Details

sample120.0ms

Algorithm

intervals

Results

77.0ms	256×	body	80	valid
6.0ms	4×	body	1280	valid
5.0ms	5×	body	320	valid
4.0ms	3×	body	640	valid
1.0ms	2×	body	160	valid

simplify1.0s

Counts: 1 → 1

prune33.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.1b

localize79.0ms

Local error

Found 3 expressions with local error:

35.1b	(cos (- (* K (/ (+ m n) 2)) M))
0.0b	(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)
0.0b	(* K (/ (+ m n) 2))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 65

Calls

3 calls:

Slowest

24.0ms	(cos (- (* K (/ (+ m n) 2)) M))
18.0ms	(* K (/ (+ m n) 2))
0.0ms	(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)

series342.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

201.0ms	(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)
82.0ms	(cos (- (* K (/ (+ m n) 2)) M))
59.0ms	(* K (/ (+ m n) 2))

simplify926.0ms

Counts: 74 → 74

prune1.4s

Pruning

4 alts after pruning (3 fresh and 1 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:

Slowest

1.0ms

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

series222.0ms

Counts

1 → 3

Calls

1 calls:

Slowest

222.0ms

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

simplify3.3s

Counts: 14 → 14

prune242.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.7b

localize49.0ms

Local error

Found 2 expressions with local error:

23.3b	(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)

series393.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

202.0ms	(posit16->real (real->posit16 (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)))
191.0ms	(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)

simplify3.7s

Counts: 28 → 28

prune813.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.7b

localize73.0ms

Local error

Found 4 expressions with local error:

35.4b	(cos (- (* (* (cbrt K) (cbrt K)) (* (cbrt K) (/ (+ m n) 2))) M))
0.5b	(cbrt K)
0.5b	(cbrt K)
0.5b	(cbrt K)

rewrite193.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
8×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
5×	`cos-sum`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `prod-diff`
1×	`cos-diff` `sub-neg`

Counts

4 → 58

Calls

4 calls:

Slowest

190.0ms	(cos (- (* (* (cbrt K) (cbrt K)) (* (cbrt K) (/ (+ m n) 2))) M))
1.0ms	(cbrt K)
1.0ms	(cbrt K)
1.0ms	(cbrt K)

series970.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

283.0ms	(cbrt K)
282.0ms	(cbrt K)
270.0ms	(cbrt K)
135.0ms	(cos (- (* (* (cbrt K) (cbrt K)) (* (cbrt K) (/ (+ m n) 2))) M))

simplify825.0ms

Counts: 70 → 70

prune1.4s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.7b

regimes445.0ms

Accuracy

0% (0.3b remaining)

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

bsearch4.0ms

end0.0ms

sample3.6s

Algorithm

intervals

Results

2.6s	8085×	body	80	valid
235.0ms	155×	body	640	valid
220.0ms	121×	body	1280	valid
102.0ms	92×	body	320	valid
19.0ms	41×	body	160	valid
1.0ms	1×	body	2560	valid