Details

sample197.0ms

Algorithm

intervals

Results

101.0ms	112×	body	1280	valid
36.0ms	22×	body	2560	valid
27.0ms	50×	body	640	valid
7.0ms	21×	body	320	valid
5.0ms	48×	body	80	valid
1.0ms	3×	body	160	valid

simplify20.0ms

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.5b

localize10.0ms

Local error

Found 2 expressions with local error:

0.9b	(- (sin (+ x eps)) (sin x))
4.2b	(sin (+ x eps))

rewrite94.0ms

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:

82.0ms	(- (sin (+ x eps)) (sin x))
11.0ms	(sin (+ x eps))

series93.0ms

Counts

2 → 6

Calls

2 calls:

64.0ms	(- (sin (+ x eps)) (sin x))
29.0ms	(sin (+ x eps))

simplify1.5s

Counts: 30 → 30

prune107.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 14.8b

localize34.0ms

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))
1.6b	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

rewrite171.0ms

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:

18.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
18.0ms	(* (sin x) (cos eps))
24.0ms	(* (cos x) (sin eps))
110.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

series426.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
65.0ms	(* (sin x) (cos eps))
62.0ms	(* (cos x) (sin eps))
164.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

simplify2.2s

Counts: 76 → 76

prune324.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize19.0ms

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))
1.7b	(- (cos eps) 1)

rewrite88.0ms

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)))
42.0ms	(* (sin x) (- (cos eps) 1))
14.0ms	(* (cos x) (sin eps))
8.0ms	(- (cos eps) 1)

series368.0ms

Counts

4 → 12

Calls

4 calls:

188.0ms	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
83.0ms	(* (sin x) (- (cos eps) 1))
66.0ms	(* (cos x) (sin eps))
32.0ms	(- (cos eps) 1)

simplify2.4s

Counts: 89 → 89

prune317.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize32.0ms

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))
0.1b	(* (cos x) (sin eps))
1.7b	(+ (* (sin x) (cos eps)) (- (sin x)))

rewrite130.0ms

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:

74.0ms	(+ (+ (* (sin x) (cos eps)) (- (sin x))) (* (cos x) (sin eps)))
13.0ms	(* (sin x) (cos eps))
17.0ms	(* (cos x) (sin eps))
25.0ms	(+ (* (sin x) (cos eps)) (- (sin x)))

series613.0ms

Counts

4 → 12

Calls

4 calls:

445.0ms	(+ (+ (* (sin x) (cos eps)) (- (sin x))) (* (cos x) (sin eps)))
55.0ms	(* (sin x) (cos eps))
47.0ms	(* (cos x) (sin eps))
65.0ms	(+ (* (sin x) (cos eps)) (- (sin x)))

simplify644.0ms

Counts: 81 → 81

prune315.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

regimes125.0ms

Accuracy

33.8% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify518.0ms

end0.0ms

sample5.9s

Algorithm

intervals

Results

3.1s	3396×	body	1280	valid
1.2s	641×	body	2560	valid
877.0ms	1805×	body	640	valid
202.0ms	745×	body	320	valid
98.0ms	1107×	body	80	valid
59.0ms	306×	body	160	valid