Details

sample54.0ms

Algorithm

intervals

Results

30.0ms	263×	body	80	valid
2.0ms	4×	body	1280	valid
1.0ms	2×	body	320	valid
0.0ms	1×	body	160	valid

simplify2.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
5	1428
4	534
3	208
2	93
1	50
0	21

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.0b

localize75.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ (* (+ m n) K) 2.0) M)
0.0b	(* (+ m n) K)
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
35.2b	(cos (- (/ (* (+ m n) K) 2.0) M))

rewrite185.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 122

Calls

4 calls:

19.0ms	(- (/ (* (+ m n) K) 2.0) M)
24.0ms	(* (+ m n) K)
94.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
44.0ms	(cos (- (/ (* (+ m n) K) 2.0) M))

series592.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(- (/ (* (+ m n) K) 2.0) M)
42.0ms	(* (+ m n) K)
382.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
92.0ms	(cos (- (/ (* (+ m n) K) 2.0) M))

simplify3.5s

Counts

134 → 134

Iterations

Iter	Nodes
done	5000
3	4484
2	1371
1	642
0	308

prune1.3s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize26.0ms

Local error

Found 1 expressions with local error:

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

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`unpow-prod-down`
5×	`*-un-lft-identity`
3×	`pow-unpow` `add-cube-cbrt`
2×	`pow1` `add-exp-log` `difference-of-squares`
1×	`expm1-log1p-u` `pow-to-exp` `pow-pow` `times-frac` `add-cbrt-cube` `pow-exp` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp` `sqr-pow`

Counts

1 → 22

Calls

1 calls:

49.0ms

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

series419.0ms

Counts

1 → 3

Calls

1 calls:

419.0ms

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

simplify2.6s

Counts

25 → 25

Iterations

Iter	Nodes
done	5007
4	2857
3	969
2	390
1	188
0	76

prune213.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.4b

localize87.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (* (* (cos (- (* (/ (+ m n) 2.0) K) M)) (cos (- (* (/ (+ m n) 2.0) K) M))) (cos (- (* (/ (+ m n) 2.0) K) M))))
35.2b	(cos (- (* (/ (+ m n) 2.0) K) M))
35.2b	(cos (- (* (/ (+ m n) 2.0) K) M))
35.2b	(cos (- (* (/ (+ m n) 2.0) K) M))

rewrite173.0ms

Algorithm

rewrite-expression-head

Rules

15×	`cos-sum`
9×	`prod-diff`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
3×	`cos-diff` `sub-neg`
1×	`cbrt-prod` `cbrt-div` `pow1/3` `pow3` `associate-*l/` `cos-mult` `rem-cbrt-cube`

Counts

4 → 58

Calls

4 calls:

72.0ms	(cbrt (* (* (cos (- (* (/ (+ m n) 2.0) K) M)) (cos (- (* (/ (+ m n) 2.0) K) M))) (cos (- (* (/ (+ m n) 2.0) K) M))))
34.0ms	(cos (- (* (/ (+ m n) 2.0) K) M))
30.0ms	(cos (- (* (/ (+ m n) 2.0) K) M))
35.0ms	(cos (- (* (/ (+ m n) 2.0) K) M))

series372.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(cbrt (* (* (cos (- (* (/ (+ m n) 2.0) K) M)) (cos (- (* (/ (+ m n) 2.0) K) M))) (cos (- (* (/ (+ m n) 2.0) K) M))))
96.0ms	(cos (- (* (/ (+ m n) 2.0) K) M))
84.0ms	(cos (- (* (/ (+ m n) 2.0) K) M))
90.0ms	(cos (- (* (/ (+ m n) 2.0) K) M))

simplify4.1s

Counts

70 → 70

Iterations

Iter	Nodes
done	5000
7	4172
6	1982
5	1181
4	692
3	404
2	245
1	158
0	94

prune916.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.4b

localize107.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (* 1 (cos (- (* (/ (+ m n) 2.0) K) M))) (cos (- (* (/ (+ m n) 2.0) K) M)))
0.5b	(cbrt (* (* 1 (cos (- (* (/ (+ m n) 2.0) K) M))) (cos (- (* (/ (+ m n) 2.0) K) M))))
35.2b	(cos (- (* (/ (+ m n) 2.0) K) M))
35.2b	(cos (- (* (/ (+ m n) 2.0) K) M))

rewrite290.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-exp-log`
10×	`cos-sum`
9×	`pow1` `add-cbrt-cube`
8×	`*-un-lft-identity`
7×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`prod-diff`
5×	`prod-exp`
4×	`cos-diff` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `pow-prod-down` `cbrt-unprod`
2×	`sub-neg`
1×	`cbrt-prod` `distribute-rgt-in` `distribute-lft-in` `pow1/3` `1-exp` `swap-sqr` `associate-l` `*-commutative`

Counts

4 → 65

Calls

4 calls:

103.0ms	(* (* 1 (cos (- (* (/ (+ m n) 2.0) K) M))) (cos (- (* (/ (+ m n) 2.0) K) M)))
75.0ms	(cbrt (* (* 1 (cos (- (* (/ (+ m n) 2.0) K) M))) (cos (- (* (/ (+ m n) 2.0) K) M))))
55.0ms	(cos (- (* (/ (+ m n) 2.0) K) M))
55.0ms	(cos (- (* (/ (+ m n) 2.0) K) M))

series706.0ms

Counts

4 → 12

Calls

4 calls:

166.0ms	(* (* 1 (cos (- (* (/ (+ m n) 2.0) K) M))) (cos (- (* (/ (+ m n) 2.0) K) M)))
328.0ms	(cbrt (* (* 1 (cos (- (* (/ (+ m n) 2.0) K) M))) (cos (- (* (/ (+ m n) 2.0) K) M))))
93.0ms	(cos (- (* (/ (+ m n) 2.0) K) M))
119.0ms	(cos (- (* (/ (+ m n) 2.0) K) M))

simplify3.3s

Counts

77 → 77

Iterations

Iter	Nodes
done	5000
5	2338
4	1073
3	691
2	468
1	269
0	120

prune857.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.4b

regimes483.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	20
1	20
0	16

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.9s	8064×	body	80	valid
158.0ms	165×	body	640	valid
101.0ms	118×	body	1280	valid
49.0ms	112×	body	320	valid
14.0ms	49×	body	160	valid
2.0ms	2×	body	2560	valid