Details

sample62.0ms

Algorithm

intervals

Results

26.0ms	254×	body	80	valid
3.0ms	5×	body	1280	valid
2.0ms	6×	body	320	valid
2.0ms	4×	body	640	valid
1.0ms	1×	body	2560	valid
0.0ms	1×	body	160	valid

simplify3.3s

Counts

1 → 1

Iterations

Useful iterations: 4 (64.0ms)

Iter	Nodes	Cost
0	21	29
1	50	29
2	92	29
3	195	29
4	428	28
5	1228	28
6	4581	28
done	5001	28

prune12.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 16.4b

Counts

2 → 1

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
0.0b	(* K (+ m n))
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
33.5b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

17×	`*-un-lft-identity`
15×	`add-sqr-sqrt`
9×	`add-log-exp`
8×	`add-cube-cbrt`
7×	`pow1` `add-exp-log`
6×	`unpow-prod-down` `add-cbrt-cube`
4×	`associate-r`
3×	`pow-unpow` `associate-l` `distribute-lft-out`
2×	`sub-neg` `cos-sum` `associate-+r+` `flip3-+` `associate-*r/` `sum-log` `flip-+` `distribute-lft-out--` `difference-of-squares`
1×	`+-commutative` `distribute-rgt-in` `cos-diff` `pow-to-exp` `associate-+r-` `pow-pow` `distribute-lft-in` `times-frac` `diff-log` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr` `sqr-pow`

Counts

4 → 70

Calls

4 calls:

21.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
7.0ms	(* K (+ m n))
11.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
9.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series115.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
6.0ms	(* K (+ m n))
42.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
22.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify1.1s

Counts

82 → 82

Iterations

Useful iterations: 3 (407.0ms)

Iter	Nodes	Cost
0	187	1188
1	442	1105
2	1006	1018
3	2697	1015
done	5000	1015

prune181.0ms

Filtered

58 candidates to 82 candidates (-41.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	78	4	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	79	4	83

Merged error: 0.8b

Counts

83 → 4

localize14.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

11×	`*-un-lft-identity`
9×	`add-sqr-sqrt`
7×	`add-log-exp`
6×	`unpow-prod-down`
4×	`add-cube-cbrt`
3×	`pow1` `add-exp-log` `pow-unpow`
2×	`associate-+r+` `sum-log` `add-cbrt-cube` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`
1×	`+-commutative` `pow-to-exp` `associate-+r-` `sub-neg` `pow-pow` `flip3-+` `times-frac` `diff-log` `pow-exp` `flip-+` `sqr-pow`

Counts

2 → 37

Calls

2 calls:

18.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
11.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series87.0ms

Counts

2 → 6

Calls

2 calls:

42.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
45.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify779.0ms

Counts

43 → 43

Iterations

Useful iterations: 3 (213.0ms)

Iter	Nodes	Cost
0	120	785
1	286	723
2	618	676
3	1763	673
done	5001	673

prune96.0ms

Filtered

31 candidates to 43 candidates (-38.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	43	0	43
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	43	4	47

Merged error: 0.8b

Counts

47 → 4

localize25.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (cos (- (/ (* K (+ m n)) 2.0) M)))
33.5b	(cos (- (/ (* K (+ m n)) 2.0) M))
33.5b	(cos (- (/ (* K (+ m n)) 2.0) M))
33.5b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

6×	`cos-sum`
5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`cbrt-prod` `cos-diff` `sub-neg`
1×	`pow1/3`

Counts

4 → 41

Calls

4 calls:

2.0ms	(cbrt (cos (- (/ (* K (+ m n)) 2.0) M)))
9.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
10.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
10.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series131.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(cbrt (cos (- (/ (* K (+ m n)) 2.0) M)))
22.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
22.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
24.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify2.3s

Counts

53 → 53

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	49	855
1	85	812
2	122	730
3	167	727
4	269	727
5	508	727
6	1327	727
done	5000	687

prune188.0ms

Filtered

43 candidates to 53 candidates (-23.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	53	0	53
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	53	4	57

Merged error: 0.8b

Counts

57 → 4

localize28.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (+ m n))
0.5b	(cbrt (+ m n))
0.5b	(cbrt (+ m n))
33.6b	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
12×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`cbrt-div`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out`
2×	`cos-sum`
1×	`cos-diff` `sub-neg`

Counts

4 → 52

Calls

4 calls:

3.0ms	(cbrt (+ m n))
4.0ms	(cbrt (+ m n))
3.0ms	(cbrt (+ m n))
17.0ms	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

series130.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(cbrt (+ m n))
32.0ms	(cbrt (+ m n))
36.0ms	(cbrt (+ m n))
29.0ms	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

simplify1.4s

Counts

64 → 64

Iterations

Useful iterations: 4 (654.0ms)

Iter	Nodes	Cost
0	102	931
1	208	895
2	406	683
3	927	593
4	2506	578
done	5000	578

prune123.0ms

Filtered

50 candidates to 64 candidates (-28.0%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	62	2	64
Fresh	0	1	1
Picked	1	0	1
Done	0	2	2
Total	63	5	68

Merged error: 0.8b

Counts

68 → 5

regimes400.0ms

Accuracy

0% (0.2b remaining)

Error of 1.5b against oracle of 1.3b and baseline of 1.5b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	19
1	20	19
done	20	19

end0.0ms

sample1.6s

Algorithm

intervals

Results

835.0ms	8065×	body	80	valid
76.0ms	120×	body	1280	valid
75.0ms	179×	body	640	valid
35.0ms	112×	body	320	valid
17.0ms	65×	body	160	valid
2.0ms	3×	body	2560	valid

Details

sample62.0ms

simplify3.3s

prune12.0ms

localize21.0ms

rewrite50.0ms

series115.0ms

simplify1.1s

prune181.0ms

localize14.0ms

rewrite30.0ms

series87.0ms

simplify779.0ms

prune96.0ms

localize25.0ms

rewrite31.0ms

series131.0ms

simplify2.3s

prune188.0ms

localize28.0ms

rewrite29.0ms

series130.0ms

simplify1.4s

prune123.0ms

regimes400.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.6s

Profiling