Details

sample194.0ms

Algorithm

intervals

Results

105.0ms	144×	body	1280	valid
34.0ms	20×	body	2560	valid
27.0ms	58×	body	640	valid
8.0ms	23×	body	320	valid
2.0ms	7×	body	160	valid
0.0ms	4×	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

prune48.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.3b

localize17.0ms

Local error

Found 2 expressions with local error:

0.8b	(- (cos (+ x eps)) (cos x))
3.6b	(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))

series108.0ms

Counts

2 → 6

Calls

2 calls:

80.0ms	(- (cos (+ x eps)) (cos x))
28.0ms	(cos (+ x eps))

simplify2.8s

Counts

30 → 30

Iterations

Useful iterations: 4 (409.0ms)

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

prune144.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.4b

localize31.0ms

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))

rewrite389.0ms

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:

131.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2))))
42.0ms	(+ (+ x eps) x)
142.0ms	(* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2)))
71.0ms	(sin (/ (+ (+ x eps) x) 2))

series228.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2))))
34.0ms	(+ (+ x eps) x)
71.0ms	(* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2)))
37.0ms	(sin (/ (+ (+ x eps) x) 2))

simplify2.3s

Counts

72 → 72

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	119	1098
1	277	1081
2	810	919
3	2388	895
done	5000	889

prune324.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.4b

localize37.0ms

Local error

Found 3 expressions with local error:

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

rewrite219.0ms

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:

55.0ms	(+ (+ x eps) x)
111.0ms	(* (* -2 (sin (/ eps 2))) (sin (/ (+ (+ x eps) x) 2)))
51.0ms	(sin (/ (+ (+ x eps) x) 2))

series180.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(+ (+ x eps) x)
101.0ms	(* (* -2 (sin (/ eps 2))) (sin (/ (+ (+ x eps) x) 2)))
41.0ms	(sin (/ (+ (+ x eps) x) 2))

simplify2.6s

Counts

49 → 49

Iterations

Useful iterations: done (2.6s)

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

prune175.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.4b

localize27.0ms

Local error

Found 4 expressions with local error:

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

rewrite232.0ms

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)))
69.0ms	(sin (/ (+ (+ x eps) x) 2))
89.0ms	(sin (/ (+ (+ x eps) x) 2))
55.0ms	(sin (/ (+ (+ x eps) x) 2))

series275.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(cbrt (sin (/ (+ (+ x eps) x) 2)))
46.0ms	(sin (/ (+ (+ x eps) x) 2))
56.0ms	(sin (/ (+ (+ x eps) x) 2))
35.0ms	(sin (/ (+ (+ x eps) x) 2))

simplify3.7s

Counts

44 → 44

Iterations

Useful iterations: 4 (413.0ms)

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

prune228.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.4b

regimes259.0ms

Accuracy

96.7% (0.5b remaining)

Error of 0.9b against oracle of 0.4b and baseline of 15.4b

bsearch117.0ms

Steps

Iters	Range		Point
9	5.155942382976535e-09	0.001020768799921521	0.00022642344448914372
4	-2657796.353906291	-1550992.7687819407	-1576820.312787291

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	51
1	35	51
done	35	51

end0.0ms

sample6.9s

Algorithm

intervals

Results

3.6s	4405×	body	1280	valid
1.0s	1886×	body	640	valid
1.0s	663×	body	2560	valid
738.0ms	700×	body	320	valid
83.0ms	248×	body	160	valid
9.0ms	98×	body	80	valid