Details

sample175.0ms

Algorithm

intervals

Results

66.0ms	103×	body	1280	valid
51.0ms	55×	body	640	valid
32.0ms	25×	body	2560	valid
6.0ms	21×	body	320	valid
4.0ms	44×	body	80	valid
1.0ms	8×	body	160	valid

simplify1.0ms

Counts: 1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.2b

localize12.0ms

Local error

Found 2 expressions with local error:

1.3b	(- (sin (+ x eps)) (sin x))
3.1b	(sin (+ x eps))

rewrite70.0ms

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:

58.0ms	(- (sin (+ x eps)) (sin x))
11.0ms	(sin (+ x eps))

series66.0ms

Counts

2 → 6

Calls

2 calls:

45.0ms	(- (sin (+ x eps)) (sin x))
21.0ms	(sin (+ x eps))

simplify116.0ms

Counts: 30 → 30

prune94.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 12.5b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
0.1b	(* (cos x) (sin eps))
0.2b	(* (sin x) (cos eps))
2.1b	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

rewrite115.0ms

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:

17.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
13.0ms	(* (cos x) (sin eps))
13.0ms	(* (sin x) (cos eps))
70.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

series345.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(+ (* (sin x) (cos eps)) (* (cos x) (sin eps)))
55.0ms	(* (cos x) (sin eps))
53.0ms	(* (sin x) (cos eps))
132.0ms	(- (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (sin x))

simplify143.0ms

Counts: 76 → 76

prune363.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize37.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (sin eps))
0.2b	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
0.2b	(* (sin x) (- (cos eps) 1))
1.2b	(- (cos eps) 1)

rewrite150.0ms

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:

18.0ms	(* (cos x) (sin eps))
44.0ms	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
57.0ms	(* (sin x) (- (cos eps) 1))
29.0ms	(- (cos eps) 1)

series347.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(* (cos x) (sin eps))
188.0ms	(+ (* (sin x) (- (cos eps) 1)) (* (cos x) (sin eps)))
66.0ms	(* (sin x) (- (cos eps) 1))
22.0ms	(- (cos eps) 1)

simplify148.0ms

Counts: 89 → 89

prune514.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (* (sin x) (log (exp (- (cos eps) 1)))) (* (cos x) (sin eps)))
0.2b	(* (sin x) (log (exp (- (cos eps) 1))))
1.2b	(- (cos eps) 1)
1.2b	(log (exp (- (cos eps) 1)))

rewrite189.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
25×	`log-prod`
22×	`*-un-lft-identity`
16×	`log-pow`
14×	`exp-prod`
13×	`add-cube-cbrt`
11×	`associate-r`
10×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in` `exp-sum`
8×	`pow1` `add-log-exp`
6×	`add-exp-log` `sub-neg` `add-cbrt-cube` `difference-of-squares`
3×	`difference-of-sqr-1` `associate-l` `distribute-lft-out--`
1×	`+-commutative` `log-div` `flip3--` `flip3-+` `exp-diff` `diff-log` `rem-log-exp` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `flip--` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 95

Calls

4 calls:

60.0ms	(+ (* (sin x) (log (exp (- (cos eps) 1)))) (* (cos x) (sin eps)))
91.0ms	(* (sin x) (log (exp (- (cos eps) 1))))
14.0ms	(- (cos eps) 1)
18.0ms	(log (exp (- (cos eps) 1)))

series326.0ms

Counts

4 → 12

Calls

4 calls:

175.0ms	(+ (* (sin x) (log (exp (- (cos eps) 1)))) (* (cos x) (sin eps)))
96.0ms	(* (sin x) (log (exp (- (cos eps) 1))))
21.0ms	(- (cos eps) 1)
34.0ms	(log (exp (- (cos eps) 1)))

simplify117.0ms

Counts: 107 → 107

prune530.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 0.0b

regimes147.0ms

Accuracy

9.7% (0.2b remaining)

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

bsearch0.0ms

simplify78.0ms

end0.0ms

sample6.2s

Algorithm

intervals

Results

3.0s	3334×	body	1280	valid
970.0ms	644×	body	2560	valid
891.0ms	1831×	body	640	valid
778.0ms	799×	body	320	valid
136.0ms	1072×	body	80	valid
106.0ms	320×	body	160	valid