Details

sample127.0ms

Algorithm

intervals

Results

82.0ms	250×	body	80	valid
8.0ms	6×	body	1280	valid
7.0ms	7×	body	640	valid
4.0ms	5×	body	320	valid
2.0ms	1×	body	2560	valid
1.0ms	4×	body	160	valid

simplify875.0ms

Counts

1 → 1

Iterations

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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.3b

localize47.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* (+ m n) K) 2)
0.0b	(+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)))
0.0b	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
36.8b	(cos (- (/ (* (+ m n) K) 2) M))

rewrite237.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 100

Calls

4 calls:

18.0ms	(/ (* (+ m n) K) 2)
36.0ms	(+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)))
155.0ms	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
27.0ms	(cos (- (/ (* (+ m n) K) 2) M))

series450.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(/ (* (+ m n) K) 2)
256.0ms	(+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)))
80.0ms	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
64.0ms	(cos (- (/ (* (+ m n) K) 2) M))

simplify822.0ms

Counts

112 → 112

Iterations

Iter	Nodes
done	2003
2	1900
1	559
0	202

prune781.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 2.7b

localize33.0ms

Local error

Found 2 expressions with local error:

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

rewrite229.0ms

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×	`distribute-rgt-in` `frac-times` `associate-+r+` `sub-neg` `distribute-lft-in` `times-frac` `add-cbrt-cube` `add-exp-log` `add-log-exp`
2×	`associate-l/` `associate-r/` `insert-posit16`
1×	`pow2` `+-commutative` `sum-log` `flip3-+` `pow-plus` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

2 → 65

Calls

2 calls:

42.0ms	(+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)))
184.0ms	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))

series374.0ms

Counts

2 → 6

Calls

2 calls:

266.0ms	(+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)))
108.0ms	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))

simplify628.0ms

Counts

71 → 71

Iterations

Iter	Nodes
done	2001
2	1187
1	349
0	119

prune350.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 2.7b

localize74.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)))
0.0b	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
24.4b	(posit16->real (real->posit16 (+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)))))

rewrite185.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 74

Calls

3 calls:

32.0ms	(+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)))
151.0ms	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
0.0ms	(posit16->real (real->posit16 (+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)))))

series506.0ms

Counts

3 → 9

Calls

3 calls:

226.0ms	(+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)))
80.0ms	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
200.0ms	(posit16->real (real->posit16 (+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)))))

simplify702.0ms

Counts

83 → 83

Iterations

Iter	Nodes
done	2000
2	1296
1	359
0	128

prune783.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 2.7b

localize68.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
0.3b	(/ (* (+ m n) K) (sqrt 2))
0.3b	(/ (/ (* (+ m n) K) (sqrt 2)) (sqrt 2))
36.7b	(cos (- (/ (/ (* (+ m n) K) (sqrt 2)) (sqrt 2)) M))

rewrite256.0ms

Algorithm

rewrite-expression-head

Rules

112×	`times-frac`
77×	`add-sqr-sqrt`
69×	`*-un-lft-identity`
60×	`sqrt-prod`
55×	`add-cube-cbrt`
20×	`add-cbrt-cube` `add-exp-log`
12×	`associate-/r*`
11×	`pow1` `associate-/l*`
9×	`div-inv`
8×	`swap-sqr` `difference-of-squares`
7×	`cbrt-undiv` `div-exp`
6×	`flip3--` `associate-r` `associate-l` `flip--` `distribute-lft-out--`
4×	`frac-times` `associate-*l/` `insert-posit16` `add-log-exp`
3×	`sub-neg` `prod-exp` `cbrt-unprod` `associate-/l/`
2×	`distribute-rgt-in` `cos-sum` `clear-num` `frac-2neg` `distribute-lft-in` `associate-*r/`
1×	`pow2` `cos-diff` `flip3-+` `pow-plus` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up` `flip-+` `unswap-sqr`

Counts

4 → 184

Calls

4 calls:

189.0ms	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
12.0ms	(/ (* (+ m n) K) (sqrt 2))
15.0ms	(/ (/ (* (+ m n) K) (sqrt 2)) (sqrt 2))
36.0ms	(cos (- (/ (/ (* (+ m n) K) (sqrt 2)) (sqrt 2)) M))

series1.0s

Counts

4 → 12

Calls

4 calls:

80.0ms	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
158.0ms	(/ (* (+ m n) K) (sqrt 2))
250.0ms	(/ (/ (* (+ m n) K) (sqrt 2)) (sqrt 2))
516.0ms	(cos (- (/ (/ (* (+ m n) K) (sqrt 2)) (sqrt 2)) M))

simplify573.0ms

Counts

196 → 196

Iterations

Iter	Nodes
done	2000
1	771
0	295

prune1.1s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 2.6b

regimes571.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	20
1	20
0	16

end0.0ms

sample3.3s

Algorithm

intervals

Results

2.5s	8119×	body	80	valid
170.0ms	139×	body	640	valid
166.0ms	137×	body	1280	valid
126.0ms	104×	body	320	valid
25.0ms	54×	body	160	valid
4.0ms	3×	body	2560	valid