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

sample134.0ms

Algorithm

intervals

Results

56.0ms	54×	body	1280	valid
24.0ms	38×	body	640	valid
19.0ms	122×	body	80	valid
11.0ms	26×	body	320	valid
5.0ms	16×	body	160	valid
3.0ms	23×	body	80	invalid
1.0ms	5×	body	80	nan

simplify479.0ms

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: 12.4b

Counts

2 → 1

localize33.0ms

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)))
5.8b	(.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))))
16.1b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (.f64 x 2.0)) (neg.f64 (/.f64 1.0 2.0)))

rewrite47.0ms

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)))

series163.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(/.f64 1.0 (tan.f64 B))
36.0ms	(*.f64 x (/.f64 1.0 (tan.f64 B)))
76.0ms	(.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))))
35.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (.f64 x 2.0)) (neg.f64 (/.f64 1.0 2.0)))

simplify79.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4933	2415
1	4933	2415

prune300.0ms

Filtered

131 candidates to 167 candidates (-27.5%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	152	15	167
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	153	15	168

Merged error: 0.0b

Counts

168 → 15

localize21.0ms

Local error

Found 4 expressions with local error:

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)))
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 x (/.f64 1.0 (tan.f64 B)))
16.1b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (.f64 2.0 x)) (/.f64 1.0 2.0))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 108

Calls

4 calls:

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))
7.0ms	(*.f64 x (/.f64 1.0 (tan.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:

92.0ms	(/.f64 F (.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (*.f64 2.0 x)) (/.f64 1.0 2.0)) (sin.f64 B)))
84.0ms	(.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (*.f64 2.0 x)) (/.f64 1.0 2.0)) (sin.f64 B))
32.0ms	(*.f64 x (/.f64 1.0 (tan.f64 B)))
27.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (.f64 2.0 x)) (/.f64 1.0 2.0))

simplify55.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5004	1848

prune194.0ms

Filtered

91 candidates to 120 candidates (-31.9%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	113	7	120
Fresh	6	8	14
Picked	1	0	1
Done	0	0	0
Total	120	15	135

Merged error: 0.0b

Counts

135 → 15

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (*.f64 x 1.0) (tan.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)))
0.3b	(.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (*.f64 2.0 x)) (/.f64 1.0 2.0)) (sin.f64 B))
16.1b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (.f64 2.0 x)) (/.f64 1.0 2.0))

rewrite41.0ms

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 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:

33.0ms	(/.f64 (*.f64 x 1.0) (tan.f64 B))
91.0ms	(/.f64 F (.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (*.f64 2.0 x)) (/.f64 1.0 2.0)) (sin.f64 B)))
84.0ms	(.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 (34.0ms)

Iter	Nodes	Cost
0	5046	1758

prune173.0ms

Filtered

82 candidates to 109 candidates (-32.9%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	105	4	109
Fresh	3	11	14
Picked	1	0	1
Done	0	0	0
Total	109	15	124

Merged error: 0.0b

Counts

124 → 15

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (*.f64 x (cos.f64 B)) (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)))
0.3b	(.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (*.f64 2.0 x)) (/.f64 1.0 2.0)) (sin.f64 B))
16.1b	(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` `*-commutative_binary64`

Counts

4 → 96

Calls

4 calls:

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

series227.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))
92.0ms	(/.f64 F (.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2.0) (*.f64 2.0 x)) (/.f64 1.0 2.0)) (sin.f64 B)))
83.0ms	(.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))

simplify67.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4974	1769
1	4974	1769

prune121.0ms

Filtered

82 candidates to 108 candidates (-31.7%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	107	1	108
Fresh	1	13	14
Picked	0	1	1
Done	0	0	0
Total	108	15	123

Merged error: 0.0b

Counts

123 → 15

regimes294.0ms

Accuracy

97.7% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 10.5b

bsearch157.0ms

Steps

Iters	Range		Point
9	0.0008170696006750185	395.6191177056823	390.90111054659343
8	-3033468113216492.0	-303997739978.316	-311106551405.7238

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	124	78
1	124	78

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.5s	1623×	body	1280	valid
794.0ms	1333×	body	640	valid
559.0ms	3980×	body	80	valid
295.0ms	690×	body	320	valid
106.0ms	709×	body	80	invalid
105.0ms	374×	body	160	valid
13.0ms	126×	body	80	nan

Details

analyze1.7s

sample134.0ms

simplify479.0ms

prune12.0ms

localize33.0ms

rewrite47.0ms

series163.0ms

simplify79.0ms

prune300.0ms

localize21.0ms

rewrite46.0ms

series236.0ms

simplify55.0ms

prune194.0ms

localize23.0ms

rewrite41.0ms

series236.0ms

simplify46.0ms

prune173.0ms

localize22.0ms

rewrite43.0ms

series227.0ms

simplify67.0ms

prune121.0ms

regimes294.0ms

bsearch157.0ms

simplify3.0ms

end0.0ms

sample3.6s

Profiling