Details

sample245.0ms

Algorithm

intervals

Results

121.0ms	137×	body	1280	valid
53.0ms	58×	body	640	valid
39.0ms	22×	body	2560	valid
14.0ms	28×	body	320	valid
3.0ms	9×	body	160	valid
0.0ms	2×	body	80	valid

simplify15.0ms

Counts: 1 → 1

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.7b

localize20.0ms

Local error

Found 2 expressions with local error:

4.5b	(cos (+ x eps))
1.6b	(- (cos (+ x eps)) (cos x))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
2×	`pow1` `cos-sum` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16`
1×	`associate--l-` `sub-neg` `flip3--` `diff-log` `diff-cos` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 26

Calls

2 calls:

Slowest

45.0ms	(- (cos (+ x eps)) (cos x))
7.0ms	(cos (+ x eps))

series97.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

73.0ms	(- (cos (+ x eps)) (cos x))
24.0ms	(cos (+ x eps))

simplify1.4s

Counts: 32 → 32

prune340.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.3b

localize51.0ms

Local error

Found 4 expressions with local error:

4.4b	(sin (/ (+ x (+ x eps)) 2))
0.3b	(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
0.0b	(+ x (+ x eps))
0.0b	(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2))))

rewrite152.0ms

Algorithm

rewrite-expression-head

Rules

12×	`*-un-lft-identity`
11×	`pow1` `add-cbrt-cube` `add-exp-log`
9×	`add-sqr-sqrt` `add-log-exp`
7×	`add-cube-cbrt`
6×	`associate-l`
4×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16`
3×	`sum-log` `distribute-lft-out`
2×	`*-commutative` `sin-mult`
1×	`+-commutative` `associate-+r+` `flip3-+` `associate-*r/` `flip-+` `unswap-sqr`

Counts

4 → 64

Calls

4 calls:

Slowest

62.0ms	(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
52.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2))))
25.0ms	(sin (/ (+ x (+ x eps)) 2))
12.0ms	(+ x (+ x eps))

series266.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

112.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2))))
76.0ms	(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
41.0ms	(+ x (+ x eps))
36.0ms	(sin (/ (+ x (+ x eps)) 2))

simplify1.0s

Counts: 76 → 76

prune864.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.2b

localize39.0ms

Local error

Found 2 expressions with local error:

4.5b	(sin (+ x (* eps 1/2)))
0.3b	(* (* -2 (sin (* eps 1/2))) (sin (+ x (* eps 1/2))))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

7×	`pow1` `add-cbrt-cube` `add-exp-log`
3×	`add-sqr-sqrt` `-un-lft-identity` `sin-sum` `associate-r*` `pow-prod-down` `prod-exp` `add-cube-cbrt` `cbrt-unprod`
2×	`insert-posit16` `add-log-exp`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-l` `*-commutative`

Counts

2 → 30

Calls

2 calls:

Slowest

57.0ms	(* (* -2 (sin (* eps 1/2))) (sin (+ x (* eps 1/2))))
8.0ms	(sin (+ x (* eps 1/2)))

series124.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

91.0ms	(* (* -2 (sin (* eps 1/2))) (sin (+ x (* eps 1/2))))
33.0ms	(sin (+ x (* eps 1/2)))

simplify2.9s

Counts: 36 → 36

prune444.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize50.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* -2 (sin (* eps 1/2))) (+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2)))))
0.2b	(* (cos x) (sin (* eps 1/2)))
0.1b	(* (sin x) (cos (* eps 1/2)))
0.1b	(+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2))))

rewrite291.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `pow1` `add-cbrt-cube` `add-exp-log`
9×	`-un-lft-identity` `associate-r*` `add-cube-cbrt`
7×	`associate-l`
6×	`add-log-exp`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`insert-posit16`
3×	`*-commutative`
2×	`flip3-+` `associate-*r/` `flip-+` `unswap-sqr`
1×	`distribute-rgt-in` `+-commutative` `sum-log` `distribute-lft-in` `sin-cos-mult`

Counts

4 → 74

Calls

4 calls:

Slowest

167.0ms	(* (* -2 (sin (* eps 1/2))) (+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2)))))
52.0ms	(+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2))))
35.0ms	(* (cos x) (sin (* eps 1/2)))
34.0ms	(* (sin x) (cos (* eps 1/2)))

series459.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

199.0ms	(* (* -2 (sin (* eps 1/2))) (+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2)))))
141.0ms	(+ (* (sin x) (cos (* eps 1/2))) (* (cos x) (sin (* eps 1/2))))
64.0ms	(* (sin x) (cos (* eps 1/2)))
55.0ms	(* (cos x) (sin (* eps 1/2)))

simplify775.0ms

Counts: 86 → 86

prune1.0s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes205.0ms

Accuracy

0% (0.4b remaining)

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

bsearch7.0ms

end0.0ms

sample8.3s

Algorithm

intervals

Results

5.3s	4478×	body	1280	valid
1.2s	1828×	body	640	valid
1.1s	648×	body	2560	valid
332.0ms	655×	body	320	valid
120.0ms	316×	body	160	valid
10.0ms	75×	body	80	valid