Details

sample89.0ms

Algorithm

intervals

Results

39.0ms	96×	body	1280	valid
17.0ms	19×	body	2560	valid
16.0ms	67×	body	640	valid
5.0ms	31×	body	320	valid
2.0ms	33×	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: 36.1b

localize8.0ms

Local error

Found 2 expressions with local error:

0.9b	(- (sin (+ x eps)) (sin x))
3.6b	(sin (+ x eps))

rewrite24.0ms

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:

19.0ms	(- (sin (+ x eps)) (sin x))
4.0ms	(sin (+ x eps))

series65.0ms

Counts

2 → 6

Calls

2 calls:

39.0ms	(- (sin (+ x eps)) (sin x))
26.0ms	(sin (+ x eps))

simplify1.5s

Counts

30 → 30

Iterations

Useful iterations: 4 (243.0ms)

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

prune70.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.3b

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)))
3.5b	(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:

12.0ms	(+ (+ x eps) x)
6.0ms	(* (sin (/ eps 2)) (cos (/ (+ (+ x eps) x) 2)))
22.0ms	(cos (/ (+ (+ x eps) x) 2))

series94.0ms

Counts

3 → 9

Calls

3 calls:

22.0ms	(+ (+ x eps) x)
49.0ms	(* (sin (/ eps 2)) (cos (/ (+ (+ x eps) x) 2)))
23.0ms	(cos (/ (+ (+ x eps) x) 2))

simplify2.5s

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

prune134.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.3b

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))
0.5b	(pow (cos (/ (+ (+ x eps) x) 2)) 3)
3.5b	(cos (/ (+ (+ x eps) x) 2))

rewrite38.0ms

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)
22.0ms	(cos (/ (+ (+ x eps) x) 2))

series143.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (sin (/ eps 2)) (cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 3)))
22.0ms	(cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 3))
48.0ms	(pow (cos (/ (+ (+ x eps) x) 2)) 3)
24.0ms	(cos (/ (+ (+ x eps) x) 2))

simplify2.1s

Counts

97 → 97

Iterations

Useful iterations: 3 (648.0ms)

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

prune234.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.3b

localize18.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 2))
0.5b	(cbrt (cos (/ (+ (+ x eps) x) 2)))
3.5b	(cos (/ (+ (+ x eps) x) 2))
3.5b	(cos (/ (+ (+ x eps) x) 2))

rewrite44.0ms

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 (pow (cos (/ (+ (+ x eps) x) 2)) 2))
1.0ms	(cbrt (cos (/ (+ (+ x eps) x) 2)))
22.0ms	(cos (/ (+ (+ x eps) x) 2))
20.0ms	(cos (/ (+ (+ x eps) x) 2))

series215.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 2))
79.0ms	(cbrt (cos (/ (+ (+ x eps) x) 2)))
23.0ms	(cos (/ (+ (+ x eps) x) 2))
23.0ms	(cos (/ (+ (+ x eps) x) 2))

simplify1.4s

Counts

53 → 53

Iterations

Useful iterations: 3 (112.0ms)

Iter	Nodes	Cost
0	71	779
1	147	704
2	299	630
3	584	608
4	1946	608
done	5001	608

prune166.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 0.3b

regimes116.0ms

Accuracy

99.5% (0.1b remaining)

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

bsearch114.0ms

Steps

Iters	Range		Point
8	1.5021325448122442e-13	3.182061564411226e-09	3.1297217212623504e-09
9	-0.04390830018224924	-3.199438276574562e-09	-8.065146023627676e-09

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

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

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.4s	3268×	body	1280	valid
591.0ms	646×	body	2560	valid
468.0ms	1864×	body	640	valid
125.0ms	771×	body	320	valid
55.0ms	1092×	body	80	valid
39.0ms	359×	body	160	valid