Details

sample76.0ms

Algorithm

intervals

Results

44.0ms	257×	body	80	valid
4.0ms	6×	body	320	valid
3.0ms	4×	body	640	valid
2.0ms	2×	body	1280	valid
1.0ms	2×	body	160	valid

simplify971.0ms

Counts

1 → 1

Iterations

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

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.2b

localize80.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ (* (+ m n) K) 2) M)
0.0b	(+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)))
0.0b	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
35.6b	(cos (- (/ (* (+ m n) K) 2) M))

rewrite292.0ms

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

Counts

4 → 91

Calls

4 calls:

25.0ms	(- (/ (* (+ m n) K) 2) M)
41.0ms	(+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)))
193.0ms	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
31.0ms	(cos (- (/ (* (+ m n) K) 2) M))

series577.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(- (/ (* (+ m n) K) 2) M)
291.0ms	(+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)))
112.0ms	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
80.0ms	(cos (- (/ (* (+ m n) K) 2) M))

simplify1.3s

Counts

103 → 103

Iterations

Iter	Nodes
done	2001
3	2001
2	1499
1	464
0	175

prune1.9s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.2b

localize38.0ms

Local error

Found 4 expressions with local error:

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

rewrite352.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 102

Calls

4 calls:

37.0ms	(exp (- (+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))) (fabs (- m n))))
46.0ms	(- (+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))) (fabs (- m n)))
35.0ms	(+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)))
232.0ms	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))

series774.0ms

Counts

4 → 12

Calls

4 calls:

185.0ms	(exp (- (+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))) (fabs (- m n))))
258.0ms	(- (+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))) (fabs (- m n)))
235.0ms	(+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)))
97.0ms	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))

simplify1.4s

Counts

114 → 114

Iterations

Iter	Nodes
done	2005
3	2005
2	1700
1	492
0	176

prune1.8s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.2b

localize64.0ms

Local error

Found 4 expressions with local error:

35.6b	(cos (- (/ (* (+ m n) K) 2) M))
37.9b	(cbrt (+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))))
37.9b	(cbrt (+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))))
37.9b	(cbrt (+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 53

Calls

4 calls:

20.0ms	(cos (- (/ (* (+ m n) K) 2) M))
2.0ms	(cbrt (+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))))
2.0ms	(cbrt (+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))))
2.0ms	(cbrt (+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))))

series2.9s

Counts

4 → 12

Calls

4 calls:

87.0ms	(cos (- (/ (* (+ m n) K) 2) M))
985.0ms	(cbrt (+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))))
905.0ms	(cbrt (+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))))
888.0ms	(cbrt (+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))))

simplify1.0s

Counts

65 → 65

Iterations

Iter	Nodes
done	2001
4	2001
3	1253
2	425
1	196
0	96

prune1.4s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.2b

localize143.0ms

Local error

Found 4 expressions with local error:

37.9b	(cbrt (+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))))
37.9b	(cbrt (+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))))
37.9b	(cbrt (+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))))
59.8b	(posit16->real (real->posit16 (cbrt (+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))))))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`cbrt-div`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`flip3-+` `pow1/3` `flip-+`
1×	`remove-posit16`

Counts

4 → 51

Calls

4 calls:

2.0ms	(cbrt (+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))))
2.0ms	(cbrt (+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))))
2.0ms	(cbrt (+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))))
0.0ms	(posit16->real (real->posit16 (cbrt (+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))))))

series3.8s

Counts

4 → 12

Calls

4 calls:

1.0s	(cbrt (+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))))
959.0ms	(cbrt (+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))))
983.0ms	(cbrt (+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))))
795.0ms	(posit16->real (real->posit16 (cbrt (+ l (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))))))

simplify1.2s

Counts

63 → 63

Iterations

Iter	Nodes
done	2000
4	2000
3	1223
2	359
1	153
0	73

prune2.4s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.2b

regimes608.0ms

Accuracy

0% (0.2b remaining)

Error of 1.4b against oracle of 1.2b and baseline of 1.4b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	20
1	20
0	16

end0.0ms

sample3.5s

Algorithm

intervals

Results

2.7s	8066×	body	80	valid
222.0ms	165×	body	640	valid
190.0ms	116×	body	1280	valid
75.0ms	105×	body	320	valid
23.0ms	46×	body	160	valid
3.0ms	1×	body	2560	valid