Details

sample93.0ms

Algorithm

intervals

Results

46.0ms	135×	body	1280	valid
21.0ms	25×	body	2560	valid
13.0ms	63×	body	640	valid
4.0ms	26×	body	320	valid
1.0ms	6×	body	160	valid
0.0ms	1×	body	80	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 39.0b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.9b	(- (cos (+ x eps)) (cos x))
3.5b	(cos (+ x eps))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `cos-sum` `*-un-lft-identity` `add-log-exp`
2×	`pow1` `add-exp-log` `+-commutative` `associate--l-` `add-cube-cbrt` `add-cbrt-cube`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `diff-cos` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 26

Calls

2 calls:

7.0ms	(- (cos (+ x eps)) (cos x))
5.0ms	(cos (+ x eps))

series76.0ms

Counts

2 → 6

Calls

2 calls:

59.0ms	(- (cos (+ x eps)) (cos x))
16.0ms	(cos (+ x eps))

simplify116.0ms

Algorithm

egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 2 (11.0ms)

Iter	Nodes	Cost
0	136	187
1	283	178
2	842	175
3	2960	175
4	5002	175

prune102.0ms

Filtered

32 candidates to 24 candidates (75.0%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	19	13	32
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	20	13	33

Merged error: 16.3b

Counts

33 → 13

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))
2.1b	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

30×	`*-un-lft-identity`
26×	`add-sqr-sqrt`
14×	`associate-l`
13×	`distribute-lft-out--`
11×	`add-log-exp`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
6×	`associate-r` `unswap-sqr`
5×	`difference-of-squares`
4×	`diff-log`
3×	`sub-neg` `cos-mult` `sin-mult`
2×	`flip3--` `pow-prod-down` `prod-exp` `associate--l+` `*-commutative` `flip--` `cbrt-unprod`
1×	`associate--l-` `frac-sub` `sub-div`

Counts

4 → 82

Calls

4 calls:

5.0ms	(* (cos x) (cos eps))
17.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
5.0ms	(* (sin x) (sin eps))
22.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

series311.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (cos x) (cos eps))
86.0ms	(- (* (cos x) (cos eps)) (* (sin x) (sin eps)))
45.0ms	(* (sin x) (sin eps))
134.0ms	(- (- (* (cos x) (cos eps)) (* (sin x) (sin eps))) (cos x))

simplify119.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	322	776
1	1089	745
2	4515	727
3	5001	727

prune266.0ms

Filtered

94 candidates to 62 candidates (66.0%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	81	13	94
Fresh	10	2	12
Picked	1	0	1
Done	0	0	0
Total	92	15	107

Merged error: 16.2b

Counts

107 → 15

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos eps) (cos x))
0.1b	(+ (* (sin x) (sin eps)) (cos x))
0.2b	(* (sin x) (sin eps))
2.1b	(- (* (cos eps) (cos x)) (+ (* (sin x) (sin eps)) (cos x)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

4.0ms	(* (cos eps) (cos x))
10.0ms	(+ (* (sin x) (sin eps)) (cos x))
5.0ms	(* (sin x) (sin eps))
23.0ms	(- (* (cos eps) (cos x)) (+ (* (sin x) (sin eps)) (cos x)))

series283.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (cos eps) (cos x))
51.0ms	(+ (* (sin x) (sin eps)) (cos x))
51.0ms	(* (sin x) (sin eps))
137.0ms	(- (* (cos eps) (cos x)) (+ (* (sin x) (sin eps)) (cos x)))

simplify44.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	340	721
1	1260	690
2	5001	682

prune245.0ms

Filtered

88 candidates to 58 candidates (65.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	83	5	88
Fresh	7	7	14
Picked	1	0	1
Done	0	0	0
Total	91	12	103

Merged error: 0.3b

Counts

103 → 12

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos eps) (cos x))
0.1b	(- (- (* (cos eps) (cos x)) (cos x)) (* (sin x) (sin eps)))
0.2b	(* (sin x) (sin eps))
1.2b	(- (* (cos eps) (cos x)) (cos x))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

31×	`*-un-lft-identity`
24×	`add-sqr-sqrt`
12×	`associate-l` `distribute-lft-out--`
11×	`add-log-exp`
10×	`add-cube-cbrt`
9×	`associate-r`
8×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`distribute-rgt-out--` `diff-log` `difference-of-squares` `unswap-sqr`
3×	`sub-neg` `flip3--` `flip--` `sin-mult`
2×	`pow-prod-down` `prod-exp` `associate--l+` `*-commutative` `frac-sub` `cbrt-unprod`
1×	`associate--l-` `cos-mult`

Counts

4 → 84

Calls

4 calls:

8.0ms	(* (cos eps) (cos x))
21.0ms	(- (- (* (cos eps) (cos x)) (cos x)) (* (sin x) (sin eps)))
5.0ms	(* (sin x) (sin eps))
10.0ms	(- (* (cos eps) (cos x)) (cos x))

series307.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (cos eps) (cos x))
136.0ms	(- (- (* (cos eps) (cos x)) (cos x)) (* (sin x) (sin eps)))
51.0ms	(* (sin x) (sin eps))
75.0ms	(- (* (cos eps) (cos x)) (cos x))

simplify41.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	330	775
1	1140	736
2	5001	720

prune238.0ms

Filtered

96 candidates to 65 candidates (67.7%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	83	13	96
Fresh	7	4	11
Picked	1	0	1
Done	0	0	0
Total	91	17	108

Merged error: 0.2b

Counts

108 → 17

regimes177.0ms

Accuracy

90.7% (0.6b remaining)

Error of 0.8b against oracle of 0.2b and baseline of 6.5b

bsearch136.0ms

Steps

Iters	Range		Point
10	7.157538394725048e-05	10451050.785873119	7.268025054873702e-05
10	-1.2252616440760547e-11	-5.2655362403227905e-23	-1.2118697881203442e-11

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	14
1	30	14

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.5s	4435×	body	1280	valid
600.0ms	685×	body	2560	valid
558.0ms	1834×	body	640	valid
99.0ms	704×	body	320	valid
28.0ms	268×	body	160	valid
4.0ms	74×	body	80	valid