Details

sample167.0ms

Algorithm

intervals

Results

87.0ms	140×	body	1280	valid
33.0ms	61×	body	640	valid
27.0ms	21×	body	2560	valid
6.0ms	22×	body	320	valid
2.0ms	10×	body	160	valid
0.0ms	2×	body	80	valid

simplify11.0ms

Counts: 1 → 1

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.0b

localize46.0ms

Local error

Found 2 expressions with local error:

2.6b	(cos (+ x eps))
1.2b	(- (cos (+ x eps)) (cos x))

rewrite35.0ms

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

21.0ms	(- (cos (+ x eps)) (cos x))
14.0ms	(cos (+ x eps))

series104.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

77.0ms	(- (cos (+ x eps)) (cos x))
27.0ms	(cos (+ x eps))

simplify577.0ms

Counts: 36 → 32

prune373.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.6b

localize37.0ms

Local error

Found 4 expressions with local error:

2.6b	(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))))

rewrite141.0ms

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

63.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2))))
47.0ms	(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
19.0ms	(sin (/ (+ x (+ x eps)) 2))
11.0ms	(+ x (+ x eps))

series249.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

104.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2))))
80.0ms	(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
40.0ms	(sin (/ (+ x (+ x eps)) 2))
24.0ms	(+ x (+ x eps))

simplify315.0ms

Counts: 76 → 76

prune668.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.6b

localize38.0ms

Local error

Found 2 expressions with local error:

2.7b	(sin (+ (* eps 1/2) (* x 1)))
0.3b	(* (* -2 (sin (* eps 1/2))) (sin (+ (* eps 1/2) (* x 1))))

rewrite74.0ms

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

50.0ms	(* (* -2 (sin (* eps 1/2))) (sin (+ (* eps 1/2) (* x 1))))
24.0ms	(sin (+ (* eps 1/2) (* x 1)))

series118.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

78.0ms	(* (* -2 (sin (* eps 1/2))) (sin (+ (* eps 1/2) (* x 1))))
39.0ms	(sin (+ (* eps 1/2) (* x 1)))

simplify678.0ms

Counts: 38 → 36

prune382.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize64.0ms

Local error

Found 4 expressions with local error:

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

rewrite562.0ms

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

455.0ms	(* (* -2 (sin (* eps 1/2))) (+ (* (sin (* eps 1/2)) (cos (* x 1))) (* (cos (* eps 1/2)) (sin (* x 1)))))
43.0ms	(+ (* (sin (* eps 1/2)) (cos (* x 1))) (* (cos (* eps 1/2)) (sin (* x 1))))
34.0ms	(* (cos (* eps 1/2)) (sin (* x 1)))
30.0ms	(* (sin (* eps 1/2)) (cos (* x 1)))

series497.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

220.0ms	(* (* -2 (sin (* eps 1/2))) (+ (* (sin (* eps 1/2)) (cos (* x 1))) (* (cos (* eps 1/2)) (sin (* x 1)))))
161.0ms	(+ (* (sin (* eps 1/2)) (cos (* x 1))) (* (cos (* eps 1/2)) (sin (* x 1))))
58.0ms	(* (cos (* eps 1/2)) (sin (* x 1)))
57.0ms	(* (sin (* eps 1/2)) (cos (* x 1)))

simplify745.0ms

Counts: 88 → 86

prune1.2s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

regimes205.0ms

Accuracy

0% (0.3b remaining)

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

bsearch4.0ms

end0.0ms

sample8.4s

Algorithm

intervals

Results

4.7s	4514×	body	1280	valid
1.8s	1867×	body	640	valid
1.3s	622×	body	2560	valid
351.0ms	659×	body	320	valid
71.0ms	257×	body	160	valid
12.0ms	81×	body	80	valid