Details

sample73.0ms

Algorithm

intervals

Results

43.0ms	260×	body	80	valid
6.0ms	7×	body	1280	valid
2.0ms	4×	body	320	valid
1.0ms	2×	body	640	valid
0.0ms	1×	body	160	valid

simplify720.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	2004
5	2004
4	821
3	262
2	104
1	51
0	21

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.5b

localize70.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ K (/ 2 (+ m n))) M)
0.0b	(/ 2 (+ m n))
0.2b	(/ K (/ 2 (+ m n)))
32.0b	(cos (- (/ K (/ 2 (+ m n))) M))

rewrite142.0ms

Algorithm

rewrite-expression-head

Rules

747×	`times-frac`
643×	`*-un-lft-identity`
492×	`add-sqr-sqrt`
483×	`add-cube-cbrt`
354×	`prod-diff`
179×	`cos-sum`
79×	`distribute-lft-out`
60×	`associate-/r/`
59×	`fma-neg`
34×	`div-inv`
26×	`flip3-+` `flip-+`
22×	`associate-/r*`
11×	`add-cbrt-cube` `add-exp-log`
6×	`associate-/l*` `add-log-exp`
4×	`expm1-log1p-u` `pow1` `cbrt-undiv` `div-exp` `insert-posit16` `log1p-expm1-u`
3×	`difference-of-squares`
2×	`clear-num` `sub-neg` `frac-2neg`
1×	`cos-diff` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 574

Calls

4 calls:

47.0ms	(- (/ K (/ 2 (+ m n))) M)
8.0ms	(/ 2 (+ m n))
10.0ms	(/ K (/ 2 (+ m n)))
61.0ms	(cos (- (/ K (/ 2 (+ m n))) M))

series223.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(- (/ K (/ 2 (+ m n))) M)
46.0ms	(/ 2 (+ m n))
43.0ms	(/ K (/ 2 (+ m n)))
68.0ms	(cos (- (/ K (/ 2 (+ m n))) M))

simplify1.9s

Counts

586 → 586

Iterations

Iter	Nodes
done	2004
2	2004
1	1876
0	1021

prune5.2s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.7b

localize39.0ms

Local error

Found 1 expressions with local error:

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

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `fma-udef` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Counts

1 → 11

Calls

1 calls:

0.0ms

(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)

series200.0ms

Counts

1 → 3

Calls

1 calls:

200.0ms

(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)

simplify958.0ms

Counts

14 → 14

Iterations

Iter	Nodes
done	2009
5	2009
4	1451
3	405
2	142
1	64
0	33

prune142.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.7b

localize62.0ms

Local error

Found 2 expressions with local error:

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

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

2×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`fma-udef` `remove-posit16`

Counts

2 → 22

Calls

2 calls:

0.0ms	(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)
0.0ms	(posit16->real (real->posit16 (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)))

series349.0ms

Counts

2 → 6

Calls

2 calls:

195.0ms	(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)
154.0ms	(posit16->real (real->posit16 (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)))

simplify968.0ms

Counts

28 → 28

Iterations

Iter	Nodes
done	2001
5	2001
4	1438
3	416
2	155
1	77
0	44

prune291.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.7b

localize46.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ K (sqrt 2)) (/ (sqrt 2) (+ m n)))
0.4b	(/ K (sqrt 2))
0.4b	(/ (sqrt 2) (+ m n))
32.2b	(cos (- (/ (/ K (sqrt 2)) (/ (sqrt 2) (+ m n))) M))

rewrite475.0ms

Algorithm

rewrite-expression-head

Rules

6996×	`times-frac`
4694×	`*-un-lft-identity`
3612×	`add-sqr-sqrt` `add-cube-cbrt`
2184×	`sqrt-prod`
1997×	`cos-sum`
1995×	`prod-diff`
541×	`distribute-lft-out`
216×	`div-inv`
184×	`associate-/r/`
90×	`flip3-+` `flip-+`
40×	`associate-/r*`
31×	`associate-/l*`
20×	`add-cbrt-cube` `add-exp-log`
10×	`cbrt-undiv` `div-exp`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg`
1×	`cos-diff` `sub-neg` `associate-/l/`

Counts

4 → 2836

Calls

4 calls:

17.0ms	(/ (/ K (sqrt 2)) (/ (sqrt 2) (+ m n)))
9.0ms	(/ K (sqrt 2))
16.0ms	(/ (sqrt 2) (+ m n))
217.0ms	(cos (- (/ (/ K (sqrt 2)) (/ (sqrt 2) (+ m n))) M))

series832.0ms

Counts

4 → 12

Calls

4 calls:

241.0ms	(/ (/ K (sqrt 2)) (/ (sqrt 2) (+ m n)))
76.0ms	(/ K (sqrt 2))
110.0ms	(/ (sqrt 2) (+ m n))
405.0ms	(cos (- (/ (/ K (sqrt 2)) (/ (sqrt 2) (+ m n))) M))

simplify8.3s

Counts

2848 → 2848

Iterations

Iter	Nodes
done	6952
0	6952

prune28.3s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.7b

regimes428.0ms

Accuracy

0% (0.3b remaining)

Error of 1.5b against oracle of 1.2b and baseline of 1.5b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	18
1	18
0	15

end0.0ms

sample3.7s

Algorithm

intervals

Results

2.5s	8096×	body	80	valid
583.0ms	140×	body	640	valid
179.0ms	132×	body	1280	valid
86.0ms	116×	body	320	valid
34.0ms	59×	body	160	valid
7.0ms	3×	body	2560	valid