Details

sample82.0ms

Algorithm

intervals

Results

45.0ms	148×	body	1280	valid
13.0ms	65×	body	640	valid
10.0ms	12×	body	2560	valid
3.0ms	19×	body	320	valid
1.0ms	10×	body	160	valid
0.0ms	2×	body	80	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: 38.1b

localize8.0ms

Local error

Found 2 expressions with local error:

1.6b	(- (cos (+ x eps)) (cos x))
2.5b	(cos (+ x eps))

rewrite30.0ms

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:

15.0ms	(- (cos (+ x eps)) (cos x))
14.0ms	(cos (+ x eps))

series71.0ms

Counts

2 → 6

Calls

2 calls:

54.0ms	(- (cos (+ x eps)) (cos x))
17.0ms	(cos (+ x eps))

simplify1.6s

Counts

30 → 30

Iterations

Useful iterations: 4 (274.0ms)

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

prune83.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.4b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ x eps) x)
0.0b	(* -2 (* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2))))
0.3b	(* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2)))
2.3b	(sin (/ (+ (+ x eps) x) 2))

rewrite240.0ms

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:

28.0ms	(+ (+ x eps) x)
80.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2))))
87.0ms	(* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2)))
43.0ms	(sin (/ (+ (+ x eps) x) 2))

series185.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(+ (+ x eps) x)
66.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2))))
61.0ms	(* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2)))
32.0ms	(sin (/ (+ (+ x eps) x) 2))

simplify1.4s

Counts

72 → 72

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	119	1098
1	277	1081
2	808	919
3	2379	895
done	5001	889

prune182.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.3b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ x eps) x)
0.3b	(* (* -2 (sin (/ eps 2))) (sin (/ (+ (+ x eps) x) 2)))
2.3b	(sin (/ (+ (+ x eps) x) 2))

rewrite153.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity`
8×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`add-sqr-sqrt` `add-cube-cbrt`
3×	`associate-r` `pow-prod-down` `prod-exp` `sum-log` `cbrt-unprod` `distribute-lft-out`
1×	`+-commutative` `associate-+l+` `flip3-+` `associate-l` `*-commutative` `flip-+`

Counts

3 → 40

Calls

3 calls:

28.0ms	(+ (+ x eps) x)
83.0ms	(* (* -2 (sin (/ eps 2))) (sin (/ (+ (+ x eps) x) 2)))
41.0ms	(sin (/ (+ (+ x eps) x) 2))

series122.0ms

Counts

3 → 9

Calls

3 calls:

23.0ms	(+ (+ x eps) x)
65.0ms	(* (* -2 (sin (/ eps 2))) (sin (/ (+ (+ x eps) x) 2)))
33.0ms	(sin (/ (+ (+ x eps) x) 2))

simplify1.4s

Counts

49 → 49

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	93	689
1	231	671
2	722	565
3	2258	545
done	5000	539

prune127.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.3b

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin (/ (+ (+ x eps) x) 2)))
2.3b	(sin (/ (+ (+ x eps) x) 2))
2.3b	(sin (/ (+ (+ x eps) x) 2))
2.3b	(sin (/ (+ (+ x eps) x) 2))

rewrite145.0ms

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:

17.0ms	(cbrt (sin (/ (+ (+ x eps) x) 2)))
42.0ms	(sin (/ (+ (+ x eps) x) 2))
42.0ms	(sin (/ (+ (+ x eps) x) 2))
43.0ms	(sin (/ (+ (+ x eps) x) 2))

series190.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(cbrt (sin (/ (+ (+ x eps) x) 2)))
33.0ms	(sin (/ (+ (+ x eps) x) 2))
30.0ms	(sin (/ (+ (+ x eps) x) 2))
31.0ms	(sin (/ (+ (+ x eps) x) 2))

simplify2.3s

Counts

44 → 44

Iterations

Useful iterations: 4 (290.0ms)

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

prune143.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.3b

regimes104.0ms

Accuracy

97.6% (0.3b remaining)

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

bsearch98.0ms

Steps

Iters	Range		Point
8	7.445648313582303e-12	4.6493452766724325e-07	4.575180546003463e-07
8	-7.406940912248032	-0.0002772006047103471	-0.0006415376531290239

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

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

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.5s	4463×	body	1280	valid
600.0ms	1845×	body	640	valid
549.0ms	641×	body	2560	valid
93.0ms	688×	body	320	valid
27.0ms	283×	body	160	valid
4.0ms	80×	body	80	valid