Details

sample137.0ms

Algorithm

intervals

Results

89.0ms	267×	body	80	valid
8.0ms	5×	body	1280	valid
6.0ms	7×	body	320	valid
4.0ms	4×	body	640	valid
1.0ms	2×	body	160	valid

simplify869.0ms

Counts: 1 → 1

prune26.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.2b

localize60.0ms

Local error

Found 4 expressions with local error:

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

rewrite663.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
11×	`pow1` `add-log-exp`
10×	`difference-of-squares`
8×	`flip3--` `swap-sqr` `add-cube-cbrt` `flip--` `distribute-lft-out--`
6×	`add-cbrt-cube` `associate-r` `associate-l` `add-exp-log`
5×	`sub-neg`
4×	`frac-times` `times-frac` `insert-posit16`
3×	`diff-log`
2×	`distribute-rgt-in` `cos-sum` `distribute-lft-in` `associate-l/` `associate-r/`
1×	`pow2` `cos-diff` `sum-log` `pow-plus` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `associate--r+` `unswap-sqr`

Counts

4 → 92

Calls

4 calls:

Slowest

560.0ms	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
54.0ms	(- (fabs (- m n)) (+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))))
24.0ms	(- (/ (* (+ m n) K) 2) M)
23.0ms	(cos (- (/ (* (+ m n) K) 2) M))

series484.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

189.0ms	(- (fabs (- m n)) (+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))))
120.0ms	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
93.0ms	(cos (- (/ (* (+ m n) K) 2) M))
83.0ms	(- (/ (* (+ m n) K) 2) M)

simplify668.0ms

Counts: 104 → 104

prune1.8s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 1.0b

localize26.0ms

Local error

Found 3 expressions with local error:

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

rewrite300.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
10×	`pow1` `add-log-exp`
9×	`difference-of-squares`
8×	`swap-sqr`
7×	`flip3--` `add-cube-cbrt` `flip--` `distribute-lft-out--`
6×	`associate-r` `associate-l`
5×	`sub-neg` `add-cbrt-cube` `add-exp-log`
4×	`distribute-rgt-in` `frac-times` `associate-+r+` `distribute-lft-in` `times-frac`
3×	`insert-posit16`
2×	`sum-log` `diff-log` `associate-l/` `associate-r/`
1×	`pow2` `+-commutative` `flip3-+` `pow-plus` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `flip-+` `associate--r+` `unswap-sqr`

Counts

3 → 82

Calls

3 calls:

Slowest

219.0ms	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
44.0ms	(+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)))
35.0ms	(- (fabs (- m n)) (+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))))

series655.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

276.0ms	(+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)))
258.0ms	(- (fabs (- m n)) (+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))))
122.0ms	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))

simplify2.0s

Counts: 91 → 91

prune1.3s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 1.0b

localize82.0ms

Local error

Found 4 expressions with local error:

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

rewrite212.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
11×	`pow1`
9×	`difference-of-squares`
8×	`swap-sqr` `add-cube-cbrt`
7×	`flip3--` `flip--` `distribute-lft-out--`
6×	`add-cbrt-cube` `associate-r` `associate-l` `add-exp-log` `add-log-exp`
4×	`frac-times` `times-frac` `insert-posit16`
3×	`sub-neg`
2×	`distribute-rgt-in` `distribute-lft-in` `associate-l/` `associate-r/`
1×	`pow2` `pow-plus` `diff-log` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `remove-posit16` `unswap-sqr`

Counts

4 → 81

Calls

4 calls:

Slowest

196.0ms	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
12.0ms	(- (/ (* (+ m n) K) 2) M)
2.0ms	(cos (posit16->real (real->posit16 (- (/ (* (+ m n) K) 2) M))))
0.0ms	(posit16->real (real->posit16 (- (/ (* (+ m n) K) 2) M)))

series326.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

100.0ms	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
83.0ms	(- (/ (* (+ m n) K) 2) M)
77.0ms	(posit16->real (real->posit16 (- (/ (* (+ m n) K) 2) M)))
65.0ms	(cos (posit16->real (real->posit16 (- (/ (* (+ m n) K) 2) M))))

simplify1.6s

Counts: 93 → 93

prune2.7s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 1.0b

localize110.0ms

Local error

Found 4 expressions with local error:

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

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `add-log-exp`
3×	`remove-posit16`

Counts

4 → 35

Calls

4 calls:

Slowest

43.0ms	(cos (* (* (cbrt (posit16->real (real->posit16 (- (/ (* (+ m n) K) 2) M)))) (cbrt (posit16->real (real->posit16 (- (/ (* (+ m n) K) 2) M))))) (cbrt (posit16->real (real->posit16 (- (/ (* (+ m n) K) 2) M))))))
1.0ms	(posit16->real (real->posit16 (- (/ (* (+ m n) K) 2) M)))
1.0ms	(posit16->real (real->posit16 (- (/ (* (+ m n) K) 2) M)))
0.0ms	(posit16->real (real->posit16 (- (/ (* (+ m n) K) 2) M)))

series334.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

89.0ms	(posit16->real (real->posit16 (- (/ (* (+ m n) K) 2) M)))
89.0ms	(cos (* (* (cbrt (posit16->real (real->posit16 (- (/ (* (+ m n) K) 2) M)))) (cbrt (posit16->real (real->posit16 (- (/ (* (+ m n) K) 2) M))))) (cbrt (posit16->real (real->posit16 (- (/ (* (+ m n) K) 2) M))))))
86.0ms	(posit16->real (real->posit16 (- (/ (* (+ m n) K) 2) M)))
70.0ms	(posit16->real (real->posit16 (- (/ (* (+ m n) K) 2) M)))

simplify1.8s

Counts: 47 → 47

prune1.4s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 1.0b

regimes488.0ms

Accuracy

0% (0.2b remaining)

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

bsearch3.0ms

end0.0ms

sample3.4s

Algorithm

intervals

Results

2.6s	8115×	body	80	valid
205.0ms	134×	body	1280	valid
151.0ms	161×	body	640	valid
92.0ms	99×	body	320	valid
24.0ms	55×	body	160	valid
3.0ms	1×	body	2560	valid