Details

sample209.0ms

Algorithm

intervals

Results

89.0ms	98×	body	1280	valid
55.0ms	22×	body	2560	valid
34.0ms	54×	body	640	valid
15.0ms	36×	body	320	valid
5.0ms	41×	body	80	valid
1.0ms	5×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.6b

localize26.0ms

Local error

Found 2 expressions with local error:

0.6b	(- (sin (+ x eps)) (sin x))
2.4b	(sin (+ x eps))

rewrite89.0ms

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:

74.0ms	(- (sin (+ x eps)) (sin x))
14.0ms	(sin (+ x eps))

series76.0ms

Counts

2 → 6

Calls

2 calls:

56.0ms	(- (sin (+ x eps)) (sin x))
20.0ms	(sin (+ x eps))

simplify937.0ms

Counts

48 → 48

Iterations

Iter	Nodes
done	2012
3	1269
2	446
1	203
0	92

prune188.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.3b

localize22.0ms

Local error

Found 2 expressions with local error:

0.2b	(* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2)))
2.4b	(cos (/ (fma 2 x eps) 2))

rewrite22.0ms

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×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `sin-cos-mult` `unswap-sqr`

Counts

2 → 32

Calls

2 calls:

18.0ms	(* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2)))
3.0ms	(cos (/ (fma 2 x eps) 2))

series89.0ms

Counts

2 → 6

Calls

2 calls:

57.0ms	(* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2)))
32.0ms	(cos (/ (fma 2 x eps) 2))

simplify728.0ms

Counts

38 → 38

Iterations

Iter	Nodes
done	2001
3	983
2	353
1	150
0	70

prune209.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.3b

localize51.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (cos (/ (fma 2 x eps) 2)))
2.4b	(cos (/ (fma 2 x eps) 2))
2.4b	(cos (/ (fma 2 x eps) 2))
2.4b	(cos (/ (fma 2 x eps) 2))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod`
1×	`pow1/3`

Counts

4 → 44

Calls

4 calls:

1.0ms	(cbrt (cos (/ (fma 2 x eps) 2)))
3.0ms	(cos (/ (fma 2 x eps) 2))
3.0ms	(cos (/ (fma 2 x eps) 2))
3.0ms	(cos (/ (fma 2 x eps) 2))

series234.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(cbrt (cos (/ (fma 2 x eps) 2)))
25.0ms	(cos (/ (fma 2 x eps) 2))
49.0ms	(cos (/ (fma 2 x eps) 2))
37.0ms	(cos (/ (fma 2 x eps) 2))

simplify1.2s

Counts

56 → 56

Iterations

Iter	Nodes
done	2000
4	1809
3	590
2	192
1	84
0	45

prune411.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.3b

localize60.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (cos (/ (fma 2 x eps) 2)))
2.4b	(cos (/ (fma 2 x eps) 2))
2.4b	(cos (/ (fma 2 x eps) 2))
2.4b	(cos (/ (fma 2 x eps) 2))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod`
1×	`pow1/3`

Counts

4 → 44

Calls

4 calls:

2.0ms	(cbrt (cos (/ (fma 2 x eps) 2)))
6.0ms	(cos (/ (fma 2 x eps) 2))
6.0ms	(cos (/ (fma 2 x eps) 2))
7.0ms	(cos (/ (fma 2 x eps) 2))

series254.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(cbrt (cos (/ (fma 2 x eps) 2)))
41.0ms	(cos (/ (fma 2 x eps) 2))
50.0ms	(cos (/ (fma 2 x eps) 2))
43.0ms	(cos (/ (fma 2 x eps) 2))

simplify969.0ms

Counts

56 → 56

Iterations

Iter	Nodes
done	2000
4	1809
3	590
2	192
1	84
0	45

prune380.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.3b

regimes231.0ms

Accuracy

99% (0.1b remaining)

Error of 0.5b against oracle of 0.4b and baseline of 14.6b

bsearch273.0ms

Steps

Iters	Range		Point
10	3.604910300985568e-30	6.892584706772745e-13	6.765190492196658e-13
10	-121993772661.31783	-0.22068356154967622	-0.22306452923435388

simplify10.0ms

Iterations

Iter	Nodes
done	32
1	32
0	24

end0.0ms

sample7.7s

Algorithm

intervals

Results

4.0s	3255×	body	1280	valid
1.5s	665×	body	2560	valid
1.3s	1781×	body	640	valid
306.0ms	781×	body	320	valid
145.0ms	1154×	body	80	valid
104.0ms	364×	body	160	valid