Details

sample134.0ms

Algorithm

intervals

Results

83.0ms	256×	body	80	valid
10.0ms	8×	body	640	valid
5.0ms	5×	body	320	valid
3.0ms	2×	body	1280	valid
2.0ms	3×	body	160	valid

simplify1.3s

Counts: 1 → 1

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.1b

localize39.0ms

Local error

Found 4 expressions with local error:

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

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

21×	`*-un-lft-identity`
20×	`add-sqr-sqrt`
16×	`associate-r`
15×	`add-cube-cbrt`
13×	`times-frac`
9×	`add-cbrt-cube` `add-exp-log`
6×	`pow1` `prod-diff` `add-log-exp`
5×	`cos-sum`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-l` `distribute-lft-out`
2×	`sub-neg` `prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`cos-diff` `cbrt-undiv` `flip3--` `fma-neg` `diff-log` `div-exp` `pow-prod-down` `associate-r/` `-commutative` `fma-udef` `div-inv` `flip--`

Counts

4 → 84

Calls

4 calls:

Slowest

57.0ms	(cos (- (* K (/ (+ m n) 2)) M))
15.0ms	(* K (/ (+ m n) 2))
14.0ms	(- (* K (/ (+ m n) 2)) M)
0.0ms	(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)

series431.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

215.0ms	(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)
86.0ms	(- (* K (/ (+ m n) 2)) M)
70.0ms	(cos (- (* K (/ (+ m n) 2)) M))
59.0ms	(* K (/ (+ m n) 2))

simplify1.2s

Counts: 96 → 96

prune1.9s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.9b

localize55.0ms

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:

Slowest

1.0ms

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

series223.0ms

Counts

1 → 3

Calls

1 calls:

Slowest

223.0ms

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

simplify3.0s

Counts: 14 → 14

prune281.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.9b

localize51.0ms

Local error

Found 2 expressions with local error:

23.1b	(posit16->real (real->posit16 (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)))
0.0b	(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:

Slowest

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

series398.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

200.0ms	(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)
197.0ms	(posit16->real (real->posit16 (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)))

simplify3.1s

Counts: 28 → 28

prune679.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.9b

localize59.0ms

Local error

Found 4 expressions with local error:

35.3b	(cos (- (* K (/ (+ m n) 2)) M))
33.1b	(posit16->real (real->posit16 (cos (- (* K (/ (+ m n) 2)) M))))
0.0b	(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)
0.0b	(- (* K (/ (+ m n) 2)) M)

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt` `*-un-lft-identity` `prod-diff` `add-cube-cbrt` `add-log-exp`
5×	`cos-sum`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
2×	`sub-neg`
1×	`cos-diff` `flip3--` `fma-neg` `diff-log` `fma-udef` `remove-posit16` `flip--`

Counts

4 → 57

Calls

4 calls:

Slowest

24.0ms	(cos (- (* K (/ (+ m n) 2)) M))
10.0ms	(- (* K (/ (+ m n) 2)) M)
0.0ms	(posit16->real (real->posit16 (cos (- (* K (/ (+ m n) 2)) M))))
0.0ms	(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)

series429.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

202.0ms	(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)
100.0ms	(- (* K (/ (+ m n) 2)) M)
64.0ms	(cos (- (* K (/ (+ m n) 2)) M))
63.0ms	(posit16->real (real->posit16 (cos (- (* K (/ (+ m n) 2)) M))))

simplify1.5s

Counts: 69 → 69

prune2.2s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.9b

regimes457.0ms

Accuracy

0% (0.3b remaining)

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

bsearch2.0ms

end0.0ms

sample3.2s

Algorithm

intervals

Results

2.3s	8109×	body	80	valid
215.0ms	166×	body	640	valid
178.0ms	124×	body	1280	valid
88.0ms	98×	body	320	valid
25.0ms	59×	body	160	valid
2.0ms	1×	body	2560	valid