Details

sample91.0ms

Algorithm

intervals

Results

47.0ms	140×	body	1280	valid
17.0ms	21×	body	2560	valid
13.0ms	65×	body	640	valid
3.0ms	19×	body	320	valid
1.0ms	9×	body	160	valid
0.0ms	2×	body	80	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	4

prune2.0ms

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: 41.7b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.7b	(- (cos (+ x eps)) (cos x))
3.9b	(cos (+ x eps))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`add-cube-cbrt` `prod-diff`
4×	`add-log-exp`
3×	`fma-neg`
2×	`pow1` `add-exp-log` `expm1-log1p-u` `cos-sum` `add-cbrt-cube` `log1p-expm1-u`
1×	`associate--l-` `sub-neg` `flip3--` `diff-log` `flip--` `diff-cos` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 40

Calls

2 calls:

7.0ms	(- (cos (+ x eps)) (cos x))
4.0ms	(cos (+ x eps))

series74.0ms

Counts

2 → 6

Calls

2 calls:

58.0ms	(- (cos (+ x eps)) (cos x))
16.0ms	(cos (+ x eps))

simplify76.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 3 (71.0ms)

Iter	Nodes	Cost
0	192	385
1	523	285
2	2519	275
3	5001	220

prune115.0ms

Filtered

46 candidates to 31 candidates (67.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	34	12	46
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	35	12	47

Merged error: 14.7b

Counts

47 → 12

localize14.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (cos x) (cos eps))
0.1b	(fma (sin x) (sin eps) (cos x))
2.2b	(- (* (cos x) (cos eps)) (fma (sin x) (sin eps) (cos x)))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`add-cube-cbrt` `*-un-lft-identity`
5×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`expm1-log1p-u` `associate-r` `associate-l` `prod-diff` `log1p-expm1-u`
2×	`fma-udef`
1×	`sub-neg` `flip3--` `fma-neg` `diff-log` `pow-prod-down` `prod-exp` `cos-mult` `*-commutative` `flip--` `cbrt-unprod` `associate--r+` `unswap-sqr`

Counts

3 → 50

Calls

3 calls:

4.0ms	(* (cos x) (cos eps))
1.0ms	(fma (sin x) (sin eps) (cos x))
5.0ms	(- (* (cos x) (cos eps)) (fma (sin x) (sin eps) (cos x)))

series233.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(* (cos x) (cos eps))
58.0ms	(fma (sin x) (sin eps) (cos x))
135.0ms	(- (* (cos x) (cos eps)) (fma (sin x) (sin eps) (cos x)))

simplify120.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 3 (110.0ms)

Iter	Nodes	Cost
0	235	486
1	832	409
2	4494	406
3	5001	404

prune213.0ms

Filtered

59 candidates to 43 candidates (72.9%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	44	15	59
Fresh	5	6	11
Picked	1	0	1
Done	0	0	0
Total	50	21	71

Merged error: 14.5b

Counts

71 → 21

localize14.0ms

Local error

Found 2 expressions with local error:

0.1b	(fma (sin x) (sin eps) (cos x))
2.2b	(fma (cos x) (cos eps) (- (fma (sin x) (sin eps) (cos x))))

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 (sin x) (sin eps) (cos x))
1.0ms	(fma (cos x) (cos eps) (- (fma (sin x) (sin eps) (cos x))))

series189.0ms

Counts

2 → 6

Calls

2 calls:

56.0ms	(fma (sin x) (sin eps) (cos x))
133.0ms	(fma (cos x) (cos eps) (- (fma (sin x) (sin eps) (cos x))))

simplify120.0ms

Algorithm

egg-herbie

Counts

26 → 26

Iterations

Useful iterations: 3 (28.0ms)

Iter	Nodes	Cost
0	93	210
1	259	183
2	932	182
3	4040	180
4	5001	180

prune131.0ms

Filtered

26 candidates to 22 candidates (84.6%)

Pruning

21 alts after pruning (20 fresh and 1 done)

	Pruned	Kept	Total
New	24	2	26
Fresh	2	18	20
Picked	0	1	1
Done	0	0	0
Total	26	21	47

Merged error: 14.5b

Counts

47 → 21

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (cos eps))
0.1b	(+ (* (sin x) (sin eps)) (cos x))
0.2b	(* (sin x) (sin eps))
2.2b	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
11×	`add-log-exp`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`prod-diff` `cos-mult`
2×	`flip3-+` `diff-log` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `frac-sub` `cbrt-unprod` `flip-+` `unswap-sqr`
1×	`+-commutative` `sub-neg` `flip3--` `fma-def` `fma-neg` `flip--` `sin-mult` `associate--r+`

Counts

4 → 78

Calls

4 calls:

4.0ms	(* (cos x) (cos eps))
6.0ms	(+ (* (sin x) (sin eps)) (cos x))
5.0ms	(* (sin x) (sin eps))
10.0ms	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

series278.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* (cos x) (cos eps))
56.0ms	(+ (* (sin x) (sin eps)) (cos x))
46.0ms	(* (sin x) (sin eps))
135.0ms	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

simplify56.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	389	759
1	1561	655
2	5001	644

prune200.0ms

Filtered

90 candidates to 66 candidates (73.3%)

Pruning

20 alts after pruning (18 fresh and 2 done)

	Pruned	Kept	Total
New	88	2	90
Fresh	3	16	19
Picked	0	1	1
Done	0	1	1
Total	91	20	111

Merged error: 14.5b

Counts

111 → 20

regimes211.0ms

Accuracy

84.7% (1.6b remaining)

Error of 15.7b against oracle of 14.1b and baseline of 24.4b

bsearch97.0ms

Steps

Iters	Range		Point
10	8.485467515044765e-21	4.846798205843289e-11	4.8007364015852064e-11
6	-3.029806383639767e-11	-2.792984742033529e-12	-2.950098860365708e-11

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	23
1	30	23

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.5s	4350×	body	1280	valid
519.0ms	620×	body	2560	valid
427.0ms	1939×	body	640	valid
106.0ms	708×	body	320	valid
29.0ms	292×	body	160	valid
5.0ms	91×	body	80	valid