Details

sample389.0ms

Algorithm

intervals

Results

323.0ms	3×	body	640	valid
34.0ms	262×	body	80	valid
3.0ms	3×	body	1280	valid
1.0ms	4×	body	320	valid
1.0ms	2×	body	160	valid

simplify1.6s

Counts

1 → 1

Iterations

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

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.6b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* K (+ m n)) 2.0)
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
0.0b	(* K (+ m n))
33.3b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite158.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

12.0ms	(/ (* K (+ m n)) 2.0)
73.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
16.0ms	(* K (+ m n))
52.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series610.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(/ (* K (+ m n)) 2.0)
392.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
46.0ms	(* K (+ m n))
114.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify1.2s

Counts

88 → 88

Iterations

Iter	Nodes
done	5001
2	1724
1	465
0	174

prune744.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 1.0b

localize23.0ms

Local error

Found 2 expressions with local error:

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

rewrite122.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 35

Calls

2 calls:

52.0ms	(- (/ (+ m n) 2.0) M)
70.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series461.0ms

Counts

2 → 6

Calls

2 calls:

40.0ms	(- (/ (+ m n) 2.0) M)
420.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify970.0ms

Counts

41 → 41

Iterations

Iter	Nodes
done	5002
3	1981
2	660
1	254
0	96

prune410.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 1.0b

localize65.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (cos (- (/ (* (+ m n) K) 2.0) M)))
33.3b	(cos (- (/ (* (+ m n) K) 2.0) M))
33.3b	(cos (- (/ (* (+ m n) K) 2.0) M))
33.3b	(cos (- (/ (* (+ m n) K) 2.0) M))

rewrite122.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 41

Calls

4 calls:

2.0ms	(cbrt (cos (- (/ (* (+ m n) K) 2.0) M)))
30.0ms	(cos (- (/ (* (+ m n) K) 2.0) M))
47.0ms	(cos (- (/ (* (+ m n) K) 2.0) M))
42.0ms	(cos (- (/ (* (+ m n) K) 2.0) M))

series504.0ms

Counts

4 → 12

Calls

4 calls:

239.0ms	(cbrt (cos (- (/ (* (+ m n) K) 2.0) M)))
85.0ms	(cos (- (/ (* (+ m n) K) 2.0) M))
99.0ms	(cos (- (/ (* (+ m n) K) 2.0) M))
81.0ms	(cos (- (/ (* (+ m n) K) 2.0) M))

simplify2.7s

Counts

53 → 53

Iterations

Iter	Nodes
done	5000
6	4446
5	1275
4	448
3	200
2	121
1	82
0	48

prune700.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 1.0b

localize45.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt 2.0)
1.0b	(cbrt 2.0)
1.0b	(cbrt 2.0)
33.6b	(cos (- (/ (/ (/ (* (+ m n) K) (cbrt 2.0)) (cbrt 2.0)) (cbrt 2.0)) M))

rewrite472.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 43

Calls

4 calls:

1.0ms	(cbrt 2.0)
1.0ms	(cbrt 2.0)
1.0ms	(cbrt 2.0)
467.0ms	(cos (- (/ (/ (/ (* (+ m n) K) (cbrt 2.0)) (cbrt 2.0)) (cbrt 2.0)) M))

series302.0ms

Counts

4 → 6

Calls

4 calls:

0.0ms	(cbrt 2.0)
0.0ms	(cbrt 2.0)
0.0ms	(cbrt 2.0)
302.0ms	(cos (- (/ (/ (/ (* (+ m n) K) (cbrt 2.0)) (cbrt 2.0)) (cbrt 2.0)) M))

simplify2.0s

Counts

49 → 49

Iterations

Iter	Nodes
done	5001
5	3750
4	883
3	365
2	185
1	108
0	62

prune464.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 1.0b

regimes508.0ms

Accuracy

0% (0.2b remaining)

Error of 1.2b against oracle of 1.0b and baseline of 1.2b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	22
2	22
1	21
0	17

end0.0ms

sample3.1s

Algorithm

intervals

Results

2.0s	8127×	body	80	valid
156.0ms	167×	body	640	valid
110.0ms	119×	body	1280	valid
62.0ms	47×	body	160	valid
54.0ms	104×	body	320	valid
4.0ms	4×	body	2560	valid