%	6.4%	9
14.8%	75.7%	9.5%	10
16%	71.4%	12.6%	11
20.9%	65.7%	13.4%	12
24.2%	60.5%	15.3%	13
24.8%	58.6%	16.6%	14

sample146.0ms

Algorithm

intervals

Results

70.0ms	68×	body	1280	valid
30.0ms	48×	body	640	valid
18.0ms	119×	body	80	valid
8.0ms	15×	body	320	valid
3.0ms	20×	body	80	invalid
2.0ms	6×	body	160	valid
0.0ms	4×	body	80	nan

simplify550.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (110.0ms)

Iter	Nodes	Cost
0	4685	21
1	4685	21

prune14.0ms

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: 14.2b

Counts

2 → 2

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 F (sin.f64 B))
0.1b	(/.f64 x (tan.f64 B))
7.2b	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
17.2b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt_binary64`
31×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
30×	`times-frac_binary64`
22×	`add-exp-log_binary64`
13×	`add-cbrt-cube_binary64` `associate-l_binary64`
8×	`unpow-prod-down_binary64`
7×	`associate-r_binary64`
6×	`associate-/r_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `associate-/l_binary64`
5×	`pow1_binary64` `div-exp_binary64`
4×	`add-log-exp_binary64` `sqr-pow_binary64`
3×	`pow-to-exp_binary64` `pow-unpow_binary64` `cbrt-undiv_binary64` `div-inv_binary64` `pow-exp_binary64`
2×	`cbrt-unprod_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`pow-pow_binary64` `associate-/r/_binary64` `tan-quot_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

4 → 115

Calls

4 calls:

4.0ms	(/.f64 F (sin.f64 B))
4.0ms	(/.f64 x (tan.f64 B))
15.0ms	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
11.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)

series114.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(/.f64 F (sin.f64 B))
29.0ms	(/.f64 x (tan.f64 B))
46.0ms	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
26.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)

simplify48.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5053	1634

prune214.0ms

Filtered

100 candidates to 127 candidates (-27.0%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	114	13	127
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	116	13	129

Merged error: 0.0b

Counts

129 → 13

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 x (tan.f64 B))
0.3b	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))
0.7b	(/.f64 (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2)) (sin.f64 B))
17.2b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64`
22×	`add-exp-log_binary64`
19×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
13×	`add-cbrt-cube_binary64`
12×	`times-frac_binary64`
7×	`associate-r_binary64` `unpow-prod-down_binary64`
6×	`associate-/r*_binary64` `prod-exp_binary64`
5×	`pow1_binary64` `div-exp_binary64`
4×	`add-log-exp_binary64` `associate-/l*_binary64`
3×	`pow-to-exp_binary64` `pow-unpow_binary64` `cbrt-undiv_binary64` `sqr-pow_binary64` `associate-l_binary64` `unswap-sqr_binary64` `pow-exp_binary64`
2×	`cbrt-unprod_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64`
1×	`pow-pow_binary64` `associate-/r/_binary64` `tan-quot_binary64` `*-commutative_binary64`

Counts

4 → 93

Calls

4 calls:

4.0ms	(/.f64 x (tan.f64 B))
12.0ms	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))
12.0ms	(/.f64 (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2)) (sin.f64 B))
8.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

series92.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(/.f64 x (tan.f64 B))
14.0ms	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))
38.0ms	(/.f64 (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2)) (sin.f64 B))
14.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

simplify48.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5010	1405

prune145.0ms

Filtered

77 candidates to 105 candidates (-36.4%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	103	2	105
Fresh	1	11	12
Picked	0	1	1
Done	0	0	0
Total	104	14	118

Merged error: 0.0b

Counts

118 → 14

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 x (tan.f64 B))
0.2b	(/.f64 1 (/.f64 (sin.f64 B) F))
7.2b	(.f64 (/.f64 1 (/.f64 (sin.f64 B) F)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
17.2b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

168×	`times-frac_binary64`
130×	`add-sqr-sqrt_binary64`
99×	`*-un-lft-identity_binary64`
93×	`add-cube-cbrt_binary64`
68×	`add-exp-log_binary64`
44×	`associate-l_binary64`
29×	`div-exp_binary64`
21×	`prod-exp_binary64`
20×	`add-cbrt-cube_binary64`
16×	`associate-/r*_binary64`
15×	`unswap-sqr_binary64`
11×	`unpow-prod-down_binary64`
10×	`div-inv_binary64`
8×	`pow-to-exp_binary64` `1-exp_binary64` `rec-exp_binary64` `pow-exp_binary64`
7×	`associate-r_binary64` `cbrt-undiv_binary64` `sqr-pow_binary64`
6×	`pow1_binary64` `associate-/l*_binary64`
4×	`add-log-exp_binary64`
3×	`pow-unpow_binary64` `cbrt-unprod_binary64` `associate-/r/_binary64`
2×	`clear-num_binary64` `frac-2neg_binary64`
1×	`pow-pow_binary64` `inv-pow_binary64` `pow-flip_binary64` `tan-quot_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

4 → 220

Calls

4 calls:

4.0ms	(/.f64 x (tan.f64 B))
6.0ms	(/.f64 1 (/.f64 (sin.f64 B) F))
22.0ms	(.f64 (/.f64 1 (/.f64 (sin.f64 B) F)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
9.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)

series101.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(/.f64 x (tan.f64 B))
12.0ms	(/.f64 1 (/.f64 (sin.f64 B) F))
49.0ms	(.f64 (/.f64 1 (/.f64 (sin.f64 B) F)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
14.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)

simplify72.0ms

Algorithm

egg-herbie

Counts

232 → 232

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4932	3334
1	4932	3334

prune250.0ms

Filtered

155 candidates to 232 candidates (-49.7%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	230	2	232
Fresh	1	11	12
Picked	1	0	1
Done	0	1	1
Total	232	14	246

Merged error: 0.0b

Counts

246 → 14

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 F (sin.f64 B))
0.3b	(/.f64 1 (/.f64 (tan.f64 B) x))
7.2b	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
17.2b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

96×	`times-frac_binary64`
78×	`add-sqr-sqrt_binary64`
65×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
31×	`add-exp-log_binary64`
16×	`associate-/r*_binary64` `add-cbrt-cube_binary64`
13×	`associate-l_binary64`
11×	`div-exp_binary64`
8×	`unpow-prod-down_binary64`
7×	`associate-r_binary64` `div-inv_binary64`
6×	`pow1_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `associate-/l*_binary64`
5×	`cbrt-undiv_binary64`
4×	`add-log-exp_binary64` `sqr-pow_binary64`
3×	`pow-to-exp_binary64` `pow-unpow_binary64` `pow-exp_binary64`
2×	`cbrt-unprod_binary64` `1-exp_binary64` `clear-num_binary64` `frac-2neg_binary64` `rec-exp_binary64`
1×	`pow-pow_binary64` `associate-/r/_binary64` `inv-pow_binary64` `pow-flip_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

4 → 163

Calls

4 calls:

4.0ms	(/.f64 F (sin.f64 B))
6.0ms	(/.f64 1 (/.f64 (tan.f64 B) x))
15.0ms	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
8.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)

series89.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(/.f64 F (sin.f64 B))
22.0ms	(/.f64 1 (/.f64 (tan.f64 B) x))
40.0ms	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
14.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)

simplify73.0ms

Algorithm

egg-herbie

Counts

175 → 175

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4943	2185
1	4943	2185

prune159.0ms

Filtered

121 candidates to 175 candidates (-44.6%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	173	2	175
Fresh	3	9	12
Picked	0	1	1
Done	0	1	1
Total	176	13	189

Merged error: 0.0b

Counts

189 → 13

regimes261.0ms

Accuracy

98.4% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 10.6b

bsearch144.0ms

Steps

Iters	Range		Point
8	3040.7324025650373	7712014.360816213	827777.6737999358
9	-1.722559145047411e+155	-9.14832067692237e+147	-1.3366524590649154e+154

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	109	67
1	109	67

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.5s	1604×	body	1280	valid
861.0ms	1400×	body	640	valid
564.0ms	3968×	body	80	valid
288.0ms	686×	body	320	valid
98.0ms	342×	body	160	valid
94.0ms	662×	body	80	invalid
12.0ms	120×	body	80	nan
0.0ms	1×	body	320	invalid

Details

analyze1.8s

sample146.0ms

simplify550.0ms

prune14.0ms

localize31.0ms

rewrite38.0ms

series114.0ms

simplify48.0ms

prune214.0ms

localize19.0ms

rewrite38.0ms

series92.0ms

simplify48.0ms

prune145.0ms

localize24.0ms

rewrite51.0ms

series101.0ms

simplify72.0ms

prune250.0ms

localize23.0ms

rewrite39.0ms

series89.0ms

simplify73.0ms

prune159.0ms

regimes261.0ms

bsearch144.0ms

simplify3.0ms

end0.0ms

sample3.7s

Profiling