Details

sample180.0ms

Algorithm

intervals

Results

112.0ms	151×	body	1280	valid
27.0ms	20×	body	2560	valid
21.0ms	50×	body	640	valid
7.0ms	21×	body	320	valid
2.0ms	11×	body	160	valid
0.0ms	3×	body	80	valid

simplify8.0ms

Counts: 1 → 1

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.4b

localize14.0ms

Local error

Found 2 expressions with local error:

3.7b	(cos (+ x eps))
0.7b	(- (cos (+ x eps)) (cos x))

rewrite42.0ms

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

29.0ms	(cos (+ x eps))
13.0ms	(- (cos (+ x eps)) (cos x))

series105.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

80.0ms	(- (cos (+ x eps)) (cos x))
25.0ms	(cos (+ x eps))

simplify978.0ms

Counts: 32 → 32

prune248.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.6b

localize29.0ms

Local error

Found 4 expressions with local error:

3.7b	(sin (/ (+ x (+ x eps)) 2))
0.3b	(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
0.2b	(/ (+ x (+ x eps)) 2)
0.0b	(+ x (+ x eps))

rewrite193.0ms

Algorithm

rewrite-expression-head

Rules

41×	`*-un-lft-identity`
18×	`add-sqr-sqrt`
16×	`add-cube-cbrt`
15×	`times-frac` `distribute-lft-out`
9×	`add-log-exp`
8×	`add-cbrt-cube` `add-exp-log`
6×	`pow1`
5×	`associate-/l*`
4×	`insert-posit16`
3×	`associate-/r` `sum-log` `associate-r` `associate-l*`
2×	`flip3-+` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `associate-+r+` `clear-num` `frac-2neg` `div-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `div-inv` `sin-mult` `unswap-sqr`

Counts

4 → 82

Calls

4 calls:

Slowest

81.0ms	(/ (+ x (+ x eps)) 2)
50.0ms	(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
38.0ms	(sin (/ (+ x (+ x eps)) 2))
23.0ms	(+ x (+ x eps))

series207.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

65.0ms	(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
57.0ms	(sin (/ (+ x (+ x eps)) 2))
56.0ms	(/ (+ x (+ x eps)) 2)
28.0ms	(+ x (+ x eps))

simplify1.0s

Counts: 94 → 94

prune1.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.3b

localize29.0ms

Local error

Found 3 expressions with local error:

3.7b	(sin (+ (* eps 1/2) x))
0.3b	(* (sin (+ (* eps 1/2) x)) (sin (/ eps 2)))
0.0b	(* -2 (* (sin (+ (* eps 1/2) x)) (sin (/ eps 2))))

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 49

Calls

3 calls:

Slowest

70.0ms	(* -2 (* (sin (+ (* eps 1/2) x)) (sin (/ eps 2))))
47.0ms	(* (sin (+ (* eps 1/2) x)) (sin (/ eps 2)))
15.0ms	(sin (+ (* eps 1/2) x))

series200.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

86.0ms	(* -2 (* (sin (+ (* eps 1/2) x)) (sin (/ eps 2))))
80.0ms	(* (sin (+ (* eps 1/2) x)) (sin (/ eps 2)))
33.0ms	(sin (+ (* eps 1/2) x))

simplify776.0ms

Counts: 58 → 58

prune635.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize42.0ms

Local error

Found 4 expressions with local error:

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

rewrite165.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

Slowest

84.0ms	(* (+ (* (sin (* eps 1/2)) (cos x)) (* (cos (* eps 1/2)) (sin x))) (sin (/ eps 2)))
28.0ms	(+ (* (sin (* eps 1/2)) (cos x)) (* (cos (* eps 1/2)) (sin x)))
27.0ms	(* (sin (* eps 1/2)) (cos x))
26.0ms	(* (cos (* eps 1/2)) (sin x))

series475.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

194.0ms	(* (+ (* (sin (* eps 1/2)) (cos x)) (* (cos (* eps 1/2)) (sin x))) (sin (/ eps 2)))
117.0ms	(+ (* (sin (* eps 1/2)) (cos x)) (* (cos (* eps 1/2)) (sin x)))
94.0ms	(* (cos (* eps 1/2)) (sin x))
70.0ms	(* (sin (* eps 1/2)) (cos x))

simplify1.4s

Counts: 84 → 84

prune1.2s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

regimes280.0ms

Accuracy

0% (0.3b remaining)

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

bsearch8.0ms

end0.0ms

sample8.6s

Algorithm

intervals

Results

5.4s	4439×	body	1280	valid
1.4s	667×	body	2560	valid
1.3s	1881×	body	640	valid
303.0ms	688×	body	320	valid
66.0ms	256×	body	160	valid
9.0ms	69×	body	80	valid