Details

sample90.0ms

Algorithm

intervals

Results

45.0ms	136×	body	1280	valid
18.0ms	22×	body	2560	valid
14.0ms	67×	body	640	valid
2.0ms	13×	body	320	valid
1.0ms	14×	body	160	valid
0.0ms	4×	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

localize13.0ms

Local error

Found 2 expressions with local error:

1.3b	(- (cos (+ x eps)) (cos x))
4.6b	(cos (+ x eps))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`add-cube-cbrt` `prod-diff`
4×	`add-log-exp`
3×	`fma-neg`
2×	`pow1` `add-exp-log` `expm1-log1p-u` `cos-sum` `add-cbrt-cube` `log1p-expm1-u`
1×	`associate--l-` `sub-neg` `flip3--` `diff-log` `flip--` `diff-cos` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 40

Calls

2 calls:

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

series63.0ms

Counts

2 → 6

Calls

2 calls:

48.0ms	(- (cos (+ x eps)) (cos x))
14.0ms	(cos (+ x eps))

simplify1.4s

Counts

46 → 46

Iterations

Useful iterations: 3 (287.0ms)

Iter	Nodes	Cost
0	91	664
1	193	540
2	465	453
3	1563	389
done	5001	389

prune113.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.7b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(* -2 (* (sin (/ (- eps 0) 2)) (sin (/ (+ (+ x eps) x) 2))))
0.0b	(+ (+ x eps) x)
0.4b	(* (sin (/ (- eps 0) 2)) (sin (/ (+ (+ x eps) x) 2)))
4.7b	(sin (/ (+ (+ x eps) x) 2))

rewrite132.0ms

Algorithm

rewrite-expression-head

Rules

15×	`*-un-lft-identity`
11×	`pow1` `add-exp-log` `add-cbrt-cube`
10×	`add-sqr-sqrt`
9×	`add-log-exp`
8×	`add-cube-cbrt`
6×	`associate-l`
4×	`expm1-log1p-u` `fma-def` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `distribute-lft-out`
3×	`sum-log`
2×	`*-commutative` `sin-mult`
1×	`+-commutative` `associate-+l+` `flip3-+` `associate-*r/` `flip-+` `unswap-sqr`

Counts

4 → 72

Calls

4 calls:

43.0ms	(* -2 (* (sin (/ (- eps 0) 2)) (sin (/ (+ (+ x eps) x) 2))))
14.0ms	(+ (+ x eps) x)
53.0ms	(* (sin (/ (- eps 0) 2)) (sin (/ (+ (+ x eps) x) 2)))
20.0ms	(sin (/ (+ (+ x eps) x) 2))

series170.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(* -2 (* (sin (/ (- eps 0) 2)) (sin (/ (+ (+ x eps) x) 2))))
21.0ms	(+ (+ x eps) x)
56.0ms	(* (sin (/ (- eps 0) 2)) (sin (/ (+ (+ x eps) x) 2)))
29.0ms	(sin (/ (+ (+ x eps) x) 2))

simplify3.3s

Counts

84 → 84

Iterations

Useful iterations: done (3.3s)

Iter	Nodes	Cost
0	129	1298
1	300	1154
2	819	995
3	2491	914
done	5000	908

prune267.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.6b

localize14.0ms

Local error

Found 2 expressions with local error:

0.4b	(* (* -2 (sin (/ eps 2))) (sin (/ (fma x 2 eps) 2)))
4.6b	(sin (/ (fma x 2 eps) 2))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

7×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`add-sqr-sqrt` `add-cube-cbrt` `-un-lft-identity` `associate-r*` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
1×	`associate-l` `*-commutative`

Counts

2 → 29

Calls

2 calls:

11.0ms	(* (* -2 (sin (/ eps 2))) (sin (/ (fma x 2 eps) 2)))
2.0ms	(sin (/ (fma x 2 eps) 2))

series95.0ms

Counts

2 → 6

Calls

2 calls:

65.0ms	(* (* -2 (sin (/ eps 2))) (sin (/ (fma x 2 eps) 2)))
30.0ms	(sin (/ (fma x 2 eps) 2))

simplify4.8s

Counts

35 → 35

Iterations

Useful iterations: 3 (482.0ms)

Iter	Nodes	Cost
0	71	552
1	168	539
2	544	447
3	1630	444
4	3562	444
done	5000	444

prune137.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.6b

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin (/ (fma x 2 eps) 2)))
4.6b	(sin (/ (fma x 2 eps) 2))
4.6b	(sin (/ (fma x 2 eps) 2))
4.6b	(sin (/ (fma x 2 eps) 2))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod`
1×	`pow1/3`

Counts

4 → 40

Calls

4 calls:

1.0ms	(cbrt (sin (/ (fma x 2 eps) 2)))
2.0ms	(sin (/ (fma x 2 eps) 2))
2.0ms	(sin (/ (fma x 2 eps) 2))
5.0ms	(sin (/ (fma x 2 eps) 2))

series187.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(cbrt (sin (/ (fma x 2 eps) 2)))
35.0ms	(sin (/ (fma x 2 eps) 2))
29.0ms	(sin (/ (fma x 2 eps) 2))
30.0ms	(sin (/ (fma x 2 eps) 2))

simplify1.6s

Counts

52 → 52

Iterations

Useful iterations: 4 (516.0ms)

Iter	Nodes	Cost
0	58	582
1	116	575
2	253	517
3	662	505
4	2332	496
done	5000	496

prune211.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 0.6b

regimes172.0ms

Accuracy

96.5% (0.5b remaining)

Error of 0.9b against oracle of 0.4b and baseline of 15.3b

bsearch99.0ms

Steps

Iters	Range		Point
7	94269.73169533648	3568380.5266111037	95617.08388190389
9	-1.1198163698016657	-1.4191042175333267e-05	-0.0009635449186787686

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	26	50
1	34	36
done	34	36

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.5s	4455×	body	1280	valid
571.0ms	654×	body	2560	valid
395.0ms	1880×	body	640	valid
103.0ms	642×	body	320	valid
34.0ms	288×	body	160	valid
4.0ms	81×	body	80	valid