Details

sample48.0ms

Algorithm

intervals

Results

21.0ms	267×	body	80	valid
3.0ms	6×	body	1280	valid
2.0ms	8×	body	320	valid
1.0ms	3×	body	640	valid
0.0ms	3×	body	160	valid

simplify3.1s

Counts

1 → 1

Iterations

Useful iterations: 4 (83.0ms)

Iter	Nodes	Cost
0	21	29
1	50	29
2	93	29
3	197	29
4	465	28
5	1141	28
6	4709	28
done	5000	28

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.6b

localize27.0ms

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	(/ (* K (+ m n)) 2.0)
34.4b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite1.0s

Algorithm

rewrite-expression-head

Rules

20×	`*-un-lft-identity`
14×	`add-log-exp`
12×	`add-sqr-sqrt`
11×	`add-exp-log` `add-cbrt-cube`
8×	`add-cube-cbrt`
6×	`pow1` `diff-log` `distribute-lft-out--`
4×	`associate-r/` `associate-r*`
3×	`sub-neg` `times-frac` `associate-l` `associate-/r*`
2×	`cbrt-undiv` `cos-sum` `distribute-rgt-neg-in` `flip3-+` `div-exp` `neg-log` `prod-exp` `cbrt-unprod` `flip-+` `associate-/l/` `associate--r+`
1×	`associate--l-` `neg-sub0` `distribute-rgt-in` `cos-diff` `flip3--` `frac-2neg` `distribute-lft-in` `pow-prod-down` `clear-num` `-commutative` `flip--` `div-inv` `distribute-lft-out` `associate-/l` `associate--r-` `difference-of-squares` `unswap-sqr`

Counts

4 → 80

Calls

4 calls:

953.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
22.0ms	(* K (+ m n))
13.0ms	(/ (* K (+ m n)) 2.0)
29.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series319.0ms

Counts

4 → 12

Calls

4 calls:

186.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
26.0ms	(* K (+ m n))
45.0ms	(/ (* K (+ m n)) 2.0)
61.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify2.0s

Counts

92 → 92

Iterations

Useful iterations: 3 (971.0ms)

Iter	Nodes	Cost
0	170	1279
1	405	1214
2	1206	1076
3	4702	1058
done	5001	1058

prune344.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 1.1b

localize16.0ms

Local error

Found 2 expressions with local error:

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

rewrite1.0s

Algorithm

rewrite-expression-head

Rules

16×	`*-un-lft-identity`
12×	`add-log-exp`
11×	`add-sqr-sqrt`
7×	`distribute-lft-out--`
6×	`unpow-prod-down` `diff-log`
4×	`add-cube-cbrt`
3×	`pow1` `add-exp-log` `pow-unpow` `difference-of-squares`
2×	`sub-neg` `distribute-rgt-neg-in` `neg-log` `add-cbrt-cube` `associate--r+`
1×	`associate--l-` `neg-sub0` `pow-to-exp` `flip3--` `pow-pow` `times-frac` `pow-exp` `flip--` `associate--r-` `sqr-pow`

Counts

2 → 44

Calls

2 calls:

58.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
963.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))

series452.0ms

Counts

2 → 6

Calls

2 calls:

263.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
190.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))

simplify947.0ms

Counts

50 → 50

Iterations

Useful iterations: done (945.0ms)

Iter	Nodes	Cost
0	122	937
1	273	879
2	632	826
3	2009	807
done	5000	799

prune172.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 1.1b

localize28.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (cos (- (/ (* K (+ m n)) 2.0) M)))
34.4b	(cos (- (/ (* K (+ m n)) 2.0) M))
34.4b	(cos (- (/ (* K (+ m n)) 2.0) M))
34.4b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite91.0ms

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)))
29.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
28.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
31.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series343.0ms

Counts

4 → 12

Calls

4 calls:

154.0ms	(cbrt (cos (- (/ (* K (+ m n)) 2.0) M)))
64.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
64.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
62.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify1.5s

Counts

53 → 53

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	48	853
1	83	812
2	122	730
3	170	727
4	282	727
5	521	727
6	1439	727
done	5000	687

prune299.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 1.1b

localize34.0ms

Local error

Found 4 expressions with local error:

34.4b	(cos (- (/ (* K (+ m n)) 2.0) M))
34.4b	(cos (- (/ (* K (+ m n)) 2.0) M))
34.4b	(cos (- (/ (* K (+ m n)) 2.0) M))
34.4b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

8×	`cos-sum`
4×	`pow1` `add-exp-log` `cos-diff` `add-sqr-sqrt` `add-cube-cbrt` `sub-neg` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`

Counts

4 → 40

Calls

4 calls:

28.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
29.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
30.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
28.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series246.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
63.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
59.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
64.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify2.1s

Counts

52 → 52

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	37	836
1	65	796
2	97	716
3	134	716
4	173	716
5	218	716
6	308	716
7	444	716
8	866	716
9	2380	716
done	5001	716

prune328.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 1.1b

regimes210.0ms

Accuracy

0% (0.2b remaining)

Error of 1.3b against oracle of 1.1b and baseline of 1.3b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 1 (1.0ms)

Iter	Nodes	Cost
0	17	20
1	21	18
done	21	18

end0.0ms

sample1.2s

Algorithm

intervals

Results

630.0ms	8087×	body	80	valid
63.0ms	133×	body	1280	valid
50.0ms	151×	body	640	valid
25.0ms	108×	body	320	valid
9.0ms	58×	body	160	valid
3.0ms	4×	body	2560	valid