Details

sample100.0ms

Algorithm

intervals

Results

47.0ms	110×	body	1280	valid
22.0ms	24×	body	2560	valid
14.0ms	56×	body	640	valid
6.0ms	32×	body	320	valid
1.0ms	27×	body	80	valid
1.0ms	7×	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: 39.7b

localize13.0ms

Local error

Found 2 expressions with local error:

1.7b	(- (sin (+ x eps)) (sin x))
3.9b	(sin (+ x eps))

rewrite26.0ms

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:

21.0ms	(- (sin (+ x eps)) (sin x))
4.0ms	(sin (+ x eps))

series63.0ms

Counts

2 → 6

Calls

2 calls:

44.0ms	(- (sin (+ x eps)) (sin x))
19.0ms	(sin (+ x eps))

simplify1.6s

Counts

30 → 30

Iterations

Useful iterations: 4 (246.0ms)

Iter	Nodes	Cost
0	64	309
1	134	295
2	295	281
3	535	275
4	1094	271
5	2492	271
done	5001	271

prune77.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ x eps) x)
0.2b	(* (sin (/ eps 2)) (cos (/ (+ (+ x eps) x) 2)))
3.9b	(cos (/ (+ (+ x eps) x) 2))

rewrite43.0ms

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:

14.0ms	(+ (+ x eps) x)
7.0ms	(* (sin (/ eps 2)) (cos (/ (+ (+ x eps) x) 2)))
21.0ms	(cos (/ (+ (+ x eps) x) 2))

series93.0ms

Counts

3 → 9

Calls

3 calls:

22.0ms	(+ (+ x eps) x)
45.0ms	(* (sin (/ eps 2)) (cos (/ (+ (+ x eps) x) 2)))
26.0ms	(cos (/ (+ (+ x eps) x) 2))

simplify2.6s

Counts

50 → 50

Iterations

Useful iterations: 4 (1.5s)

Iter	Nodes	Cost
0	91	656
1	212	646
2	526	566
3	1350	556
4	4390	540
done	5001	540

prune144.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.4b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (/ eps 2)) (cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 3)))
0.5b	(cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 3))
0.5b	(pow (cos (/ (+ (+ x eps) x) 2)) 3)
3.9b	(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:

12.0ms	(* (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)
21.0ms	(cos (/ (+ (+ x eps) x) 2))

series144.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* (sin (/ eps 2)) (cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 3)))
22.0ms	(cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 3))
44.0ms	(pow (cos (/ (+ (+ x eps) x) 2)) 3)
26.0ms	(cos (/ (+ (+ x eps) x) 2))

simplify2.4s

Counts

97 → 97

Iterations

Useful iterations: 3 (662.0ms)

Iter	Nodes	Cost
0	117	1733
1	254	1447
2	735	1279
3	3629	1259
done	5001	1259

prune237.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.4b

localize18.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (cos (/ (+ (+ x eps) x) 2)))
0.5b	(cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 2))
3.9b	(cos (/ (+ (+ x eps) x) 2))
3.9b	(cos (/ (+ (+ x eps) x) 2))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

11×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`unpow-prod-down`
2×	`pow1/3`
1×	`unpow2` `sqr-pow`

Counts

4 → 41

Calls

4 calls:

1.0ms	(cbrt (cos (/ (+ (+ x eps) x) 2)))
1.0ms	(cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 2))
21.0ms	(cos (/ (+ (+ x eps) x) 2))
24.0ms	(cos (/ (+ (+ x eps) x) 2))

series213.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(cbrt (cos (/ (+ (+ x eps) x) 2)))
89.0ms	(cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 2))
25.0ms	(cos (/ (+ (+ x eps) x) 2))
24.0ms	(cos (/ (+ (+ x eps) x) 2))

simplify1.2s

Counts

53 → 53

Iterations

Useful iterations: 3 (117.0ms)

Iter	Nodes	Cost
0	71	779
1	147	704
2	299	630
3	586	608
4	1950	608
done	5001	608

prune159.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.4b

regimes132.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.5b against oracle of 0.4b and baseline of 15.1b

bsearch138.0ms

Steps

Iters	Range		Point
11	2.28145452431431e-18	2231369.5462890854	1.174838876346265e-08
10	-925426.909356872	-1.1036397448000079e-07	-1.1161292204334507e-07

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	25	51
1	35	38
done	35	38

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.5s	3333×	body	1280	valid
601.0ms	666×	body	2560	valid
475.0ms	1791×	body	640	valid
131.0ms	779×	body	320	valid
56.0ms	1083×	body	80	valid
39.0ms	348×	body	160	valid