Details

sample84.0ms

Algorithm

intervals

Results

42.0ms	108×	body	1280	valid
16.0ms	68×	body	640	valid
10.0ms	12×	body	2560	valid
3.0ms	21×	body	320	valid
2.0ms	41×	body	80	valid
1.0ms	6×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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: 34.6b

localize8.0ms

Local error

Found 2 expressions with local error:

0.9b	(- (sin (+ x eps)) (sin x))
2.4b	(sin (+ x eps))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 24

Calls

2 calls:

44.0ms	(- (sin (+ x eps)) (sin x))
9.0ms	(sin (+ x eps))

series64.0ms

Counts

2 → 6

Calls

2 calls:

43.0ms	(- (sin (+ x eps)) (sin x))
21.0ms	(sin (+ x eps))

simplify1.9s

Counts

30 → 30

Iterations

Useful iterations: 4 (300.0ms)

Iter	Nodes	Cost
0	64	309
1	135	295
2	284	281
3	572	275
4	1162	271
5	2763	271
done	5000	271

prune73.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.3b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ x eps) x)
0.2b	(* (sin (/ eps 2)) (cos (/ (+ (+ x eps) x) 2)))
2.1b	(cos (/ (+ (+ x eps) x) 2))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 41

Calls

3 calls:

25.0ms	(+ (+ x eps) x)
18.0ms	(* (sin (/ eps 2)) (cos (/ (+ (+ x eps) x) 2)))
39.0ms	(cos (/ (+ (+ x eps) x) 2))

series101.0ms

Counts

3 → 9

Calls

3 calls:

24.0ms	(+ (+ x eps) x)
51.0ms	(* (sin (/ eps 2)) (cos (/ (+ (+ x eps) x) 2)))
25.0ms	(cos (/ (+ (+ x eps) x) 2))

simplify2.8s

Counts

50 → 50

Iterations

Useful iterations: 4 (1.7s)

Iter	Nodes	Cost
0	91	656
1	213	646
2	546	566
3	1366	548
4	4627	540
done	5000	540

prune122.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (cos (/ (+ (+ x eps) x) 2)))
2.1b	(cos (/ (+ (+ x eps) x) 2))
2.1b	(cos (/ (+ (+ x eps) x) 2))
2.1b	(cos (/ (+ (+ x eps) x) 2))

rewrite121.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 32

Calls

4 calls:

1.0ms	(cbrt (cos (/ (+ (+ x eps) x) 2)))
40.0ms	(cos (/ (+ (+ x eps) x) 2))
38.0ms	(cos (/ (+ (+ x eps) x) 2))
41.0ms	(cos (/ (+ (+ x eps) x) 2))

series161.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(cbrt (cos (/ (+ (+ x eps) x) 2)))
25.0ms	(cos (/ (+ (+ x eps) x) 2))
27.0ms	(cos (/ (+ (+ x eps) x) 2))
25.0ms	(cos (/ (+ (+ x eps) x) 2))

simplify1.7s

Counts

44 → 44

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	42	551
1	88	540
2	162	466
3	289	447
4	509	447
5	831	447
6	1833	447
done	5000	415

prune163.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.3b

localize17.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (* (sin (/ eps 2)) (cos (/ (+ (+ x eps) x) 2))))
2.1b	(cos (/ (+ (+ x eps) x) 2))
2.1b	(cos (/ (+ (+ x eps) x) 2))
2.1b	(cos (/ (+ (+ x eps) x) 2))

rewrite125.0ms

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`
1×	`cbrt-prod` `cbrt-div` `pow1/3` `sin-cos-mult`

Counts

4 → 31

Calls

4 calls:

5.0ms	(cbrt (* (sin (/ eps 2)) (cos (/ (+ (+ x eps) x) 2))))
40.0ms	(cos (/ (+ (+ x eps) x) 2))
38.0ms	(cos (/ (+ (+ x eps) x) 2))
41.0ms	(cos (/ (+ (+ x eps) x) 2))

series189.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(cbrt (* (sin (/ eps 2)) (cos (/ (+ (+ x eps) x) 2))))
25.0ms	(cos (/ (+ (+ x eps) x) 2))
25.0ms	(cos (/ (+ (+ x eps) x) 2))
28.0ms	(cos (/ (+ (+ x eps) x) 2))

simplify1.5s

Counts

43 → 43

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	65	617
1	133	609
2	240	527
3	533	497
4	1538	489
done	5000	488

prune153.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.3b

regimes88.0ms

Accuracy

99.4% (0.1b remaining)

Error of 0.4b against oracle of 0.4b and baseline of 14.8b

bsearch112.0ms

Steps

Iters	Range		Point
8	5.712072376485207e-16	7.445648313582303e-12	7.263195155747594e-12
10	-9.588134368690297e-05	-2.110491317952259e-15	-6.839223651471605e-09

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	25	51
1	35	38
done	35	38

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.4s	3264×	body	1280	valid
583.0ms	641×	body	2560	valid
424.0ms	1781×	body	640	valid
115.0ms	763×	body	320	valid
64.0ms	1201×	body	80	valid
35.0ms	350×	body	160	valid