Details

sample59.0ms

Algorithm

intervals

Results

31.0ms	261×	body	80	valid
4.0ms	5×	body	1280	valid
3.0ms	4×	body	640	valid
1.0ms	2×	body	320	valid
0.0ms	1×	body	160	valid

simplify4.6s

Counts

1 → 1

Iterations

Useful iterations: 4 (127.0ms)

Iter	Nodes	Cost
0	21	29
1	50	29
2	93	29
3	197	29
4	465	28
5	1141	28
6	4709	28
done	5000	28

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.1b

localize56.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
0.0b	(* K (+ m n))
0.0b	(exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
32.9b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite4.2s

Algorithm

rewrite-expression-head

Rules

29×	`*-un-lft-identity`
25×	`add-log-exp`
13×	`add-sqr-sqrt`
12×	`diff-log` `distribute-lft-out--`
8×	`exp-prod`
7×	`add-cube-cbrt`
6×	`pow1` `add-exp-log` `add-cbrt-cube`
5×	`rem-exp-log`
4×	`sub-neg` `distribute-rgt-neg-in` `associate-r` `neg-log`
3×	`associate-l` `exp-sum`
2×	`cos-sum` `associate-*r/` `associate--r+` `associate--r-` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `distribute-rgt-in` `cos-diff` `flip3--` `distribute-lft-in` `flip3-+` `exp-diff` `pow-prod-down` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `flip-+` `distribute-lft-out` `unswap-sqr`

Counts

4 → 81

Calls

4 calls:

1.5s	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
20.0ms	(* K (+ m n))
2.6s	(exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
66.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series636.0ms

Counts

4 → 12

Calls

4 calls:

288.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
36.0ms	(* K (+ m n))
195.0ms	(exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
116.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify2.8s

Counts

93 → 93

Iterations

Useful iterations: 3 (1.2s)

Iter	Nodes	Cost
0	164	1461
1	389	1405
2	1102	1260
3	4188	1229
done	5000	1229

prune675.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 1.0b

localize18.0ms

Local error

Found 3 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))))
0.0b	(exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))

rewrite4.1s

Algorithm

rewrite-expression-head

Rules

28×	`*-un-lft-identity`
24×	`add-log-exp`
15×	`add-sqr-sqrt`
13×	`distribute-lft-out--`
12×	`diff-log`
8×	`exp-prod`
6×	`add-cube-cbrt` `unpow-prod-down`
5×	`rem-exp-log`
4×	`pow1` `add-exp-log` `distribute-rgt-neg-in` `neg-log` `difference-of-squares`
3×	`sub-neg` `pow-unpow` `exp-sum` `add-cbrt-cube`
2×	`associate--r+` `associate--r-`
1×	`associate--l-` `neg-sub0` `pow-to-exp` `flip3--` `pow-pow` `times-frac` `exp-diff` `pow-exp` `flip--` `sqr-pow`

Counts

3 → 68

Calls

3 calls:

79.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
1.5s	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
2.6s	(exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))

series874.0ms

Counts

3 → 9

Calls

3 calls:

383.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
298.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
193.0ms	(exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))

simplify2.1s

Counts

77 → 77

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	152	1395
1	352	1325
2	914	1223
3	3516	1191
done	5001	1183

prune366.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 1.0b

localize40.0ms

Local error

Found 3 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))))
0.0b	(pow E (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))

rewrite2.6s

Algorithm

rewrite-expression-head

Rules

29×	`*-un-lft-identity`
16×	`add-sqr-sqrt`
13×	`distribute-lft-out--` `add-log-exp`
11×	`pow-unpow`
9×	`unpow-prod-down`
7×	`add-cube-cbrt`
6×	`diff-log`
5×	`pow1` `add-exp-log`
4×	`distribute-rgt-neg-in` `difference-of-squares`
3×	`unpow-prod-up` `sub-neg` `pow-exp` `add-cbrt-cube`
2×	`pow-to-exp` `pow-pow` `neg-log` `associate--r+` `associate--r-` `sqr-pow`
1×	`associate--l-` `neg-sub0` `e-exp-1` `flip3--` `times-frac` `flip--` `pow-sub`

Counts

3 → 71

Calls

3 calls:

79.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
1.6s	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
920.0ms	(pow E (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))

series877.0ms

Counts

3 → 9

Calls

3 calls:

390.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
269.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
217.0ms	(pow E (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))

simplify2.6s

Counts

80 → 80

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	169	1662
1	403	1541
2	1036	1446
3	3852	1403
done	5001	1388

prune325.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 1.0b

localize48.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (cos (- (/ (* K (+ m n)) 2.0) M)))
32.9b	(cos (- (/ (* K (+ m n)) 2.0) M))
32.9b	(cos (- (/ (* K (+ m n)) 2.0) M))
32.9b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 41

Calls

4 calls:

2.0ms	(cbrt (cos (- (/ (* K (+ m n)) 2.0) M)))
33.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
29.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
50.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series447.0ms

Counts

4 → 12

Calls

4 calls:

213.0ms	(cbrt (cos (- (/ (* K (+ m n)) 2.0) M)))
78.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
83.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
73.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify2.2s

Counts

53 → 53

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	48	853
1	83	812
2	122	730
3	170	727
4	282	727
5	521	727
6	1439	727
done	5000	687

prune434.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 1.0b

regimes221.0ms

Accuracy

0% (0.2b remaining)

Error of 1.4b against oracle of 1.1b and baseline of 1.4b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	18	21
1	23	19
done	23	19

end0.0ms

sample3.0s

Algorithm

intervals

Results

2.1s	8103×	body	80	valid
180.0ms	133×	body	1280	valid
158.0ms	161×	body	640	valid
62.0ms	113×	body	320	valid
17.0ms	53×	body	160	valid
4.0ms	3×	body	2560	valid