Details

sample72.0ms

Algorithm

intervals

Results

47.0ms	260×	body	80	valid
4.0ms	4×	body	1280	valid
2.0ms	3×	body	640	valid
1.0ms	2×	body	320	valid

simplify2.2s

Counts

1 → 1

Iterations

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

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.0b

localize64.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
0.0b	(pow (- (/ (+ m n) 2) M) 2)
0.0b	(- (/ (* K (+ m n)) 2) M)
33.3b	(cos (- (/ (* K (+ m n)) 2) M))

rewrite766.0ms

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:

675.0ms	(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
49.0ms	(pow (- (/ (+ m n) 2) M) 2)
17.0ms	(- (/ (* K (+ m n)) 2) M)
24.0ms	(cos (- (/ (* K (+ m n)) 2) M))

series417.0ms

Counts

4 → 12

Calls

4 calls:

185.0ms	(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
93.0ms	(pow (- (/ (+ m n) 2) M) 2)
68.0ms	(- (/ (* K (+ m n)) 2) M)
70.0ms	(cos (- (/ (* K (+ m n)) 2) M))

simplify1.8s

Counts

85 → 85

Iterations

Iter	Nodes
done	5002
3	3521
2	1001
1	397
0	162

prune566.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.8b

localize47.0ms

Local error

Found 3 expressions with local error:

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

rewrite762.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 63

Calls

3 calls:

29.0ms	(- (/ (+ m n) 2) M)
684.0ms	(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
47.0ms	(pow (- (/ (+ m n) 2) M) 2)

series359.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(- (/ (+ m n) 2) M)
213.0ms	(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
117.0ms	(pow (- (/ (+ m n) 2) M) 2)

simplify1.7s

Counts

72 → 72

Iterations

Iter	Nodes
done	5000
3	2960
2	897
1	345
0	129

prune453.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.8b

localize71.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ (+ n m) 2) M)
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))
22.6b	(posit16->real (real->posit16 (* (- (/ (+ n m) 2) M) (- (/ (+ n m) 2) M))))

rewrite209.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
34×	`*-un-lft-identity`
16×	`add-log-exp`
13×	`distribute-lft-out--`
11×	`pow1` `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` `times-frac`
4×	`frac-times` `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 → 99

Calls

4 calls:

43.0ms	(- (/ (+ n m) 2) M)
16.0ms	(- (- (posit16->real (real->posit16 (* (- (/ (+ n m) 2) M) (- (/ (+ n m) 2) M))))) (- l (fabs (- m n))))
148.0ms	(* (- (/ (+ n m) 2) M) (- (/ (+ n m) 2) M))
0.0ms	(posit16->real (real->posit16 (* (- (/ (+ n m) 2) M) (- (/ (+ n m) 2) M))))

series377.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(- (/ (+ n m) 2) M)
157.0ms	(- (- (posit16->real (real->posit16 (* (- (/ (+ n m) 2) M) (- (/ (+ n m) 2) M))))) (- l (fabs (- m n))))
90.0ms	(* (- (/ (+ n m) 2) M) (- (/ (+ n m) 2) M))
99.0ms	(posit16->real (real->posit16 (* (- (/ (+ n m) 2) M) (- (/ (+ n m) 2) M))))

simplify1.4s

Counts

111 → 111

Iterations

Iter	Nodes
done	5001
2	1340
1	409
0	156

prune965.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.8b

localize79.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (- (/ (+ m n) 2) M) 2)
0.0b	(- (/ (* K (+ m n)) 2) M)
31.8b	(posit16->real (real->posit16 (cos (- (/ (* K (+ m n)) 2) M))))
33.3b	(cos (- (/ (* K (+ m n)) 2) M))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
6×	`unpow-prod-down` `add-cube-cbrt` `add-log-exp`
5×	`pow1` `add-exp-log`
4×	`add-cbrt-cube` `insert-posit16`
3×	`pow-unpow` `difference-of-squares`
2×	`cos-sum` `sub-neg` `distribute-lft-out--`
1×	`cos-diff` `pow-to-exp` `pow-pow` `times-frac` `flip3--` `diff-log` `pow-exp` `remove-posit16` `flip--` `unpow2` `sqr-pow`

Counts

4 → 57

Calls

4 calls:

46.0ms	(pow (- (/ (+ m n) 2) M) 2)
12.0ms	(- (/ (* K (+ m n)) 2) M)
0.0ms	(posit16->real (real->posit16 (cos (- (/ (* K (+ m n)) 2) M))))
20.0ms	(cos (- (/ (* K (+ m n)) 2) M))

series304.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(pow (- (/ (+ m n) 2) M) 2)
61.0ms	(- (/ (* K (+ m n)) 2) M)
67.0ms	(posit16->real (real->posit16 (cos (- (/ (* K (+ m n)) 2) M))))
92.0ms	(cos (- (/ (* K (+ m n)) 2) M))

simplify1.4s

Counts

69 → 69

Iterations

Iter	Nodes
done	5008
3	2211
2	733
1	305
0	127

prune881.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.8b

regimes315.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	21
1	21
0	17

end0.0ms

sample3.4s

Algorithm

intervals

Results

2.4s	8117×	body	80	valid
151.0ms	121×	body	1280	valid
114.0ms	127×	body	640	valid
70.0ms	116×	body	320	valid
23.0ms	55×	body	160	valid
5.0ms	3×	body	2560	valid