Details

sample109.0ms

Algorithm

intervals

Results

46.0ms	95×	body	1280	valid
22.0ms	23×	body	2560	valid
21.0ms	70×	body	640	valid
4.0ms	18×	body	320	valid
2.0ms	38×	body	80	valid
2.0ms	12×	body	160	valid

simplify2.0ms

Counts: 1 → 1

prune29.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.6b

localize12.0ms

Local error

Found 2 expressions with local error:

1.5b	(- (sin (+ x eps)) (sin x))
3.2b	(sin (+ x eps))

rewrite59.0ms

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:

48.0ms	(- (sin (+ x eps)) (sin x))
10.0ms	(sin (+ x eps))

series65.0ms

Counts

2 → 6

Calls

2 calls:

44.0ms	(- (sin (+ x eps)) (sin x))
21.0ms	(sin (+ x eps))

simplify134.0ms

Counts: 30 → 30

prune88.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 15.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
0.1b	(* (sin x) (cos eps))
0.1b	(* (cos x) (sin eps))
2.6b	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

rewrite99.0ms

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:

15.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
11.0ms	(* (sin x) (cos eps))
12.0ms	(* (cos x) (sin eps))
59.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

series327.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
53.0ms	(* (sin x) (cos eps))
47.0ms	(* (cos x) (sin eps))
130.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

simplify41.0ms

Counts: 76 → 76

prune228.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize20.0ms

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))
0.1b	(* (cos x) (sin eps))
2.4b	(- (cos eps) 1)

rewrite79.0ms

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:

23.0ms	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
28.0ms	(* (sin x) (- (cos eps) 1))
18.0ms	(* (cos x) (sin eps))
8.0ms	(- (cos eps) 1)

series252.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
54.0ms	(* (sin x) (- (cos eps) 1))
48.0ms	(* (cos x) (sin eps))
24.0ms	(- (cos eps) 1)

simplify40.0ms

Counts: 89 → 89

prune282.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin eps))
0.6b	(cbrt (sin eps))
0.6b	(cbrt (sin eps))
2.4b	(- (cos eps) 1)

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
9×	`cbrt-prod`
7×	`add-cube-cbrt`
6×	`add-log-exp`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`pow1/3`
2×	`difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `difference-of-sqr-1` `flip--` `distribute-lft-out--`

Counts

4 → 49

Calls

4 calls:

1.0ms	(cbrt (sin eps))
1.0ms	(cbrt (sin eps))
1.0ms	(cbrt (sin eps))
8.0ms	(- (cos eps) 1)

series353.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(cbrt (sin eps))
109.0ms	(cbrt (sin eps))
112.0ms	(cbrt (sin eps))
22.0ms	(- (cos eps) 1)

simplify60.0ms

Counts: 61 → 61

prune207.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

regimes155.0ms

Accuracy

80.2% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 1.6b

bsearch177.0ms

Steps

Iters	Range		Point
8	0.000352901875324175	20.983827299779215	0.032687227737141666
8	-58.92542956775719	-0.023229637516429813	-0.030506529006046484

simplify2.0ms

end0.0ms

sample4.9s

Algorithm

intervals

Results

2.2s	3364×	body	1280	valid
1.1s	624×	body	2560	valid
1.0s	1859×	body	640	valid
206.0ms	737×	body	320	valid
121.0ms	1076×	body	80	valid
47.0ms	340×	body	160	valid