Details

sample233.0ms

Algorithm

intervals

Results

113.0ms	98×	body	1280	valid
41.0ms	22×	body	2560	valid
40.0ms	54×	body	640	valid
17.0ms	36×	body	320	valid
6.0ms	41×	body	80	valid
1.0ms	5×	body	160	valid

simplify8.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.6b

localize38.0ms

Local error

Found 2 expressions with local error:

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

rewrite47.0ms

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:

36.0ms	(- (sin (+ x eps)) (sin x))
10.0ms	(sin (+ x eps))

series79.0ms

Counts

2 → 6

Calls

2 calls:

51.0ms	(- (sin (+ x eps)) (sin x))
29.0ms	(sin (+ x eps))

simplify823.0ms

Counts

32 → 32

Iterations

Iter	Nodes
done	2002
4	1723
3	751
2	308
1	137
0	65

prune167.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.3b

localize22.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (+ x eps))
0.2b	(* (sin (* 1/2 eps)) (cos (/ (+ x (+ x eps)) 2)))
2.4b	(cos (/ (+ x (+ x eps)) 2))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity`
8×	`add-log-exp`
7×	`add-sqr-sqrt`
5×	`pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
3×	`sum-log` `associate-r` `associate-l` `insert-posit16` `distribute-lft-out`
1×	`+-commutative` `associate-+r+` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `sin-cos-mult` `unswap-sqr`

Counts

3 → 44

Calls

3 calls:

22.0ms	(+ x (+ x eps))
37.0ms	(* (sin (* 1/2 eps)) (cos (/ (+ x (+ x eps)) 2)))
33.0ms	(cos (/ (+ x (+ x eps)) 2))

series135.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(+ x (+ x eps))
75.0ms	(* (sin (* 1/2 eps)) (cos (/ (+ x (+ x eps)) 2)))
26.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify487.0ms

Counts

53 → 53

Iterations

Iter	Nodes
done	2001
2	654
1	221
0	92

prune276.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.3b

localize56.0ms

Local error

Found 4 expressions with local error:

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

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 36

Calls

4 calls:

1.0ms	(cbrt (cos (/ (+ x (+ x eps)) 2)))
23.0ms	(cos (/ (+ x (+ x eps)) 2))
31.0ms	(cos (/ (+ x (+ x eps)) 2))
42.0ms	(cos (/ (+ x (+ x eps)) 2))

series196.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(cbrt (cos (/ (+ x (+ x eps)) 2)))
29.0ms	(cos (/ (+ x (+ x eps)) 2))
36.0ms	(cos (/ (+ x (+ x eps)) 2))
27.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify853.0ms

Counts

48 → 48

Iterations

Iter	Nodes
done	2004
4	1626
3	543
2	186
1	91
0	44

prune321.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.3b

localize70.0ms

Local error

Found 4 expressions with local error:

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

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 36

Calls

4 calls:

2.0ms	(cbrt (cos (/ (+ x (+ x eps)) 2)))
47.0ms	(cos (/ (+ x (+ x eps)) 2))
32.0ms	(cos (/ (+ x (+ x eps)) 2))
24.0ms	(cos (/ (+ x (+ x eps)) 2))

series225.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(cbrt (cos (/ (+ x (+ x eps)) 2)))
25.0ms	(cos (/ (+ x (+ x eps)) 2))
40.0ms	(cos (/ (+ x (+ x eps)) 2))
42.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify787.0ms

Counts

48 → 48

Iterations

Iter	Nodes
done	2004
4	1626
3	543
2	186
1	91
0	44

prune349.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.3b

regimes188.0ms

Accuracy

99% (0.1b remaining)

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

bsearch261.0ms

Steps

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

simplify6.0ms

Iterations

Iter	Nodes
done	37
1	37
0	26

end0.0ms

sample8.2s

Algorithm

intervals

Results

4.3s	3255×	body	1280	valid
1.8s	665×	body	2560	valid
1.2s	1781×	body	640	valid
346.0ms	781×	body	320	valid
155.0ms	1154×	body	80	valid
131.0ms	364×	body	160	valid