Details

sample49.0ms

Algorithm

intervals

Results

25.0ms	263×	body	80	valid
1.0ms	3×	body	640	valid
1.0ms	2×	body	1280	valid
1.0ms	3×	body	160	valid
0.0ms	1×	body	320	valid

simplify6.9s

Counts

1 → 1

Iterations

Useful iterations: 4 (280.0ms)

Iter	Nodes	Cost
0	21	826
1	50	826
2	91	826
3	198	826
4	501	786
5	1382	786
6	4997	786
done	5001	786

prune29.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.6b

localize44.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ (* K (+ m n)) 2.0) M)
0.0b	(* K (+ m n))
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
34.6b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite206.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 67

Calls

4 calls:

31.0ms	(- (/ (* K (+ m n)) 2.0) M)
30.0ms	(* K (+ m n))
96.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
44.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series591.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(- (/ (* K (+ m n)) 2.0) M)
32.0ms	(* K (+ m n))
417.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
71.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify2.8s

Counts

79 → 79

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	164	24197
1	409	22248
2	999	22088
3	3109	21888
done	5000	21848

prune622.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize36.0ms

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)

rewrite482.0ms

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` `pow-unpow` `add-exp-log`
2×	`associate-+r+` `sum-log` `add-cbrt-cube` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`
1×	`pow-to-exp` `+-commutative` `associate-+r-` `sub-neg` `pow-pow` `flip3-+` `times-frac` `diff-log` `pow-exp` `flip-+` `sqr-pow`

Counts

2 → 37

Calls

2 calls:

424.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
57.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series612.0ms

Counts

2 → 6

Calls

2 calls:

265.0ms	(+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))
347.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify2.5s

Counts

43 → 43

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	110	22335
1	282	20346
2	658	20186
3	2108	20186
done	5008	20146

prune301.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.4b

localize73.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (+ m n))
0.6b	(cbrt (+ m n))
0.6b	(cbrt (+ m n))
34.0b	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

rewrite414.0ms

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-cbrt-cube` `add-exp-log` `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:

8.0ms	(cbrt (+ m n))
7.0ms	(cbrt (+ m n))
6.0ms	(cbrt (+ m n))
391.0ms	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

series690.0ms

Counts

4 → 12

Calls

4 calls:

166.0ms	(cbrt (+ m n))
184.0ms	(cbrt (+ m n))
185.0ms	(cbrt (+ m n))
154.0ms	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

simplify2.6s

Counts

64 → 64

Iterations

Useful iterations: 4 (1.0s)

Iter	Nodes	Cost
0	91	24306
1	188	20177
2	409	20097
3	916	17537
4	2363	17417
done	5000	17417

prune646.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.4b

localize211.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (+ m n))
34.0b	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))
34.0b	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))
34.0b	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

rewrite867.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 44

Calls

4 calls:

3.0ms	(cbrt (+ m n))
283.0ms	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))
256.0ms	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))
322.0ms	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

series619.0ms

Counts

4 → 12

Calls

4 calls:

186.0ms	(cbrt (+ m n))
146.0ms	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))
152.0ms	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))
134.0ms	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

simplify2.8s

Counts

56 → 56

Iterations

Useful iterations: 4 (995.0ms)

Iter	Nodes	Cost
0	91	25798
1	188	23995
2	409	23755
3	916	17355
4	2363	17315
done	5000	17315

prune731.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.4b

regimes499.0ms

Accuracy

0% (0.1b remaining)

Error of 1.2b against oracle of 1.1b and baseline of 1.2b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	606
1	20	606
done	20	606

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.9s	8109×	body	80	valid
129.0ms	140×	body	640	valid
87.0ms	103×	body	1280	valid
45.0ms	106×	body	320	valid
35.0ms	3×	body	2560	valid
20.0ms	76×	body	160	valid