Details

sample437.0ms

Algorithm

intervals

Results

110.0ms	51×	body	2560	valid
54.0ms	86×	body	1280	valid
15.0ms	58×	body	640	valid
4.0ms	25×	body	320	valid
3.0ms	22×	body	160	valid
1.0ms	14×	body	80	valid

simplify13.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	13	5
1	17	5
2	19	5
3	19	5

prune5.0ms

Filtered

1 candidates to 0 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: 32.3b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.4b	(- x (tan x))
1.4b	(- x (sin x))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

57×	`add-sqr-sqrt` `*-un-lft-identity`
29×	`add-cube-cbrt`
25×	`times-frac`
18×	`prod-diff`
14×	`distribute-lft-out--` `difference-of-squares`
7×	`add-log-exp`
6×	`fma-neg`
5×	`add-exp-log` `associate-/r` `add-cbrt-cube` `associate-/l`
4×	`flip3--` `flip--`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

3 → 110

Calls

3 calls:

9.0ms	(/ (- x (sin x)) (- x (tan x)))
4.0ms	(- x (tan x))
7.0ms	(- x (sin x))

series177.0ms

Counts

3 → 9

Calls

3 calls:

76.0ms	(/ (- x (sin x)) (- x (tan x)))
59.0ms	(- x (tan x))
42.0ms	(- x (sin x))

simplify57.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	472	1059
1	1737	854
2	5001	854

prune215.0ms

Filtered

119 candidates to 79 candidates (66.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	117	2	119
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	117	3	120

Merged error: 0.0b

Counts

120 → 3

localize11.0ms

Local error

Found 2 expressions with local error:

0.3b	(fma 27/2800 (pow x 4) 1/2)
13.6b	(fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

2×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

2 → 20

Calls

2 calls:

1.0ms	(fma 27/2800 (pow x 4) 1/2)
1.0ms	(fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))

series130.0ms

Counts

2 → 6

Calls

2 calls:

84.0ms	(fma 27/2800 (pow x 4) 1/2)
45.0ms	(fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))

simplify149.0ms

Algorithm

egg-herbie

Counts

26 → 26

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	51	133
1	162	117
2	626	117
3	3552	117
4	5001	117

prune57.0ms

Filtered

26 candidates to 20 candidates (76.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	26	0	26
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	26	3	29

Merged error: 0.0b

Counts

29 → 3

localize15.0ms

Local error

Found 4 expressions with local error:

1.4b	(- x (tan x))
1.4b	(- x (sin x))
1.4b	(- x (sin x))
1.4b	(- x (sin x))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt` `*-un-lft-identity`
36×	`prod-diff`
32×	`add-cube-cbrt`
12×	`fma-neg` `add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 112

Calls

4 calls:

4.0ms	(- x (tan x))
4.0ms	(- x (sin x))
4.0ms	(- x (sin x))
5.0ms	(- x (sin x))

series147.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(- x (tan x))
30.0ms	(- x (sin x))
34.0ms	(- x (sin x))
31.0ms	(- x (sin x))

simplify97.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 3 (88.0ms)

Iter	Nodes	Cost
0	258	969
1	749	605
2	3295	569
3	5001	401

prune222.0ms

Filtered

124 candidates to 73 candidates (58.9%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	124	0	124
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	124	3	127

Merged error: 0.0b

Counts

127 → 3

regimes48.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.9b

bsearch80.0ms

Steps

Iters	Range		Point
9	2.1846438371975785e-05	719.5386143167987	0.027312182699548947
10	-43540924890.08803	-0.0051836583041924315	-0.029125160038493098

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	10
1	25	10

end0.0ms

sample6.3s

Algorithm

intervals

Results

3.7s	1551×	body	2560	valid
1.7s	2869×	body	1280	valid
491.0ms	1852×	body	640	valid
157.0ms	919×	body	320	valid
58.0ms	471×	body	160	valid
30.0ms	338×	body	80	valid