Details

sample64.0ms

Algorithm

intervals

Results

28.0ms	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

simplify575.0ms

Counts

1 → 1

Iterations

Useful iterations: 4 (55.0ms)

Iter	Nodes	Cost
0	21	29
1	50	29
2	92	29
3	202	29
4	449	28
5	1423	28
done	5000	28

prune18.0ms

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))

rewrite47.0ms

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:

18.0ms	(+ (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))

series121.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
7.0ms	(* K (+ m n))
44.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
26.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify834.0ms

Counts

82 → 82

Iterations

Useful iterations: 3 (332.0ms)

Iter	Nodes	Cost
0	187	1188
1	449	1105
2	1132	1018
3	3127	1015
done	5000	1015

prune182.0ms

Filtered

60 candidates to 82 candidates (-36.7%)

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

localize16.0ms

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)

rewrite31.0ms

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:

19.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
11.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series90.0ms

Counts

2 → 6

Calls

2 calls:

46.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
44.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify585.0ms

Counts

43 → 43

Iterations

Useful iterations: 3 (191.0ms)

Iter	Nodes	Cost
0	120	785
1	289	723
2	685	676
3	2018	673
done	5001	673

prune94.0ms

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

localize28.0ms

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))

rewrite32.0ms

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)))
10.0ms	(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))

series133.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(cbrt (cos (- (/ (* K (+ m n)) 2.0) M)))
26.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
23.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
22.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify661.0ms

Counts

53 → 53

Iterations

Useful iterations: 3 (35.0ms)

Iter	Nodes	Cost
0	49	855
1	86	812
2	127	730
3	180	727
4	289	727
5	541	727
6	1414	727
done	5000	727

prune184.0ms

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

localize25.0ms

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))

rewrite32.0ms

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))
3.0ms	(cbrt (+ m n))
3.0ms	(cbrt (+ m n))
18.0ms	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

series132.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(cbrt (+ m n))
35.0ms	(cbrt (+ m n))
33.0ms	(cbrt (+ m n))
29.0ms	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

simplify701.0ms

Counts

64 → 64

Iterations

Useful iterations: 4 (272.0ms)

Iter	Nodes	Cost
0	102	931
1	208	895
2	434	683
3	995	593
4	2245	578
done	5000	578

prune125.0ms

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

regimes404.0ms

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

852.0ms	8065×	body	80	valid
82.0ms	179×	body	640	valid
75.0ms	120×	body	1280	valid
48.0ms	112×	body	320	valid
18.0ms	65×	body	160	valid
3.0ms	3×	body	2560	valid

Details

sample64.0ms

simplify575.0ms

prune18.0ms

localize21.0ms

rewrite47.0ms

series121.0ms

simplify834.0ms

prune182.0ms

localize16.0ms

rewrite31.0ms

series90.0ms

simplify585.0ms

prune94.0ms

localize28.0ms

rewrite32.0ms

series133.0ms

simplify661.0ms

prune184.0ms

localize25.0ms

rewrite32.0ms

series132.0ms

simplify701.0ms

prune125.0ms

regimes404.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.6s

Profiling