Details

sample90.0ms

Algorithm

intervals

Results

47.0ms	109×	body	1280	valid
16.0ms	72×	body	640	valid
12.0ms	14×	body	2560	valid
3.0ms	23×	body	320	valid
1.0ms	31×	body	80	valid
1.0ms	7×	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: 37.5b

localize8.0ms

Local error

Found 2 expressions with local error:

1.7b	(- (sin (+ x eps)) (sin x))
3.8b	(sin (+ x eps))

rewrite27.0ms

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))
5.0ms	(sin (+ x eps))

series62.0ms

Counts

2 → 6

Calls

2 calls:

43.0ms	(- (sin (+ x eps)) (sin x))
19.0ms	(sin (+ x eps))

simplify141.0ms

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

prune78.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 14.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
0.2b	(* (cos x) (sin eps))
0.2b	(* (sin x) (cos eps))
3.8b	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

rewrite35.0ms

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:

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

series290.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
47.0ms	(* (cos x) (sin eps))
43.0ms	(* (sin x) (cos eps))
112.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

simplify41.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (35.0ms)

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

prune213.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.4b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
0.2b	(* (sin x) (- (cos eps) 1))
0.2b	(* (cos x) (sin eps))
2.6b	(- (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)))
12.0ms	(* (sin x) (- (cos eps) 1))
4.0ms	(* (cos x) (sin eps))
3.0ms	(- (cos eps) 1)

series228.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
44.0ms	(* (sin x) (- (cos eps) 1))
47.0ms	(* (cos x) (sin eps))
19.0ms	(- (cos eps) 1)

simplify43.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (36.0ms)

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

prune266.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin x) (- (* (cos eps) (cos eps)) 1))
0.3b	(* (cos eps) (cos eps))
0.3b	(+ (cos eps) 1)
2.5b	(- (* (cos eps) (cos eps)) 1)

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
14×	`*-un-lft-identity`
13×	`pow1`
10×	`add-cube-cbrt`
9×	`associate-r`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
6×	`associate-l`
4×	`sqr-cos` `difference-of-squares`
3×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `swap-sqr` `associate--l+`
2×	`flip3--` `difference-of-sqr-1` `associate-r/` `pow-prod-down` `prod-exp` `sub-1-cos` `-commutative` `flip--` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `pow2` `flip3-+` `pow-plus` `diff-log` `sum-log` `pow-sqr` `cos-mult` `pow-prod-up` `distribute-rgt-neg-out` `flip-+` `distribute-lft-out`

Counts

4 → 86

Calls

4 calls:

16.0ms	(* (sin x) (- (* (cos eps) (cos eps)) 1))
7.0ms	(* (cos eps) (cos eps))
3.0ms	(+ (cos eps) 1)
4.0ms	(- (* (cos eps) (cos eps)) 1)

series118.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* (sin x) (- (* (cos eps) (cos eps)) 1))
16.0ms	(* (cos eps) (cos eps))
10.0ms	(+ (cos eps) 1)
34.0ms	(- (* (cos eps) (cos eps)) 1)

simplify48.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	310	519
1	1426	442
2	5001	434

prune291.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

regimes130.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	13
1	35	13
2	35	13

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.4s	3282×	body	1280	valid
580.0ms	658×	body	2560	valid
438.0ms	1821×	body	640	valid
126.0ms	784×	body	320	valid
54.0ms	1125×	body	80	valid
34.0ms	330×	body	160	valid