Details

sample76.0ms

Algorithm

intervals

Results

44.0ms	258×	body	80	valid
2.0ms	3×	body	640	valid
2.0ms	3×	body	1280	valid
2.0ms	4×	body	320	valid
1.0ms	4×	body	160	valid

simplify744.0ms

Counts: 1 → 1

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.2b

localize39.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* K (+ m n)) 2.0)
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
0.0b	(* K (+ m n))
31.6b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite206.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

26.0ms	(/ (* K (+ m n)) 2.0)
91.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
34.0ms	(* K (+ m n))
51.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series601.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(/ (* K (+ m n)) 2.0)
417.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
36.0ms	(* K (+ m n))
86.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify805.0ms

Counts: 88 → 88

prune604.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 1.0b

localize30.0ms

Local error

Found 1 expressions with local error:

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

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`unpow-prod-down`
5×	`*-un-lft-identity`
3×	`add-cube-cbrt` `pow-unpow`
2×	`pow1` `add-exp-log` `difference-of-squares`
1×	`pow-to-exp` `pow-pow` `times-frac` `pow-exp` `add-cbrt-cube` `distribute-lft-out--` `add-log-exp` `sqr-pow`

Counts

1 → 20

Calls

1 calls:

70.0ms

(pow (- (/ (+ m n) 2.0) M) 2.0)

series439.0ms

Counts

1 → 3

Calls

1 calls:

439.0ms

(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify2.5s

Counts: 23 → 23

prune123.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 1.0b

localize42.0ms

Local error

Found 4 expressions with local error:

16.9b	(cbrt (/ (* K (+ m n)) 2.0))
16.9b	(cbrt (/ (* K (+ m n)) 2.0))
16.9b	(cbrt (/ (* K (+ m n)) 2.0))
31.8b	(cos (- (* (* (cbrt (/ (* K (+ m n)) 2.0)) (cbrt (/ (* K (+ m n)) 2.0))) (cbrt (/ (* K (+ m n)) 2.0))) M))

rewrite150.0ms

Algorithm

rewrite-expression-head

Rules

21×	`cbrt-prod`
10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`cbrt-div` `pow1/3` `div-inv`
2×	`cos-sum`
1×	`cos-diff` `sub-neg`

Counts

4 → 58

Calls

4 calls:

13.0ms	(cbrt (/ (* K (+ m n)) 2.0))
13.0ms	(cbrt (/ (* K (+ m n)) 2.0))
11.0ms	(cbrt (/ (* K (+ m n)) 2.0))
110.0ms	(cos (- (* (* (cbrt (/ (* K (+ m n)) 2.0)) (cbrt (/ (* K (+ m n)) 2.0))) (cbrt (/ (* K (+ m n)) 2.0))) M))

series1.1s

Counts

4 → 12

Calls

4 calls:

294.0ms	(cbrt (/ (* K (+ m n)) 2.0))
236.0ms	(cbrt (/ (* K (+ m n)) 2.0))
260.0ms	(cbrt (/ (* K (+ m n)) 2.0))
281.0ms	(cos (- (* (* (cbrt (/ (* K (+ m n)) 2.0)) (cbrt (/ (* K (+ m n)) 2.0))) (cbrt (/ (* K (+ m n)) 2.0))) M))

simplify1.6s

Counts: 70 → 70

prune628.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 1.0b

localize117.0ms

Local error

Found 4 expressions with local error:

16.9b	(cbrt (/ (* K (+ m n)) 2.0))
31.8b	(cos (- (* (* (cbrt (/ (* K (+ m n)) 2.0)) (cbrt (/ (* K (+ m n)) 2.0))) (cbrt (/ (* K (+ m n)) 2.0))) M))
31.8b	(cos (- (* (* (cbrt (/ (* K (+ m n)) 2.0)) (cbrt (/ (* K (+ m n)) 2.0))) (cbrt (/ (* K (+ m n)) 2.0))) M))
31.8b	(cos (- (* (* (cbrt (/ (* K (+ m n)) 2.0)) (cbrt (/ (* K (+ m n)) 2.0))) (cbrt (/ (* K (+ m n)) 2.0))) M))

rewrite439.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 46

Calls

4 calls:

12.0ms	(cbrt (/ (* K (+ m n)) 2.0))
146.0ms	(cos (- (* (* (cbrt (/ (* K (+ m n)) 2.0)) (cbrt (/ (* K (+ m n)) 2.0))) (cbrt (/ (* K (+ m n)) 2.0))) M))
143.0ms	(cos (- (* (* (cbrt (/ (* K (+ m n)) 2.0)) (cbrt (/ (* K (+ m n)) 2.0))) (cbrt (/ (* K (+ m n)) 2.0))) M))
136.0ms	(cos (- (* (* (cbrt (/ (* K (+ m n)) 2.0)) (cbrt (/ (* K (+ m n)) 2.0))) (cbrt (/ (* K (+ m n)) 2.0))) M))

series1.1s

Counts

4 → 12

Calls

4 calls:

263.0ms	(cbrt (/ (* K (+ m n)) 2.0))
298.0ms	(cos (- (* (* (cbrt (/ (* K (+ m n)) 2.0)) (cbrt (/ (* K (+ m n)) 2.0))) (cbrt (/ (* K (+ m n)) 2.0))) M))
305.0ms	(cos (- (* (* (cbrt (/ (* K (+ m n)) 2.0)) (cbrt (/ (* K (+ m n)) 2.0))) (cbrt (/ (* K (+ m n)) 2.0))) M))
272.0ms	(cos (- (* (* (cbrt (/ (* K (+ m n)) 2.0)) (cbrt (/ (* K (+ m n)) 2.0))) (cbrt (/ (* K (+ m n)) 2.0))) M))

simplify1.6s

Counts: 58 → 58

prune618.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 1.0b

regimes246.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify701.0ms

end0.0ms

sample3.1s

Algorithm

intervals

Results

2.1s	8109×	body	80	valid
136.0ms	101×	body	1280	valid
134.0ms	155×	body	640	valid
50.0ms	109×	body	320	valid
19.0ms	62×	body	160	valid
4.0ms	3×	body	2560	valid