Details

sample151.0ms

Algorithm

intervals

Results

84.0ms	145×	body	1280	valid
24.0ms	16×	body	2560	valid
23.0ms	55×	body	640	valid
7.0ms	26×	body	320	valid
2.0ms	10×	body	160	valid
0.0ms	4×	body	80	valid

simplify3.0ms

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: 41.3b

localize47.0ms

Local error

Found 2 expressions with local error:

1.1b	(- (cos (+ x eps)) (cos x))
3.7b	(cos (+ x eps))

rewrite37.0ms

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))
20.0ms	(cos (+ x eps))

series523.0ms

Counts

2 → 6

Calls

2 calls:

500.0ms	(- (cos (+ x eps)) (cos x))
23.0ms	(cos (+ x eps))

simplify2.5s

Counts

30 → 30

Iterations

Useful iterations: 4 (403.0ms)

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

prune130.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

localize14.0ms

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))

rewrite370.0ms

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:

105.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2))))
41.0ms	(+ (+ x eps) x)
132.0ms	(* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2)))
89.0ms	(sin (/ (+ (+ x eps) x) 2))

series306.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2))))
47.0ms	(+ (+ x eps) x)
100.0ms	(* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2)))
42.0ms	(sin (/ (+ (+ x eps) x) 2))

simplify2.1s

Counts

72 → 72

Iterations

Useful iterations: done (2.1s)

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

prune332.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.2b

localize20.0ms

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))

rewrite205.0ms

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:

32.0ms	(+ (+ x eps) x)
123.0ms	(* (* -2 (sin (/ eps 2))) (sin (/ (+ (+ x eps) x) 2)))
48.0ms	(sin (/ (+ (+ x eps) x) 2))

series181.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(+ (+ x eps) x)
99.0ms	(* (* -2 (sin (/ eps 2))) (sin (/ (+ (+ x eps) x) 2)))
39.0ms	(sin (/ (+ (+ x eps) x) 2))

simplify2.1s

Counts

49 → 49

Iterations

Useful iterations: done (2.1s)

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

prune171.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.2b

localize19.0ms

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

rewrite88.0ms

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)))
81.0ms	(sin (/ (+ (+ x eps) x) 2))

series450.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(cbrt (sin (/ eps 2)))
157.0ms	(cbrt (sin (/ eps 2)))
118.0ms	(cbrt (sin (/ eps 2)))
35.0ms	(sin (/ (+ (+ x eps) x) 2))

simplify2.1s

Counts

52 → 52

Iterations

Useful iterations: done (2.1s)

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

prune180.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.2b

regimes244.0ms

Accuracy

97.9% (0.3b remaining)

Error of 0.7b against oracle of 0.4b and baseline of 15.3b

bsearch139.0ms

Steps

Iters	Range		Point
9	0.04058914318552966	3991008.2413703846	0.04140103919524168
7	-0.22637101271021068	-0.008005822963963436	-0.00815188689103541

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample6.8s

Algorithm

intervals

Results

4.1s	4400×	body	1280	valid
1.0s	633×	body	2560	valid
900.0ms	1942×	body	640	valid
342.0ms	651×	body	320	valid
54.0ms	284×	body	160	valid
9.0ms	90×	body	80	valid