Details

sample103.0ms

Algorithm

intervals

Results

58.0ms	145×	body	1280	valid
14.0ms	19×	body	2560	valid
12.0ms	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))

simplify1.0s

Counts

30 → 30

Iterations

Useful iterations: 4 (165.0ms)

Iter	Nodes	Cost
0	65	311
1	134	299
2	287	283
3	578	275
4	1129	273
5	2550	273
done	5000	273

prune60.0ms

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))

rewrite27.0ms

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)
12.0ms	(* (sin (/ (+ (+ x eps) x) 2)) (sin (/ eps 2)))
8.0ms	(sin (/ (+ (+ x eps) x) 2))

series28.0ms

Counts

3 → 9

Calls

3 calls:

4.0ms	(+ (+ x eps) x)
17.0ms	(* (sin (/ (+ (+ x eps) x) 2)) (sin (/ eps 2)))
7.0ms	(sin (/ (+ (+ x eps) x) 2))

simplify1.2s

Counts

50 → 50

Iterations

Useful iterations: 4 (494.0ms)

Iter	Nodes	Cost
0	91	656
1	207	650
2	551	571
3	1432	552
4	4440	544
done	5000	544

prune130.0ms

Filtered

37 candidates to 50 candidates (-35.1%)

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

localize18.0ms

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)))
9.0ms	(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)))
7.0ms	(sin (/ (+ (+ x eps) x) 2))
7.0ms	(sin (/ (+ (+ x eps) x) 2))
7.0ms	(sin (/ (+ (+ x eps) x) 2))

simplify1.5s

Counts

44 → 44

Iterations

Useful iterations: 4 (167.0ms)

Iter	Nodes	Cost
0	57	570
1	119	567
2	261	501
3	599	473
4	1523	467
5	4774	467
done	5000	467

prune407.0ms

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

localize17.0ms

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))

rewrite19.0ms

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:

5.0ms	(cbrt (sin (/ eps 2)))
2.0ms	(cbrt (sin (/ eps 2)))
2.0ms	(cbrt (sin (/ eps 2)))
8.0ms	(sin (/ (+ (+ x eps) x) 2))

series70.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(cbrt (sin (/ eps 2)))
21.0ms	(cbrt (sin (/ eps 2)))
21.0ms	(cbrt (sin (/ eps 2)))
7.0ms	(sin (/ (+ (+ x eps) x) 2))

simplify599.0ms

Counts

52 → 52

Iterations

Useful iterations: 4 (179.0ms)

Iter	Nodes	Cost
0	60	558
1	121	549
2	235	503
3	570	457
4	1746	439
done	5001	439

prune164.0ms

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

regimes316.0ms

Accuracy

97.7% (0.3b remaining)

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

bsearch68.0ms

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 (1.0ms)

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

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.6s	4421×	body	1280	valid
535.0ms	668×	body	2560	valid
452.0ms	1853×	body	640	valid
112.0ms	668×	body	320	valid
39.0ms	298×	body	160	valid
5.0ms	92×	body	80	valid

Details

sample103.0ms

simplify3.0ms

prune3.0ms

localize8.0ms

rewrite12.0ms

series15.0ms

simplify1.0s

prune60.0ms

localize13.0ms

rewrite27.0ms

series28.0ms

simplify1.2s

prune130.0ms

localize18.0ms

rewrite32.0ms

series45.0ms

simplify1.5s

prune407.0ms

localize17.0ms

rewrite19.0ms

series70.0ms

simplify599.0ms

prune164.0ms

regimes316.0ms

bsearch68.0ms

simplify3.0ms

end0.0ms

sample3.1s

Profiling