Details

analyze1.7s

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

69.0ms	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

simplify441.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4951	26
1	4951	26

prune12.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 14.3b

Counts

2 → 1

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 F (sin.f64 B))
0.2b	(*.f64 x (/.f64 1.0 (tan.f64 B)))
7.2b	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (*.f64 x 2.0)) (neg.f64 (/.f64 1.0 2.0))))
17.2b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (.f64 x 2.0)) (neg.f64 (/.f64 1.0 2.0)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

63×	`add-sqr-sqrt_binary64`
49×	`times-frac_binary64`
45×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
30×	`pow-unpow_binary64`
25×	`add-exp-log_binary64`
21×	`associate-r_binary64`
16×	`add-cbrt-cube_binary64` `associate-l_binary64`
13×	`distribute-lft-neg-in_binary64` `distribute-rgt-neg-in_binary64`
8×	`unswap-sqr_binary64` `unpow-prod-down_binary64` `prod-exp_binary64`
7×	`pow1_binary64`
5×	`div-inv_binary64` `div-exp_binary64`
4×	`add-log-exp_binary64` `cbrt-unprod_binary64` `sqr-pow_binary64` `pow-neg_binary64`
3×	`pow-to-exp_binary64` `associate-/r_binary64` `neg-sub0_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `pow-sub_binary64` `associate-/l*_binary64` `pow-exp_binary64`
2×	`frac-times_binary64` `*-commutative_binary64`
1×	`pow-prod-down_binary64` `pow-pow_binary64` `neg-mul-1_binary64` `associate-/r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `un-div-inv_binary64` `tan-quot_binary64` `associate-*l/_binary64`

Counts

4 → 154

Calls

4 calls:

4.0ms	(/.f64 F (sin.f64 B))
7.0ms	(*.f64 x (/.f64 1.0 (tan.f64 B)))
15.0ms	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (*.f64 x 2.0)) (neg.f64 (/.f64 1.0 2.0))))
13.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (.f64 x 2.0)) (neg.f64 (/.f64 1.0 2.0)))

series157.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(/.f64 F (sin.f64 B))
34.0ms	(*.f64 x (/.f64 1.0 (tan.f64 B)))
69.0ms	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (*.f64 x 2.0)) (neg.f64 (/.f64 1.0 2.0))))
42.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (.f64 x 2.0)) (neg.f64 (/.f64 1.0 2.0)))

simplify67.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4935	2393
1	4935	2393

prune295.0ms

Filtered

129 candidates to 166 candidates (-28.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	153	13	166
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	154	13	167

Merged error: 0.0b

Counts

167 → 13

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(*.f64 x (/.f64 1.0 (tan.f64 B)))
0.3b	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (*.f64 2.0 x)) (neg.f64 (/.f64 1.0 2.0))))
0.7b	(/.f64 (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (*.f64 2.0 x)) (neg.f64 (/.f64 1.0 2.0)))) (sin.f64 B))
17.2b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (.f64 2.0 x)) (neg.f64 (/.f64 1.0 2.0)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt_binary64`
33×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
31×	`times-frac_binary64`
30×	`pow-unpow_binary64`
25×	`add-exp-log_binary64`
21×	`associate-r_binary64`
16×	`add-cbrt-cube_binary64`
13×	`distribute-lft-neg-in_binary64` `distribute-rgt-neg-in_binary64`
8×	`prod-exp_binary64`
7×	`pow1_binary64` `unpow-prod-down_binary64`
6×	`associate-l_binary64`
5×	`associate-*r/_binary64` `unswap-sqr_binary64` `pow-neg_binary64` `div-exp_binary64`
4×	`add-log-exp_binary64` `cbrt-unprod_binary64` `div-inv_binary64`
3×	`pow-to-exp_binary64` `associate-/l/_binary64` `associate-/r*_binary64` `neg-sub0_binary64` `cbrt-undiv_binary64` `sqr-pow_binary64` `pow-sub_binary64` `pow-exp_binary64`
2×	`un-div-inv_binary64` `*-commutative_binary64`
1×	`pow-prod-down_binary64` `pow-pow_binary64` `neg-mul-1_binary64` `associate-/r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `tan-quot_binary64`

Counts

4 → 133

Calls

4 calls:

7.0ms	(*.f64 x (/.f64 1.0 (tan.f64 B)))
12.0ms	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (*.f64 2.0 x)) (neg.f64 (/.f64 1.0 2.0))))
12.0ms	(/.f64 (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (*.f64 2.0 x)) (neg.f64 (/.f64 1.0 2.0)))) (sin.f64 B))
11.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (.f64 2.0 x)) (neg.f64 (/.f64 1.0 2.0)))

series153.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(*.f64 x (/.f64 1.0 (tan.f64 B)))
32.0ms	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (*.f64 2.0 x)) (neg.f64 (/.f64 1.0 2.0))))
69.0ms	(/.f64 (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (*.f64 2.0 x)) (neg.f64 (/.f64 1.0 2.0)))) (sin.f64 B))
24.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (.f64 2.0 x)) (neg.f64 (/.f64 1.0 2.0)))

simplify39.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5131	2183

prune227.0ms

Filtered

108 candidates to 145 candidates (-34.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	139	6	145
Fresh	5	7	12
Picked	1	0	1
Done	0	0	0
Total	145	13	158

Merged error: 0.0b

Counts

158 → 13

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (*.f64 x 1.0) (tan.f64 B))
0.3b	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (*.f64 2.0 x)) (neg.f64 (/.f64 1.0 2.0))))
0.7b	(/.f64 (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (*.f64 2.0 x)) (neg.f64 (/.f64 1.0 2.0)))) (sin.f64 B))
17.2b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (.f64 2.0 x)) (neg.f64 (/.f64 1.0 2.0)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt_binary64`
30×	`pow-unpow_binary64`
27×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
25×	`add-exp-log_binary64`
24×	`times-frac_binary64`
16×	`add-cbrt-cube_binary64`
13×	`distribute-lft-neg-in_binary64` `distribute-rgt-neg-in_binary64`
7×	`associate-r_binary64` `unpow-prod-down_binary64` `prod-exp_binary64`
6×	`associate-/r*_binary64` `div-exp_binary64`
5×	`pow1_binary64` `pow-neg_binary64`
4×	`add-log-exp_binary64` `cbrt-undiv_binary64` `associate-*r/_binary64` `div-inv_binary64`
3×	`pow-to-exp_binary64` `associate-/l/_binary64` `cbrt-unprod_binary64` `neg-sub0_binary64` `sqr-pow_binary64` `associate-l_binary64` `unswap-sqr_binary64` `pow-sub_binary64` `pow-exp_binary64`
2×	`clear-num_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `un-div-inv_binary64`
1×	`pow-pow_binary64` `neg-mul-1_binary64` `associate-/r/_binary64` `tan-quot_binary64` `*-commutative_binary64`

Counts

4 → 122

Calls

4 calls:

5.0ms	(/.f64 (*.f64 x 1.0) (tan.f64 B))
12.0ms	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (*.f64 2.0 x)) (neg.f64 (/.f64 1.0 2.0))))
12.0ms	(/.f64 (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (*.f64 2.0 x)) (neg.f64 (/.f64 1.0 2.0)))) (sin.f64 B))
11.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (.f64 2.0 x)) (neg.f64 (/.f64 1.0 2.0)))

series154.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(/.f64 (*.f64 x 1.0) (tan.f64 B))
33.0ms	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (*.f64 2.0 x)) (neg.f64 (/.f64 1.0 2.0))))
66.0ms	(/.f64 (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (*.f64 2.0 x)) (neg.f64 (/.f64 1.0 2.0)))) (sin.f64 B))
27.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (.f64 2.0 x)) (neg.f64 (/.f64 1.0 2.0)))

simplify50.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4945	2100
1	4945	2100

prune197.0ms

Filtered

101 candidates to 134 candidates (-32.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	129	5	134
Fresh	6	6	12
Picked	1	0	1
Done	0	0	0
Total	136	11	147

Merged error: 0.0b

Counts

147 → 11

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (*.f64 x 1.0) (tan.f64 B))
0.2b	(/.f64 F (.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (*.f64 2.0 x)) (/.f64 1.0 2.0)) (sin.f64 B)))
0.2b	(.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (*.f64 2.0 x)) (/.f64 1.0 2.0)) (sin.f64 B))
17.2b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (.f64 2.0 x)) (/.f64 1.0 2.0))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 97

Calls

4 calls:

5.0ms	(/.f64 (*.f64 x 1.0) (tan.f64 B))
13.0ms	(/.f64 F (.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (*.f64 2.0 x)) (/.f64 1.0 2.0)) (sin.f64 B)))
12.0ms	(.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (*.f64 2.0 x)) (/.f64 1.0 2.0)) (sin.f64 B))
10.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (.f64 2.0 x)) (/.f64 1.0 2.0))

series236.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(/.f64 (*.f64 x 1.0) (tan.f64 B))
86.0ms	(/.f64 F (.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (*.f64 2.0 x)) (/.f64 1.0 2.0)) (sin.f64 B)))
95.0ms	(.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (*.f64 2.0 x)) (/.f64 1.0 2.0)) (sin.f64 B))
27.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (.f64 2.0 x)) (/.f64 1.0 2.0))

simplify46.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	4974	1776
1	4974	1776

prune132.0ms

Filtered

84 candidates to 109 candidates (-29.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	106	3	109
Fresh	3	7	10
Picked	0	1	1
Done	0	0	0
Total	109	11	120

Merged error: 0.0b

Counts

120 → 11

regimes242.0ms

Accuracy

98.2% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 10.6b

bsearch140.0ms

Steps

Iters	Range		Point
8	3040.7324025650373	7712014.360816213	6874909.974872331
9	-2.166553379375817e+30	-4.0218625629144235e+21	-1.1305106783563191e+26

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	104	75
1	104	75

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.5s	1604×	body	1280	valid
860.0ms	1400×	body	640	valid
557.0ms	3968×	body	80	valid
289.0ms	686×	body	320	valid
98.0ms	342×	body	160	valid
97.0ms	662×	body	80	invalid
12.0ms	120×	body	80	nan
0.0ms	1×	body	320	invalid

Details

analyze1.7s

sample146.0ms

simplify441.0ms

prune12.0ms

localize34.0ms

rewrite46.0ms

series157.0ms

simplify67.0ms

prune295.0ms

localize23.0ms

rewrite49.0ms

series153.0ms

simplify39.0ms

prune227.0ms

localize23.0ms

rewrite44.0ms

series154.0ms

simplify50.0ms

prune197.0ms

localize21.0ms

rewrite43.0ms

series236.0ms

simplify46.0ms

prune132.0ms

regimes242.0ms

bsearch140.0ms

simplify3.0ms

end0.0ms

sample3.7s

Profiling