Details

sample64.0ms

Algorithm

intervals

Results

32.0ms	258×	body	80	valid
3.0ms	6×	body	640	valid
2.0ms	2×	body	1280	valid
1.0ms	3×	body	320	valid
0.0ms	1×	body	160	valid

simplify49.0ms

Counts

1 → 1

Iterations

Useful iterations: 3 (9.0ms)

Iter	Nodes	Cost
0	50	16
1	95	16
2	211	16
3	553	15
4	1974	15
5	5001	15
done	5001	15

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(- l (fabs (- m n)))
0.0b	(* K (+ m n))
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
34.4b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite126.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
34×	`*-un-lft-identity`
30×	`prod-diff`
28×	`add-cube-cbrt`
23×	`cos-sum`
10×	`times-frac`
7×	`pow1` `add-exp-log`
6×	`unpow-prod-down` `add-cbrt-cube` `add-log-exp`
4×	`expm1-log1p-u` `associate-r` `log1p-expm1-u`
3×	`pow-unpow` `fma-neg` `associate-l` `div-inv` `difference-of-squares`
2×	`sub-neg` `associate-*r/` `distribute-lft-out--`
1×	`distribute-rgt-in` `cos-diff` `pow-to-exp` `flip3--` `pow-pow` `distribute-lft-in` `flip3-+` `diff-log` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `flip-+` `distribute-lft-out` `unswap-sqr` `sqr-pow`

Counts

4 → 108

Calls

4 calls:

7.0ms	(- l (fabs (- m n)))
20.0ms	(* K (+ m n))
58.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
38.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series378.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(- l (fabs (- m n)))
32.0ms	(* K (+ m n))
268.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
65.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify60.0ms

Counts

120 → 120

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	655	1498
1	1934	1154
2	5002	1153
done	5002	1153

prune436.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.6b

localize19.0ms

Local error

Found 3 expressions with local error:

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

rewrite1.3s

Algorithm

rewrite-expression-head

Rules

189×	`add-sqr-sqrt`
158×	`*-un-lft-identity`
138×	`prod-diff`
78×	`unpow-prod-down`
72×	`add-cube-cbrt`
62×	`distribute-rgt-neg-in`
60×	`distribute-lft-neg-in`
52×	`difference-of-squares`
44×	`distribute-lft-out--`
27×	`fma-neg`
15×	`add-log-exp`
13×	`times-frac` `sqr-pow`
11×	`associate--r+`
7×	`diff-log`
6×	`neg-mul-1`
4×	`pow1` `add-exp-log`
3×	`expm1-log1p-u` `sub-neg` `pow-unpow` `add-cbrt-cube` `log1p-expm1-u`
2×	`flip3--` `neg-log` `flip--`
1×	`associate--l-` `neg-sub0` `pow-to-exp` `pow-pow` `pow-exp` `associate--r-`

Counts

3 → 229

Calls

3 calls:

1.2s	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
8.0ms	(- l (fabs (- m n)))
58.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series486.0ms

Counts

3 → 9

Calls

3 calls:

199.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
13.0ms	(- l (fabs (- m n)))
274.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify85.0ms

Counts

238 → 238

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	650	5353
1	1864	3800
2	5001	3192
done	5001	3192

prune431.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.6b

localize44.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt 2.0)
1.0b	(cbrt 2.0)
34.3b	(cos (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))
34.5b	(sin (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

6×	`cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow1/3` `fma-udef`
1×	`cos-sum` `sin-sum`

Counts

4 → 46

Calls

4 calls:

1.0ms	(cbrt 2.0)
1.0ms	(cbrt 2.0)
2.0ms	(cos (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))
3.0ms	(sin (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))

series434.0ms

Counts

4 → 8

Calls

4 calls:

0.0ms	(cbrt 2.0)
0.0ms	(cbrt 2.0)
215.0ms	(cos (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))
219.0ms	(sin (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))

simplify131.0ms

Counts

54 → 54

Iterations

Useful iterations: 3 (28.0ms)

Iter	Nodes	Cost
0	162	538
1	381	481
2	991	472
3	3226	466
4	5001	466
done	5001	466

prune456.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.6b

localize50.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt 2.0)
1.0b	(cbrt 2.0)
34.3b	(cos (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))
34.5b	(sin (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

6×	`cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow1/3` `fma-udef`
1×	`cos-sum` `sin-sum`

Counts

4 → 46

Calls

4 calls:

1.0ms	(cbrt 2.0)
1.0ms	(cbrt 2.0)
3.0ms	(cos (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))
3.0ms	(sin (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))

series432.0ms

Counts

4 → 8

Calls

4 calls:

0.0ms	(cbrt 2.0)
0.0ms	(cbrt 2.0)
213.0ms	(cos (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))
218.0ms	(sin (fma (/ K (* (cbrt 2.0) (cbrt 2.0))) (/ (+ m n) (cbrt 2.0)) (- (* M 1))))

simplify65.0ms

Counts

54 → 54

Iterations

Useful iterations: 3 (18.0ms)

Iter	Nodes	Cost
0	122	474
1	273	419
2	641	414
3	1470	412
4	5002	412
done	5002	412

prune482.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.6b

regimes121.0ms

Accuracy

0% (0.2b remaining)

Error of 1.3b against oracle of 1.2b and baseline of 1.3b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	10
1	23	10
2	23	10
done	23	10

end0.0ms

sample1.1s

Algorithm

intervals

Results

601.0ms	8079×	body	80	valid
52.0ms	113×	body	1280	valid
47.0ms	150×	body	640	valid
25.0ms	97×	body	320	valid
9.0ms	62×	body	160	valid