Details

sample46.0ms

Algorithm

intervals

Results

25.0ms	268×	body	80	valid
2.0ms	4×	body	640	valid
1.0ms	5×	body	320	valid
1.0ms	2×	body	1280	valid
0.0ms	1×	body	160	valid

simplify1.1s

Counts

1 → 1

Iterations

Useful iterations: 4 (62.0ms)

Iter	Nodes	Cost
0	21	29
1	50	29
2	94	29
3	212	29
4	506	28
5	1813	28
done	5000	28

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(* K (+ m n))
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
0.0b	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
31.7b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite1.0s

Algorithm

rewrite-expression-head

Rules

198×	`add-sqr-sqrt`
167×	`*-un-lft-identity`
150×	`prod-diff`
81×	`add-cube-cbrt`
78×	`unpow-prod-down`
62×	`distribute-rgt-neg-in`
60×	`distribute-lft-neg-in`
51×	`difference-of-squares`
43×	`distribute-lft-out--`
24×	`fma-neg`
23×	`cos-sum`
22×	`times-frac`
14×	`add-log-exp`
13×	`sqr-pow`
11×	`associate--r+`
7×	`pow1` `add-exp-log`
6×	`neg-mul-1` `diff-log` `add-cbrt-cube`
4×	`expm1-log1p-u` `associate-r` `log1p-expm1-u`
3×	`sub-neg` `pow-unpow` `associate-l` `div-inv`
2×	`associate-*r/` `neg-log`
1×	`associate--l-` `neg-sub0` `distribute-rgt-in` `cos-diff` `pow-to-exp` `flip3--` `pow-pow` `distribute-lft-in` `flip3-+` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `flip-+` `distribute-lft-out` `associate--r-` `unswap-sqr`

Counts

4 → 259

Calls

4 calls:

18.0ms	(* K (+ m n))
65.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
872.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
26.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series641.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(* K (+ m n))
357.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
197.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
55.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify1.4s

Counts

271 → 271

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	478	11285
1	1003	8855
2	2742	7233
done	5000	7165

prune846.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.8b

localize21.0ms

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))))

rewrite910.0ms

Algorithm

rewrite-expression-head

Rules

179×	`add-sqr-sqrt`
148×	`*-un-lft-identity`
129×	`prod-diff`
78×	`unpow-prod-down`
64×	`add-cube-cbrt`
62×	`distribute-rgt-neg-in`
60×	`distribute-lft-neg-in`
51×	`difference-of-squares`
43×	`distribute-lft-out--`
24×	`fma-neg`
13×	`times-frac` `sqr-pow`
12×	`add-log-exp`
11×	`associate--r+`
6×	`neg-mul-1` `diff-log`
3×	`pow1` `add-exp-log` `pow-unpow`
2×	`expm1-log1p-u` `sub-neg` `neg-log` `add-cbrt-cube` `log1p-expm1-u`
1×	`associate--l-` `neg-sub0` `pow-to-exp` `flip3--` `pow-pow` `pow-exp` `flip--` `associate--r-`

Counts

2 → 201

Calls

2 calls:

37.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
851.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))

series515.0ms

Counts

2 → 6

Calls

2 calls:

304.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
210.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))

simplify874.0ms

Counts

207 → 207

Iterations

Useful iterations: done (864.0ms)

Iter	Nodes	Cost
0	274	9396
1	615	7377
2	1655	6047
done	5000	5979

prune561.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.8b

localize34.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt K)
0.6b	(cbrt K)
0.6b	(cbrt K)
31.7b	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

23×	`cos-sum`
21×	`prod-diff`
20×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`cbrt-prod` `times-frac`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `div-inv`
1×	`cos-diff` `sub-neg`

Counts

4 → 72

Calls

4 calls:

0.0ms	(cbrt K)
0.0ms	(cbrt K)
0.0ms	(cbrt K)
51.0ms	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

series783.0ms

Counts

4 → 12

Calls

4 calls:

229.0ms	(cbrt K)
201.0ms	(cbrt K)
242.0ms	(cbrt K)
110.0ms	(cos (- (/ (* (* (cbrt K) (cbrt K)) (* (cbrt K) (+ m n))) 2.0) M))

simplify1.8s

Counts

84 → 84

Iterations

Useful iterations: 3 (376.0ms)

Iter	Nodes	Cost
0	202	2442
1	359	2034
2	757	1440
3	2339	963
done	5001	963

prune404.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.8b

localize37.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (+ m n) (sqrt 2.0))
0.5b	(/ (+ m n) (sqrt 2.0))
31.6b	(cos (fma (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)) (- M)))
31.7b	(sin (fma (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)) (- M)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

66×	`*-un-lft-identity`
48×	`times-frac`
38×	`add-sqr-sqrt` `add-cube-cbrt`
30×	`sqrt-prod`
14×	`distribute-lft-out`
12×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `associate-/l/` `add-log-exp`
2×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `fma-udef` `div-inv`
1×	`cos-sum` `sin-sum`

Counts

4 → 120

Calls

4 calls:

9.0ms	(/ (+ m n) (sqrt 2.0))
9.0ms	(/ (+ m n) (sqrt 2.0))
1.0ms	(cos (fma (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)) (- M)))
1.0ms	(sin (fma (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)) (- M)))

series765.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(/ (+ m n) (sqrt 2.0))
120.0ms	(/ (+ m n) (sqrt 2.0))
272.0ms	(cos (fma (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)) (- M)))
263.0ms	(sin (fma (/ K (sqrt 2.0)) (/ (+ m n) (sqrt 2.0)) (- M)))

simplify1.5s

Counts

132 → 132

Iterations

Useful iterations: 3 (272.0ms)

Iter	Nodes	Cost
0	128	1746
1	230	1660
2	570	1544
3	2083	1428
done	5000	1428

prune996.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.8b

regimes186.0ms

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
2	23	18
done	23	18

end0.0ms

sample1.1s

Algorithm

intervals

Results

674.0ms	8117×	body	80	valid
60.0ms	160×	body	640	valid
53.0ms	102×	body	1280	valid
28.0ms	109×	body	320	valid
9.0ms	50×	body	160	valid
5.0ms	6×	body	2560	valid