Details

sample153.0ms

Algorithm

intervals

Results

74.0ms	112×	body	1280	valid
33.0ms	20×	body	2560	valid
23.0ms	53×	body	640	valid
8.0ms	22×	body	320	valid
4.0ms	38×	body	80	valid
2.0ms	11×	body	160	valid

simplify10.0ms

Counts: 1 → 1

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.9b

localize55.0ms

Local error

Found 2 expressions with local error:

3.5b	(sin (+ x eps))
1.0b	(- (sin (+ x eps)) (sin x))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 26

Calls

2 calls:

Slowest

51.0ms	(- (sin (+ x eps)) (sin x))
12.0ms	(sin (+ x eps))

series96.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

72.0ms	(- (sin (+ x eps)) (sin x))
24.0ms	(sin (+ x eps))

simplify1.2s

Counts: 32 → 32

prune256.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.5b

localize36.0ms

Local error

Found 4 expressions with local error:

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

rewrite113.0ms

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-cos-mult` `unswap-sqr`

Counts

4 → 82

Calls

4 calls:

Slowest

51.0ms	(/ (+ x (+ x eps)) 2)
28.0ms	(cos (/ (+ x (+ x eps)) 2))
19.0ms	(* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2)))
14.0ms	(+ x (+ x eps))

series179.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

62.0ms	(* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2)))
51.0ms	(/ (+ x (+ x eps)) 2)
34.0ms	(+ x (+ x eps))
31.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify1.2s

Counts: 94 → 94

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.3b

localize41.0ms

Local error

Found 2 expressions with local error:

3.7b	(cos (+ (* 1/2 eps) x))
0.2b	(* (sin (/ eps 2)) (cos (+ (* 1/2 eps) x)))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 29

Calls

2 calls:

Slowest

40.0ms	(* (sin (/ eps 2)) (cos (+ (* 1/2 eps) x)))
25.0ms	(cos (+ (* 1/2 eps) x))

series102.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

75.0ms	(* (sin (/ eps 2)) (cos (+ (* 1/2 eps) x)))
26.0ms	(cos (+ (* 1/2 eps) x))

simplify1.1s

Counts: 35 → 35

prune359.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize35.0ms

Local error

Found 4 expressions with local error:

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

rewrite264.0ms

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`
5×	`cos-mult` `sin-mult`
4×	`associate-*r/` `insert-posit16`
3×	`sub-neg` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`distribute-rgt-in` `distribute-lft-in` `flip3--` `frac-sub` `flip--` `sub-div`
1×	`diff-log`

Counts

4 → 82

Calls

4 calls:

Slowest

173.0ms	(* (sin (/ eps 2)) (- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x))))
43.0ms	(- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x)))
27.0ms	(* (sin (* 1/2 eps)) (sin x))
19.0ms	(* (cos (* 1/2 eps)) (cos x))

series329.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

130.0ms	(* (sin (/ eps 2)) (- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x))))
94.0ms	(- (* (cos (* 1/2 eps)) (cos x)) (* (sin (* 1/2 eps)) (sin x)))
57.0ms	(* (sin (* 1/2 eps)) (sin x))
49.0ms	(* (cos (* 1/2 eps)) (cos x))

simplify1.0s

Counts: 94 → 94

prune892.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

regimes119.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch2.0ms

end0.0ms

sample6.0s

Algorithm

intervals

Results

3.5s	3268×	body	1280	valid
963.0ms	667×	body	2560	valid
883.0ms	1871×	body	640	valid
242.0ms	768×	body	320	valid
114.0ms	1106×	body	80	valid
98.0ms	320×	body	160	valid