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

sample140.0ms

Algorithm

intervals

Results

60.0ms	64×	body	1280	valid
26.0ms	42×	body	640	valid
18.0ms	120×	body	80	valid
8.0ms	18×	body	320	valid
8.0ms	20×	body	80	invalid
4.0ms	12×	body	160	valid
1.0ms	5×	body	80	nan

simplify472.0ms

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: 15.7b

Counts

2 → 1

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1.0 (tan.f64 B))
0.3b	(*.f64 x (/.f64 1.0 (tan.f64 B)))
7.7b	(.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))))
18.8b	(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×	`associate-/r/_binary64` `frac-times_binary64` `tan-quot_binary64` `*-commutative_binary64`
1×	`pow-prod-down_binary64` `pow-pow_binary64` `neg-mul-1_binary64` `clear-num_binary64` `frac-2neg_binary64` `un-div-inv_binary64` `associate-*l/_binary64`

Counts

4 → 155

Calls

4 calls:

4.0ms	(/.f64 1.0 (tan.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)))

series152.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(/.f64 1.0 (tan.f64 B))
32.0ms	(*.f64 x (/.f64 1.0 (tan.f64 B)))
72.0ms	(.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))))
34.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (.f64 x 2.0)) (neg.f64 (/.f64 1.0 2.0)))

simplify57.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4970	2407
1	4970	2407

prune319.0ms

Filtered

131 candidates to 167 candidates (-27.5%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	149	18	167
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	150	18	168

Merged error: 0.0b

Counts

168 → 18

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (*.f64 2.0 x)) (neg.f64 (/.f64 1.0 2.0))))
0.3b	(*.f64 x (/.f64 1.0 (tan.f64 B)))
0.4b	(/.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))
18.8b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (.f64 2.0 x)) (neg.f64 (/.f64 1.0 2.0)))

rewrite46.0ms

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:

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

series145.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (*.f64 2.0 x)) (neg.f64 (/.f64 1.0 2.0))))
26.0ms	(*.f64 x (/.f64 1.0 (tan.f64 B)))
65.0ms	(/.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))
23.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (.f64 2.0 x)) (neg.f64 (/.f64 1.0 2.0)))

simplify38.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5131	2183

prune228.0ms

Filtered

108 candidates to 145 candidates (-34.3%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	142	3	145
Fresh	4	13	17
Picked	1	0	1
Done	0	0	0
Total	147	16	163

Merged error: 0.0b

Counts

163 → 16

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.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))))
0.4b	(/.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))
18.8b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (.f64 2.0 x)) (neg.f64 (/.f64 1.0 2.0)))

rewrite43.0ms

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))
11.0ms	(.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)))

series145.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(/.f64 (*.f64 x 1.0) (tan.f64 B))
30.0ms	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (*.f64 2.0 x)) (neg.f64 (/.f64 1.0 2.0))))
65.0ms	(/.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))
23.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (.f64 2.0 x)) (neg.f64 (/.f64 1.0 2.0)))

simplify51.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	4945	2100
1	4945	2100

prune211.0ms

Filtered

102 candidates to 134 candidates (-31.4%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	130	4	134
Fresh	5	10	15
Picked	1	0	1
Done	0	0	0
Total	136	14	150

Merged error: 0.0b

Counts

150 → 14

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (*.f64 x 1.0) (tan.f64 B))
0.3b	(.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (*.f64 2.0 x)) (/.f64 1.0 2.0)) (sin.f64 B))
0.3b	(/.f64 F (.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (*.f64 2.0 x)) (/.f64 1.0 2.0)) (sin.f64 B)))
18.7b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (.f64 2.0 x)) (/.f64 1.0 2.0))

rewrite42.0ms

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))
11.0ms	(.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (*.f64 2.0 x)) (/.f64 1.0 2.0)) (sin.f64 B))
11.0ms	(/.f64 F (.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (*.f64 2.0 x)) (/.f64 1.0 2.0)) (sin.f64 B)))
10.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (.f64 2.0 x)) (/.f64 1.0 2.0))

series221.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(/.f64 (*.f64 x 1.0) (tan.f64 B))
89.0ms	(.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (*.f64 2.0 x)) (/.f64 1.0 2.0)) (sin.f64 B))
80.0ms	(/.f64 F (.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (*.f64 2.0 x)) (/.f64 1.0 2.0)) (sin.f64 B)))
26.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (.f64 2.0 x)) (/.f64 1.0 2.0))

simplify45.0ms

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

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	105	4	109
Fresh	3	10	13
Picked	1	0	1
Done	0	0	0
Total	109	14	123

Merged error: 0.0b

Counts

123 → 14

regimes291.0ms

Accuracy

97.9% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 11.0b

bsearch126.0ms

Steps

Iters	Range		Point
7	4.8615426410334854e+20	2.4574456530104413e+22	4.9267265883090964e+20
7	-9.098051782367158e+111	-2.6583604369437583e+110	-1.0279393567136411e+111

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	100	70
1	100	70

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.5s	1689×	body	1280	valid
813.0ms	1353×	body	640	valid
544.0ms	3904×	body	80	valid
290.0ms	700×	body	320	valid
101.0ms	354×	body	160	valid
87.0ms	618×	body	80	invalid
10.0ms	102×	body	80	nan
1.0ms	2×	body	640	invalid
1.0ms	1×	body	1280	invalid
0.0ms	1×	body	320	invalid

Details

analyze1.8s

sample140.0ms

simplify472.0ms

prune12.0ms

localize35.0ms

rewrite46.0ms

series152.0ms

simplify57.0ms

prune319.0ms

localize25.0ms

rewrite46.0ms

series145.0ms

simplify38.0ms

prune228.0ms

localize25.0ms

rewrite43.0ms

series145.0ms

simplify51.0ms

prune211.0ms

localize21.0ms

rewrite42.0ms

series221.0ms

simplify45.0ms

prune132.0ms

regimes291.0ms

bsearch126.0ms

simplify3.0ms

end0.0ms

sample3.6s

Profiling