Details

sample41.0ms

Algorithm

intervals

Results

20.0ms	259×	body	80	valid
2.0ms	6×	body	640	valid
1.0ms	4×	body	320	valid
1.0ms	1×	body	2560	valid
0.0ms	1×	body	1280	valid

simplify2.3s

Counts

1 → 1

Iterations

Useful iterations: 4 (59.0ms)

Iter	Nodes	Cost
0	21	29
1	50	29
2	94	29
3	205	29
4	460	28
5	1278	28
6	4692	28
done	5000	28

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.6b

localize29.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (/ (* K (+ m n)) 2.0) M)
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
35.4b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

42×	`prod-diff`
40×	`add-sqr-sqrt`
37×	`*-un-lft-identity`
33×	`add-cube-cbrt`
23×	`cos-sum`
22×	`times-frac`
7×	`fma-neg` `div-inv`
6×	`unpow-prod-down`
5×	`add-log-exp`
4×	`pow1` `add-exp-log`
3×	`expm1-log1p-u` `pow-unpow` `add-cbrt-cube` `log1p-expm1-u` `difference-of-squares`
2×	`sub-neg` `distribute-lft-out--`
1×	`cos-diff` `pow-to-exp` `flip3--` `pow-pow` `diff-log` `pow-exp` `flip--` `sqr-pow`

Counts

3 → 99

Calls

3 calls:

14.0ms	(- (/ (* K (+ m n)) 2.0) M)
31.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
20.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series374.0ms

Counts

3 → 9

Calls

3 calls:

58.0ms	(- (/ (* K (+ m n)) 2.0) M)
262.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
53.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify1.2s

Counts

108 → 108

Iterations

Useful iterations: 3 (429.0ms)

Iter	Nodes	Cost
0	268	2992
1	494	2362
2	901	2014
3	2545	1779
done	5001	1779

prune362.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 1.0b

localize15.0ms

Local error

Found 1 expressions with local error:

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

rewrite33.0ms

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×	`expm1-log1p-u` `pow-to-exp` `pow-pow` `times-frac` `pow-exp` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp` `sqr-pow`

Counts

1 → 22

Calls

1 calls:

31.0ms

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

series258.0ms

Counts

1 → 3

Calls

1 calls:

258.0ms

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

simplify1.1s

Counts

25 → 25

Iterations

Useful iterations: 4 (339.0ms)

Iter	Nodes	Cost
0	76	357
1	160	338
2	317	325
3	714	324
4	1839	316
done	5000	316

prune107.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 1.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
0.6b	(pow (cbrt (/ (* K (+ m n)) 2.0)) 3)
15.1b	(cbrt (/ (* K (+ m n)) 2.0))
35.5b	(cos (+ (- (pow (cbrt (/ (* K (+ m n)) 2.0)) 3) M) (- M M)))

rewrite237.0ms

Algorithm

rewrite-expression-head

Rules

21×	`cbrt-prod`
20×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
16×	`unpow-prod-down`
15×	`add-cube-cbrt`
10×	`times-frac` `cube-prod`
6×	`pow1` `add-exp-log` `pow-unpow`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow-pow` `div-inv`
2×	`cos-diff` `pow-to-exp` `cbrt-div` `pow1/3` `pow-exp` `difference-of-squares` `sqr-pow`
1×	`cube-div` `cube-mult` `associate-+l-` `associate-+r-` `cos-sum` `unpow3` `distribute-lft-out--` `rem-cube-cbrt`

Counts

4 → 93

Calls

4 calls:

33.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
3.0ms	(pow (cbrt (/ (* K (+ m n)) 2.0)) 3)
3.0ms	(cbrt (/ (* K (+ m n)) 2.0))
195.0ms	(cos (+ (- (pow (cbrt (/ (* K (+ m n)) 2.0)) 3) M) (- M M)))

series762.0ms

Counts

4 → 12

Calls

4 calls:

270.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
156.0ms	(pow (cbrt (/ (* K (+ m n)) 2.0)) 3)
157.0ms	(cbrt (/ (* K (+ m n)) 2.0))
180.0ms	(cos (+ (- (pow (cbrt (/ (* K (+ m n)) 2.0)) 3) M) (- M M)))

simplify2.0s

Counts

105 → 105

Iterations

Useful iterations: 3 (566.0ms)

Iter	Nodes	Cost
0	212	1672
1	485	1352
2	1088	1212
3	4258	1207
done	5000	1207

prune485.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 1.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
0.5b	(cbrt (pow (cos (- (* K (/ (+ m n) 2.0)) M)) 3))
0.6b	(pow (cos (- (* K (/ (+ m n) 2.0)) M)) 3)
35.4b	(cos (- (* K (/ (+ m n) 2.0)) M))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
15×	`*-un-lft-identity`
13×	`add-cube-cbrt`
12×	`cbrt-prod` `unpow-prod-down`
6×	`pow1` `add-exp-log` `pow-unpow` `cube-prod`
5×	`cos-sum` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`prod-diff` `sqr-pow`
2×	`cube-mult` `pow-to-exp` `pow-pow` `unpow3` `pow-exp` `difference-of-squares`
1×	`cos-diff` `sub-neg` `times-frac` `pow1/3` `rem-cbrt-cube` `distribute-lft-out--` `rem-cube-cbrt`

Counts

4 → 85

Calls

4 calls:

31.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
3.0ms	(cbrt (pow (cos (- (* K (/ (+ m n) 2.0)) M)) 3))
4.0ms	(pow (cos (- (* K (/ (+ m n) 2.0)) M)) 3)
13.0ms	(cos (- (* K (/ (+ m n) 2.0)) M))

series500.0ms

Counts

4 → 12

Calls

4 calls:

267.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
56.0ms	(cbrt (pow (cos (- (* K (/ (+ m n) 2.0)) M)) 3))
120.0ms	(pow (cos (- (* K (/ (+ m n) 2.0)) M)) 3)
57.0ms	(cos (- (* K (/ (+ m n) 2.0)) M))

simplify1.4s

Counts

97 → 97

Iterations

Useful iterations: 3 (366.0ms)

Iter	Nodes	Cost
0	184	1791
1	355	1523
2	767	1361
3	2752	1354
done	5000	1354

prune386.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 1.0b

regimes211.0ms

Accuracy

0% (0.3b remaining)

Error of 1.4b against oracle of 1.2b and baseline of 1.4b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 1 (1.0ms)

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

end0.0ms

sample1.1s

Algorithm

intervals

Results

640.0ms	8091×	body	80	valid
54.0ms	160×	body	640	valid
50.0ms	103×	body	1280	valid
32.0ms	120×	body	320	valid
10.0ms	56×	body	160	valid
2.0ms	2×	body	2560	valid