Details

sample91.0ms

Algorithm

intervals

Results

42.0ms	102×	body	1280	valid
19.0ms	22×	body	2560	valid
15.0ms	65×	body	640	valid
3.0ms	20×	body	320	valid
2.0ms	37×	body	80	valid
1.0ms	10×	body	160	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: 38.5b

localize8.0ms

Local error

Found 2 expressions with local error:

0.6b	(- (sin (+ x eps)) (sin x))
4.7b	(sin (+ x eps))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
2×	`pow1` `add-exp-log` `add-cube-cbrt` `sin-sum` `add-cbrt-cube`
1×	`sub-neg` `flip3--` `diff-log` `diff-sin` `associate--l+` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 24

Calls

2 calls:

20.0ms	(- (sin (+ x eps)) (sin x))
4.0ms	(sin (+ x eps))

series62.0ms

Counts

2 → 6

Calls

2 calls:

39.0ms	(- (sin (+ x eps)) (sin x))
23.0ms	(sin (+ x eps))

simplify1.7s

Counts

30 → 30

Iterations

Useful iterations: 4 (265.0ms)

Iter	Nodes	Cost
0	64	309
1	134	295
2	296	281
3	544	275
4	1111	271
5	2498	271
done	5001	271

prune76.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.6b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ x eps) x)
0.3b	(* (sin (/ eps 2)) (cos (/ (+ (+ x eps) x) 2)))
4.8b	(cos (/ (+ (+ x eps) x) 2))

rewrite41.0ms

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` `sin-cos-mult` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

3 → 41

Calls

3 calls:

13.0ms	(+ (+ x eps) x)
6.0ms	(* (sin (/ eps 2)) (cos (/ (+ (+ x eps) x) 2)))
20.0ms	(cos (/ (+ (+ x eps) x) 2))

series98.0ms

Counts

3 → 9

Calls

3 calls:

23.0ms	(+ (+ x eps) x)
51.0ms	(* (sin (/ eps 2)) (cos (/ (+ (+ x eps) x) 2)))
24.0ms	(cos (/ (+ (+ x eps) x) 2))

simplify3.1s

Counts

50 → 50

Iterations

Useful iterations: 4 (1.7s)

Iter	Nodes	Cost
0	91	656
1	212	646
2	526	566
3	1353	556
4	4191	540
done	5000	540

prune133.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.5b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin (/ eps 2)) (cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 3)))
0.5b	(cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 3))
0.6b	(pow (cos (/ (+ (+ x eps) x) 2)) 3)
4.8b	(cos (/ (+ (+ x eps) x) 2))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

28×	`cbrt-prod`
24×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `-un-lft-identity` `associate-r*`
10×	`unpow-prod-down` `cube-prod`
7×	`pow1` `add-exp-log`
6×	`add-cbrt-cube`
5×	`unswap-sqr`
4×	`add-log-exp` `sqr-pow`
3×	`cube-mult` `pow-unpow` `unpow3` `associate-l`
1×	`pow-to-exp` `pow-pow` `pow1/3` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `rem-cbrt-cube` `cbrt-unprod` `rem-cube-cbrt`

Counts

4 → 85

Calls

4 calls:

11.0ms	(* (sin (/ eps 2)) (cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 3)))
1.0ms	(cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 3))
1.0ms	(pow (cos (/ (+ (+ x eps) x) 2)) 3)
22.0ms	(cos (/ (+ (+ x eps) x) 2))

series141.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (sin (/ eps 2)) (cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 3)))
23.0ms	(cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 3))
48.0ms	(pow (cos (/ (+ (+ x eps) x) 2)) 3)
24.0ms	(cos (/ (+ (+ x eps) x) 2))

simplify2.7s

Counts

97 → 97

Iterations

Useful iterations: 3 (769.0ms)

Iter	Nodes	Cost
0	117	1733
1	255	1447
2	736	1279
3	3661	1259
done	5000	1259

prune227.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.5b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (cos (/ (+ (+ x eps) x) 2)))
0.3b	(* (sin (/ eps 2)) (log (exp (cos (/ (+ (+ x eps) x) 2)))))
0.6b	(log (exp (cos (/ (+ (+ x eps) x) 2))))
4.8b	(cos (/ (+ (+ x eps) x) 2))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `*-un-lft-identity`
9×	`log-prod` `exp-prod`
8×	`pow1` `log-pow`
7×	`associate-r`
6×	`add-exp-log` `add-cbrt-cube`
5×	`add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `associate-l`
1×	`rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `rem-exp-log` `unswap-sqr`

Counts

4 → 61

Calls

4 calls:

17.0ms	(exp (cos (/ (+ (+ x eps) x) 2)))
26.0ms	(* (sin (/ eps 2)) (log (exp (cos (/ (+ (+ x eps) x) 2)))))
37.0ms	(log (exp (cos (/ (+ (+ x eps) x) 2))))
20.0ms	(cos (/ (+ (+ x eps) x) 2))

series142.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(exp (cos (/ (+ (+ x eps) x) 2)))
46.0ms	(* (sin (/ eps 2)) (log (exp (cos (/ (+ (+ x eps) x) 2)))))
22.0ms	(log (exp (cos (/ (+ (+ x eps) x) 2))))
27.0ms	(cos (/ (+ (+ x eps) x) 2))

simplify2.0s

Counts

73 → 73

Iterations

Useful iterations: 4 (808.0ms)

Iter	Nodes	Cost
0	107	1191
1	208	1093
2	483	951
3	1067	945
4	2386	927
done	5000	927

prune186.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.5b

regimes106.0ms

Accuracy

99.6% (0.1b remaining)

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

bsearch101.0ms

Steps

Iters	Range		Point
9	7.573771271304567e-12	1.8324855427473017e-05	1.3462536641985354e-08
7	-1.4745663415654705e-08	-9.168401155690507e-11	-1.2375327809157776e-08

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	51
1	35	51
done	35	51

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.4s	3323×	body	1280	valid
589.0ms	654×	body	2560	valid
458.0ms	1883×	body	640	valid
124.0ms	730×	body	320	valid
59.0ms	1059×	body	80	valid
42.0ms	351×	body	160	valid