Details

sample276.0ms

Algorithm

intervals

Results

135.0ms	106×	body	1280	valid
71.0ms	34×	body	2560	valid
35.0ms	47×	body	640	valid
16.0ms	32×	body	320	valid
4.0ms	25×	body	80	valid
4.0ms	12×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
3	10
2	10
1	9
0	6

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.7b

localize13.0ms

Local error

Found 2 expressions with local error:

2.2b	(- (sin (+ x eps)) (sin x))
3.5b	(sin (+ x eps))

rewrite76.0ms

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:

41.0ms	(- (sin (+ x eps)) (sin x))
34.0ms	(sin (+ x eps))

series105.0ms

Counts

2 → 6

Calls

2 calls:

72.0ms	(- (sin (+ x eps)) (sin x))
34.0ms	(sin (+ x eps))

simplify1.5s

Counts

32 → 32

Iterations

Iter	Nodes
5	3374
4	1441
3	637
2	294
1	137
0	65

prune253.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.3b

localize33.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (+ x eps))
0.3b	(* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2)))
3.6b	(cos (/ (+ x (+ x eps)) 2))

rewrite49.0ms

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:

11.0ms	(+ x (+ x eps))
15.0ms	(* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2)))
21.0ms	(cos (/ (+ x (+ x eps)) 2))

series123.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(+ x (+ x eps))
53.0ms	(* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2)))
34.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify5.0s

Counts

53 → 53

Iterations

Iter	Nodes
4	7454
3	1757
2	596
1	221
0	94

prune432.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.3b

localize47.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (* (* (cos (/ (+ x (+ x eps)) 2)) (cos (/ (+ x (+ x eps)) 2))) (cos (/ (+ x (+ x eps)) 2))))
3.6b	(cos (/ (+ x (+ x eps)) 2))
3.6b	(cos (/ (+ x (+ x eps)) 2))
3.6b	(cos (/ (+ x (+ x eps)) 2))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `add-log-exp`
1×	`cbrt-prod` `cbrt-div` `pow1/3` `pow3` `associate-*l/` `cos-mult` `rem-cbrt-cube`

Counts

4 → 36

Calls

4 calls:

13.0ms	(cbrt (* (* (cos (/ (+ x (+ x eps)) 2)) (cos (/ (+ x (+ x eps)) 2))) (cos (/ (+ x (+ x eps)) 2))))
23.0ms	(cos (/ (+ x (+ x eps)) 2))
22.0ms	(cos (/ (+ x (+ x eps)) 2))
26.0ms	(cos (/ (+ x (+ x eps)) 2))

series138.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(cbrt (* (* (cos (/ (+ x (+ x eps)) 2)) (cos (/ (+ x (+ x eps)) 2))) (cos (/ (+ x (+ x eps)) 2))))
38.0ms	(cos (/ (+ x (+ x eps)) 2))
37.0ms	(cos (/ (+ x (+ x eps)) 2))
26.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify3.5s

Counts

48 → 48

Iterations

Iter	Nodes
8	4119
7	1495
6	924
5	652
4	431
3	248
2	129
1	80
0	45

prune625.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.2b

localize62.0ms

Local error

Found 4 expressions with local error:

3.6b	(cos (/ (+ x (+ x eps)) 2))
3.6b	(cos (/ (+ x (+ x eps)) 2))
3.6b	(cos (/ (+ x (+ x eps)) 2))
3.6b	(cos (/ (+ x (+ x eps)) 2))

rewrite122.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `add-log-exp`

Counts

4 → 32

Calls

4 calls:

35.0ms	(cos (/ (+ x (+ x eps)) 2))
38.0ms	(cos (/ (+ x (+ x eps)) 2))
29.0ms	(cos (/ (+ x (+ x eps)) 2))
20.0ms	(cos (/ (+ x (+ x eps)) 2))

series151.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(cos (/ (+ x (+ x eps)) 2))
37.0ms	(cos (/ (+ x (+ x eps)) 2))
40.0ms	(cos (/ (+ x (+ x eps)) 2))
39.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify1.9s

Counts

44 → 44

Iterations

Iter	Nodes
9	2889
8	1502
7	748
6	527
5	355
4	251
3	165
2	92
1	57
0	27

prune467.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 0.2b

regimes197.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.4b against oracle of 0.3b and baseline of 14.6b

bsearch298.0ms

Steps

Iters	Range		Point
10	1.578644681612568e-16	0.0001688282409805197	1.2412047115655244e-08
11	-145.89507053458865	-6.948120050383171e-19	-9.108842191445869e-09

simplify12.0ms

Iterations

Iter	Nodes
2	35
1	35
0	27

end0.0ms

sample6.9s

Algorithm

intervals

Results

3.6s	3376×	body	1280	valid
1.1s	645×	body	2560	valid
1.0s	1731×	body	640	valid
693.0ms	792×	body	320	valid
145.0ms	380×	body	160	valid
122.0ms	1076×	body	80	valid