Details

sample227.0ms

Algorithm

intervals

Results

124.0ms	112×	body	1280	valid
38.0ms	20×	body	2560	valid
33.0ms	53×	body	640	valid
10.0ms	22×	body	320	valid
5.0ms	38×	body	80	valid
3.0ms	11×	body	160	valid

simplify9.0ms

Counts: 1 → 1

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.9b

localize19.0ms

Local error

Found 2 expressions with local error:

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

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`prod-diff` `add-cube-cbrt`
4×	`add-log-exp`
3×	`fma-neg`
2×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `sin-sum` `add-exp-log` `insert-posit16` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `diff-sin` `associate--l+` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 42

Calls

2 calls:

Slowest

60.0ms	(- (sin (+ x eps)) (sin x))
34.0ms	(sin (+ x eps))

series92.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

58.0ms	(- (sin (+ x eps)) (sin x))
33.0ms	(sin (+ x eps))

simplify1.4s

Counts: 48 → 48

prune477.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.5b

localize29.0ms

Local error

Found 4 expressions with local error:

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

rewrite137.0ms

Algorithm

rewrite-expression-head

Rules

42×	`*-un-lft-identity`
19×	`add-sqr-sqrt`
17×	`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×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r` `sum-log` `fma-def` `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 → 93

Calls

4 calls:

Slowest

72.0ms	(/ (+ x (+ eps x)) 2)
27.0ms	(cos (/ (+ x (+ eps x)) 2))
18.0ms	(* (sin (/ eps 2)) (cos (/ (+ x (+ eps x)) 2)))
16.0ms	(+ x (+ eps x))

series180.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

80.0ms	(* (sin (/ eps 2)) (cos (/ (+ x (+ eps x)) 2)))
44.0ms	(/ (+ x (+ eps x)) 2)
28.0ms	(cos (/ (+ x (+ eps x)) 2))
28.0ms	(+ x (+ eps x))

simplify1.5s

Counts: 105 → 105

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.3b

localize41.0ms

Local error

Found 2 expressions with local error:

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

rewrite28.0ms

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×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`cos-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `sin-cos-mult` `unswap-sqr`

Counts

2 → 33

Calls

2 calls:

Slowest

23.0ms	(* (sin (/ eps 2)) (cos (fma eps 1/2 x)))
5.0ms	(cos (fma eps 1/2 x))

series89.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

55.0ms	(* (sin (/ eps 2)) (cos (fma eps 1/2 x)))
34.0ms	(cos (fma eps 1/2 x))

simplify1.6s

Counts: 39 → 39

prune401.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize39.0ms

Local error

Found 4 expressions with local error:

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

rewrite247.0ms

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×	`expm1-log1p-u` `associate-*r/` `insert-posit16` `log1p-expm1-u`
3×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `prod-diff` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`flip3--` `frac-sub` `flip--` `sub-div`
1×	`fma-neg` `diff-log`

Counts

4 → 94

Calls

4 calls:

Slowest

163.0ms	(* (sin (/ eps 2)) (- (* (cos (* eps 1/2)) (cos x)) (* (sin (* eps 1/2)) (sin x))))
45.0ms	(- (* (cos (* eps 1/2)) (cos x)) (* (sin (* eps 1/2)) (sin x)))
20.0ms	(* (cos (* eps 1/2)) (cos x))
18.0ms	(* (sin (* eps 1/2)) (sin x))

series457.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

185.0ms	(* (sin (/ eps 2)) (- (* (cos (* eps 1/2)) (cos x)) (* (sin (* eps 1/2)) (sin x))))
126.0ms	(- (* (cos (* eps 1/2)) (cos x)) (* (sin (* eps 1/2)) (sin x)))
78.0ms	(* (sin (* eps 1/2)) (sin x))
67.0ms	(* (cos (* eps 1/2)) (cos x))

simplify1.8s

Counts: 106 → 106

prune1.5s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes163.0ms

Accuracy

0% (0.3b remaining)

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

bsearch4.0ms

end0.0ms

sample7.5s

Algorithm

intervals

Results

3.9s	3268×	body	1280	valid
1.3s	1871×	body	640	valid
1.1s	667×	body	2560	valid
551.0ms	1106×	body	80	valid
341.0ms	768×	body	320	valid
128.0ms	320×	body	160	valid