Details

sample87.0ms

Algorithm

intervals

Results

44.0ms	136×	body	1280	valid
16.0ms	19×	body	2560	valid
13.0ms	60×	body	640	valid
4.0ms	26×	body	320	valid
1.0ms	11×	body	160	valid
0.0ms	4×	body	80	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	6	7
1	9	7
2	10	7
done	10	7

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.5b

localize8.0ms

Local error

Found 2 expressions with local error:

1.1b	(- (cos (+ x eps)) (cos x))
3.5b	(cos (+ x eps))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
2×	`pow1` `add-exp-log` `add-cube-cbrt` `cos-sum` `add-cbrt-cube`
1×	`associate--l-` `sub-neg` `flip3--` `diff-log` `flip--` `diff-cos` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 24

Calls

2 calls:

7.0ms	(- (cos (+ x eps)) (cos x))
5.0ms	(cos (+ x eps))

series73.0ms

Counts

2 → 6

Calls

2 calls:

51.0ms	(- (cos (+ x eps)) (cos x))
22.0ms	(cos (+ x eps))

simplify2.3s

Counts

30 → 30

Iterations

Useful iterations: 4 (382.0ms)

Iter	Nodes	Cost
0	65	311
1	134	299
2	274	283
3	590	275
4	1492	273
5	4153	273
done	5001	273

prune86.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.3b

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite129.0ms

Algorithm

rewrite-expression-head

Rules

12×	`*-un-lft-identity`
11×	`pow1` `add-exp-log` `add-cbrt-cube`
9×	`add-sqr-sqrt` `add-log-exp`
7×	`add-cube-cbrt`
6×	`associate-l`
4×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
3×	`sum-log` `distribute-lft-out`
2×	`*-commutative` `sin-mult`
1×	`+-commutative` `associate-+l+` `flip3-+` `associate-*r/` `flip-+` `unswap-sqr`

Counts

4 → 60

Calls

4 calls:

40.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2))))
14.0ms	(+ (+ x eps) x)
49.0ms	(* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2)))
23.0ms	(sin (/ (+ (+ x eps) x) 2))

series180.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2))))
28.0ms	(+ (+ x eps) x)
54.0ms	(* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2)))
32.0ms	(sin (/ (+ (+ x eps) x) 2))

simplify2.6s

Counts

72 → 72

Iterations

Useful iterations: 3 (478.0ms)

Iter	Nodes	Cost
0	119	1098
1	278	1081
2	766	919
3	2363	907
done	5000	907

prune198.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.3b

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin (/ eps 2)))
0.6b	(cbrt (sin (/ eps 2)))
0.6b	(cbrt (sin (/ eps 2)))
3.6b	(sin (/ (+ (+ x eps) x) 2))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`pow1/3`

Counts

4 → 40

Calls

4 calls:

1.0ms	(cbrt (sin (/ eps 2)))
1.0ms	(cbrt (sin (/ eps 2)))
1.0ms	(cbrt (sin (/ eps 2)))
23.0ms	(sin (/ (+ (+ x eps) x) 2))

series372.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(cbrt (sin (/ eps 2)))
111.0ms	(cbrt (sin (/ eps 2)))
114.0ms	(cbrt (sin (/ eps 2)))
33.0ms	(sin (/ (+ (+ x eps) x) 2))

simplify1.8s

Counts

52 → 52

Iterations

Useful iterations: 4 (711.0ms)

Iter	Nodes	Cost
0	60	558
1	121	549
2	238	503
3	654	461
4	2876	439
done	5000	439

prune210.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0.3b

localize18.0ms

Local error

Found 4 expressions with local error:

3.6b	(sin (/ (+ (+ x eps) x) 2))
5.1b	(cbrt (* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2))))
5.1b	(cbrt (* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2))))
5.1b	(cbrt (* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2))))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`
3×	`cbrt-prod` `cbrt-div` `pow1/3` `sin-mult`

Counts

4 → 37

Calls

4 calls:

22.0ms	(sin (/ (+ (+ x eps) x) 2))
12.0ms	(cbrt (* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2))))
12.0ms	(cbrt (* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2))))
15.0ms	(cbrt (* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2))))

series473.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(sin (/ (+ (+ x eps) x) 2))
153.0ms	(cbrt (* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2))))
144.0ms	(cbrt (* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2))))
147.0ms	(cbrt (* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2))))

simplify1.2s

Counts

49 → 49

Iterations

Useful iterations: 4 (356.0ms)

Iter	Nodes	Cost
0	66	924
1	136	918
2	271	818
3	573	767
4	1704	721
done	5000	721

prune191.0ms

Pruning

15 alts after pruning (12 fresh and 3 done)

Merged error: 0.2b

regimes180.0ms

Accuracy

97.9% (0.3b remaining)

Error of 0.7b against oracle of 0.4b and baseline of 15.1b

bsearch121.0ms

Steps

Iters	Range		Point
9	3.182061564411226e-09	0.0591185632533196	9.949689884521833e-06
9	-0.04390830018224924	-3.199438276574562e-09	-7.455928426940857e-05

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	26	51
1	35	38
done	35	38

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.5s	4395×	body	1280	valid
564.0ms	646×	body	2560	valid
390.0ms	1879×	body	640	valid
112.0ms	708×	body	320	valid
37.0ms	301×	body	160	valid
4.0ms	71×	body	80	valid