Details

sample90.0ms

Algorithm

intervals

Results

43.0ms	135×	body	1280	valid
21.0ms	25×	body	2560	valid
13.0ms	63×	body	640	valid
3.0ms	24×	body	320	valid
1.0ms	7×	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: 39.8b

Counts

2 → 1

localize14.0ms

Local error

Found 2 expressions with local error:

0.9b	(- (cos (+ x eps)) (cos x))
4.6b	(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))
5.0ms	(cos (+ x eps))

series65.0ms

Counts

2 → 6

Calls

2 calls:

50.0ms	(- (cos (+ x eps)) (cos x))
15.0ms	(cos (+ x eps))

simplify75.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 3 (70.0ms)

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

prune122.0ms

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: 13.9b

Counts

47 → 13

localize13.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (cos x) (cos eps))
0.1b	(fma (sin x) (sin eps) (cos x))
1.8b	(- (* (cos x) (cos eps)) (fma (sin x) (sin eps) (cos x)))

rewrite14.0ms

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)))

series228.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(* (cos x) (cos eps))
57.0ms	(fma (sin x) (sin eps) (cos x))
131.0ms	(- (* (cos x) (cos eps)) (fma (sin x) (sin eps) (cos x)))

simplify117.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 3 (111.0ms)

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

prune205.0ms

Filtered

59 candidates to 43 candidates (72.9%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	49	10	59
Fresh	6	6	12
Picked	1	0	1
Done	0	0	0
Total	56	16	72

Merged error: 13.8b

Counts

72 → 16

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))
1.8b	(- (* (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))
5.0ms	(+ (* (sin x) (sin eps)) (cos x))
5.0ms	(* (sin x) (sin eps))
10.0ms	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

series280.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (cos x) (cos eps))
56.0ms	(+ (* (sin x) (sin eps)) (cos x))
45.0ms	(* (sin x) (sin eps))
134.0ms	(- (* (cos x) (cos eps)) (+ (* (sin x) (sin eps)) (cos x)))

simplify52.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 2 (44.0ms)

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

prune253.0ms

Filtered

90 candidates to 64 candidates (71.1%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	85	5	90
Fresh	4	11	15
Picked	1	0	1
Done	0	0	0
Total	90	16	106

Merged error: 13.7b

Counts

106 → 16

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (sin x) (sin eps) (cos x))
0.2b	(expm1 (log1p (* (cos x) (cos eps))))
0.4b	(log1p (* (cos x) (cos eps)))
18.7b	(- (expm1 (log1p (* (cos x) (cos eps)))) (fma (sin x) (sin eps) (cos x)))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 62

Calls

4 calls:

1.0ms	(fma (sin x) (sin eps) (cos x))
1.0ms	(expm1 (log1p (* (cos x) (cos eps))))
1.0ms	(log1p (* (cos x) (cos eps)))
8.0ms	(- (expm1 (log1p (* (cos x) (cos eps)))) (fma (sin x) (sin eps) (cos x)))

series371.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(fma (sin x) (sin eps) (cos x))
73.0ms	(expm1 (log1p (* (cos x) (cos eps))))
71.0ms	(log1p (* (cos x) (cos eps)))
170.0ms	(- (expm1 (log1p (* (cos x) (cos eps)))) (fma (sin x) (sin eps) (cos x)))

simplify115.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 3 (107.0ms)

Iter	Nodes	Cost
0	227	893
1	727	654
2	4069	605
3	5001	602

prune181.0ms

Filtered

74 candidates to 50 candidates (67.6%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	72	2	74
Fresh	0	15	15
Picked	0	1	1
Done	0	0	0
Total	72	18	90

Merged error: 13.7b

Counts

90 → 18

regimes200.0ms

Accuracy

84.1% (1.6b remaining)

Error of 16.0b against oracle of 14.4b and baseline of 24.6b

bsearch123.0ms

Steps

Iters	Range		Point
9	2.5055192714849007e-19	1.2000045585397406e-10	1.100010266646646e-10
10	-3.0624602319297156e-13	-7.300870368480786e-24	-3.0233319669493137e-13

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	27
1	37	27

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.5s	4499×	body	1280	valid
515.0ms	614×	body	2560	valid
382.0ms	1853×	body	640	valid
101.0ms	683×	body	320	valid
25.0ms	263×	body	160	valid
4.0ms	88×	body	80	valid