Details

sample100.0ms

Algorithm

intervals

Results

50.0ms	120×	body	1280	valid
15.0ms	19×	body	2560	valid
15.0ms	56×	body	640	valid
5.0ms	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))

rewrite18.0ms

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

series14.0ms

Counts

2 → 6

Calls

2 calls:

9.0ms	(- (sin (+ x eps)) (sin x))
5.0ms	(sin (+ x eps))

simplify973.0ms

Counts

30 → 30

Iterations

Useful iterations: 4 (183.0ms)

Iter	Nodes	Cost
0	63	309
1	134	295
2	304	281
3	654	275
4	1355	271
5	3068	271
done	5000	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

localize12.0ms

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))

rewrite24.0ms

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:

9.0ms	(+ (+ x eps) x)
6.0ms	(* (cos (/ (+ (+ x eps) x) 2)) (sin (/ eps 2)))
7.0ms	(cos (/ (+ (+ x eps) x) 2))

series24.0ms

Counts

3 → 9

Calls

3 calls:

4.0ms	(+ (+ x eps) x)
14.0ms	(* (cos (/ (+ (+ x eps) x) 2)) (sin (/ eps 2)))
6.0ms	(cos (/ (+ (+ x eps) x) 2))

simplify1.1s

Counts

49 → 49

Iterations

Useful iterations: 4 (516.0ms)

Iter	Nodes	Cost
0	86	633
1	206	621
2	533	541
3	1449	521
4	4338	513
done	5000	513

prune114.0ms

Filtered

35 candidates to 49 candidates (-40.0%)

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))

rewrite25.0ms

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

series36.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(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))

simplify753.0ms

Counts

44 → 44

Iterations

Useful iterations: 3 (43.0ms)

Iter	Nodes	Cost
0	43	553
1	91	540
2	182	466
3	367	447
4	727	447
5	1227	447
6	2391	447
done	5000	447

prune164.0ms

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

localize23.0ms

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))

rewrite33.0ms

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

series23.0ms

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))

simplify1.5s

Counts

40 → 40

Iterations

Useful iterations: 3 (29.0ms)

Iter	Nodes	Cost
0	26	476
1	56	468
2	102	396
3	198	380
4	359	380
5	520	380
6	914	380
7	1281	380
8	1825	380
9	3813	380
done	5001	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

regimes159.0ms

Accuracy

99.3% (0.1b remaining)

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

bsearch57.0ms

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

sample3.1s

Algorithm

intervals

Results

1.4s	3317×	body	1280	valid
586.0ms	668×	body	2560	valid
487.0ms	1800×	body	640	valid
141.0ms	749×	body	320	valid
68.0ms	1117×	body	80	valid
45.0ms	349×	body	160	valid

Details

sample100.0ms

simplify3.0ms

prune3.0ms

localize8.0ms

rewrite18.0ms

series14.0ms

simplify973.0ms

prune46.0ms

localize12.0ms

rewrite24.0ms

series24.0ms

simplify1.1s

prune114.0ms

localize17.0ms

rewrite25.0ms

series36.0ms

simplify753.0ms

prune164.0ms

localize23.0ms

rewrite33.0ms

series23.0ms

simplify1.5s

prune183.0ms

regimes159.0ms

bsearch57.0ms

simplify3.0ms

end0.0ms

sample3.1s

Profiling