Details

sample236.0ms

Algorithm

intervals

Results

143.0ms	144×	body	1280	valid
35.0ms	21×	body	2560	valid
27.0ms	54×	body	640	valid
8.0ms	22×	body	320	valid
3.0ms	9×	body	160	valid
1.0ms	6×	body	80	valid

simplify9.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	9	7
2	10	7
done	10	7

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.6b

localize19.0ms

Local error

Found 2 expressions with local error:

1.2b	(- (cos (+ x eps)) (cos x))
3.5b	(cos (+ x eps))

rewrite45.0ms

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:

23.0ms	(- (cos (+ x eps)) (cos x))
21.0ms	(cos (+ x eps))

series123.0ms

Counts

2 → 6

Calls

2 calls:

72.0ms	(- (cos (+ x eps)) (cos x))
51.0ms	(cos (+ x eps))

simplify832.0ms

Counts

30 → 30

Iterations

Useful iterations: done (831.0ms)

Iter	Nodes	Cost
0	65	311
1	135	299
2	339	283
3	1210	275
done	5000	273

prune102.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.3b

localize30.0ms

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))

rewrite375.0ms

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:

112.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2))))
59.0ms	(+ (+ x eps) x)
132.0ms	(* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2)))
69.0ms	(sin (/ (+ (+ x eps) x) 2))

series239.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2))))
32.0ms	(+ (+ x eps) x)
66.0ms	(* (sin (/ eps 2)) (sin (/ (+ (+ x eps) x) 2)))
35.0ms	(sin (/ (+ (+ x eps) x) 2))

simplify811.0ms

Counts

72 → 72

Iterations

Useful iterations: done (808.0ms)

Iter	Nodes	Cost
0	119	1098
1	284	1081
2	1056	923
done	5001	895

prune302.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.2b

localize23.0ms

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))

rewrite220.0ms

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:

47.0ms	(+ (+ x eps) x)
110.0ms	(* (* -2 (sin (/ eps 2))) (sin (/ (+ (+ x eps) x) 2)))
60.0ms	(sin (/ (+ (+ x eps) x) 2))

series192.0ms

Counts

3 → 9

Calls

3 calls:

25.0ms	(+ (+ x eps) x)
115.0ms	(* (* -2 (sin (/ eps 2))) (sin (/ (+ (+ x eps) x) 2)))
51.0ms	(sin (/ (+ (+ x eps) x) 2))

simplify888.0ms

Counts

49 → 49

Iterations

Useful iterations: done (886.0ms)

Iter	Nodes	Cost
0	93	689
1	235	673
2	1089	567
done	5001	545

prune242.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.2b

localize39.0ms

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))

rewrite207.0ms

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:

24.0ms	(cbrt (sin (/ (+ (+ x eps) x) 2)))
54.0ms	(sin (/ (+ (+ x eps) x) 2))
68.0ms	(sin (/ (+ (+ x eps) x) 2))
59.0ms	(sin (/ (+ (+ x eps) x) 2))

series322.0ms

Counts

4 → 12

Calls

4 calls:

187.0ms	(cbrt (sin (/ (+ (+ x eps) x) 2)))
38.0ms	(sin (/ (+ (+ x eps) x) 2))
49.0ms	(sin (/ (+ (+ x eps) x) 2))
48.0ms	(sin (/ (+ (+ x eps) x) 2))

simplify4.8s

Counts

44 → 44

Iterations

Useful iterations: 4 (1.4s)

Iter	Nodes	Cost
0	57	570
1	120	567
2	304	501
3	1056	477
4	4975	467
done	5001	467

prune281.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.2b

regimes264.0ms

Accuracy

97.4% (0.4b remaining)

Error of 0.7b against oracle of 0.4b and baseline of 14.8b

bsearch208.0ms

Steps

Iters	Range		Point
10	5.2366538615162886e-09	44039.89650146889	9.76354326473103e-05
8	-527.3133570883257	-0.03117879455470207	-0.03196418493759398

simplify8.0ms

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

3.3s	4477×	body	1280	valid
1.4s	1831×	body	640	valid
1.2s	647×	body	2560	valid
661.0ms	671×	body	320	valid
58.0ms	292×	body	160	valid
8.0ms	82×	body	80	valid