Details

sample81.0ms

Algorithm

intervals

Results

55.0ms	262×	body	80	valid
5.0ms	4×	body	1280	valid
3.0ms	6×	body	320	valid
1.0ms	2×	body	640	valid
1.0ms	2×	body	160	valid

simplify305.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

305.0ms

(* (cos (- (/ (* K (+ m n)) 2) M)) (exp (- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))))

prune32.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.5b

localize68.0ms

Local error

Found 4 expressions with local error:

32.4b	(cos (- (* (/ K 2) (+ m n)) M))
0.0b	(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)
0.0b	(* (/ K 2) (+ m n))
0.0b	(- (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l) (fabs (- m n)))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
20×	`add-cube-cbrt`
13×	`associate-l`
12×	`prod-diff`
10×	`times-frac`
9×	`add-cbrt-cube` `add-exp-log`
7×	`cos-sum`
6×	`pow1` `add-log-exp`
4×	`expm1-log1p-u` `associate-r` `insert-posit16` `log1p-expm1-u`
3×	`fma-neg` `associate--l+`
2×	`distribute-rgt-in` `frac-times` `sub-neg` `distribute-lft-in` `flip3-+` `prod-exp` `associate-*r/` `cbrt-unprod` `flip-+` `fma-udef` `unswap-sqr`
1×	`cos-diff` `cbrt-undiv` `flip3--` `diff-log` `div-exp` `pow-prod-down` `associate-l/` `-commutative` `div-inv` `flip--` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 101

Calls

4 calls:

Slowest

39.0ms	(cos (- (* (/ K 2) (+ m n)) M))
18.0ms	(* (/ K 2) (+ m n))
5.0ms	(- (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l) (fabs (- m n)))
0.0ms	(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)

series569.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

205.0ms	(- (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l) (fabs (- m n)))
199.0ms	(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)
101.0ms	(cos (- (* (/ K 2) (+ m n)) M))
63.0ms	(* (/ K 2) (+ m n))

simplify10.0s

Counts

78 → 113

Calls

78 calls:

Slowest

909.0ms	(fma 1 (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l) (- (* (sqrt (fabs (- m n))) (sqrt (fabs (- m n))))))
562.0ms	(fma 1 (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l) (- (* (cbrt (fabs (- m n))) (* (cbrt (fabs (- m n))) (cbrt (fabs (- m n)))))))
476.0ms	(fma 1 (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l) (- (* (fabs (- m n)) 1)))
430.0ms	(/ (exp (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)) (exp (fabs (- m n))))
343.0ms	(* 2 (+ (* m m) (- (* n n) (* m n))))

prune1.9s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.1b

localize43.0ms

Local error

Found 2 expressions with local error:

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

rewrite12.0ms

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` `associate--l+` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 41

Calls

2 calls:

Slowest

11.0ms	(- (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l) (fabs (- m n)))
1.0ms	(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)

series422.0ms

Counts

2 → 6

Calls

2 calls:

Slowest

214.0ms	(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)
208.0ms	(- (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l) (fabs (- m n)))

simplify6.3s

Counts

31 → 47

Calls

31 calls:

Slowest

513.0ms	(fma 1 (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l) (- (* (cbrt (fabs (- m n))) (* (cbrt (fabs (- m n))) (cbrt (fabs (- m n)))))))
478.0ms	(fma 1 (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l) (- (* (sqrt (fabs (- m n))) (sqrt (fabs (- m n))))))
434.0ms	(fma 1 (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l) (- (* (fabs (- m n)) 1)))
398.0ms	(/ (exp (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)) (exp (fabs (- m n))))
308.0ms	(fma (* (cbrt (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)) (cbrt (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l))) (cbrt (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)) (- (* (cbrt (fabs (- m n))) (* (cbrt (fabs (- m n))) (cbrt (fabs (- m n)))))))

prune752.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.1b

localize130.0ms

Local error

Found 4 expressions with local error:

25.5b	(cos (* m (/ K 2)))
25.2b	(sin (* m (/ K 2)))
24.6b	(cos (- (* n (/ K 2)) M))
24.6b	(sin (- (* n (/ K 2)) M))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 52

Calls

4 calls:

Slowest

33.0ms	(cos (- (* n (/ K 2)) M))
23.0ms	(sin (- (* n (/ K 2)) M))
14.0ms	(sin (* m (/ K 2)))
13.0ms	(cos (* m (/ K 2)))

series164.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

80.0ms	(sin (- (* n (/ K 2)) M))
54.0ms	(cos (- (* n (/ K 2)) M))
18.0ms	(sin (* m (/ K 2)))
12.0ms	(cos (* m (/ K 2)))

simplify1.1s

Counts

24 → 64

Calls

24 calls:

Slowest

110.0ms	(* (sin (fma n (/ K 2) (- (* (cbrt M) (* (cbrt M) (cbrt M)))))) (cos (fma (- (cbrt M)) (* (cbrt M) (cbrt M)) (* (cbrt M) (* (cbrt M) (cbrt M))))))
95.0ms	(* (cos (fma n (/ K 2) (- (* (sqrt M) (sqrt M))))) (cos (fma (- (sqrt M)) (sqrt M) (* (sqrt M) (sqrt M)))))
94.0ms	(* (cos (fma n (/ K 2) (- (* (cbrt M) (* (cbrt M) (cbrt M)))))) (cos (fma (- (cbrt M)) (* (cbrt M) (cbrt M)) (* (cbrt M) (* (cbrt M) (cbrt M))))))
72.0ms	(* (cos (* n (/ K 2))) (cos (- M)))
71.0ms	(* (cos (fma n (/ K 2) (- (* M 1)))) (cos (fma (- M) 1 (* M 1))))

prune1.7s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.1b

localize150.0ms

Local error

Found 4 expressions with local error:

41.8b	(posit16->real (real->posit16 (sin (* m (/ K 2)))))
25.5b	(cos (* m (/ K 2)))
25.2b	(sin (* m (/ K 2)))
24.6b	(cos (- (* n (/ K 2)) M))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 47

Calls

4 calls:

Slowest

40.0ms	(cos (- (* n (/ K 2)) M))
7.0ms	(sin (* m (/ K 2)))
7.0ms	(cos (* m (/ K 2)))
0.0ms	(posit16->real (real->posit16 (sin (* m (/ K 2)))))

series111.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

44.0ms	(cos (- (* n (/ K 2)) M))
30.0ms	(posit16->real (real->posit16 (sin (* m (/ K 2)))))
19.0ms	(cos (* m (/ K 2)))
18.0ms	(sin (* m (/ K 2)))

simplify698.0ms

Counts

19 → 59

Calls

19 calls:

Slowest

109.0ms	(* (cos (fma n (/ K 2) (- (* (cbrt M) (* (cbrt M) (cbrt M)))))) (cos (fma (- (cbrt M)) (* (cbrt M) (cbrt M)) (* (cbrt M) (* (cbrt M) (cbrt M))))))
71.0ms	(* (cos (* n (/ K 2))) (cos (- M)))
66.0ms	(* (cos (fma n (/ K 2) (- (* M 1)))) (cos (fma (- M) 1 (* M 1))))
57.0ms	(* (cos (fma n (/ K 2) (- (* (sqrt M) (sqrt M))))) (cos (fma (- (sqrt M)) (sqrt M) (* (sqrt M) (sqrt M)))))
44.0ms	(* (cos (* n (/ K 2))) (cos (- M)))

prune2.5s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.1b

regimes597.0ms

Accuracy

0% (0.2b remaining)

Error of 1.2b against oracle of 1.0b and baseline of 1.2b

bsearch2.0ms

end0.0ms

sample3.3s

Algorithm

intervals

Results

2.6s	8135×	body	80	valid
207.0ms	125×	body	1280	valid
170.0ms	149×	body	640	valid
68.0ms	103×	body	320	valid
56.0ms	64×	body	160	valid
6.0ms	3×	body	2560	valid