Details

sample100.0ms

Algorithm

intervals

Results

43.0ms	106×	body	1280	valid
28.0ms	26×	body	2560	valid
12.0ms	50×	body	640	valid
5.0ms	27×	body	320	valid
2.0ms	34×	body	80	valid
1.0ms	13×	body	160	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: 36.9b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

1.4b	(- (sin (+ x eps)) (sin x))
4.7b	(sin (+ x eps))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 24

Calls

2 calls:

6.0ms	(- (sin (+ x eps)) (sin x))
4.0ms	(sin (+ x eps))

series61.0ms

Counts

2 → 6

Calls

2 calls:

43.0ms	(- (sin (+ x eps)) (sin x))
18.0ms	(sin (+ x eps))

simplify139.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 2 (10.0ms)

Iter	Nodes	Cost
0	133	175
1	301	166
2	937	164
3	3445	164
4	5001	164

prune272.0ms

Filtered

30 candidates to 23 candidates (76.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	23	7	30
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	24	7	31

Merged error: 14.7b

Counts

31 → 7

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 64

Calls

4 calls:

6.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
5.0ms	(* (cos x) (sin eps))
5.0ms	(* (sin x) (cos eps))
9.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

series284.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
42.0ms	(* (cos x) (sin eps))
46.0ms	(* (sin x) (cos eps))
110.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

simplify43.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	308	589
1	1168	555
2	5001	543

prune211.0ms

Filtered

76 candidates to 54 candidates (71.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	65	11	76
Fresh	5	1	6
Picked	1	0	1
Done	0	0	0
Total	71	12	83

Merged error: 0.2b

Counts

83 → 12

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
0.1b	(* (sin x) (- (cos eps) 1))
0.1b	(* (cos x) (sin eps))
1.7b	(- (cos eps) 1)

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 77

Calls

4 calls:

9.0ms	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
8.0ms	(* (sin x) (- (cos eps) 1))
5.0ms	(* (cos x) (sin eps))
4.0ms	(- (cos eps) 1)

series215.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
44.0ms	(* (sin x) (- (cos eps) 1))
46.0ms	(* (cos x) (sin eps))
19.0ms	(- (cos eps) 1)

simplify48.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	337	548
1	1280	501
2	5001	499

prune211.0ms

Filtered

89 candidates to 55 candidates (61.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	80	9	89
Fresh	8	3	11
Picked	1	0	1
Done	0	0	0
Total	89	12	101

Merged error: 0.0b

Counts

101 → 12

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (- (cos eps) 1))
0.1b	(* (cos x) (sin eps))
1.7b	(- (cos eps) 1)
1.7b	(log (exp (- (cos eps) 1)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
18×	`*-un-lft-identity`
14×	`exp-prod`
9×	`add-cube-cbrt` `add-log-exp`
8×	`log-pow`
7×	`pow1`
6×	`add-exp-log` `add-cbrt-cube` `difference-of-squares`
5×	`log-prod`
4×	`exp-sum`
3×	`sub-neg` `difference-of-sqr-1` `associate-r` `associate-l` `distribute-lft-out--`
2×	`exp-diff` `diff-log` `rem-exp-log`
1×	`log-div` `flip3--` `rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `unswap-sqr`

Counts

4 → 75

Calls

4 calls:

5.0ms	(exp (- (cos eps) 1))
4.0ms	(* (cos x) (sin eps))
4.0ms	(- (cos eps) 1)
5.0ms	(log (exp (- (cos eps) 1)))

series127.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(exp (- (cos eps) 1))
42.0ms	(* (cos x) (sin eps))
21.0ms	(- (cos eps) 1)
19.0ms	(log (exp (- (cos eps) 1)))

simplify92.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 2 (23.0ms)

Iter	Nodes	Cost
0	228	371
1	753	325
2	2804	324
3	5001	324

prune198.0ms

Filtered

87 candidates to 57 candidates (65.5%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	87	0	87
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	87	12	99

Merged error: 0.0b

Counts

99 → 12

regimes104.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	10
1	18	10

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.4s	3317×	body	1280	valid
559.0ms	603×	body	2560	valid
464.0ms	1839×	body	640	valid
128.0ms	768×	body	320	valid
58.0ms	1107×	body	80	valid
41.0ms	366×	body	160	valid