Details

sample128.0ms

Algorithm

intervals

Results

58.0ms	97×	body	1280	valid
24.0ms	21×	body	2560	valid
19.0ms	52×	body	640	valid
7.0ms	26×	body	320	valid
3.0ms	42×	body	80	valid
3.0ms	18×	body	160	valid

simplify2.0ms

Counts: 1 → 1

prune32.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.7b

localize14.0ms

Local error

Found 2 expressions with local error:

2.4b	(- (sin (+ x eps)) (sin x))
4.2b	(sin (+ x eps))

rewrite67.0ms

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:

56.0ms	(- (sin (+ x eps)) (sin x))
10.0ms	(sin (+ x eps))

series63.0ms

Counts

2 → 6

Calls

2 calls:

43.0ms	(- (sin (+ x eps)) (sin x))
20.0ms	(sin (+ x eps))

simplify89.0ms

Counts: 30 → 30

prune88.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 14.1b

localize16.0ms

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))
3.4b	(+ (* (sin x) (cos eps)) (- (* (cos x) (sin eps)) (sin x)))

rewrite80.0ms

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:

13.0ms	(- (* (cos x) (sin eps)) (sin x))
16.0ms	(* (sin x) (cos eps))
11.0ms	(* (cos x) (sin eps))
38.0ms	(+ (* (sin x) (cos eps)) (- (* (cos x) (sin eps)) (sin x)))

series336.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(- (* (cos x) (sin eps)) (sin x))
63.0ms	(* (sin x) (cos eps))
52.0ms	(* (cos x) (sin eps))
142.0ms	(+ (* (sin x) (cos eps)) (- (* (cos x) (sin eps)) (sin x)))

simplify41.0ms

Counts: 78 → 78

prune325.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize32.0ms

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))
1.6b	(- (cos eps) 1)

rewrite125.0ms

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:

25.0ms	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
58.0ms	(* (sin x) (- (cos eps) 1))
24.0ms	(* (cos x) (sin eps))
14.0ms	(- (cos eps) 1)

series310.0ms

Counts

4 → 12

Calls

4 calls:

151.0ms	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
54.0ms	(* (sin x) (- (cos eps) 1))
66.0ms	(* (cos x) (sin eps))
38.0ms	(- (cos eps) 1)

simplify146.0ms

Counts: 89 → 89

prune334.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos eps) (cos eps))
0.3b	(pow (cos eps) 3)
0.4b	(+ (* 1 1) (* (cos eps) 1))
1.5b	(- (pow (cos eps) 3) (pow 1 3))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
24×	`difference-of-squares`
21×	`unpow-prod-down` `cube-prod`
12×	`pow1`
11×	`add-cube-cbrt` `sqr-pow`
8×	`add-log-exp`
7×	`add-exp-log` `add-cbrt-cube`
6×	`distribute-lft-out--`
3×	`pow-unpow` `swap-sqr` `associate-r` `associate-l`
2×	`cube-mult`
1×	`difference-cubes` `+-commutative` `pow2` `pow-to-exp` `sub-neg` `sqr-cos` `distribute-rgt-out` `flip3--` `pow-pow` `flip3-+` `pow-plus` `diff-log` `unpow3` `pow-prod-down` `pow-exp` `prod-exp` `sum-log` `pow-sqr` `cos-mult` `*-commutative` `pow-prod-up` `flip--` `cbrt-unprod` `flip-+` `rem-cube-cbrt` `unswap-sqr`

Counts

4 → 105

Calls

4 calls:

17.0ms	(* (cos eps) (cos eps))
6.0ms	(pow (cos eps) 3)
18.0ms	(+ (* 1 1) (* (cos eps) 1))
41.0ms	(- (pow (cos eps) 3) (pow 1 3))

series155.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(* (cos eps) (cos eps))
30.0ms	(pow (cos eps) 3)
12.0ms	(+ (* 1 1) (* (cos eps) 1))
83.0ms	(- (pow (cos eps) 3) (pow 1 3))

simplify63.0ms

Counts: 117 → 117

prune557.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.1b

regimes169.0ms

Accuracy

-8% (0.2b remaining)

Error of 0.4b against oracle of 0.2b and baseline of 0.4b

bsearch0.0ms

simplify65.0ms

end0.0ms

sample5.5s

Algorithm

intervals

Results

2.5s	3293×	body	1280	valid
1.2s	674×	body	2560	valid
1.2s	1847×	body	640	valid
213.0ms	731×	body	320	valid
82.0ms	1063×	body	80	valid
74.0ms	392×	body	160	valid