Details

sample87.0ms

Algorithm

intervals

Results

54.0ms	259×	body	80	valid
3.0ms	6×	body	320	valid
2.0ms	4×	body	640	valid
2.0ms	2×	body	1280	valid
0.0ms	1×	body	160	valid

simplify2.4s

Counts

1 → 1

Iterations

Iter	Nodes
done	5052
5	3741
4	818
3	257
2	102
1	51
0	21

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.4b

localize51.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ (* K (+ m n)) 2) M)
0.0b	(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
0.0b	(pow (- (/ (+ m n) 2) M) 2)
32.7b	(cos (- (/ (* K (+ m n)) 2) M))

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

20×	`*-un-lft-identity`
16×	`add-log-exp`
15×	`add-sqr-sqrt`
8×	`distribute-lft-out--`
7×	`diff-log`
6×	`unpow-prod-down` `add-cube-cbrt`
5×	`pow1` `add-exp-log`
4×	`sub-neg` `add-cbrt-cube` `insert-posit16` `difference-of-squares`
3×	`pow-unpow`
2×	`cos-sum` `distribute-rgt-neg-in` `flip3--` `neg-log` `flip--` `associate--r+`
1×	`associate--l-` `neg-sub0` `cos-diff` `pow-to-exp` `pow-pow` `times-frac` `pow-exp` `unpow2` `associate--r-` `sqr-pow`

Counts

4 → 73

Calls

4 calls:

16.0ms	(- (/ (* K (+ m n)) 2) M)
1.1s	(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
52.0ms	(pow (- (/ (+ m n) 2) M) 2)
27.0ms	(cos (- (/ (* K (+ m n)) 2) M))

series388.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(- (/ (* K (+ m n)) 2) M)
166.0ms	(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
76.0ms	(pow (- (/ (+ m n) 2) M) 2)
63.0ms	(cos (- (/ (* K (+ m n)) 2) M))

simplify1.9s

Counts

85 → 85

Iterations

Iter	Nodes
done	5000
3	3691
2	1023
1	395
0	162

prune587.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.8b

localize33.0ms

Local error

Found 3 expressions with local error:

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

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
15×	`add-log-exp`
14×	`add-sqr-sqrt`
8×	`distribute-lft-out--`
7×	`diff-log`
6×	`unpow-prod-down`
5×	`add-cube-cbrt`
4×	`pow1` `add-exp-log` `difference-of-squares`
3×	`pow-unpow` `sub-neg` `add-cbrt-cube` `insert-posit16`
2×	`distribute-rgt-neg-in` `flip3--` `neg-log` `flip--` `associate--r+`
1×	`associate--l-` `neg-sub0` `pow-to-exp` `pow-pow` `times-frac` `pow-exp` `unpow2` `associate--r-` `sqr-pow`

Counts

3 → 62

Calls

3 calls:

5.0ms	(- l (fabs (- m n)))
1.2s	(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
59.0ms	(pow (- (/ (+ m n) 2) M) 2)

series293.0ms

Counts

3 → 9

Calls

3 calls:

17.0ms	(- l (fabs (- m n)))
179.0ms	(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
97.0ms	(pow (- (/ (+ m n) 2) M) 2)

simplify1.5s

Counts

71 → 71

Iterations

Iter	Nodes
done	5001
3	2591
2	796
1	325
0	127

prune527.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.8b

localize74.0ms

Local error

Found 4 expressions with local error:

0.0b	(- l (fabs (- m n)))
0.0b	(- (- (posit16->real (real->posit16 (* (- (/ (+ n m) 2) M) (- (/ (+ n m) 2) M))))) (- l (fabs (- m n))))
0.0b	(* (- (/ (+ n m) 2) M) (- (/ (+ n m) 2) M))
25.6b	(posit16->real (real->posit16 (* (- (/ (+ n m) 2) M) (- (/ (+ n m) 2) M))))

rewrite345.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt` `*-un-lft-identity`
16×	`add-log-exp`
13×	`distribute-lft-out--`
11×	`pow1`
10×	`difference-of-squares`
8×	`flip3--` `swap-sqr` `add-cube-cbrt` `flip--`
7×	`diff-log`
6×	`add-cbrt-cube` `associate-r` `associate-l` `add-exp-log`
5×	`sub-neg`
4×	`frac-times` `times-frac` `insert-posit16`
2×	`distribute-rgt-in` `distribute-rgt-neg-in` `distribute-lft-in` `neg-log` `associate-l/` `associate-r/` `associate--r+`
1×	`associate--l-` `pow2` `neg-sub0` `pow-plus` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `remove-posit16` `associate--r-` `unswap-sqr`

Counts

4 → 98

Calls

4 calls:

8.0ms	(- l (fabs (- m n)))
21.0ms	(- (- (posit16->real (real->posit16 (* (- (/ (+ n m) 2) M) (- (/ (+ n m) 2) M))))) (- l (fabs (- m n))))
311.0ms	(* (- (/ (+ n m) 2) M) (- (/ (+ n m) 2) M))
1.0ms	(posit16->real (real->posit16 (* (- (/ (+ n m) 2) M) (- (/ (+ n m) 2) M))))

series462.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(- l (fabs (- m n)))
222.0ms	(- (- (posit16->real (real->posit16 (* (- (/ (+ n m) 2) M) (- (/ (+ n m) 2) M))))) (- l (fabs (- m n))))
117.0ms	(* (- (/ (+ n m) 2) M) (- (/ (+ n m) 2) M))
105.0ms	(posit16->real (real->posit16 (* (- (/ (+ n m) 2) M) (- (/ (+ n m) 2) M))))

simplify1.5s

Counts

110 → 110

Iterations

Iter	Nodes
done	5000
2	1388
1	434
0	167

prune1.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.8b

localize85.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ (+ m n) (/ 2 K)) M)
0.0b	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
0.2b	(/ (+ m n) (/ 2 K))
32.8b	(cos (- (/ (+ m n) (/ 2 K)) M))

rewrite663.0ms

Algorithm

rewrite-expression-head

Rules

104×	`times-frac`
101×	`*-un-lft-identity`
88×	`add-sqr-sqrt`
57×	`add-cube-cbrt`
14×	`distribute-lft-out`
13×	`associate-/r*`
11×	`pow1` `add-cbrt-cube` `add-exp-log` `difference-of-squares`
8×	`swap-sqr`
7×	`flip3--` `flip--` `distribute-lft-out--`
6×	`associate-r` `associate-l` `div-inv` `add-log-exp`
4×	`frac-times` `sub-neg` `insert-posit16` `associate-/l*`
3×	`cbrt-undiv` `div-exp`
2×	`distribute-rgt-in` `cos-sum` `distribute-lft-in` `associate-l/` `associate-r/` `associate-/l/`
1×	`pow2` `cos-diff` `clear-num` `frac-2neg` `flip3-+` `pow-plus` `diff-log` `pow-prod-down` `prod-exp` `associate-/r/` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 164

Calls

4 calls:

92.0ms	(- (/ (+ m n) (/ 2 K)) M)
396.0ms	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
33.0ms	(/ (+ m n) (/ 2 K))
131.0ms	(cos (- (/ (+ m n) (/ 2 K)) M))

series330.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(- (/ (+ m n) (/ 2 K)) M)
97.0ms	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
56.0ms	(/ (+ m n) (/ 2 K))
117.0ms	(cos (- (/ (+ m n) (/ 2 K)) M))

simplify2.0s

Counts

176 → 176

Iterations

Iter	Nodes
done	5007
2	2494
1	797
0	299

prune1.3s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 1.7b

regimes692.0ms

Accuracy

0% (0.3b remaining)

Error of 1.4b against oracle of 1.2b and baseline of 1.4b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	21
1	21
0	17

end0.0ms

sample2.6s

Algorithm

intervals

Results

2.0s	8088×	body	80	valid
161.0ms	121×	body	1280	valid
98.0ms	151×	body	640	valid
47.0ms	103×	body	320	valid
18.0ms	62×	body	160	valid
4.0ms	4×	body	2560	valid