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

sample141.0ms

Algorithm

intervals

Results

66.0ms	66×	body	1280	valid
30.0ms	50×	body	640	valid
16.0ms	113×	body	80	valid
7.0ms	16×	body	320	valid
4.0ms	24×	body	80	invalid
3.0ms	11×	body	160	valid
0.0ms	3×	body	80	nan

simplify514.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (108.0ms)

Iter	Nodes	Cost
0	4685	21
1	4685	21

prune12.0ms

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: 12.8b

Counts

2 → 2

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 F (sin.f64 B))
0.1b	(/.f64 x (tan.f64 B))
6.2b	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
15.0b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)

rewrite39.0ms

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)

series100.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(/.f64 F (sin.f64 B))
25.0ms	(/.f64 x (tan.f64 B))
41.0ms	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
24.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)

simplify47.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5053	1634

prune158.0ms

Filtered

100 candidates to 127 candidates (-27.0%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	113	14	127
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	115	14	129

Merged error: 0.0b

Counts

129 → 14

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 x (tan.f64 B))
0.3b	(.f64 F (/.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2) (sin.f64 B)))
0.4b	(/.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2) (sin.f64 B))
15.0b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 138

Calls

4 calls:

4.0ms	(/.f64 x (tan.f64 B))
15.0ms	(.f64 F (/.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2) (sin.f64 B)))
12.0ms	(/.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2) (sin.f64 B))
9.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

series96.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(/.f64 x (tan.f64 B))
32.0ms	(.f64 F (/.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2) (sin.f64 B)))
31.0ms	(/.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2) (sin.f64 B))
13.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

simplify76.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4931	2549
1	4931	2549

prune146.0ms

Filtered

115 candidates to 150 candidates (-30.4%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	146	4	150
Fresh	5	8	13
Picked	0	1	1
Done	0	0	0
Total	151	13	164

Merged error: 0.0b

Counts

164 → 13

localize27.0ms

Local error

Found 4 expressions with local error:

0.4b	(/.f64 (pow.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) (*.f64 (cbrt.f64 -1/2) (cbrt.f64 -1/2))) (cbrt.f64 -1/2)) (sin.f64 B))
1.0b	(*.f64 (cbrt.f64 -1/2) (cbrt.f64 -1/2))
10.1b	(pow.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) (*.f64 (cbrt.f64 -1/2) (cbrt.f64 -1/2))) (cbrt.f64 -1/2))
10.5b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) (*.f64 (cbrt.f64 -1/2) (cbrt.f64 -1/2)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

53×	`unpow-prod-down_binary64`
49×	`add-sqr-sqrt_binary64`
41×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
33×	`times-frac_binary64`
19×	`cbrt-prod_binary64`
17×	`add-exp-log_binary64`
12×	`pow1_binary64`
11×	`sqr-pow_binary64` `associate-/l*_binary64`
9×	`pow-exp_binary64`
7×	`pow-unpow_binary64`
6×	`swap-sqr_binary64` `associate-r_binary64` `pow1/3_binary64` `add-cbrt-cube_binary64` `associate-l_binary64`
5×	`pow-to-exp_binary64` `div-exp_binary64`
4×	`add-log-exp_binary64` `unswap-sqr_binary64`
3×	`associate-/r*_binary64`
2×	`pow-prod-down_binary64` `pow-prod-up_binary64` `pow-pow_binary64` `pow-sqr_binary64`
1×	`cbrt-unprod_binary64` `cbrt-undiv_binary64` `pow-plus_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 144

Calls

4 calls:

14.0ms	(/.f64 (pow.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) (*.f64 (cbrt.f64 -1/2) (cbrt.f64 -1/2))) (cbrt.f64 -1/2)) (sin.f64 B))
6.0ms	(*.f64 (cbrt.f64 -1/2) (cbrt.f64 -1/2))
10.0ms	(pow.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) (*.f64 (cbrt.f64 -1/2) (cbrt.f64 -1/2))) (cbrt.f64 -1/2))
9.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) (*.f64 (cbrt.f64 -1/2) (cbrt.f64 -1/2)))

series185.0ms

Counts

4 → 10

Calls

4 calls:

83.0ms	(/.f64 (pow.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) (*.f64 (cbrt.f64 -1/2) (cbrt.f64 -1/2))) (cbrt.f64 -1/2)) (sin.f64 B))
0.0ms	(*.f64 (cbrt.f64 -1/2) (cbrt.f64 -1/2))
51.0ms	(pow.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) (*.f64 (cbrt.f64 -1/2) (cbrt.f64 -1/2))) (cbrt.f64 -1/2))
51.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) (*.f64 (cbrt.f64 -1/2) (cbrt.f64 -1/2)))

simplify67.0ms

Algorithm

egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4909	3340
1	4909	3340

prune212.0ms

Filtered

116 candidates to 154 candidates (-32.8%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	154	0	154
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	154	13	167

Merged error: 0.0b

Counts

167 → 13

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (tan.f64 B) x)
0.2b	(/.f64 1 (/.f64 (tan.f64 B) x))
6.2b	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
15.0b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)

rewrite40.0ms

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×	`associate-/l/_binary64` `pow-pow_binary64` `associate-/r/_binary64` `inv-pow_binary64` `pow-flip_binary64` `tan-quot_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

4 → 164

Calls

4 calls:

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

series79.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(/.f64 (tan.f64 B) x)
18.0ms	(/.f64 1 (/.f64 (tan.f64 B) x))
36.0ms	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
12.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)

simplify72.0ms

Algorithm

egg-herbie

Counts

176 → 176

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4919	2204
1	4919	2204

prune108.0ms

Filtered

123 candidates to 176 candidates (-43.1%)

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	175	1	176
Fresh	1	9	10
Picked	0	1	1
Done	0	2	2
Total	176	13	189

Merged error: 0.0b

Counts

189 → 13

regimes202.0ms

Accuracy

98.4% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 10.9b

bsearch171.0ms

Steps

Iters	Range		Point
9	156990.6063368243	13788715467.834576	64768006.58827289
10	-433543364.2827886	-0.0001239539780877448	-762427.8971967286

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	96	65
1	96	65

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.5s	1652×	body	1280	valid
830.0ms	1399×	body	640	valid
538.0ms	3886×	body	80	valid
300.0ms	728×	body	320	valid
95.0ms	667×	body	80	invalid
94.0ms	335×	body	160	valid
11.0ms	116×	body	80	nan
1.0ms	1×	body	640	invalid

Details

analyze1.8s

sample141.0ms

simplify514.0ms

prune12.0ms

localize32.0ms

rewrite39.0ms

series100.0ms

simplify47.0ms

prune158.0ms

localize19.0ms

rewrite44.0ms

series96.0ms

simplify76.0ms

prune146.0ms

localize27.0ms

rewrite44.0ms

series185.0ms

simplify67.0ms

prune212.0ms

localize21.0ms

rewrite40.0ms

series79.0ms

simplify72.0ms

prune108.0ms

regimes202.0ms

bsearch171.0ms

simplify3.0ms

end0.0ms

sample3.6s

Profiling