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

sample131.0ms

Algorithm

intervals

Results

48.0ms	50×	body	1280	valid
30.0ms	48×	body	640	valid
24.0ms	129×	body	80	valid
8.0ms	19×	body	320	valid
3.0ms	21×	body	80	invalid
3.0ms	10×	body	160	valid
1.0ms	5×	body	80	nan

simplify705.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (193.0ms)

Iter	Nodes	Cost
0	4665	32
1	4665	32

prune8.0ms

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: 16.0b

Counts

2 → 2

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 x (tan.f64 B))
0.1b	(/.f64 F (sin.f64 B))
8.1b	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
18.4b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)

rewrite37.0ms

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 x (tan.f64 B))
3.0ms	(/.f64 F (sin.f64 B))
14.0ms	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
10.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)

series391.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(/.f64 x (tan.f64 B))
50.0ms	(/.f64 F (sin.f64 B))
154.0ms	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
71.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)

simplify82.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5156	2525

prune177.0ms

Filtered

100 candidates to 127 candidates (-27.0%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	115	12	127
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	117	12	129

Merged error: 0.0b

Counts

129 → 12

localize20.0ms

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))
0.5b	(/.f64 (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2)) (sin.f64 B))
18.4b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

rewrite40.0ms

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))
13.0ms	(.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)

series339.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(/.f64 x (tan.f64 B))
48.0ms	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))
137.0ms	(/.f64 (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2)) (sin.f64 B))
47.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

simplify81.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4970	2141
1	4970	2141

prune112.0ms

Filtered

77 candidates to 105 candidates (-36.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	102	3	105
Fresh	3	8	11
Picked	1	0	1
Done	0	0	0
Total	106	11	117

Merged error: 0.0b

Counts

117 → 11

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 x (tan.f64 B))
0.3b	(/.f64 F (/.f64 (sin.f64 B) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)))
0.3b	(/.f64 (sin.f64 B) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2))
18.4b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

189×	`times-frac_binary64`
112×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
51×	`unpow-prod-down_binary64`
35×	`associate-/r*_binary64`
22×	`add-exp-log_binary64`
17×	`sqr-pow_binary64`
13×	`add-cbrt-cube_binary64`
11×	`div-exp_binary64`
9×	`associate-/l*_binary64`
7×	`div-inv_binary64`
5×	`pow1_binary64` `cbrt-undiv_binary64`
4×	`add-log-exp_binary64`
3×	`pow-to-exp_binary64` `pow-unpow_binary64` `clear-num_binary64` `frac-2neg_binary64` `pow-exp_binary64`
2×	`associate-/r/_binary64`
1×	`pow-pow_binary64` `tan-quot_binary64`

Counts

4 → 210

Calls

4 calls:

4.0ms	(/.f64 x (tan.f64 B))
14.0ms	(/.f64 F (/.f64 (sin.f64 B) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)))
10.0ms	(/.f64 (sin.f64 B) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2))
8.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

series499.0ms

Counts

4 → 12

Calls

4 calls:

171.0ms	(/.f64 x (tan.f64 B))
183.0ms	(/.f64 F (/.f64 (sin.f64 B) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)))
95.0ms	(/.f64 (sin.f64 B) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2))
51.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

simplify149.0ms

Algorithm

egg-herbie

Counts

222 → 222

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	4944	7920
1	4944	7920

prune412.0ms

Filtered

174 candidates to 222 candidates (-27.6%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	221	1	222
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	222	11	233

Merged error: 0.0b

Counts

233 → 11

localize41.0ms

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B))
0.2b	(/.f64 x (sin.f64 B))
8.1b	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
18.4b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 119

Calls

4 calls:

8.0ms	(*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B))
4.0ms	(/.f64 x (sin.f64 B))
19.0ms	(.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)

series442.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B))
60.0ms	(/.f64 x (sin.f64 B))
154.0ms	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
84.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)

simplify180.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (130.0ms)

Iter	Nodes	Cost
0	4966	2635
1	4966	2635

prune160.0ms

Filtered

102 candidates to 131 candidates (-28.4%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	130	1	131
Fresh	1	8	9
Picked	0	1	1
Done	0	1	1
Total	131	11	142

Merged error: 0.0b

Counts

142 → 11

regimes144.0ms

Accuracy

98.4% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 10.5b

bsearch322.0ms

Steps

Iters	Range		Point
10	0.0033294837586715664	31513296664.731464	51281.2123343461
9	-1.7238392751307282e+24	-1.0262202425614834e+18	-1.0378427485936736e+18

simplify5.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	86	90
1	86	90

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.6s	1590×	body	1280	valid
963.0ms	1413×	body	640	valid
620.0ms	3920×	body	80	valid
349.0ms	732×	body	320	valid
109.0ms	345×	body	160	valid
108.0ms	652×	body	80	invalid
13.0ms	115×	body	80	nan
1.0ms	1×	body	640	invalid
0.0ms	1×	body	320	invalid

Details

analyze1.8s

sample131.0ms

simplify705.0ms

prune8.0ms

localize22.0ms

rewrite37.0ms

series391.0ms

simplify82.0ms

prune177.0ms

localize20.0ms

rewrite40.0ms

series339.0ms

simplify81.0ms

prune112.0ms

localize20.0ms

rewrite46.0ms

series499.0ms

simplify149.0ms

prune412.0ms

localize41.0ms

rewrite51.0ms

series442.0ms

simplify180.0ms

prune160.0ms

regimes144.0ms

bsearch322.0ms

simplify5.0ms

end0.0ms

sample4.1s

Profiling