Details

sample92.0ms

Algorithm

intervals

Results

47.0ms	145×	body	1280	valid
20.0ms	24×	body	2560	valid
12.0ms	59×	body	640	valid
3.0ms	24×	body	320	valid
0.0ms	3×	body	160	valid
0.0ms	1×	body	80	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 41.0b

localize8.0ms

Local error

Found 2 expressions with local error:

1.0b	(- (cos (+ x eps)) (cos x))
4.2b	(cos (+ x eps))

rewrite12.0ms

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:

7.0ms	(- (cos (+ x eps)) (cos x))
5.0ms	(cos (+ x eps))

series72.0ms

Counts

2 → 6

Calls

2 calls:

50.0ms	(- (cos (+ x eps)) (cos x))
22.0ms	(cos (+ x eps))

simplify1.3s

Counts

30 → 30

Iterations

Useful iterations: 4 (423.0ms)

Iter	Nodes	Cost
0	65	311
1	134	299
2	274	283
3	643	275
4	1979	273
done	5000	273

prune82.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(* -2 (* (sin (* eps 1/2)) (sin (/ (+ (+ x eps) x) 2))))
0.0b	(+ (+ x eps) x)
0.3b	(* (sin (* eps 1/2)) (sin (/ (+ (+ x eps) x) 2)))
4.1b	(sin (/ (+ (+ x eps) x) 2))

rewrite129.0ms

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:

42.0ms	(* -2 (* (sin (* eps 1/2)) (sin (/ (+ (+ x eps) x) 2))))
16.0ms	(+ (+ x eps) x)
47.0ms	(* (sin (* eps 1/2)) (sin (/ (+ (+ x eps) x) 2)))
23.0ms	(sin (/ (+ (+ x eps) x) 2))

series172.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(* -2 (* (sin (* eps 1/2)) (sin (/ (+ (+ x eps) x) 2))))
22.0ms	(+ (+ x eps) x)
57.0ms	(* (sin (* eps 1/2)) (sin (/ (+ (+ x eps) x) 2)))
29.0ms	(sin (/ (+ (+ x eps) x) 2))

simplify1.6s

Counts

72 → 72

Iterations

Useful iterations: 3 (529.0ms)

Iter	Nodes	Cost
0	119	1098
1	278	1077
2	803	919
3	3184	907
done	5000	907

prune351.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.2b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ x eps) x)
0.3b	(* (* -2 (sin (* eps 1/2))) (sin (/ (+ (+ x eps) x) 2)))
4.1b	(sin (/ (+ (+ x eps) x) 2))

rewrite82.0ms

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:

14.0ms	(+ (+ x eps) x)
44.0ms	(* (* -2 (sin (* eps 1/2))) (sin (/ (+ (+ x eps) x) 2)))
22.0ms	(sin (/ (+ (+ x eps) x) 2))

series116.0ms

Counts

3 → 9

Calls

3 calls:

22.0ms	(+ (+ x eps) x)
65.0ms	(* (* -2 (sin (* eps 1/2))) (sin (/ (+ (+ x eps) x) 2)))
29.0ms	(sin (/ (+ (+ x eps) x) 2))

simplify1.6s

Counts

49 → 49

Iterations

Useful iterations: 3 (498.0ms)

Iter	Nodes	Cost
0	93	689
1	230	673
2	739	563
3	2986	553
done	5001	553

prune136.0ms

Pruning

13 alts after pruning (12 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)))
4.1b	(sin (/ (+ (+ x eps) x) 2))
4.1b	(sin (/ (+ (+ x eps) x) 2))
4.1b	(sin (/ (+ (+ x eps) x) 2))

rewrite80.0ms

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:

10.0ms	(cbrt (sin (/ (+ (+ x eps) x) 2)))
22.0ms	(sin (/ (+ (+ x eps) x) 2))
23.0ms	(sin (/ (+ (+ x eps) x) 2))
25.0ms	(sin (/ (+ (+ x eps) x) 2))

series180.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(cbrt (sin (/ (+ (+ x eps) x) 2)))
28.0ms	(sin (/ (+ (+ x eps) x) 2))
27.0ms	(sin (/ (+ (+ x eps) x) 2))
31.0ms	(sin (/ (+ (+ x eps) x) 2))

simplify2.2s

Counts

44 → 44

Iterations

Useful iterations: 4 (731.0ms)

Iter	Nodes	Cost
0	57	570
1	119	567
2	256	501
3	773	493
4	4220	483
done	5000	483

prune161.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.2b

regimes243.0ms

Accuracy

97.8% (0.3b remaining)

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

bsearch139.0ms

Steps

Iters	Range		Point
11	2.28145452431431e-18	2231369.5462890854	1.2384991687240798e-05
10	-925426.909356872	-1.1036397448000079e-07	-0.0002414674700011765

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	27	51
1	37	38
done	37	38

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.6s	4511×	body	1280	valid
579.0ms	666×	body	2560	valid
391.0ms	1784×	body	640	valid
106.0ms	691×	body	320	valid
25.0ms	259×	body	160	valid
4.0ms	89×	body	80	valid