Details

sample92.0ms

Algorithm

intervals

Results

46.0ms	102×	body	1280	valid
15.0ms	17×	body	2560	valid
14.0ms	58×	body	640	valid
6.0ms	36×	body	320	valid
2.0ms	32×	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.7b

localize8.0ms

Local error

Found 2 expressions with local error:

1.8b	(- (sin (+ x eps)) (sin x))
3.2b	(sin (+ x eps))

rewrite25.0ms

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:

20.0ms	(- (sin (+ x eps)) (sin x))
4.0ms	(sin (+ x eps))

series60.0ms

Counts

2 → 6

Calls

2 calls:

42.0ms	(- (sin (+ x eps)) (sin x))
18.0ms	(sin (+ x eps))

simplify142.0ms

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

prune80.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 14.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
0.2b	(* (sin x) (cos eps))
0.2b	(* (cos x) (sin eps))
3.5b	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

rewrite34.0ms

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	(* (sin x) (cos eps))
7.0ms	(* (cos x) (sin eps))
18.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

series286.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
45.0ms	(* (sin x) (cos eps))
43.0ms	(* (cos x) (sin eps))
109.0ms	(- (+ (* (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

prune220.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.3b

localize15.0ms

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))
0.2b	(* (cos x) (sin eps))
1.7b	(- (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:

7.0ms	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
11.0ms	(* (sin x) (- (cos eps) 1))
4.0ms	(* (cos x) (sin eps))
3.0ms	(- (cos eps) 1)

series215.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
44.0ms	(* (sin x) (- (cos eps) 1))
45.0ms	(* (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	333	552
1	1271	503
2	5001	501

prune249.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos x) (sin eps))
0.2b	(* (sin x) (- (* (sin eps) (sin eps))))
0.3b	(* (sin eps) (sin eps))
0.4b	(+ (cos eps) 1)

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
15×	`pow1`
14×	`*-un-lft-identity`
12×	`add-cube-cbrt` `associate-r`
10×	`add-exp-log` `add-cbrt-cube`
9×	`associate-l`
6×	`add-log-exp`
3×	`swap-sqr` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`sin-mult`
1×	`+-commutative` `pow2` `distribute-lft-neg-in` `neg-mul-1` `distribute-rgt-neg-in` `flip3-+` `pow-plus` `associate-*r/` `sum-log` `pow-sqr` `pow-prod-up` `distribute-rgt-neg-out` `flip-+` `sqr-sin` `distribute-neg-frac` `distribute-lft-out`

Counts

4 → 80

Calls

4 calls:

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

series138.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (cos x) (sin eps))
59.0ms	(* (sin x) (- (* (sin eps) (sin eps))))
22.0ms	(* (sin eps) (sin eps))
10.0ms	(+ (cos eps) 1)

simplify62.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	374	459
1	1897	403
2	5001	393

prune277.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes99.0ms

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	29	14
1	37	14
2	37	14

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.4s	3309×	body	1280	valid
565.0ms	623×	body	2560	valid
460.0ms	1864×	body	640	valid
121.0ms	772×	body	320	valid
58.0ms	1077×	body	80	valid
44.0ms	355×	body	160	valid