Details

sample96.0ms

Algorithm

intervals

Results

53.0ms	253×	body	80	valid
12.0ms	9×	body	1280	valid
3.0ms	3×	body	640	valid
2.0ms	3×	body	320	valid
1.0ms	1×	body	160	valid

simplify1.2s

Counts: 1 → 1

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.1b

localize37.0ms

Local error

Found 4 expressions with local error:

32.1b	(cos (- (* K (/ (+ m n) 2)) M))
0.0b	(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)
0.0b	(* (exp (- (fabs (- m n)) (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l))) (cos (- (* K (/ (+ m n) 2)) M)))
0.0b	(- (* K (/ (+ m n) 2)) M)

rewrite124.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
15×	`prod-diff`
14×	`-un-lft-identity` `associate-l*` `add-cube-cbrt`
11×	`exp-sum`
6×	`pow1` `add-cbrt-cube` `add-log-exp`
5×	`cos-sum` `add-exp-log`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`cos-diff` `sub-neg` `associate-r`
1×	`distribute-rgt-in` `distribute-lft-in` `flip3--` `exp-diff` `fma-neg` `diff-log` `pow-prod-down` `associate-l/` `prod-exp` `-commutative` `cbrt-unprod` `fma-udef` `flip--` `unswap-sqr`

Counts

4 → 81

Calls

4 calls:

Slowest

73.0ms	(* (exp (- (fabs (- m n)) (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l))) (cos (- (* K (/ (+ m n) 2)) M)))
31.0ms	(cos (- (* K (/ (+ m n) 2)) M))
18.0ms	(- (* K (/ (+ m n) 2)) M)
0.0ms	(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)

series602.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

300.0ms	(* (exp (- (fabs (- m n)) (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l))) (cos (- (* K (/ (+ m n) 2)) M)))
163.0ms	(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)
71.0ms	(cos (- (* K (/ (+ m n) 2)) M))
68.0ms	(- (* K (/ (+ m n) 2)) M)

simplify1.8s

Counts: 93 → 93

prune1.5s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.8b

localize42.0ms

Local error

Found 4 expressions with local error:

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

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

96×	`*-un-lft-identity`
75×	`add-sqr-sqrt`
66×	`prod-diff` `add-cube-cbrt`
49×	`times-frac`
19×	`fma-neg`
12×	`distribute-lft-out`
11×	`exp-sum` `add-log-exp`
5×	`exp-prod`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `div-inv` `difference-of-squares`
3×	`sub-neg` `diff-log` `distribute-lft-out--`
2×	`flip3--` `fma-udef` `flip--` `rem-exp-log`
1×	`exp-diff` `associate--r+`

Counts

4 → 152

Calls

4 calls:

Slowest

37.0ms	(- (/ (+ m n) 2) M)
16.0ms	(exp (- (fabs (- m n)) (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)))
6.0ms	(- (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)

series545.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

198.0ms	(- (fabs (- m n)) (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l))
176.0ms	(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)
143.0ms	(exp (- (fabs (- m n)) (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)))
27.0ms	(- (/ (+ m n) 2) M)

simplify1.6s

Counts: 164 → 164

prune2.5s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.8b

localize39.0ms

Local error

Found 4 expressions with local error:

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

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-udef`

Counts

4 → 54

Calls

4 calls:

Slowest

1.0ms	(sqrt (fabs (- m n)))
1.0ms	(sqrt (fabs (- m n)))
0.0ms	(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)
0.0ms	(fma (sqrt (fabs (- m n))) (sqrt (fabs (- m n))) (- (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)))

series447.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

223.0ms	(fma (sqrt (fabs (- m n))) (sqrt (fabs (- m n))) (- (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)))
200.0ms	(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)
14.0ms	(sqrt (fabs (- m n)))
10.0ms	(sqrt (fabs (- m n)))

simplify739.0ms

Counts: 66 → 66

prune948.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.8b

localize86.0ms

Local error

Found 4 expressions with local error:

0.8b	(posit16->real (real->posit16 (exp (- (fabs (- m n)) (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)))))
0.0b	(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)
0.0b	(exp (- (fabs (- m n)) (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))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 81

Calls

4 calls:

Slowest

19.0ms	(exp (- (fabs (- m n)) (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)))
11.0ms	(- (fabs (- m n)) (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l))
1.0ms	(posit16->real (real->posit16 (exp (- (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)

series676.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

191.0ms	(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)
186.0ms	(- (fabs (- m n)) (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l))
150.0ms	(exp (- (fabs (- m n)) (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)))
148.0ms	(posit16->real (real->posit16 (exp (- (fabs (- m n)) (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)))))

simplify900.0ms

Counts: 93 → 93

prune2.6s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 1.8b

regimes613.0ms

Accuracy

0% (0.3b remaining)

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

bsearch6.0ms

end0.0ms

sample3.6s

Algorithm

intervals

Results

2.7s	8087×	body	80	valid
226.0ms	167×	body	640	valid
187.0ms	139×	body	1280	valid
114.0ms	103×	body	320	valid
25.0ms	51×	body	160	valid
7.0ms	4×	body	2560	valid