Details

sample57.0ms

Algorithm

intervals

Results

27.0ms	258×	body	80	valid
3.0ms	5×	body	1280	valid
1.0ms	3×	body	640	valid
1.0ms	4×	body	160	valid

simplify1.5s

Counts

1 → 1

Iterations

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

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.5b

localize53.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
0.0b	(* (/ K 2.0) (+ m n))
0.0b	(- (* (/ K 2.0) (+ m n)) M)
33.5b	(cos (- (* (/ K 2.0) (+ m n)) M))

rewrite150.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 85

Calls

4 calls:

54.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
30.0ms	(* (/ K 2.0) (+ m n))
12.0ms	(- (* (/ K 2.0) (+ m n)) M)
51.0ms	(cos (- (* (/ K 2.0) (+ m n)) M))

series618.0ms

Counts

4 → 12

Calls

4 calls:

391.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
59.0ms	(* (/ K 2.0) (+ m n))
87.0ms	(- (* (/ K 2.0) (+ m n)) M)
80.0ms	(cos (- (* (/ K 2.0) (+ m n)) M))

simplify1.2s

Counts

97 → 97

Iterations

Iter	Nodes
done	5002
2	2281
1	613
0	214

prune844.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.0b

localize42.0ms

Local error

Found 2 expressions with local error:

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

rewrite202.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
8×	`*-un-lft-identity`
7×	`unpow-prod-down`
5×	`difference-of-squares`
4×	`add-cube-cbrt` `add-log-exp`
3×	`pow1` `pow-unpow` `add-exp-log`
2×	`add-cbrt-cube` `distribute-lft-out--` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `pow-pow` `times-frac` `flip3--` `diff-log` `pow-exp` `flip--`

Counts

2 → 36

Calls

2 calls:

147.0ms	(- (fabs (- m n)) (pow (- (/ (+ m n) 2.0) M) 2.0))
54.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series584.0ms

Counts

2 → 6

Calls

2 calls:

174.0ms	(- (fabs (- m n)) (pow (- (/ (+ m n) 2.0) M) 2.0))
409.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify1.2s

Counts

42 → 42

Iterations

Iter	Nodes
done	5000
3	2373
2	712
1	284
0	113

prune385.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (/ K 2.0))
0.7b	(cbrt (/ K 2.0))
0.7b	(cbrt (/ K 2.0))
33.3b	(cos (- (* (* (cbrt (/ K 2.0)) (cbrt (/ K 2.0))) (* (+ n m) (cbrt (/ K 2.0)))) M))

rewrite231.0ms

Algorithm

rewrite-expression-head

Rules

39×	`cbrt-prod`
27×	`times-frac`
25×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`cbrt-div` `pow1/3` `div-inv`
2×	`cos-sum`
1×	`cos-diff` `sub-neg`

Counts

4 → 76

Calls

4 calls:

2.0ms	(cbrt (/ K 2.0))
2.0ms	(cbrt (/ K 2.0))
2.0ms	(cbrt (/ K 2.0))
223.0ms	(cos (- (* (* (cbrt (/ K 2.0)) (cbrt (/ K 2.0))) (* (+ n m) (cbrt (/ K 2.0)))) M))

series1.3s

Counts

4 → 12

Calls

4 calls:

339.0ms	(cbrt (/ K 2.0))
351.0ms	(cbrt (/ K 2.0))
332.0ms	(cbrt (/ K 2.0))
283.0ms	(cos (- (* (* (cbrt (/ K 2.0)) (cbrt (/ K 2.0))) (* (+ n m) (cbrt (/ K 2.0)))) M))

simplify1.0s

Counts

88 → 88

Iterations

Iter	Nodes
done	5000
3	970
2	315
1	158
0	100

prune995.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.0b

localize71.0ms

Local error

Found 4 expressions with local error:

21.7b	(sin (- (/ (* K n) 2.0) M))
21.9b	(cos (- (/ (* K n) 2.0) M))
29.7b	(sin (* (/ K 2.0) m))
30.1b	(cos (* (/ K 2.0) m))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `add-log-exp`
2×	`cos-sum` `sub-neg` `sin-sum`
1×	`cos-diff` `sin-diff`

Counts

4 → 34

Calls

4 calls:

19.0ms	(sin (- (/ (* K n) 2.0) M))
31.0ms	(cos (- (/ (* K n) 2.0) M))
10.0ms	(sin (* (/ K 2.0) m))
11.0ms	(cos (* (/ K 2.0) m))

series122.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(sin (- (/ (* K n) 2.0) M))
39.0ms	(cos (- (/ (* K n) 2.0) M))
20.0ms	(sin (* (/ K 2.0) m))
16.0ms	(cos (* (/ K 2.0) m))

simplify1.8s

Counts

46 → 46

Iterations

Iter	Nodes
done	5001
8	4020
7	1371
6	646
5	312
4	179
3	148
2	123
1	97
0	69

prune557.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.0b

regimes578.0ms

Accuracy

0% (0.2b remaining)

Error of 1.3b against oracle of 1.1b and baseline of 1.3b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	21
2	21
1	20
0	16

end0.0ms

sample2.9s

Algorithm

intervals

Results

2.0s	8096×	body	80	valid
145.0ms	164×	body	640	valid
108.0ms	124×	body	1280	valid
48.0ms	101×	body	320	valid
24.0ms	55×	body	160	valid
2.0ms	1×	body	2560	valid