Details

sample114.0ms

Algorithm

intervals

Results

66.0ms	267×	body	80	valid
14.0ms	5×	body	1280	valid
5.0ms	7×	body	320	valid
3.0ms	4×	body	640	valid
1.0ms	2×	body	160	valid

simplify993.0ms

Counts: 1 → 1

prune30.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.2b

localize63.0ms

Local error

Found 4 expressions with local error:

34.1b	(cos (- (* K (/ (+ m n) 2)) M))
0.0b	(- (* K (/ (+ m n) 2)) M)
0.0b	(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)
0.0b	(- (fabs (- m n)) (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt` `*-un-lft-identity` `prod-diff`
13×	`add-cube-cbrt`
8×	`add-log-exp`
5×	`cos-sum`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `fma-neg` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`sub-neg`
2×	`flip3--` `diff-log` `fma-udef` `flip--`
1×	`cos-diff` `associate--r+` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 76

Calls

4 calls:

Slowest

25.0ms	(cos (- (* K (/ (+ m n) 2)) M))
20.0ms	(- (* K (/ (+ m n) 2)) M)
10.0ms	(- (fabs (- m n)) (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l))
0.0ms	(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)

series584.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

220.0ms	(- (fabs (- m n)) (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l))
206.0ms	(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))

simplify989.0ms

Counts: 88 → 88

prune1.7s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 1.0b

localize50.0ms

Local error

Found 2 expressions with local error:

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

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`prod-diff` `add-cube-cbrt`
4×	`add-log-exp`
3×	`fma-neg`
2×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `fma-udef` `insert-posit16` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `associate--r+` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 41

Calls

2 calls:

Slowest

5.0ms	(- (fabs (- m n)) (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l))
0.0ms	(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)

series399.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

203.0ms	(- (fabs (- m n)) (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l))
196.0ms	(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)

simplify2.4s

Counts: 47 → 47

prune840.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 1.0b

localize60.0ms

Local error

Found 4 expressions with local error:

54.0b	(posit16->real (real->posit16 (- (* K (/ (+ m n) 2)) M)))
34.1b	(cos (posit16->real (real->posit16 (- (* K (/ (+ m n) 2)) M))))
0.0b	(- (* K (/ (+ m n) 2)) M)
0.0b	(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 51

Calls

4 calls:

Slowest

25.0ms	(- (* K (/ (+ m n) 2)) M)
5.0ms	(cos (posit16->real (real->posit16 (- (* K (/ (+ m n) 2)) M))))
1.0ms	(posit16->real (real->posit16 (- (* K (/ (+ m n) 2)) M)))
0.0ms	(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)

series439.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

183.0ms	(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)
86.0ms	(cos (posit16->real (real->posit16 (- (* K (/ (+ m n) 2)) M))))
85.0ms	(- (* K (/ (+ m n) 2)) M)
84.0ms	(posit16->real (real->posit16 (- (* K (/ (+ m n) 2)) M)))

simplify2.2s

Counts: 63 → 63

prune2.0s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 1.0b

localize113.0ms

Local error

Found 4 expressions with local error:

54.0b	(posit16->real (real->posit16 (- (* K (/ (+ m n) 2)) M)))
54.0b	(posit16->real (real->posit16 (- (* K (/ (+ m n) 2)) M)))
54.0b	(posit16->real (real->posit16 (- (* K (/ (+ m n) 2)) M)))
45.8b	(cos (* (* (cbrt (posit16->real (real->posit16 (- (* K (/ (+ m n) 2)) M)))) (cbrt (posit16->real (real->posit16 (- (* K (/ (+ m n) 2)) M))))) (cbrt (posit16->real (real->posit16 (- (* K (/ (+ m n) 2)) M))))))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

4×	`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`
3×	`remove-posit16`

Counts

4 → 43

Calls

4 calls:

Slowest

57.0ms	(cos (* (* (cbrt (posit16->real (real->posit16 (- (* K (/ (+ m n) 2)) M)))) (cbrt (posit16->real (real->posit16 (- (* K (/ (+ m n) 2)) M))))) (cbrt (posit16->real (real->posit16 (- (* K (/ (+ m n) 2)) M))))))
1.0ms	(posit16->real (real->posit16 (- (* K (/ (+ m n) 2)) M)))
0.0ms	(posit16->real (real->posit16 (- (* K (/ (+ m n) 2)) M)))
0.0ms	(posit16->real (real->posit16 (- (* K (/ (+ m n) 2)) M)))

series381.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

100.0ms	(posit16->real (real->posit16 (- (* K (/ (+ m n) 2)) M)))
99.0ms	(posit16->real (real->posit16 (- (* K (/ (+ m n) 2)) M)))
98.0ms	(posit16->real (real->posit16 (- (* K (/ (+ m n) 2)) M)))
83.0ms	(cos (* (* (cbrt (posit16->real (real->posit16 (- (* K (/ (+ m n) 2)) M)))) (cbrt (posit16->real (real->posit16 (- (* K (/ (+ m n) 2)) M))))) (cbrt (posit16->real (real->posit16 (- (* K (/ (+ m n) 2)) M))))))

simplify2.8s

Counts: 55 → 55

prune1.9s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 1.0b

regimes425.0ms

Accuracy

0% (0.2b remaining)

Error of 1.3b against oracle of 1.1b and baseline of 1.3b

bsearch4.0ms

end0.0ms

sample3.9s

Algorithm

intervals

Results

2.7s	8115×	body	80	valid
547.0ms	161×	body	640	valid
188.0ms	134×	body	1280	valid
82.0ms	99×	body	320	valid
28.0ms	55×	body	160	valid
1.0ms	1×	body	2560	valid