Details

sample94.0ms

Algorithm

intervals

Results

42.0ms	105×	body	1280	valid
22.0ms	25×	body	2560	valid
14.0ms	61×	body	640	valid
5.0ms	28×	body	320	valid
1.0ms	28×	body	80	valid
1.0ms	9×	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: 37.4b

Counts

2 → 1

localize14.0ms

Local error

Found 2 expressions with local error:

1.2b	(- (sin (+ x eps)) (sin x))
3.6b	(sin (+ x eps))

rewrite12.0ms

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:

7.0ms	(- (sin (+ x eps)) (sin x))
4.0ms	(sin (+ x eps))

series56.0ms

Counts

2 → 6

Calls

2 calls:

38.0ms	(- (sin (+ x eps)) (sin x))
18.0ms	(sin (+ x eps))

simplify137.0ms

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

prune87.0ms

Filtered

30 candidates to 23 candidates (76.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	22	8	30
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	23	8	31

Merged error: 16.4b

Counts

31 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (sin eps))
0.1b	(* (sin x) (cos eps))
0.1b	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
2.4b	(- (+ (* (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:

5.0ms	(* (cos x) (sin eps))
5.0ms	(* (sin x) (cos eps))
6.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
8.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

series289.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (cos x) (sin eps))
47.0ms	(* (sin x) (cos eps))
90.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
111.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

simplify39.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (33.0ms)

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

prune229.0ms

Filtered

76 candidates to 54 candidates (71.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	67	9	76
Fresh	6	1	7
Picked	1	0	1
Done	0	0	0
Total	74	10	84

Merged error: 0.3b

Counts

84 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (sin eps))
0.1b	(* (sin x) (- (cos eps) 1))
0.2b	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
1.1b	(- (cos eps) 1)

rewrite27.0ms

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:

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

series226.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (cos x) (sin eps))
45.0ms	(* (sin x) (- (cos eps) 1))
110.0ms	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
24.0ms	(- (cos eps) 1)

simplify42.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	337	548
1	1280	501
2	5002	499

prune282.0ms

Filtered

89 candidates to 58 candidates (65.2%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	77	12	89
Fresh	5	4	9
Picked	1	0	1
Done	0	0	0
Total	83	16	99

Merged error: 0.1b

Counts

99 → 16

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-log-exp`
12×	`add-sqr-sqrt`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
7×	`sum-log`
6×	`associate-r` `associate-l`
3×	`associate-+l-`
2×	`+-commutative` `neg-sub0` `associate-+r-` `flip3-+` `unsub-neg` `pow-prod-down` `neg-log` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `unswap-sqr`
1×	`associate-+l+` `sin-cos-mult`

Counts

4 → 69

Calls

4 calls:

5.0ms	(* (cos x) (sin eps))
5.0ms	(* (sin x) (cos eps))
10.0ms	(+ (+ (* (sin x) (cos eps)) (- (sin x))) (* (cos x) (sin eps)))
6.0ms	(+ (* (sin x) (cos eps)) (- (sin x)))

series261.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (cos x) (sin eps))
42.0ms	(* (sin x) (cos eps))
110.0ms	(+ (+ (* (sin x) (cos eps)) (- (sin x))) (* (cos x) (sin eps)))
61.0ms	(+ (* (sin x) (cos eps)) (- (sin x)))

simplify44.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	339	587
1	1426	530
2	5001	517

prune226.0ms

Filtered

81 candidates to 56 candidates (69.1%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	73	8	81
Fresh	9	6	15
Picked	1	0	1
Done	0	0	0
Total	83	14	97

Merged error: 0.1b

Counts

97 → 14

regimes136.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	10
1	22	10
2	22	10

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.6s	3261×	body	1280	valid
608.0ms	685×	body	2560	valid
445.0ms	1820×	body	640	valid
122.0ms	776×	body	320	valid
57.0ms	1143×	body	80	valid
33.0ms	315×	body	160	valid