Details

sample155.0ms

Algorithm

intervals

Results

75.0ms	140×	body	1280	valid
37.0ms	28×	body	2560	valid
21.0ms	61×	body	640	valid
5.0ms	19×	body	320	valid
1.0ms	6×	body	160	valid
0.0ms	2×	body	80	valid

simplify8.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune41.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.9b

localize13.0ms

Local error

Found 2 expressions with local error:

0.8b	(- (cos (+ x eps)) (cos x))
4.6b	(cos (+ x eps))

rewrite27.0ms

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:

16.0ms	(- (cos (+ x eps)) (cos x))
10.0ms	(cos (+ x eps))

series119.0ms

Counts

2 → 6

Calls

2 calls:

97.0ms	(- (cos (+ x eps)) (cos x))
22.0ms	(cos (+ x eps))

simplify2.7s

Counts

30 → 30

Iterations

Useful iterations: 4 (417.0ms)

Iter	Nodes	Cost
0	65	311
1	135	299
2	266	283
3	540	275
4	1076	273
5	2577	273
done	5001	273

prune163.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.3b

localize24.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ x eps) x)
0.3b	(* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2)))
4.4b	(sin (/ (+ (+ x eps) x) 2))

rewrite218.0ms

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` `cbrt-unprod` `flip-+` `sin-mult` `unswap-sqr`

Counts

3 → 41

Calls

3 calls:

38.0ms	(+ (+ x eps) x)
122.0ms	(* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2)))
56.0ms	(sin (/ (+ (+ x eps) x) 2))

series172.0ms

Counts

3 → 9

Calls

3 calls:

32.0ms	(+ (+ x eps) x)
107.0ms	(* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2)))
33.0ms	(sin (/ (+ (+ x eps) x) 2))

simplify3.8s

Counts

50 → 50

Iterations

Useful iterations: 4 (2.3s)

Iter	Nodes	Cost
0	91	654
1	206	646
2	540	568
3	1301	550
4	4556	544
done	5000	544

prune162.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.2b

localize43.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin (/ (+ (+ x eps) x) 2)))
4.4b	(sin (/ (+ (+ x eps) x) 2))
4.4b	(sin (/ (+ (+ x eps) x) 2))
4.4b	(sin (/ (+ (+ x eps) x) 2))

rewrite229.0ms

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:

34.0ms	(cbrt (sin (/ (+ (+ x eps) x) 2)))
88.0ms	(sin (/ (+ (+ x eps) x) 2))
53.0ms	(sin (/ (+ (+ x eps) x) 2))
53.0ms	(sin (/ (+ (+ x eps) x) 2))

series312.0ms

Counts

4 → 12

Calls

4 calls:

179.0ms	(cbrt (sin (/ (+ (+ x eps) x) 2)))
38.0ms	(sin (/ (+ (+ x eps) x) 2))
42.0ms	(sin (/ (+ (+ x eps) x) 2))
52.0ms	(sin (/ (+ (+ x eps) x) 2))

simplify3.9s

Counts

44 → 44

Iterations

Useful iterations: 4 (443.0ms)

Iter	Nodes	Cost
0	57	570
1	120	567
2	251	501
3	519	477
4	1308	467
5	3961	467
done	5000	467

prune252.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.2b

localize28.0ms

Local error

Found 4 expressions with local error:

4.4b	(sin (/ (+ (+ x eps) x) 2))
6.3b	(cbrt (* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2))))
6.3b	(cbrt (* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2))))
6.3b	(cbrt (* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2))))

rewrite148.0ms

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:

58.0ms	(sin (/ (+ (+ x eps) x) 2))
22.0ms	(cbrt (* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2))))
30.0ms	(cbrt (* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2))))
38.0ms	(cbrt (* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2))))

series586.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(sin (/ (+ (+ x eps) x) 2))
171.0ms	(cbrt (* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2))))
183.0ms	(cbrt (* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2))))
200.0ms	(cbrt (* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2))))

simplify2.2s

Counts

49 → 49

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	66	924
1	136	918
2	274	818
3	622	751
4	1784	721
done	5001	712

prune290.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0.2b

regimes202.0ms

Accuracy

97.6% (0.4b remaining)

Error of 0.7b against oracle of 0.4b and baseline of 14.9b

bsearch212.0ms

Steps

Iters	Range		Point
10	2.714148548773617e-15	3495.1882749471233	3.028675491606891e-06
10	-7.35943201301068	-4.7981562703001505e-12	-0.00026844987953330624

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

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

end0.0ms

sample6.7s

Algorithm

intervals

Results

3.5s	4478×	body	1280	valid
1.5s	625×	body	2560	valid
938.0ms	1802×	body	640	valid
242.0ms	732×	body	320	valid
85.0ms	279×	body	160	valid
7.0ms	84×	body	80	valid