Details

sample466.0ms

Algorithm

intervals

Results

134.0ms	49×	body	2560	valid
59.0ms	92×	body	1280	valid
16.0ms	63×	body	640	valid
6.0ms	30×	body	320	valid
2.0ms	16×	body	160	valid
0.0ms	6×	body	80	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune4.0ms

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: 29.1b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
0.7b	(- x (tan x))
0.7b	(- x (sin x))

rewrite42.0ms

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:

25.0ms	(/ (- x (sin x)) (- x (tan x)))
4.0ms	(- x (tan x))
7.0ms	(- x (sin x))

series175.0ms

Counts

3 → 9

Calls

3 calls:

76.0ms	(/ (- x (sin x)) (- x (tan x)))
57.0ms	(- x (tan x))
41.0ms	(- x (sin x))

simplify56.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 1 (12.0ms)

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

prune203.0ms

Filtered

119 candidates to 79 candidates (66.4%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	118	1	119
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	118	2	120

Merged error: 0b

Counts

120 → 2

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma 27/2800 (pow x 4) 1/2)
17.6b	(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)))

series128.0ms

Counts

2 → 6

Calls

2 calls:

83.0ms	(fma 27/2800 (pow x 4) 1/2)
44.0ms	(fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))

simplify146.0ms

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

prune61.0ms

Filtered

26 candidates to 20 candidates (76.9%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	26	0	26
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	26	2	28

Merged error: 0b

Counts

28 → 2

regimes40.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.2b

bsearch92.0ms

Steps

Iters	Range		Point
11	3.029362037509861e-19	14.716166499582775	0.03081552158575834
11	-2193661101726697.2	-1.4639597033977343e-08	-0.02942964392520356

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	10
1	25	10

end0.0ms

sample6.7s

Algorithm

intervals

Results

4.2s	1609×	body	2560	valid
1.6s	2775×	body	1280	valid
493.0ms	1850×	body	640	valid
160.0ms	923×	body	320	valid
58.0ms	470×	body	160	valid
28.0ms	373×	body	80	valid