Details

sample58.0ms

Algorithm

intervals

Results

32.0ms	259×	body	80	valid
2.0ms	4×	body	640	valid
2.0ms	3×	body	1280	valid
1.0ms	2×	body	320	valid
0.0ms	1×	body	160	valid

simplify1.8s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
5	3032
4	640
3	210
2	93
1	50
0	21

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.7b

localize66.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (- (- (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)))))
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
32.6b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite9.0s

Algorithm

rewrite-expression-head

Rules

21×	`*-un-lft-identity`
18×	`add-sqr-sqrt`
15×	`add-log-exp`
9×	`add-cube-cbrt`
8×	`exp-prod`
7×	`pow1` `distribute-lft-out--`
6×	`unpow-prod-down` `add-cbrt-cube` `diff-log` `associate-r` `exp-sum` `add-exp-log`
5×	`rem-exp-log`
3×	`pow-unpow` `sub-neg` `associate-l` `difference-of-squares`
2×	`cos-sum` `distribute-rgt-neg-in` `exp-diff` `neg-log` `associate--r-`
1×	`cos-diff` `pow-to-exp` `pow-pow` `times-frac` `pow-prod-down` `pow-exp` `prod-exp` `associate-r/` `-commutative` `cbrt-unprod` `unswap-sqr` `sqr-pow`

Counts

4 → 76

Calls

4 calls:

6.7s	(* (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))))
2.2s	(exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
65.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
28.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series1.3s

Counts

4 → 12

Calls

4 calls:

638.0ms	(* (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))))
174.0ms	(exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
405.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
89.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify679.0ms

Counts

88 → 88

Iterations

Iter	Nodes
done	5000
2	1312
1	421
0	175

prune921.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 1.1b

localize26.0ms

Local error

Found 3 expressions with local error:

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

rewrite3.5s

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×	`unpow-prod-down` `add-cube-cbrt`
5×	`rem-exp-log`
4×	`pow1` `distribute-rgt-neg-in` `neg-log` `add-exp-log` `difference-of-squares`
3×	`pow-unpow` `sub-neg` `add-cbrt-cube` `exp-sum`
2×	`associate--r+` `associate--r-`
1×	`associate--l-` `neg-sub0` `pow-to-exp` `pow-pow` `times-frac` `flip3--` `exp-diff` `pow-exp` `flip--` `sqr-pow`

Counts

3 → 68

Calls

3 calls:

1.2s	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
2.2s	(exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
63.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series773.0ms

Counts

3 → 9

Calls

3 calls:

287.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
161.0ms	(exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
324.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify668.0ms

Counts

77 → 77

Iterations

Iter	Nodes
done	5000
2	1235
1	397
0	152

prune669.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 1.1b

localize55.0ms

Local error

Found 3 expressions with local error:

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

rewrite1.9s

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` `add-cbrt-cube` `pow-exp`
2×	`pow-to-exp` `pow-pow` `neg-log` `associate--r+` `associate--r-` `sqr-pow`
1×	`associate--l-` `neg-sub0` `e-exp-1` `times-frac` `flip3--` `flip--` `pow-sub`

Counts

3 → 71

Calls

3 calls:

1.1s	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
656.0ms	(pow E (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
94.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series815.0ms

Counts

3 → 9

Calls

3 calls:

245.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
178.0ms	(pow E (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
391.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify854.0ms

Counts

80 → 80

Iterations

Iter	Nodes
done	5001
2	1649
1	475
0	169

prune564.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 1.1b

localize93.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (sqrt (exp (- (+ (pow (- (/ (+ n m) 2.0) M) 2.0) (- l (fabs (- m n))))))) (sqrt (exp (- (+ (pow (- (/ (+ n m) 2.0) M) 2.0) (- l (fabs (- m n))))))))
0.0b	(pow (- (/ (+ n m) 2.0) M) 2.0)
0.0b	(pow (- (/ (+ n m) 2.0) M) 2.0)
32.6b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite13.9s

Algorithm

rewrite-expression-head

Rules

308×	`*-un-lft-identity`
212×	`sqrt-pow1`
204×	`exp-prod`
88×	`distribute-lft-out`
84×	`distribute-rgt-neg-in`
72×	`distribute-lft-neg-in`
56×	`add-sqr-sqrt`
46×	`distribute-lft-out--`
41×	`pow-prod-down`
37×	`pow-prod-up`
35×	`pow-sqr`
34×	`add-cube-cbrt`
22×	`sqrt-prod`
21×	`pow1`
12×	`neg-mul-1` `unpow-prod-down` `sqrt-div`
9×	`swap-sqr`
8×	`pow1/2` `add-exp-log`
7×	`associate-r` `associate-l`
6×	`neg-sub0` `exp-neg` `pow-unpow` `add-cbrt-cube` `exp-diff`
4×	`frac-times` `distribute-neg-in` `exp-sum` `add-log-exp` `difference-of-squares` `unswap-sqr`
2×	`pow-to-exp` `cos-sum` `pow-pow` `times-frac` `associate-l/` `pow-exp` `associate-r/` `sqr-pow`
1×	`pow2` `cos-diff` `sub-neg` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 212

Calls

4 calls:

13.7s	(* (sqrt (exp (- (+ (pow (- (/ (+ n m) 2.0) M) 2.0) (- l (fabs (- m n))))))) (sqrt (exp (- (+ (pow (- (/ (+ n m) 2.0) M) 2.0) (- l (fabs (- m n))))))))
72.0ms	(pow (- (/ (+ n m) 2.0) M) 2.0)
74.0ms	(pow (- (/ (+ n m) 2.0) M) 2.0)
23.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series1.1s

Counts

4 → 12

Calls

4 calls:

250.0ms	(* (sqrt (exp (- (+ (pow (- (/ (+ n m) 2.0) M) 2.0) (- l (fabs (- m n))))))) (sqrt (exp (- (+ (pow (- (/ (+ n m) 2.0) M) 2.0) (- l (fabs (- m n))))))))
421.0ms	(pow (- (/ (+ n m) 2.0) M) 2.0)
359.0ms	(pow (- (/ (+ n m) 2.0) M) 2.0)
88.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify2.7s

Counts

224 → 224

Iterations

Iter	Nodes
done	5000
2	2711
1	594
0	256

prune1.3s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 1.1b

regimes487.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	24
2	24
1	23
0	18

end0.0ms

sample2.9s

Algorithm

intervals

Results

2.2s	8067×	body	80	valid
142.0ms	137×	body	640	valid
91.0ms	99×	body	1280	valid
59.0ms	117×	body	320	valid
25.0ms	70×	body	160	valid
3.0ms	2×	body	2560	valid