Details

sample91.0ms

Algorithm

intervals

Results

51.0ms	147×	body	1280	valid
15.0ms	18×	body	2560	valid
12.0ms	55×	body	640	valid
3.0ms	23×	body	320	valid
1.0ms	9×	body	160	valid
0.0ms	4×	body	80	valid

simplify10.0ms

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: 39.4b

Counts

2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

2.5b	(- (cos (+ x eps)) (cos x))
4.4b	(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))

series73.0ms

Counts

2 → 6

Calls

2 calls:

56.0ms	(- (cos (+ x eps)) (cos x))
17.0ms	(cos (+ x eps))

simplify108.0ms

Algorithm

egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 2 (10.0ms)

Iter	Nodes	Cost
0	134	187
1	274	178
2	810	175
3	2813	175
4	5001	175

prune80.0ms

Filtered

32 candidates to 24 candidates (75.0%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	20	12	32
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	21	12	33

Merged error: 13.1b

Counts

33 → 12

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos eps) (cos x))
0.1b	(+ (* (sin eps) (sin x)) (cos x))
0.2b	(* (sin eps) (sin x))
3.9b	(- (* (cos eps) (cos x)) (+ (* (sin eps) (sin x)) (cos x)))

rewrite44.0ms

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:

7.0ms	(* (cos eps) (cos x))
10.0ms	(+ (* (sin eps) (sin x)) (cos x))
5.0ms	(* (sin eps) (sin x))
20.0ms	(- (* (cos eps) (cos x)) (+ (* (sin eps) (sin x)) (cos x)))

series299.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (cos eps) (cos x))
65.0ms	(+ (* (sin eps) (sin x)) (cos x))
50.0ms	(* (sin eps) (sin x))
142.0ms	(- (* (cos eps) (cos x)) (+ (* (sin eps) (sin x)) (cos x)))

simplify44.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	337	721
1	1268	690
2	5002	682

prune207.0ms

Filtered

88 candidates to 60 candidates (68.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	78	10	88
Fresh	10	1	11
Picked	1	0	1
Done	0	0	0
Total	89	11	100

Merged error: 0.2b

Counts

100 → 11

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (- (* (cos eps) (cos x)) (cos x)) (* (sin eps) (sin x)))
0.1b	(* (cos eps) (cos x))
0.2b	(* (sin eps) (sin x))
3.1b	(- (* (cos eps) (cos x)) (cos x))

rewrite44.0ms

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:

22.0ms	(- (- (* (cos eps) (cos x)) (cos x)) (* (sin eps) (sin x)))
5.0ms	(* (cos eps) (cos x))
5.0ms	(* (sin eps) (sin x))
10.0ms	(- (* (cos eps) (cos x)) (cos x))

series324.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(- (- (* (cos eps) (cos x)) (cos x)) (* (sin eps) (sin x)))
43.0ms	(* (cos eps) (cos x))
51.0ms	(* (sin eps) (sin x))
81.0ms	(- (* (cos eps) (cos x)) (cos x))

simplify42.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	322	775
1	1107	736
2	5001	719

prune240.0ms

Filtered

96 candidates to 62 candidates (64.6%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	81	15	96
Fresh	6	4	10
Picked	1	0	1
Done	0	0	0
Total	88	19	107

Merged error: 0.1b

Counts

107 → 19

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos x) (- (cos eps) 1)) (* (sin eps) (sin x)))
0.1b	(* (cos x) (- (cos eps) 1))
0.2b	(* (sin eps) (sin x))
3.0b	(- (cos eps) 1)

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 89

Calls

4 calls:

22.0ms	(- (* (cos x) (- (cos eps) 1)) (* (sin eps) (sin x)))
9.0ms	(* (cos x) (- (cos eps) 1))
5.0ms	(* (sin eps) (sin x))
5.0ms	(- (cos eps) 1)

series280.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(- (* (cos x) (- (cos eps) 1)) (* (sin eps) (sin x)))
73.0ms	(* (cos x) (- (cos eps) 1))
51.0ms	(* (sin eps) (sin x))
20.0ms	(- (cos eps) 1)

simplify46.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	349	734
1	1299	686
2	5002	679

prune200.0ms

Filtered

101 candidates to 64 candidates (63.4%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	94	7	101
Fresh	12	6	18
Picked	0	1	1
Done	0	0	0
Total	106	14	120

Merged error: 0.0b

Counts

120 → 14

regimes117.0ms

Accuracy

0% (0.6b remaining)

Error of 0.6b against oracle of 0.1b and baseline of 0.6b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	13
1	30	13
2	31	13
3	31	13

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.6s	4494×	body	1280	valid
518.0ms	603×	body	2560	valid
412.0ms	1876×	body	640	valid
113.0ms	669×	body	320	valid
28.0ms	276×	body	160	valid
5.0ms	82×	body	80	valid