Details

sample134.0ms

Algorithm

intervals

Results

90.0ms	268×	body	80	valid
6.0ms	4×	body	1280	valid
4.0ms	5×	body	320	valid
3.0ms	3×	body	640	valid
1.0ms	2×	body	160	valid

simplify1.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	2000
5	2000
4	818
3	257
2	102
1	51
0	21

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ (* K (+ m n)) 2) M)
0.0b	(* K (+ m n))
0.0b	(pow (- (/ (+ m n) 2) M) 2)
35.5b	(cos (- (/ (* K (+ m n)) 2) M))

rewrite120.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
14×	`*-un-lft-identity`
8×	`add-cube-cbrt`
7×	`pow1` `add-exp-log`
6×	`unpow-prod-down` `add-cbrt-cube` `add-log-exp`
4×	`associate-r` `insert-posit16`
3×	`pow-unpow` `associate-l` `difference-of-squares`
2×	`cos-sum` `sub-neg` `associate-*r/` `distribute-lft-out--`
1×	`distribute-rgt-in` `cos-diff` `pow-to-exp` `pow-pow` `distribute-lft-in` `flip3-+` `times-frac` `flip3--` `diff-log` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `flip--` `distribute-lft-out` `unpow2` `unswap-sqr` `sqr-pow`

Counts

4 → 72

Calls

4 calls:

12.0ms	(- (/ (* K (+ m n)) 2) M)
24.0ms	(* K (+ m n))
57.0ms	(pow (- (/ (+ m n) 2) M) 2)
25.0ms	(cos (- (/ (* K (+ m n)) 2) M))

series345.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(- (/ (* K (+ m n)) 2) M)
48.0ms	(* K (+ m n))
104.0ms	(pow (- (/ (+ m n) 2) M) 2)
86.0ms	(cos (- (/ (* K (+ m n)) 2) M))

simplify1.2s

Counts

84 → 84

Iterations

Iter	Nodes
done	2015
3	2015
2	1161
1	408
0	155

prune865.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.6b

localize35.0ms

Local error

Found 1 expressions with local error:

0.0b	(pow (- (/ (+ m n) 2) M) 2)

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`unpow-prod-down`
5×	`*-un-lft-identity`
3×	`pow-unpow` `add-cube-cbrt`
2×	`pow1` `add-exp-log` `difference-of-squares`
1×	`pow-to-exp` `pow-pow` `times-frac` `add-cbrt-cube` `pow-exp` `insert-posit16` `distribute-lft-out--` `unpow2` `add-log-exp` `sqr-pow`

Counts

1 → 22

Calls

1 calls:

71.0ms

(pow (- (/ (+ m n) 2) M) 2)

series113.0ms

Counts

1 → 3

Calls

1 calls:

113.0ms

(pow (- (/ (+ m n) 2) M) 2)

simplify1.0s

Counts

25 → 25

Iterations

Iter	Nodes
done	2016
4	2016
3	1097
2	403
1	180
0	62

prune234.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.6b

localize69.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (- (/ (+ n m) 2) M) (- (/ (+ n m) 2) M))
18.4b	(posit16->real (real->posit16 (* (- (/ (+ n m) 2) M) (- (/ (+ n m) 2) M))))

rewrite232.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 58

Calls

2 calls:

230.0ms	(* (- (/ (+ n m) 2) M) (- (/ (+ n m) 2) M))
0.0ms	(posit16->real (real->posit16 (* (- (/ (+ n m) 2) M) (- (/ (+ n m) 2) M))))

series247.0ms

Counts

2 → 6

Calls

2 calls:

131.0ms	(* (- (/ (+ n m) 2) M) (- (/ (+ n m) 2) M))
116.0ms	(posit16->real (real->posit16 (* (- (/ (+ n m) 2) M) (- (/ (+ n m) 2) M))))

simplify1.4s

Counts

64 → 64

Iterations

Iter	Nodes
done	2005
3	2005
2	989
1	291
0	103

prune818.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.6b

localize109.0ms

Local error

Found 4 expressions with local error:

0.0b	(* K (+ m n))
0.0b	(pow (- (/ (+ m n) 2) M) 2)
35.5b	(cos (- (/ (posit16->real (real->posit16 (* K (+ m n)))) 2) M))
53.9b	(posit16->real (real->posit16 (* K (+ m n))))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
8×	`add-cube-cbrt`
7×	`pow1` `add-exp-log`
6×	`unpow-prod-down` `add-cbrt-cube`
4×	`associate-r` `insert-posit16` `add-log-exp`
3×	`pow-unpow` `associate-l`
2×	`cos-sum` `associate-*r/` `difference-of-squares`
1×	`distribute-rgt-in` `cos-diff` `pow-to-exp` `sub-neg` `pow-pow` `distribute-lft-in` `flip3-+` `times-frac` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `remove-posit16` `distribute-lft-out` `distribute-lft-out--` `unpow2` `unswap-sqr` `sqr-pow`

Counts

4 → 66

Calls

4 calls:

14.0ms	(* K (+ m n))
52.0ms	(pow (- (/ (+ m n) 2) M) 2)
15.0ms	(cos (- (/ (posit16->real (real->posit16 (* K (+ m n)))) 2) M))
0.0ms	(posit16->real (real->posit16 (* K (+ m n))))

series322.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* K (+ m n))
132.0ms	(pow (- (/ (+ m n) 2) M) 2)
113.0ms	(cos (- (/ (posit16->real (real->posit16 (* K (+ m n)))) 2) M))
37.0ms	(posit16->real (real->posit16 (* K (+ m n))))

simplify1.3s

Counts

78 → 78

Iterations

Iter	Nodes
done	2009
3	2009
2	932
1	358
0	140

prune1.2s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.6b

regimes537.0ms

Accuracy

0% (0.1b remaining)

Error of 1.3b against oracle of 1.2b and baseline of 1.3b

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	21
1	21
0	17

end0.0ms

sample4.2s

Algorithm

intervals

Results

3.2s	8091×	body	80	valid
208.0ms	130×	body	1280	valid
201.0ms	159×	body	640	valid
134.0ms	109×	body	320	valid
29.0ms	50×	body	160	valid
6.0ms	4×	body	2560	valid