Details

sample109.0ms

Algorithm

intervals

Results

57.0ms	120×	body	1280	valid
16.0ms	19×	body	2560	valid
15.0ms	56×	body	640	valid
6.0ms	28×	body	320	valid
2.0ms	27×	body	80	valid
1.0ms	6×	body	160	valid

simplify3.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	6	7
1	9	7
2	10	7
done	10	7

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 36.2b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.7b	(- (sin (+ x eps)) (sin x))
3.5b	(sin (+ x eps))

rewrite12.0ms

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:

7.0ms	(- (sin (+ x eps)) (sin x))
4.0ms	(sin (+ x eps))

series16.0ms

Counts

2 → 6

Calls

2 calls:

10.0ms	(- (sin (+ x eps)) (sin x))
6.0ms	(sin (+ x eps))

simplify1.1s

Counts

30 → 30

Iterations

Useful iterations: 4 (191.0ms)

Iter	Nodes	Cost
0	63	309
1	134	295
2	306	281
3	630	275
4	1320	271
5	2970	271
done	5001	271

prune46.0ms

Filtered

23 candidates to 30 candidates (-30.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	27	3	30
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	28	3	31

Merged error: 0.5b

Counts

31 → 3

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ x eps) x)
0.2b	(* (cos (/ (+ (+ x eps) x) 2)) (sin (/ eps 2)))
3.7b	(cos (/ (+ (+ x eps) x) 2))

rewrite21.0ms

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-+` `unswap-sqr`

Counts

3 → 40

Calls

3 calls:

7.0ms	(+ (+ x eps) x)
6.0ms	(* (cos (/ (+ (+ x eps) x) 2)) (sin (/ eps 2)))
8.0ms	(cos (/ (+ (+ x eps) x) 2))

series25.0ms

Counts

3 → 9

Calls

3 calls:

4.0ms	(+ (+ x eps) x)
15.0ms	(* (cos (/ (+ (+ x eps) x) 2)) (sin (/ eps 2)))
6.0ms	(cos (/ (+ (+ x eps) x) 2))

simplify1.1s

Counts

49 → 49

Iterations

Useful iterations: 4 (478.0ms)

Iter	Nodes	Cost
0	86	633
1	206	622
2	565	542
3	1388	521
4	3867	513
done	5000	513

prune111.0ms

Filtered

37 candidates to 49 candidates (-32.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	44	5	49
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	44	8	52

Merged error: 0.4b

Counts

52 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (cos (/ (+ (+ x eps) x) 2)))
3.7b	(cos (/ (+ (+ x eps) x) 2))
3.7b	(cos (/ (+ (+ x eps) x) 2))
3.7b	(cos (/ (+ (+ x eps) x) 2))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 32

Calls

4 calls:

1.0ms	(cbrt (cos (/ (+ (+ x eps) x) 2)))
8.0ms	(cos (/ (+ (+ x eps) x) 2))
8.0ms	(cos (/ (+ (+ x eps) x) 2))
12.0ms	(cos (/ (+ (+ x eps) x) 2))

series38.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(cbrt (cos (/ (+ (+ x eps) x) 2)))
6.0ms	(cos (/ (+ (+ x eps) x) 2))
6.0ms	(cos (/ (+ (+ x eps) x) 2))
6.0ms	(cos (/ (+ (+ x eps) x) 2))

simplify997.0ms

Counts

44 → 44

Iterations

Useful iterations: 3 (44.0ms)

Iter	Nodes	Cost
0	43	553
1	91	540
2	178	466
3	328	447
4	601	447
5	1024	447
6	2276	447
done	5001	447

prune167.0ms

Filtered

37 candidates to 44 candidates (-18.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	43	1	44
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	44	8	52

Merged error: 0.4b

Counts

52 → 8

localize24.0ms

Local error

Found 4 expressions with local error:

3.7b	(cos (/ (+ (+ x eps) x) 2))
3.7b	(cos (/ (+ (+ x eps) x) 2))
3.7b	(cos (/ (+ (+ x eps) x) 2))
3.7b	(cos (/ (+ (+ x eps) x) 2))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`

Counts

4 → 28

Calls

4 calls:

8.0ms	(cos (/ (+ (+ x eps) x) 2))
9.0ms	(cos (/ (+ (+ x eps) x) 2))
8.0ms	(cos (/ (+ (+ x eps) x) 2))
8.0ms	(cos (/ (+ (+ x eps) x) 2))

series24.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(cos (/ (+ (+ x eps) x) 2))
6.0ms	(cos (/ (+ (+ x eps) x) 2))
6.0ms	(cos (/ (+ (+ x eps) x) 2))
6.0ms	(cos (/ (+ (+ x eps) x) 2))

simplify1.0s

Counts

40 → 40

Iterations

Useful iterations: 3 (29.0ms)

Iter	Nodes	Cost
0	26	476
1	56	468
2	102	396
3	177	380
4	288	380
5	387	380
6	615	380
7	1232	380
8	2221	380
done	5000	380

prune183.0ms

Filtered

36 candidates to 40 candidates (-11.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	39	1	40
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	40	8	48

Merged error: 0.4b

Counts

48 → 8

regimes158.0ms

Accuracy

99.3% (0.1b remaining)

Error of 0.5b against oracle of 0.4b and baseline of 14.9b

bsearch61.0ms

Steps

Iters	Range		Point
8	5.972365790103743e-15	5.691295351696058e-12	5.621069998466474e-12
5	-0.0004813576712207844	-0.0001616040529746431	-0.0001647469450861392

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

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

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.5s	3317×	body	1280	valid
579.0ms	668×	body	2560	valid
514.0ms	1800×	body	640	valid
146.0ms	749×	body	320	valid
77.0ms	1117×	body	80	valid
52.0ms	349×	body	160	valid

Details

sample109.0ms

simplify3.0ms

prune3.0ms

localize8.0ms

rewrite12.0ms

series16.0ms

simplify1.1s

prune46.0ms

localize16.0ms

rewrite21.0ms

series25.0ms

simplify1.1s

prune111.0ms

localize17.0ms

rewrite30.0ms

series38.0ms

simplify997.0ms

prune167.0ms

localize24.0ms

rewrite34.0ms

series24.0ms

simplify1.0s

prune183.0ms

regimes158.0ms

bsearch61.0ms

simplify3.0ms

end0.0ms

sample3.2s

Profiling