Details

sample117.0ms

Algorithm

intervals

Results

63.0ms	265×	body	80	valid
18.0ms	3×	body	640	valid
2.0ms	1×	body	2560	valid
2.0ms	2×	body	320	valid
1.0ms	1×	body	1280	valid
1.0ms	2×	body	160	valid

simplify839.0ms

Counts

1 → 1

Iterations

Iter	Nodes
5	3045
4	783
3	250
2	102
1	51
0	21

prune29.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.7b

localize63.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ (* (+ m n) K) 2) M)
0.0b	(* (+ m n) K)
0.0b	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
35.3b	(cos (- (/ (* (+ m n) K) 2) M))

rewrite317.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
13×	`pow1`
10×	`associate-l` `add-cube-cbrt`
9×	`associate-r` `difference-of-squares`
8×	`add-cbrt-cube` `swap-sqr` `add-exp-log`
7×	`flip3--` `flip--` `distribute-lft-out--`
6×	`add-log-exp`
4×	`frac-times` `sub-neg` `times-frac` `associate-*l/` `insert-posit16`
2×	`distribute-rgt-in` `cos-sum` `distribute-lft-in` `pow-prod-down` `prod-exp` `associate-r/` `-commutative` `cbrt-unprod` `unswap-sqr`
1×	`pow2` `cos-diff` `flip3-+` `pow-plus` `diff-log` `pow-sqr` `pow-prod-up` `flip-+` `distribute-lft-out`

Counts

4 → 97

Calls

4 calls:

12.0ms	(- (/ (* (+ m n) K) 2) M)
20.0ms	(* (+ m n) K)
244.0ms	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
38.0ms	(cos (- (/ (* (+ m n) K) 2) M))

series350.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(- (/ (* (+ m n) K) 2) M)
44.0ms	(* (+ m n) K)
111.0ms	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
107.0ms	(cos (- (/ (* (+ m n) K) 2) M))

simplify2.1s

Counts

109 → 109

Iterations

Iter	Nodes
3	5823
2	1570
1	475
0	186

prune1.8s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize43.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)))
0.0b	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))

rewrite238.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
20×	`*-un-lft-identity`
9×	`pow1`
8×	`swap-sqr` `difference-of-squares`
6×	`flip3--` `associate-r` `associate-l` `add-cube-cbrt` `flip--` `distribute-lft-out--`
4×	`distribute-rgt-in` `frac-times` `associate-+r+` `sub-neg` `distribute-lft-in` `times-frac` `add-cbrt-cube` `add-exp-log` `add-log-exp`
2×	`associate-l/` `associate-r/` `insert-posit16`
1×	`pow2` `+-commutative` `sum-log` `flip3-+` `pow-plus` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

2 → 65

Calls

2 calls:

40.0ms	(+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)))
198.0ms	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))

series358.0ms

Counts

2 → 6

Calls

2 calls:

271.0ms	(+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)))
87.0ms	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))

simplify1.4s

Counts

71 → 71

Iterations

Iter	Nodes
3	5023
2	1141
1	340
0	119

prune1.1s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.4b

localize84.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ m n) K)
0.0b	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
32.9b	(posit16->real (real->posit16 (cos (- (/ (* (+ m n) K) 2) M))))
35.3b	(cos (- (/ (* (+ m n) K) 2) M))

rewrite258.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
13×	`pow1`
10×	`associate-l` `add-cube-cbrt`
9×	`associate-r`
8×	`add-cbrt-cube` `swap-sqr` `add-exp-log` `difference-of-squares`
6×	`flip3--` `flip--` `distribute-lft-out--`
4×	`frac-times` `times-frac` `associate-*l/` `insert-posit16` `add-log-exp`
3×	`sub-neg`
2×	`distribute-rgt-in` `cos-sum` `distribute-lft-in` `pow-prod-down` `prod-exp` `associate-r/` `-commutative` `cbrt-unprod` `unswap-sqr`
1×	`pow2` `cos-diff` `flip3-+` `pow-plus` `pow-sqr` `pow-prod-up` `flip-+` `remove-posit16` `distribute-lft-out`

Counts

4 → 91

Calls

4 calls:

28.0ms	(* (+ m n) K)
207.0ms	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
0.0ms	(posit16->real (real->posit16 (cos (- (/ (* (+ m n) K) 2) M))))
20.0ms	(cos (- (/ (* (+ m n) K) 2) M))

series299.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* (+ m n) K)
113.0ms	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
83.0ms	(posit16->real (real->posit16 (cos (- (/ (* (+ m n) K) 2) M))))
68.0ms	(cos (- (/ (* (+ m n) K) 2) M))

simplify2.2s

Counts

103 → 103

Iterations

Iter	Nodes
3	5690
2	1472
1	426
0	170

prune3.2s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.4b

localize95.0ms

Local error

Found 4 expressions with local error:

32.9b	(posit16->real (real->posit16 (cos (- (/ (* (+ m n) K) 2) M))))
35.3b	(cos (- (/ (* (+ m n) K) 2) M))
35.3b	(cos (- (/ (* (+ m n) K) 2) M))
35.3b	(cos (- (/ (* (+ m n) K) 2) M))

rewrite89.0ms

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` `insert-posit16` `add-log-exp`
3×	`cos-diff` `sub-neg`
1×	`remove-posit16`

Counts

4 → 42

Calls

4 calls:

0.0ms	(posit16->real (real->posit16 (cos (- (/ (* (+ m n) K) 2) M))))
23.0ms	(cos (- (/ (* (+ m n) K) 2) M))
43.0ms	(cos (- (/ (* (+ m n) K) 2) M))
22.0ms	(cos (- (/ (* (+ m n) K) 2) M))

series389.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(posit16->real (real->posit16 (cos (- (/ (* (+ m n) K) 2) M))))
110.0ms	(cos (- (/ (* (+ m n) K) 2) M))
74.0ms	(cos (- (/ (* (+ m n) K) 2) M))
82.0ms	(cos (- (/ (* (+ m n) K) 2) M))

simplify7.3s

Counts

54 → 54

Iterations

Iter	Nodes
10	7853
9	1836
8	766
7	437
6	277
5	190
4	140
3	122
2	100
1	75
0	47

prune2.4s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.4b

regimes288.0ms

Accuracy

0% (0.2b remaining)

Error of 1.4b against oracle of 1.1b and baseline of 1.4b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
2	21
1	21
0	16

end0.0ms

sample3.5s

Algorithm

intervals

Results

2.7s	8092×	body	80	valid
234.0ms	154×	body	640	valid
161.0ms	127×	body	1280	valid
66.0ms	92×	body	320	valid
30.0ms	62×	body	160	valid
8.0ms	4×	body	2560	valid