Details

sample79.0ms

Algorithm

intervals

Results

43.0ms	260×	body	80	valid
6.0ms	8×	body	640	valid
2.0ms	2×	body	1280	valid
1.0ms	2×	body	320	valid

simplify2.3s

Counts

1 → 1

Iterations

Iter	Nodes
done	5052
5	3741
4	818
3	257
2	102
1	51
0	21

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.8b

localize64.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
0.0b	(* K (+ m n))
0.0b	(pow (- (/ (+ m n) 2) M) 2)
35.2b	(cos (- (/ (* K (+ m n)) 2) M))

rewrite1.4s

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
17×	`add-sqr-sqrt`
14×	`add-log-exp`
8×	`add-cube-cbrt`
7×	`pow1` `add-exp-log` `distribute-lft-out--`
6×	`unpow-prod-down` `add-cbrt-cube` `diff-log`
4×	`associate-r` `insert-posit16`
3×	`pow-unpow` `sub-neg` `associate-l` `difference-of-squares`
2×	`cos-sum` `distribute-rgt-neg-in` `neg-log` `associate-*r/` `associate--r+`
1×	`associate--l-` `neg-sub0` `distribute-rgt-in` `cos-diff` `pow-to-exp` `pow-pow` `distribute-lft-in` `flip3-+` `times-frac` `flip3--` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `flip--` `distribute-lft-out` `unpow2` `associate--r-` `unswap-sqr` `sqr-pow`

Counts

4 → 82

Calls

4 calls:

1.3s	(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
20.0ms	(* K (+ m n))
59.0ms	(pow (- (/ (+ m n) 2) M) 2)
54.0ms	(cos (- (/ (* K (+ m n)) 2) M))

series413.0ms

Counts

4 → 12

Calls

4 calls:

186.0ms	(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
44.0ms	(* K (+ m n))
97.0ms	(pow (- (/ (+ m n) 2) M) 2)
86.0ms	(cos (- (/ (* K (+ m n)) 2) M))

simplify1.1s

Counts

94 → 94

Iterations

Iter	Nodes
done	5001
2	1280
1	451
0	175

prune755.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.8b

localize44.0ms

Local error

Found 2 expressions with local error:

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

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

16×	`*-un-lft-identity`
12×	`add-log-exp`
11×	`add-sqr-sqrt`
7×	`distribute-lft-out--`
6×	`unpow-prod-down` `diff-log`
4×	`add-cube-cbrt`
3×	`pow1` `pow-unpow` `add-exp-log` `difference-of-squares`
2×	`sub-neg` `distribute-rgt-neg-in` `add-cbrt-cube` `neg-log` `insert-posit16` `associate--r+`
1×	`associate--l-` `neg-sub0` `pow-to-exp` `pow-pow` `times-frac` `flip3--` `pow-exp` `flip--` `unpow2` `associate--r-` `sqr-pow`

Counts

2 → 47

Calls

2 calls:

1.1s	(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
63.0ms	(pow (- (/ (+ m n) 2) M) 2)

series288.0ms

Counts

2 → 6

Calls

2 calls:

185.0ms	(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
103.0ms	(pow (- (/ (+ m n) 2) M) 2)

simplify1.6s

Counts

53 → 53

Iterations

Iter	Nodes
done	5000
3	2394
2	714
1	284
0	107

prune408.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.8b

localize129.0ms

Local error

Found 4 expressions with local error:

0.0b	(* K (+ m n))
0.0b	(pow (- (/ (+ m n) 2) M) 2)
32.8b	(posit16->real (real->posit16 (cos (- (/ (* K (+ m n)) 2) M))))
35.2b	(cos (- (/ (* K (+ m n)) 2) M))

rewrite178.0ms

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:

31.0ms	(* K (+ m n))
90.0ms	(pow (- (/ (+ m n) 2) M) 2)
0.0ms	(posit16->real (real->posit16 (cos (- (/ (* K (+ m n)) 2) M))))
54.0ms	(cos (- (/ (* K (+ m n)) 2) M))

series315.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* K (+ m n))
112.0ms	(pow (- (/ (+ m n) 2) M) 2)
67.0ms	(posit16->real (real->posit16 (cos (- (/ (* K (+ m n)) 2) M))))
90.0ms	(cos (- (/ (* K (+ m n)) 2) M))

simplify2.4s

Counts

78 → 78

Iterations

Iter	Nodes
done	5000
3	3633
2	914
1	359
0	140

prune1.0s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.8b

localize59.0ms

Local error

Found 4 expressions with local error:

14.1b	(cbrt (* K (+ m n)))
14.1b	(cbrt (* K (+ m n)))
14.1b	(cbrt (* K (+ m n)))
35.7b	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2) M))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

6×	`cbrt-div` `associate-*r/`
4×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `add-log-exp`
3×	`cbrt-prod` `flip3-+` `pow1/3` `flip-+`
2×	`cos-sum`
1×	`cos-diff` `sub-neg`

Counts

4 → 47

Calls

4 calls:

12.0ms	(cbrt (* K (+ m n)))
11.0ms	(cbrt (* K (+ m n)))
9.0ms	(cbrt (* K (+ m n)))
58.0ms	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2) M))

series456.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(cbrt (* K (+ m n)))
141.0ms	(cbrt (* K (+ m n)))
111.0ms	(cbrt (* K (+ m n)))
68.0ms	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2) M))

simplify1.2s

Counts

59 → 59

Iterations

Iter	Nodes
done	5001
4	2035
3	689
2	351
1	187
0	88

prune583.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 1.7b

regimes891.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	21
1	21
0	17

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.8s	8124×	body	80	valid
147.0ms	154×	body	640	valid
145.0ms	120×	body	1280	valid
41.0ms	96×	body	320	valid
16.0ms	56×	body	160	valid
4.0ms	4×	body	2560	valid