Details

sample85.0ms

Algorithm

intervals

Results

42.0ms	105×	body	1280	valid
15.0ms	61×	body	640	valid
11.0ms	13×	body	2560	valid
4.0ms	24×	body	320	valid
2.0ms	40×	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.1b

localize8.0ms

Local error

Found 2 expressions with local error:

1.3b	(- (sin (+ x eps)) (sin x))
4.3b	(sin (+ x eps))

rewrite26.0ms

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:

21.0ms	(- (sin (+ x eps)) (sin x))
4.0ms	(sin (+ x eps))

series62.0ms

Counts

2 → 6

Calls

2 calls:

38.0ms	(- (sin (+ x eps)) (sin x))
24.0ms	(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

prune81.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 12.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos x) (sin eps)) (sin x))
0.1b	(* (sin x) (cos eps))
0.2b	(* (cos x) (sin eps))
3.2b	(+ (* (sin x) (cos eps)) (- (* (cos x) (sin eps)) (sin x)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 66

Calls

4 calls:

4.0ms	(- (* (cos x) (sin eps)) (sin x))
4.0ms	(* (sin x) (cos eps))
4.0ms	(* (cos x) (sin eps))
11.0ms	(+ (* (sin x) (cos eps)) (- (* (cos x) (sin eps)) (sin x)))

series255.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(- (* (cos x) (sin eps)) (sin x))
42.0ms	(* (sin x) (cos eps))
45.0ms	(* (cos x) (sin eps))
107.0ms	(+ (* (sin x) (cos eps)) (- (* (cos x) (sin eps)) (sin x)))

simplify43.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	348	614
1	1352	581
2	5002	565

prune229.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
0.2b	(* (cos x) (sin eps))
0.2b	(* (sin x) (- (cos eps) 1))
2.5b	(- (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:

7.0ms	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
4.0ms	(* (cos x) (sin eps))
12.0ms	(* (sin x) (- (cos eps) 1))
3.0ms	(- (cos eps) 1)

series218.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
44.0ms	(* (cos x) (sin eps))
45.0ms	(* (sin x) (- (cos eps) 1))
21.0ms	(- (cos eps) 1)

simplify44.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (37.0ms)

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

prune254.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (+ (* (sin x) (cos eps)) (- (sin x))) (* (cos x) (sin eps)))
0.1b	(* (sin x) (cos eps))
0.2b	(* (cos x) (sin eps))
2.5b	(+ (* (sin x) (cos eps)) (- (sin x)))

rewrite49.0ms

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:

31.0ms	(+ (+ (* (sin x) (cos eps)) (- (sin x))) (* (cos x) (sin eps)))
4.0ms	(* (sin x) (cos eps))
7.0ms	(* (cos x) (sin eps))
6.0ms	(+ (* (sin x) (cos eps)) (- (sin x)))

series254.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(+ (+ (* (sin x) (cos eps)) (- (sin x))) (* (cos x) (sin eps)))
47.0ms	(* (sin x) (cos eps))
42.0ms	(* (cos x) (sin eps))
58.0ms	(+ (* (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

prune212.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.0b

regimes132.0ms

Accuracy

0% (0.5b 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	20	13
1	20	13

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.4s	3316×	body	1280	valid
576.0ms	632×	body	2560	valid
455.0ms	1829×	body	640	valid
132.0ms	768×	body	320	valid
61.0ms	1129×	body	80	valid
35.0ms	326×	body	160	valid