Details

sample214.0ms

Algorithm

intervals

Results

140.0ms	159×	body	1280	valid
32.0ms	52×	body	640	valid
23.0ms	14×	body	2560	valid
6.0ms	19×	body	320	valid
3.0ms	10×	body	160	valid
0.0ms	2×	body	80	valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.6b

localize13.0ms

Local error

Found 2 expressions with local error:

0.7b	(- (cos (+ x eps)) (cos x))
2.0b	(cos (+ x eps))

rewrite50.0ms

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:

42.0ms	(- (cos (+ x eps)) (cos x))
8.0ms	(cos (+ x eps))

series76.0ms

Counts

2 → 6

Calls

2 calls:

57.0ms	(- (cos (+ x eps)) (cos x))
19.0ms	(cos (+ x eps))

simplify2.6s

Counts

48 → 48

Iterations

Iter	Nodes
done	5001
4	3872
3	1291
2	456
1	202
0	93

prune274.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.5b

localize29.0ms

Local error

Found 3 expressions with local error:

0.0b	(* -2 (* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2))))
0.3b	(* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2)))
2.1b	(sin (/ (fma 2 x eps) 2))

rewrite75.0ms

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:

44.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2))))
27.0ms	(* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2)))
3.0ms	(sin (/ (fma 2 x eps) 2))

series198.0ms

Counts

3 → 9

Calls

3 calls:

83.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2))))
70.0ms	(* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2)))
45.0ms	(sin (/ (fma 2 x eps) 2))

simplify2.4s

Counts

63 → 63

Iterations

Iter	Nodes
done	5000
3	2363
2	617
1	226
0	102

prune396.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.4b

localize30.0ms

Local error

Found 2 expressions with local error:

0.3b	(* (* (sin (fma 1/2 eps x)) -2) (sin (* eps 1/2)))
2.1b	(sin (fma 1/2 eps x))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

7×	`pow1` `add-cbrt-cube` `add-exp-log`
3×	`add-sqr-sqrt` `-un-lft-identity` `associate-r*` `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-l` `*-commutative` `fma-udef`

Counts

2 → 32

Calls

2 calls:

48.0ms	(* (* (sin (fma 1/2 eps x)) -2) (sin (* eps 1/2)))
5.0ms	(sin (fma 1/2 eps x))

series126.0ms

Counts

2 → 6

Calls

2 calls:

101.0ms	(* (* (sin (fma 1/2 eps x)) -2) (sin (* eps 1/2)))
25.0ms	(sin (fma 1/2 eps x))

simplify2.6s

Counts

38 → 38

Iterations

Iter	Nodes
done	5001
3	2536
2	692
1	174
0	78

prune328.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize52.0ms

Local error

Found 4 expressions with local error:

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

rewrite324.0ms

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×	`expm1-log1p-u` `associate-*l/` `insert-posit16` `log1p-expm1-u`
3×	`*-commutative`
2×	`flip3-+` `flip-+` `unswap-sqr`
1×	`+-commutative` `sum-log` `fma-def` `sin-cos-mult`

Counts

4 → 81

Calls

4 calls:

38.0ms	(* (cos (* 1/2 eps)) (sin x))
58.0ms	(+ (* (sin (* 1/2 eps)) (cos x)) (* (cos (* 1/2 eps)) (sin x)))
38.0ms	(* (sin (* 1/2 eps)) (cos x))
188.0ms	(* (* (+ (* (sin (* 1/2 eps)) (cos x)) (* (cos (* 1/2 eps)) (sin x))) -2) (sin (* eps 1/2)))

series521.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(* (cos (* 1/2 eps)) (sin x))
146.0ms	(+ (* (sin (* 1/2 eps)) (cos x)) (* (cos (* 1/2 eps)) (sin x)))
76.0ms	(* (sin (* 1/2 eps)) (cos x))
236.0ms	(* (* (+ (* (sin (* 1/2 eps)) (cos x)) (* (cos (* 1/2 eps)) (sin x))) -2) (sin (* eps 1/2)))

simplify1.6s

Counts

93 → 93

Iterations

Iter	Nodes
done	5001
2	1536
1	431
0	172

prune603.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

regimes226.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	26
2	26
1	25
0	19

end0.0ms

sample8.3s

Algorithm

intervals

Results

4.4s	4425×	body	1280	valid
1.2s	1901×	body	640	valid
1.1s	618×	body	2560	valid
779.0ms	711×	body	320	valid
633.0ms	277×	body	160	valid
8.0ms	68×	body	80	valid