Details

sample219.0ms

Algorithm

intervals

Results

135.0ms	145×	body	1280	valid
34.0ms	21×	body	2560	valid
32.0ms	64×	body	640	valid
4.0ms	12×	body	320	valid
3.0ms	11×	body	160	valid
0.0ms	3×	body	80	valid

simplify14.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

14.0ms

(- (cos (+ x eps)) (cos x))

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.6b

localize24.0ms

Local error

Found 2 expressions with local error:

2.7b	(cos (+ x eps))
1.6b	(- (cos (+ x eps)) (cos x))

rewrite31.0ms

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

18.0ms	(- (cos (+ x eps)) (cos x))
12.0ms	(cos (+ x eps))

series150.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

91.0ms	(- (cos (+ x eps)) (cos x))
59.0ms	(cos (+ x eps))

simplify491.0ms

Counts

13 → 32

Calls

13 calls:

Slowest

159.0ms	(- 1 (+ (* x eps) (* 1/2 (pow x 2))))
149.0ms	(- (* 1/6 (* (pow x 3) eps)) (+ (* 1/2 (pow eps 2)) (* x eps)))
59.0ms	(* (sin (/ (- (+ x eps) x) 2)) (sin (/ (+ (+ x eps) x) 2)))
33.0ms	(/ (exp (cos (+ x eps))) (exp (cos x)))
17.0ms	(- (cos (+ x eps)) (cos x))

prune332.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.7b

localize32.0ms

Local error

Found 3 expressions with local error:

2.7b	(sin (/ (+ x (+ eps x)) 2))
0.3b	(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
0.0b	(+ x (+ eps x))

rewrite120.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity`
8×	`add-log-exp`
7×	`add-sqr-sqrt`
5×	`pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
3×	`sum-log` `associate-r` `associate-l` `insert-posit16` `distribute-lft-out`
1×	`+-commutative` `associate-+r+` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `sin-mult` `unswap-sqr`

Counts

3 → 44

Calls

3 calls:

Slowest

62.0ms	(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
39.0ms	(sin (/ (+ x (+ eps x)) 2))
19.0ms	(+ x (+ eps x))

series204.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

137.0ms	(* (sin (/ (+ x (+ eps x)) 2)) (sin (/ eps 2)))
36.0ms	(sin (/ (+ x (+ eps x)) 2))
30.0ms	(+ x (+ eps x))

simplify1.4s

Counts

24 → 53

Calls

24 calls:

Slowest

384.0ms	(* (* (* (sin (/ (+ x (+ eps x)) 2)) (sin (/ (+ x (+ eps x)) 2))) (sin (/ (+ x (+ eps x)) 2))) (* (* (sin (/ eps 2)) (sin (/ eps 2))) (sin (/ eps 2))))
227.0ms	(- (+ x (* 1/2 eps)) (* 1/6 (pow x 3)))
226.0ms	(- (+ (* 1/4 (pow eps 2)) (* 1/2 (* x eps))) (* 1/12 (* (pow x 3) eps)))
70.0ms	(* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 eps)))
47.0ms	(sin (* 1/2 (+ (* 2 x) eps)))

prune651.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.6b

localize33.0ms

Local error

Found 2 expressions with local error:

2.8b	(sin (+ (* eps 1/2) x))
0.3b	(* (sin (* eps 1/2)) (sin (+ (* eps 1/2) x)))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 31

Calls

2 calls:

Slowest

49.0ms	(* (sin (* eps 1/2)) (sin (+ (* eps 1/2) x)))
13.0ms	(sin (+ (* eps 1/2) x))

series135.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

90.0ms	(* (sin (* eps 1/2)) (sin (+ (* eps 1/2) x)))
45.0ms	(sin (+ (* eps 1/2) x))

simplify1.6s

Counts

20 → 37

Calls

20 calls:

Slowest

560.0ms	(- (cos (- (* eps 1/2) (+ (* eps 1/2) x))) (cos (+ (* eps 1/2) (+ (* eps 1/2) x))))
389.0ms	(* (* (* (sin (* eps 1/2)) (sin (* eps 1/2))) (sin (* eps 1/2))) (* (* (sin (+ (* eps 1/2) x)) (sin (+ (* eps 1/2) x))) (sin (+ (* eps 1/2) x))))
238.0ms	(- (+ x (* 1/2 eps)) (* 1/48 (pow eps 3)))
187.0ms	(- (+ (* 1/2 (* x eps)) (* 1/4 (pow eps 2))) (* 1/48 (pow eps 4)))
32.0ms	(* (* (cos (* eps 1/2)) (sin x)) (sin (* eps 1/2)))

prune408.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize35.0ms

Local error

Found 4 expressions with local error:

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

rewrite208.0ms

Algorithm

rewrite-expression-head

Rules

18×	`pow1` `add-cbrt-cube` `add-exp-log`
14×	`add-sqr-sqrt`
12×	`associate-l`
10×	`*-un-lft-identity` `add-cube-cbrt`
8×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`*-commutative` `insert-posit16` `add-log-exp`
2×	`sin-cos-mult` `unswap-sqr`
1×	`associate-*r/`

Counts

4 → 78

Calls

4 calls:

Slowest

73.0ms	(* (sin (* eps 1/2)) (* (cos (* eps 1/2)) (sin x)))
64.0ms	(* (sin (* eps 1/2)) (* (sin (* eps 1/2)) (cos x)))
35.0ms	(* (cos (* eps 1/2)) (sin x))
34.0ms	(* (sin (* eps 1/2)) (cos x))

series358.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

121.0ms	(* (sin (* eps 1/2)) (* (cos (* eps 1/2)) (sin x)))
86.0ms	(* (sin (* eps 1/2)) (cos x))
80.0ms	(* (cos (* eps 1/2)) (sin x))
71.0ms	(* (sin (* eps 1/2)) (* (sin (* eps 1/2)) (cos x)))

simplify4.0s

Counts

51 → 90

Calls

51 calls:

Slowest

568.0ms	(* (* (* (sin (* eps 1/2)) (sin (* eps 1/2))) (sin (* eps 1/2))) (* (* (* (cos (* eps 1/2)) (sin x)) (* (cos (* eps 1/2)) (sin x))) (* (cos (* eps 1/2)) (sin x))))
456.0ms	(* (* (* (sin (* eps 1/2)) (sin (* eps 1/2))) (sin (* eps 1/2))) (* (* (* (cos (* eps 1/2)) (cos (* eps 1/2))) (cos (* eps 1/2))) (* (* (sin x) (sin x)) (sin x))))
372.0ms	(* (* (* (sin (* eps 1/2)) (sin (* eps 1/2))) (sin (* eps 1/2))) (* (* (* (sin (* eps 1/2)) (cos x)) (* (sin (* eps 1/2)) (cos x))) (* (sin (* eps 1/2)) (cos x))))
346.0ms	(* (* (* (sin (* eps 1/2)) (sin (* eps 1/2))) (sin (* eps 1/2))) (* (* (cos x) (cos x)) (cos x)))
336.0ms	(* (* (* (cos (* eps 1/2)) (cos (* eps 1/2))) (cos (* eps 1/2))) (* (* (sin x) (sin x)) (sin x)))

prune1.3s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

regimes181.0ms

Accuracy

0% (0.3b remaining)

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

bsearch5.0ms

end0.0ms

sample8.2s

Algorithm

intervals

Results

4.7s	4392×	body	1280	valid
1.5s	616×	body	2560	valid
1.4s	1944×	body	640	valid
263.0ms	662×	body	320	valid
127.0ms	313×	body	160	valid
9.0ms	73×	body	80	valid