Details

sample91.0ms

Algorithm

intervals

Results

46.0ms	103×	body	1280	valid
16.0ms	68×	body	640	valid
14.0ms	17×	body	2560	valid
3.0ms	18×	body	320	valid
2.0ms	39×	body	80	valid
1.0ms	11×	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 (100.0%)

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: 37.9b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

1.9b	(- (sin (+ x eps)) (sin x))
2.3b	(sin (+ x eps))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 26

Calls

2 calls:

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

series65.0ms

Counts

2 → 6

Calls

2 calls:

46.0ms	(- (sin (+ x eps)) (sin x))
19.0ms	(sin (+ x eps))

simplify137.0ms

Algorithm

egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 2 (10.0ms)

Iter	Nodes	Cost
0	133	186
1	298	177
2	920	175
3	3386	175
4	5001	175

prune62.0ms

Filtered

32 candidates to 25 candidates (21.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	29	3	32
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	30	3	33

Merged error: 0.4b

Counts

33 → 3

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin eps) (cos x))
0.1b	(* (cos eps) (sin x))
0.2b	(+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x)))
1.7b	(- (* (cos eps) (sin x)) (sin x))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 80

Calls

4 calls:

7.0ms	(* (sin eps) (cos x))
4.0ms	(* (cos eps) (sin x))
19.0ms	(+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x)))
9.0ms	(- (* (cos eps) (sin x)) (sin x))

series275.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (sin eps) (cos x))
43.0ms	(* (cos eps) (sin x))
123.0ms	(+ (* (sin eps) (cos x)) (- (* (cos eps) (sin x)) (sin x)))
62.0ms	(- (* (cos eps) (sin x)) (sin x))

simplify42.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	353	723
1	1239	687
2	5001	670

prune221.0ms

Filtered

92 candidates to 62 candidates (32.6%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	76	16	92
Fresh	2	0	2
Picked	1	0	1
Done	0	0	0
Total	79	16	95

Merged error: 0.3b

Counts

95 → 16

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin x) (- (cos eps) 1))
0.1b	(* (sin eps) (cos x))
0.2b	(+ (* (sin eps) (cos x)) (* (sin x) (- (cos eps) 1)))
1.6b	(- (cos eps) 1)

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 84

Calls

4 calls:

7.0ms	(* (sin x) (- (cos eps) 1))
4.0ms	(* (sin eps) (cos x))
22.0ms	(+ (* (sin eps) (cos x)) (* (sin x) (- (cos eps) 1)))
4.0ms	(- (cos eps) 1)

series234.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* (sin x) (- (cos eps) 1))
47.0ms	(* (sin eps) (cos x))
117.0ms	(+ (* (sin eps) (cos x)) (* (sin x) (- (cos eps) 1)))
19.0ms	(- (cos eps) 1)

simplify49.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	376	633
1	1544	590
2	5001	587

prune219.0ms

Filtered

96 candidates to 62 candidates (35.4%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	87	9	96
Fresh	10	5	15
Picked	1	0	1
Done	0	0	0
Total	98	14	112

Merged error: 0.1b

Counts

112 → 14

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cbrt (- (cos eps) 1)) (cbrt (- (cos eps) 1)))
1.6b	(- (cos eps) 1)
1.6b	(- (cos eps) 1)
1.6b	(- (cos eps) 1)

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-sqr-sqrt`
41×	`*-un-lft-identity`
40×	`cbrt-prod`
16×	`difference-of-squares`
14×	`swap-sqr`
12×	`add-cube-cbrt` `cbrt-div`
11×	`pow1`
10×	`associate-r` `associate-l` `add-log-exp`
9×	`flip3--` `difference-of-sqr-1` `flip--` `distribute-lft-out--`
8×	`add-cbrt-cube`
6×	`add-exp-log` `pow1/3`
4×	`frac-times` `cbrt-unprod` `unswap-sqr`
3×	`sub-neg` `diff-log`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative`

Counts

4 → 115

Calls

4 calls:

12.0ms	(* (cbrt (- (cos eps) 1)) (cbrt (- (cos eps) 1)))
4.0ms	(- (cos eps) 1)
4.0ms	(- (cos eps) 1)
4.0ms	(- (cos eps) 1)

series204.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(* (cbrt (- (cos eps) 1)) (cbrt (- (cos eps) 1)))
19.0ms	(- (cos eps) 1)
19.0ms	(- (cos eps) 1)
23.0ms	(- (cos eps) 1)

simplify126.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 3 (115.0ms)

Iter	Nodes	Cost
0	248	976
1	874	892
2	4101	814
3	5002	797

prune288.0ms

Filtered

127 candidates to 72 candidates (43.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	125	2	127
Fresh	2	11	13
Picked	1	0	1
Done	0	0	0
Total	128	13	141

Merged error: 0.1b

Counts

141 → 13

regimes118.0ms

Accuracy

0% (0.5b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	28
1	40	28
2	40	28

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.6s	3305×	body	1280	valid
531.0ms	610×	body	2560	valid
457.0ms	1850×	body	640	valid
118.0ms	758×	body	320	valid
70.0ms	1102×	body	80	valid
39.0ms	375×	body	160	valid