Details

sample93.0ms

Algorithm

intervals

Results

42.0ms	135×	body	1280	valid
21.0ms	25×	body	2560	valid
12.0ms	64×	body	640	valid
5.0ms	19×	body	320	valid
1.0ms	11×	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: 40.6b

localize8.0ms

Local error

Found 2 expressions with local error:

1.7b	(- (cos (+ x eps)) (cos x))
2.3b	(cos (+ x eps))

rewrite24.0ms

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:

14.0ms	(- (cos (+ x eps)) (cos x))
10.0ms	(cos (+ x eps))

series73.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify1.6s

Counts

30 → 30

Iterations

Useful iterations: 4 (282.0ms)

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

prune74.0ms

Pruning

6 alts after pruning (6 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)))
2.3b	(sin (/ (+ (+ x eps) x) 2))

rewrite223.0ms

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:

74.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2))))
25.0ms	(+ (+ x eps) x)
81.0ms	(* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2)))
42.0ms	(sin (/ (+ (+ x eps) x) 2))

series181.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2))))
23.0ms	(+ (+ x eps) x)
56.0ms	(* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2)))
34.0ms	(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	810	919
3	2388	895
done	5000	889

prune174.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.2b

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))

rewrite134.0ms

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:

16.0ms	(cbrt (sin (/ (+ (+ x eps) x) 2)))
38.0ms	(sin (/ (+ (+ x eps) x) 2))
38.0ms	(sin (/ (+ (+ x eps) x) 2))
41.0ms	(sin (/ (+ (+ x eps) x) 2))

series185.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(cbrt (sin (/ (+ (+ x eps) x) 2)))
33.0ms	(sin (/ (+ (+ x eps) x) 2))
29.0ms	(sin (/ (+ (+ x eps) x) 2))
29.0ms	(sin (/ (+ (+ x eps) x) 2))

simplify2.3s

Counts

44 → 44

Iterations

Useful iterations: 4 (294.0ms)

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

prune176.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.2b

localize16.0ms

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

rewrite48.0ms

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:

2.0ms	(cbrt (sin (/ eps 2)))
2.0ms	(cbrt (sin (/ eps 2)))
2.0ms	(cbrt (sin (/ eps 2)))
41.0ms	(sin (/ (+ (+ x eps) x) 2))

series359.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(cbrt (sin (/ eps 2)))
110.0ms	(cbrt (sin (/ eps 2)))
112.0ms	(cbrt (sin (/ eps 2)))
29.0ms	(sin (/ (+ (+ x eps) x) 2))

simplify1.7s

Counts

52 → 52

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	60	558
1	122	549
2	232	503
3	540	457
4	1795	439
done	5001	430

prune159.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.2b

regimes91.0ms

Accuracy

97.7% (0.3b remaining)

Error of 0.7b against oracle of 0.4b and baseline of 14.6b

bsearch117.0ms

Steps

Iters	Range		Point
9	0.00037885794385599284	510463.6686732238	0.0005448146684575088
11	-2.8163082396285558e+17	-1.4864914298183363e-09	-2.8506138935394462e-06

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

1.4s	4401×	body	1280	valid
602.0ms	678×	body	2560	valid
378.0ms	1861×	body	640	valid
92.0ms	688×	body	320	valid
27.0ms	290×	body	160	valid
4.0ms	82×	body	80	valid