Details

analyze2.0s

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

sample127.0ms

Algorithm

intervals

Results

65.0ms	79×	body	1024	valid
18.0ms	119×	body	128	valid
17.0ms	34×	body	512	valid
7.0ms	23×	body	256	valid
3.0ms	21×	body	128	invalid
1.0ms	1×	body	2048	valid
0.0ms	1×	body	128	nan

simplify308.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (140.0ms)

Iter	Nodes	Cost
0	4852	32
1	4852	32

prune15.0ms

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: 13.1b

Counts

2 → 2

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 F (sin.f64 B))
0.2b	(/.f64 x (tan.f64 B))
6.9b	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
15.2b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)

rewrite46.0ms

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)

series745.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(/.f64 F (sin.f64 B))
212.0ms	(/.f64 x (tan.f64 B))
296.0ms	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
144.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)

simplify71.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5252	2525

prune181.0ms

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

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 x (tan.f64 B))
0.3b	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))
0.4b	(/.f64 (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2)) (sin.f64 B))
15.2b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

rewrite45.0ms

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))
12.0ms	(.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)

series669.0ms

Counts

4 → 12

Calls

4 calls:

212.0ms	(/.f64 x (tan.f64 B))
90.0ms	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))
246.0ms	(/.f64 (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2)) (sin.f64 B))
121.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

simplify68.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4989	2141
1	4989	2141

prune118.0ms

Filtered

76 candidates to 105 candidates (-38.2%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	102	3	105
Fresh	3	10	13
Picked	0	1	1
Done	0	0	0
Total	105	14	119

Merged error: 0.0b

Counts

119 → 14

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 x (tan.f64 B))
0.2b	(.f64 F (/.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2) (sin.f64 B)))
0.3b	(/.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2) (sin.f64 B))
15.2b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

rewrite55.0ms

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))
16.0ms	(.f64 F (/.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2) (sin.f64 B)))
11.0ms	(/.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)

series794.0ms

Counts

4 → 12

Calls

4 calls:

202.0ms	(/.f64 x (tan.f64 B))
261.0ms	(.f64 F (/.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2) (sin.f64 B)))
227.0ms	(/.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2) (sin.f64 B))
103.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

simplify104.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4923	3927
1	4923	3927

prune177.0ms

Filtered

114 candidates to 150 candidates (-31.6%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	149	1	150
Fresh	0	12	12
Picked	1	0	1
Done	0	1	1
Total	150	14	164

Merged error: 0.0b

Counts

164 → 14

localize28.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 F)
0.5b	(cbrt.f64 F)
0.5b	(cbrt.f64 F)
15.2b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `cbrt-prod_binary64`
5×	`pow1_binary64` `add-exp-log_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64`
3×	`pow-unpow_binary64` `pow1/3_binary64` `unpow-prod-down_binary64`
1×	`pow-to-exp_binary64` `pow-pow_binary64` `sqr-pow_binary64` `pow-exp_binary64`

Counts

4 → 50

Calls

4 calls:

1.0ms	(cbrt.f64 F)
1.0ms	(cbrt.f64 F)
1.0ms	(cbrt.f64 F)
9.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

series563.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(cbrt.f64 F)
151.0ms	(cbrt.f64 F)
163.0ms	(cbrt.f64 F)
106.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

simplify61.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4884	683
1	4884	683

prune64.0ms

Filtered

51 candidates to 62 candidates (-21.6%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	62	0	62
Fresh	0	12	12
Picked	0	1	1
Done	0	1	1
Total	62	14	76

Merged error: 0.0b

Counts

76 → 14

regimes122.0ms

Accuracy

98.4% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 10.7b

bsearch155.0ms

Steps

Iters	Range		Point
8	55.94141630524473	45637.308962806776	11899.074426921257
9	-3.5818005339014134e+54	-7.643947389091419e+46	-3.5054901799938445e+54

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	67	90
1	67	90

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.7s	2226×	body	1024	valid
597.0ms	4104×	body	128	valid
523.0ms	1088×	body	512	valid
177.0ms	572×	body	256	valid
100.0ms	661×	body	128	invalid
15.0ms	113×	body	128	nan
14.0ms	10×	body	2048	valid
1.0ms	1×	body	1024	invalid
0.0ms	1×	body	256	invalid

Details

analyze2.0s

sample127.0ms

simplify308.0ms

prune15.0ms

localize22.0ms

rewrite46.0ms

series745.0ms

simplify71.0ms

prune181.0ms

localize20.0ms

rewrite45.0ms

series669.0ms

simplify68.0ms

prune118.0ms

localize20.0ms

rewrite55.0ms

series794.0ms

simplify104.0ms

prune177.0ms

localize28.0ms

rewrite17.0ms

series563.0ms

simplify61.0ms

prune64.0ms

regimes122.0ms

bsearch155.0ms

simplify3.0ms

end0.0ms

sample3.4s

Profiling