Details

sample87.0ms

Algorithm

intervals

Results

43.0ms	135×	body	1280	valid
19.0ms	24×	body	2560	valid
12.0ms	60×	body	640	valid
3.0ms	25×	body	320	valid
1.0ms	10×	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: 40.0b

localize8.0ms

Local error

Found 2 expressions with local error:

1.6b	(- (cos (+ x eps)) (cos x))
1.9b	(cos (+ x eps))

rewrite11.0ms

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:

6.0ms	(- (cos (+ x eps)) (cos x))
4.0ms	(cos (+ x eps))

series71.0ms

Counts

2 → 6

Calls

2 calls:

56.0ms	(- (cos (+ x eps)) (cos x))
15.0ms	(cos (+ x eps))

simplify1.3s

Counts

30 → 30

Iterations

Useful iterations: 4 (328.0ms)

Iter	Nodes	Cost
0	65	311
1	134	299
2	280	283
3	728	275
4	2068	273
done	5001	273

prune81.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.5b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ x eps) x)
0.3b	(* (sin (* eps 1/2)) (sin (/ (+ (+ x eps) x) 2)))
2.0b	(sin (/ (+ (+ x eps) x) 2))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity`
8×	`add-log-exp`
7×	`add-sqr-sqrt`
5×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
3×	`associate-r` `associate-l` `sum-log` `distribute-lft-out`
1×	`+-commutative` `associate-+l+` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `sin-mult` `unswap-sqr`

Counts

3 → 41

Calls

3 calls:

15.0ms	(+ (+ x eps) x)
43.0ms	(* (sin (* eps 1/2)) (sin (/ (+ (+ x eps) x) 2)))
24.0ms	(sin (/ (+ (+ x eps) x) 2))

series110.0ms

Counts

3 → 9

Calls

3 calls:

22.0ms	(+ (+ x eps) x)
58.0ms	(* (sin (* eps 1/2)) (sin (/ (+ (+ x eps) x) 2)))
29.0ms	(sin (/ (+ (+ x eps) x) 2))

simplify1.1s

Counts

50 → 50

Iterations

Useful iterations: 3 (227.0ms)

Iter	Nodes	Cost
0	91	654
1	206	646
2	559	568
3	1848	558
done	5000	558

prune151.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.5b

localize14.0ms

Local error

Found 2 expressions with local error:

0.3b	(* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 eps)))
2.0b	(sin (* 1/2 (+ (* 2 x) eps)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
3×	`associate-r` `associate-l`
2×	`sin-sum` `add-log-exp`
1×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `sin-mult` `unswap-sqr`

Counts

2 → 28

Calls

2 calls:

12.0ms	(* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 eps)))
5.0ms	(sin (* 1/2 (+ (* 2 x) eps)))

series106.0ms

Counts

2 → 6

Calls

2 calls:

78.0ms	(* (sin (* 1/2 (+ (* 2 x) eps))) (sin (* 1/2 eps)))
28.0ms	(sin (* 1/2 (+ (* 2 x) eps)))

simplify853.0ms

Counts

34 → 34

Iterations

Useful iterations: 3 (165.0ms)

Iter	Nodes	Cost
0	75	555
1	158	540
2	416	472
3	1475	390
done	5000	390

prune126.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* (sin x) (cos (* 1/2 eps))) (* (sin (* 1/2 eps)) (cos x)))
0.1b	(* (sin x) (cos (* 1/2 eps)))
0.1b	(* (sin (* 1/2 eps)) (cos x))
0.2b	(* (+ (* (sin x) (cos (* 1/2 eps))) (* (sin (* 1/2 eps)) (cos x))) (sin (* 1/2 eps)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
9×	`associate-r` `associate-l`
6×	`sin-cos-mult` `add-log-exp`
3×	`pow-prod-down` `associate-l/` `prod-exp` `-commutative` `cbrt-unprod` `unswap-sqr`
2×	`flip3-+` `frac-add` `flip-+`
1×	`+-commutative` `sum-log`

Counts

4 → 71

Calls

4 calls:

6.0ms	(+ (* (sin x) (cos (* 1/2 eps))) (* (sin (* 1/2 eps)) (cos x)))
5.0ms	(* (sin x) (cos (* 1/2 eps)))
5.0ms	(* (sin (* 1/2 eps)) (cos x))
23.0ms	(* (+ (* (sin x) (cos (* 1/2 eps))) (* (sin (* 1/2 eps)) (cos x))) (sin (* 1/2 eps)))

series357.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(+ (* (sin x) (cos (* 1/2 eps))) (* (sin (* 1/2 eps)) (cos x)))
52.0ms	(* (sin x) (cos (* 1/2 eps)))
52.0ms	(* (sin (* 1/2 eps)) (cos x))
153.0ms	(* (+ (* (sin x) (cos (* 1/2 eps))) (* (sin (* 1/2 eps)) (cos x))) (sin (* 1/2 eps)))

simplify532.0ms

Counts

83 → 83

Iterations

Useful iterations: done (530.0ms)

Iter	Nodes	Cost
0	146	1462
1	362	1414
2	1250	1272
done	5000	1266

prune259.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes128.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	16	24
1	24	22
2	26	22
done	26	22

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.5s	4415×	body	1280	valid
560.0ms	649×	body	2560	valid
377.0ms	1833×	body	640	valid
96.0ms	712×	body	320	valid
29.0ms	307×	body	160	valid
4.0ms	84×	body	80	valid