Details

sample92.0ms

Algorithm

intervals

Results

51.0ms	151×	body	1280	valid
16.0ms	54×	body	640	valid
12.0ms	14×	body	2560	valid
3.0ms	23×	body	320	valid
1.0ms	12×	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: 38.7b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

1.4b	(- (cos (+ x eps)) (cos x))
2.8b	(cos (+ x eps))

rewrite12.0ms

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))

series70.0ms

Counts

2 → 6

Calls

2 calls:

55.0ms	(- (cos (+ x eps)) (cos x))
15.0ms	(cos (+ x eps))

simplify72.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 3 (67.0ms)

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

prune110.0ms

Filtered

46 candidates to 31 candidates (67.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	33	13	46
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	34	13	47

Merged error: 14.3b

Counts

47 → 13

localize17.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (cos x) (cos eps))
0.1b	(fma (sin x) (sin eps) (cos x))
2.3b	(- (* (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)))

series219.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(* (cos x) (cos eps))
55.0ms	(fma (sin x) (sin eps) (cos x))
127.0ms	(- (* (cos x) (cos eps)) (fma (sin x) (sin eps) (cos x)))

simplify112.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 3 (107.0ms)

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

prune204.0ms

Filtered

59 candidates to 43 candidates (72.9%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	48	11	59
Fresh	5	7	12
Picked	1	0	1
Done	0	0	0
Total	54	18	72

Merged error: 14.2b

Counts

72 → 18

localize18.0ms

Local error

Found 2 expressions with local error:

0.1b	(fma (sin x) (sin eps) (cos x))
2.3b	(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))))

series183.0ms

Counts

2 → 6

Calls

2 calls:

54.0ms	(fma (sin x) (sin eps) (cos x))
129.0ms	(fma (cos x) (cos eps) (- (fma (sin x) (sin eps) (cos x))))

simplify118.0ms

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

prune129.0ms

Filtered

26 candidates to 23 candidates (88.5%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	25	1	26
Fresh	1	16	17
Picked	0	1	1
Done	0	0	0
Total	26	18	44

Merged error: 14.1b

Counts

44 → 18

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (cos eps))
0.1b	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
0.2b	(* (sin x) (sin eps))
2.3b	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
15×	`add-cube-cbrt`
11×	`prod-diff` `add-log-exp`
8×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `fma-neg` `diff-log` `log1p-expm1-u`
3×	`sub-neg` `associate--l+` `cos-mult` `sin-mult`
2×	`flip3--` `pow-prod-down` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `unswap-sqr`
1×	`associate--l-` `frac-sub` `distribute-lft-out--` `sub-div` `difference-of-squares`

Counts

4 → 93

Calls

4 calls:

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

series298.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(* (cos x) (cos eps))
84.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
49.0ms	(* (sin x) (sin eps))
126.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify49.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	381	988
1	1342	837
2	5002	822

prune240.0ms

Filtered

105 candidates to 74 candidates (70.5%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	98	7	105
Fresh	2	14	16
Picked	1	0	1
Done	1	0	1
Total	102	21	123

Merged error: 14.1b

Counts

123 → 21

regimes214.0ms

Accuracy

83.4% (1.6b remaining)

Error of 16.3b against oracle of 14.6b and baseline of 24.5b

bsearch113.0ms

Steps

Iters	Range		Point
8	1.3803315812694795e-08	1.8094954886202674e-05	1.6985852405271936e-07
8	-1.2056568586554778e-13	-1.4903061489544405e-16	-1.184078211908822e-13

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	44
1	40	44

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.6s	4486×	body	1280	valid
553.0ms	634×	body	2560	valid
414.0ms	1841×	body	640	valid
110.0ms	671×	body	320	valid
36.0ms	299×	body	160	valid
4.0ms	69×	body	80	valid