Details

sample105.0ms

Algorithm

intervals

Results

60.0ms	145×	body	1280	valid
15.0ms	19×	body	2560	valid
13.0ms	55×	body	640	valid
5.0ms	27×	body	320	valid
1.0ms	8×	body	160	valid
0.0ms	2×	body	80	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: 38.1b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

1.2b	(- (cos (+ x eps)) (cos x))
3.6b	(cos (+ 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` `cos-sum` `add-cbrt-cube`
1×	`associate--l-` `sub-neg` `flip3--` `diff-log` `flip--` `diff-cos` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 24

Calls

2 calls:

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

series15.0ms

Counts

2 → 6

Calls

2 calls:

10.0ms	(- (cos (+ x eps)) (cos x))
5.0ms	(cos (+ x eps))

simplify2.6s

Counts

30 → 30

Iterations

Useful iterations: 4 (413.0ms)

Iter	Nodes	Cost
0	65	311
1	134	299
2	274	283
3	592	275
4	1501	273
5	4161	273
done	5001	273

prune61.0ms

Filtered

23 candidates to 30 candidates (-30.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	24	6	30
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	25	6	31

Merged error: 0.5b

Counts

31 → 6

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ x eps) x)
0.3b	(* (sin (/ (+ (+ x eps) x) 2)) (sin (/ eps 2)))
3.6b	(sin (/ (+ (+ x eps) x) 2))

rewrite29.0ms

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-+` `sin-mult` `unswap-sqr`

Counts

3 → 41

Calls

3 calls:

7.0ms	(+ (+ x eps) x)
14.0ms	(* (sin (/ (+ (+ x eps) x) 2)) (sin (/ eps 2)))
8.0ms	(sin (/ (+ (+ x eps) x) 2))

series29.0ms

Counts

3 → 9

Calls

3 calls:

4.0ms	(+ (+ x eps) x)
16.0ms	(* (sin (/ (+ (+ x eps) x) 2)) (sin (/ eps 2)))
8.0ms	(sin (/ (+ (+ x eps) x) 2))

simplify2.5s

Counts

50 → 50

Iterations

Useful iterations: 4 (1.4s)

Iter	Nodes	Cost
0	91	656
1	204	648
2	516	570
3	1298	560
4	3845	544
done	5000	544

prune129.0ms

Filtered

36 candidates to 50 candidates (-38.9%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	42	8	50
Fresh	2	3	5
Picked	0	1	1
Done	0	0	0
Total	44	12	56

Merged error: 0.4b

Counts

56 → 12

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin (/ (+ (+ x eps) x) 2)))
3.6b	(sin (/ (+ (+ x eps) x) 2))
3.6b	(sin (/ (+ (+ x eps) x) 2))
3.6b	(sin (/ (+ (+ x eps) x) 2))

rewrite32.0ms

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:

7.0ms	(cbrt (sin (/ (+ (+ x eps) x) 2)))
8.0ms	(sin (/ (+ (+ x eps) x) 2))
8.0ms	(sin (/ (+ (+ x eps) x) 2))
8.0ms	(sin (/ (+ (+ x eps) x) 2))

series45.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(cbrt (sin (/ (+ (+ x eps) x) 2)))
6.0ms	(sin (/ (+ (+ x eps) x) 2))
6.0ms	(sin (/ (+ (+ x eps) x) 2))
7.0ms	(sin (/ (+ (+ x eps) x) 2))

simplify1.6s

Counts

44 → 44

Iterations

Useful iterations: 4 (651.0ms)

Iter	Nodes	Cost
0	57	570
1	119	567
2	252	501
3	618	489
4	2331	467
done	5000	467

prune181.0ms

Filtered

37 candidates to 44 candidates (-18.9%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	42	2	44
Fresh	1	9	10
Picked	1	0	1
Done	0	1	1
Total	44	12	56

Merged error: 0.4b

Counts

56 → 12

localize19.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin (/ eps 2)))
0.6b	(cbrt (sin (/ eps 2)))
0.6b	(cbrt (sin (/ eps 2)))
3.6b	(sin (/ (+ (+ x eps) x) 2))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 40

Calls

4 calls:

3.0ms	(cbrt (sin (/ eps 2)))
2.0ms	(cbrt (sin (/ eps 2)))
2.0ms	(cbrt (sin (/ eps 2)))
9.0ms	(sin (/ (+ (+ x eps) x) 2))

series67.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify1.9s

Counts

52 → 52

Iterations

Useful iterations: 4 (790.0ms)

Iter	Nodes	Cost
0	60	558
1	121	549
2	238	503
3	652	461
4	2910	439
done	5000	439

prune154.0ms

Filtered

42 candidates to 52 candidates (-23.8%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	51	1	52
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	51	13	64

Merged error: 0.4b

Counts

64 → 13

regimes310.0ms

Accuracy

97.7% (0.3b remaining)

Error of 0.7b against oracle of 0.4b and baseline of 15.0b

bsearch64.0ms

Steps

Iters	Range		Point
11	0.0007984694048976103	2.3885905512890262e+30	0.0010712813958775483
5	-0.0004813576712207844	-0.0001616040529746431	-0.0002864983603080275

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	26	51
1	35	38
done	35	38

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.7s	4421×	body	1280	valid
540.0ms	668×	body	2560	valid
434.0ms	1853×	body	640	valid
116.0ms	668×	body	320	valid
39.0ms	298×	body	160	valid
5.0ms	92×	body	80	valid

Details

sample105.0ms

simplify3.0ms

prune3.0ms

localize8.0ms

rewrite12.0ms

series15.0ms

simplify2.6s

prune61.0ms

localize13.0ms

rewrite29.0ms

series29.0ms

simplify2.5s

prune129.0ms

localize17.0ms

rewrite32.0ms

series45.0ms

simplify1.6s

prune181.0ms

localize19.0ms

rewrite18.0ms

series67.0ms

simplify1.9s

prune154.0ms

regimes310.0ms

bsearch64.0ms

simplify3.0ms

end0.0ms

sample3.1s

Profiling