Details

sample59.0ms

Algorithm

intervals

Results

36.0ms	263×	body	80	valid
2.0ms	4×	body	1280	valid
1.0ms	2×	body	320	valid
0.0ms	1×	body	160	valid

simplify3.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
6	4997
5	1382
4	501
3	198
2	91
1	50
0	21

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.0b

localize51.0ms

Local error

Found 4 expressions with local error:

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

rewrite136.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
18×	`*-un-lft-identity`
14×	`add-cube-cbrt`
13×	`associate-r`
11×	`times-frac`
10×	`add-exp-log`
9×	`add-cbrt-cube`
7×	`pow1`
6×	`unpow-prod-down` `add-log-exp`
4×	`associate-l`
3×	`pow-unpow`
2×	`frac-times` `cos-sum` `sub-neg` `flip3-+` `associate-*l/` `prod-exp` `cbrt-unprod` `flip-+` `difference-of-squares` `unswap-sqr`
1×	`cos-diff` `pow-to-exp` `cbrt-undiv` `pow-pow` `flip3--` `diff-log` `div-exp` `pow-prod-down` `pow-exp` `associate-r/` `-commutative` `div-inv` `flip--` `distribute-lft-out` `distribute-lft-out--` `sqr-pow`

Counts

4 → 79

Calls

4 calls:

11.0ms	(- (* (+ m n) (/ K 2.0)) M)
26.0ms	(* (+ m n) (/ K 2.0))
64.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
33.0ms	(cos (- (* (+ m n) (/ K 2.0)) M))

series528.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(- (* (+ m n) (/ K 2.0)) M)
48.0ms	(* (+ m n) (/ K 2.0))
325.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
70.0ms	(cos (- (* (+ m n) (/ K 2.0)) M))

simplify1.4s

Counts

91 → 91

Iterations

Iter	Nodes
done	5000
2	1464
1	514
0	202

prune883.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize38.0ms

Local error

Found 1 expressions with local error:

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

rewrite75.0ms

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×	`pow-to-exp` `pow-pow` `times-frac` `add-cbrt-cube` `pow-exp` `distribute-lft-out--` `add-log-exp` `sqr-pow`

Counts

1 → 20

Calls

1 calls:

74.0ms

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

series362.0ms

Counts

1 → 3

Calls

1 calls:

362.0ms

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

simplify2.2s

Counts

23 → 23

Iterations

Iter	Nodes
done	5000
4	2641
3	921
2	379
1	184
0	74

prune230.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.4b

localize118.0ms

Local error

Found 4 expressions with local error:

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

rewrite294.0ms

Algorithm

rewrite-expression-head

Rules

6×	`cos-sum`
4×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `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 → 41

Calls

4 calls:

142.0ms	(cbrt (* (* (cos (- (* (+ m n) (/ K 2.0)) M)) (cos (- (* (+ m n) (/ K 2.0)) M))) (cos (- (* (+ m n) (/ K 2.0)) M))))
54.0ms	(cos (- (* (+ m n) (/ K 2.0)) M))
53.0ms	(cos (- (* (+ m n) (/ K 2.0)) M))
43.0ms	(cos (- (* (+ m n) (/ K 2.0)) M))

series352.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(cbrt (* (* (cos (- (* (+ m n) (/ K 2.0)) M)) (cos (- (* (+ m n) (/ K 2.0)) M))) (cos (- (* (+ m n) (/ K 2.0)) M))))
86.0ms	(cos (- (* (+ m n) (/ K 2.0)) M))
76.0ms	(cos (- (* (+ m n) (/ K 2.0)) M))
91.0ms	(cos (- (* (+ m n) (/ K 2.0)) M))

simplify2.4s

Counts

53 → 53

Iterations

Iter	Nodes
done	5002
5	2299
4	1040
3	378
2	163
1	92
0	55

prune685.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.4b

localize62.0ms

Local error

Found 4 expressions with local error:

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

rewrite316.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1`
10×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`add-cbrt-cube` `add-exp-log`
4×	`cos-diff` `cos-sum` `add-log-exp`
3×	`swap-sqr` `associate-r` `associate-l`
2×	`sub-neg` `cos-mult`
1×	`cbrt-prod` `pow2` `distribute-rgt-in` `sqr-cos` `cbrt-div` `distribute-lft-in` `pow-plus` `pow1/3` `pow-prod-down` `associate-l/` `prod-exp` `pow-sqr` `-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`

Counts

4 → 59

Calls

4 calls:

90.0ms	(* (cos (- (* (+ m n) (/ K 2.0)) M)) (cos (- (* (+ m n) (/ K 2.0)) M)))
117.0ms	(cbrt (* (* (cos (- (* (+ m n) (/ K 2.0)) M)) (cos (- (* (+ m n) (/ K 2.0)) M))) 1))
61.0ms	(cos (- (* (+ m n) (/ K 2.0)) M))
45.0ms	(cos (- (* (+ m n) (/ K 2.0)) M))

series660.0ms

Counts

4 → 12

Calls

4 calls:

184.0ms	(* (cos (- (* (+ m n) (/ K 2.0)) M)) (cos (- (* (+ m n) (/ K 2.0)) M)))
270.0ms	(cbrt (* (* (cos (- (* (+ m n) (/ K 2.0)) M)) (cos (- (* (+ m n) (/ K 2.0)) M))) 1))
94.0ms	(cos (- (* (+ m n) (/ K 2.0)) M))
113.0ms	(cos (- (* (+ m n) (/ K 2.0)) M))

simplify2.9s

Counts

71 → 71

Iterations

Iter	Nodes
done	5000
4	3067
3	960
2	444
1	192
0	86

prune759.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.4b

regimes477.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	20
1	20
0	16

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.8s	8064×	body	80	valid
180.0ms	118×	body	1280	valid
131.0ms	165×	body	640	valid
90.0ms	112×	body	320	valid
13.0ms	49×	body	160	valid
3.0ms	2×	body	2560	valid