Details

sample91.0ms

Algorithm

intervals

Results

45.0ms	133×	body	1280	valid
19.0ms	22×	body	2560	valid
14.0ms	67×	body	640	valid
3.0ms	19×	body	320	valid
1.0ms	13×	body	160	valid
0.0ms	2×	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: 37.5b

localize14.0ms

Local error

Found 2 expressions with local error:

1.0b	(- (cos (+ x eps)) (cos x))
4.0b	(cos (+ x eps))

rewrite13.0ms

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:

8.0ms	(- (cos (+ x eps)) (cos x))
5.0ms	(cos (+ x eps))

series66.0ms

Counts

2 → 6

Calls

2 calls:

51.0ms	(- (cos (+ x eps)) (cos x))
15.0ms	(cos (+ x eps))

simplify2.4s

Counts

30 → 30

Iterations

Useful iterations: 4 (311.0ms)

Iter	Nodes	Cost
0	65	311
1	134	299
2	274	283
3	590	275
4	1496	273
5	4159	273
done	5000	273

prune78.0ms

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

rewrite132.0ms

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 2)) (sin (/ (+ (+ x eps) x) 2))))
15.0ms	(+ (+ x eps) x)
50.0ms	(* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2)))
23.0ms	(sin (/ (+ (+ x eps) x) 2))

series174.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2))))
22.0ms	(+ (+ x eps) x)
57.0ms	(* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2)))
29.0ms	(sin (/ (+ (+ x eps) x) 2))

simplify1.4s

Counts

72 → 72

Iterations

Useful iterations: 3 (359.0ms)

Iter	Nodes	Cost
0	119	1098
1	278	1081
2	766	919
3	2362	907
done	5000	907

prune178.0ms

Pruning

11 alts after pruning (11 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)))
4.1b	(sin (/ (+ (+ x eps) x) 2))

rewrite84.0ms

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:

15.0ms	(+ (+ x eps) x)
42.0ms	(* (* -2 (sin (/ eps 2))) (sin (/ (+ (+ x eps) x) 2)))
26.0ms	(sin (/ (+ (+ x eps) x) 2))

series120.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(+ (+ x eps) x)
62.0ms	(* (* -2 (sin (/ eps 2))) (sin (/ (+ (+ x eps) x) 2)))
31.0ms	(sin (/ (+ (+ x eps) x) 2))

simplify1.4s

Counts

49 → 49

Iterations

Useful iterations: 3 (364.0ms)

Iter	Nodes	Cost
0	93	689
1	232	671
2	714	565
3	2195	553
done	5000	553

prune131.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.3b

localize18.0ms

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)))
4.1b	(sin (/ (+ (+ x eps) x) 2))

rewrite28.0ms

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:

1.0ms	(cbrt (sin (/ eps 2)))
1.0ms	(cbrt (sin (/ eps 2)))
1.0ms	(cbrt (sin (/ eps 2)))
23.0ms	(sin (/ (+ (+ x eps) x) 2))

series372.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(cbrt (sin (/ eps 2)))
113.0ms	(cbrt (sin (/ eps 2)))
118.0ms	(cbrt (sin (/ eps 2)))
29.0ms	(sin (/ (+ (+ x eps) x) 2))

simplify1.7s

Counts

52 → 52

Iterations

Useful iterations: 4 (472.0ms)

Iter	Nodes	Cost
0	60	558
1	121	549
2	238	503
3	654	461
4	2869	443
done	5000	443

prune346.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.3b

regimes189.0ms

Accuracy

97.9% (0.3b remaining)

Error of 0.7b against oracle of 0.4b and baseline of 15.2b

bsearch111.0ms

Steps

Iters	Range		Point
8	9.143643357499823e-08	5.968040026638966e-05	2.684800803254601e-05
9	-4030.930838101798	-2.879878352494296e-05	-4.402851865399074e-05

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.6s	4457×	body	1280	valid
585.0ms	686×	body	2560	valid
392.0ms	1837×	body	640	valid
105.0ms	656×	body	320	valid
40.0ms	292×	body	160	valid
4.0ms	72×	body	80	valid