Details

sample186.0ms

Algorithm

intervals

Results

85.0ms	135×	body	1280	valid
37.0ms	24×	body	2560	valid
26.0ms	63×	body	640	valid
6.0ms	20×	body	320	valid
2.0ms	10×	body	160	valid
0.0ms	4×	body	80	valid

simplify24.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune37.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.3b

localize25.0ms

Local error

Found 2 expressions with local error:

0.8b	(- (cos (+ x eps)) (cos x))
2.9b	(cos (+ x eps))

rewrite55.0ms

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` `cos-sum` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
1×	`associate--l-` `sub-neg` `flip3--` `diff-log` `diff-cos` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 42

Calls

2 calls:

37.0ms	(- (cos (+ x eps)) (cos x))
15.0ms	(cos (+ x eps))

series163.0ms

Counts

2 → 6

Calls

2 calls:

130.0ms	(- (cos (+ x eps)) (cos x))
33.0ms	(cos (+ x eps))

simplify6.8s

Counts

48 → 48

Iterations

Iter	Nodes
done	5003
4	3387
3	1175
2	433
1	202
0	93

prune613.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.5b

localize55.0ms

Local error

Found 3 expressions with local error:

0.0b	(* -2 (* (sin (* eps 1/2)) (sin (/ (fma 2 x eps) 2))))
0.3b	(* (sin (* eps 1/2)) (sin (/ (fma 2 x eps) 2)))
2.7b	(sin (/ (fma 2 x eps) 2))

rewrite157.0ms

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×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`*-commutative` `sin-mult`
1×	`associate-*r/` `unswap-sqr`

Counts

3 → 54

Calls

3 calls:

83.0ms	(* -2 (* (sin (* eps 1/2)) (sin (/ (fma 2 x eps) 2))))
63.0ms	(* (sin (* eps 1/2)) (sin (/ (fma 2 x eps) 2)))
6.0ms	(sin (/ (fma 2 x eps) 2))

series372.0ms

Counts

3 → 9

Calls

3 calls:

170.0ms	(* -2 (* (sin (* eps 1/2)) (sin (/ (fma 2 x eps) 2))))
119.0ms	(* (sin (* eps 1/2)) (sin (/ (fma 2 x eps) 2)))
83.0ms	(sin (/ (fma 2 x eps) 2))

simplify5.3s

Counts

63 → 63

Iterations

Iter	Nodes
done	5001
3	2077
2	601
1	226
0	102

prune1000.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.4b

localize50.0ms

Local error

Found 2 expressions with local error:

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

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

7×	`pow1` `add-cbrt-cube` `add-exp-log`
3×	`add-sqr-sqrt` `-un-lft-identity` `associate-l*` `pow-prod-down` `prod-exp` `add-cube-cbrt` `cbrt-unprod`
2×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`sin-sum` `associate-r` `*-commutative` `fma-udef`

Counts

2 → 32

Calls

2 calls:

48.0ms	(* (sin (/ eps 2)) (* (sin (fma 1/2 eps x)) -2))
8.0ms	(sin (fma 1/2 eps x))

series163.0ms

Counts

2 → 6

Calls

2 calls:

125.0ms	(* (sin (/ eps 2)) (* (sin (fma 1/2 eps x)) -2))
38.0ms	(sin (fma 1/2 eps x))

simplify6.0s

Counts

38 → 38

Iterations

Iter	Nodes
done	5014
4	3081
3	1218
2	428
1	163
0	75

prune577.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize79.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin (* 1/2 eps)) (cos x))
0.1b	(+ (* (sin (* 1/2 eps)) (cos x)) (* (cos (* 1/2 eps)) (sin x)))
0.2b	(* (cos (* 1/2 eps)) (sin x))
0.3b	(* (sin (/ eps 2)) (* (+ (* (sin (* 1/2 eps)) (cos x)) (* (cos (* 1/2 eps)) (sin x))) -2))

rewrite428.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `pow1` `add-cbrt-cube` `add-exp-log`
9×	`-un-lft-identity` `associate-l*` `add-cube-cbrt`
7×	`associate-r`
6×	`add-log-exp`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`*-commutative`
2×	`flip3-+` `associate-l/` `associate-r/` `flip-+` `unswap-sqr`
1×	`+-commutative` `sum-log` `fma-def` `sin-cos-mult`

Counts

4 → 81

Calls

4 calls:

36.0ms	(* (sin (* 1/2 eps)) (cos x))
54.0ms	(+ (* (sin (* 1/2 eps)) (cos x)) (* (cos (* 1/2 eps)) (sin x)))
38.0ms	(* (cos (* 1/2 eps)) (sin x))
296.0ms	(* (sin (/ eps 2)) (* (+ (* (sin (* 1/2 eps)) (cos x)) (* (cos (* 1/2 eps)) (sin x))) -2))

series857.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(* (sin (* 1/2 eps)) (cos x))
241.0ms	(+ (* (sin (* 1/2 eps)) (cos x)) (* (cos (* 1/2 eps)) (sin x)))
111.0ms	(* (cos (* 1/2 eps)) (sin x))
377.0ms	(* (sin (/ eps 2)) (* (+ (* (sin (* 1/2 eps)) (cos x)) (* (cos (* 1/2 eps)) (sin x))) -2))

simplify3.3s

Counts

93 → 93

Iterations

Iter	Nodes
done	5001
2	1399
1	426
0	170

prune1.2s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

regimes658.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify10.0ms

Iterations

Iter	Nodes
done	17
1	17
0	13

end0.0ms

sample6.3s

Algorithm

intervals

Results

3.9s	4388×	body	1280	valid
914.0ms	649×	body	2560	valid
824.0ms	1901×	body	640	valid
226.0ms	689×	body	320	valid
50.0ms	290×	body	160	valid
7.0ms	83×	body	80	valid