Details

sample141.0ms

Algorithm

intervals

Results

99.0ms	268×	body	80	valid
7.0ms	4×	body	1280	valid
3.0ms	5×	body	320	valid
3.0ms	3×	body	640	valid
1.0ms	2×	body	160	valid

simplify1.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	2004
5	2004
4	821
3	262
2	104
1	51
0	21

prune33.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.0b

localize53.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ K (/ 2 (+ m n))) M)
0.0b	(/ 2 (+ m n))
0.2b	(/ K (/ 2 (+ m n)))
35.4b	(cos (- (/ K (/ 2 (+ m n))) M))

rewrite265.0ms

Algorithm

rewrite-expression-head

Rules

747×	`times-frac`
643×	`*-un-lft-identity`
492×	`add-sqr-sqrt`
483×	`add-cube-cbrt`
354×	`prod-diff`
179×	`cos-sum`
79×	`distribute-lft-out`
60×	`associate-/r/`
59×	`fma-neg`
34×	`div-inv`
26×	`flip3-+` `flip-+`
22×	`associate-/r*`
11×	`add-cbrt-cube` `add-exp-log`
6×	`associate-/l*` `add-log-exp`
4×	`expm1-log1p-u` `pow1` `cbrt-undiv` `div-exp` `insert-posit16` `log1p-expm1-u`
3×	`difference-of-squares`
2×	`clear-num` `sub-neg` `frac-2neg`
1×	`cos-diff` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 574

Calls

4 calls:

90.0ms	(- (/ K (/ 2 (+ m n))) M)
16.0ms	(/ 2 (+ m n))
19.0ms	(/ K (/ 2 (+ m n)))
109.0ms	(cos (- (/ K (/ 2 (+ m n))) M))

series372.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(- (/ K (/ 2 (+ m n))) M)
78.0ms	(/ 2 (+ m n))
74.0ms	(/ K (/ 2 (+ m n)))
110.0ms	(cos (- (/ K (/ 2 (+ m n))) M))

simplify2.0s

Counts

586 → 586

Iterations

Iter	Nodes
done	2004
2	2004
1	1876
0	1021

prune6.6s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.6b

localize38.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)
0.0b	(/ 1 (exp (- (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l) (fabs (- m n)))))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-sqr-sqrt` `*-un-lft-identity`
48×	`exp-sum`
47×	`add-cube-cbrt`
45×	`times-frac`
36×	`prod-diff`
15×	`associate-/r*`
6×	`pow-flip`
5×	`exp-prod` `fma-udef`
4×	`sub-neg` `add-cbrt-cube` `associate--l+`
3×	`pow1` `add-exp-log` `associate-/l*`
2×	`expm1-log1p-u` `div-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `rec-exp` `clear-num` `frac-2neg` `exp-diff` `1-exp` `associate-/r/` `div-inv` `distribute-lft-out--` `inv-pow` `difference-of-squares`

Counts

2 → 99

Calls

2 calls:

0.0ms	(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)
37.0ms	(/ 1 (exp (- (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l) (fabs (- m n)))))

series407.0ms

Counts

2 → 6

Calls

2 calls:

214.0ms	(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)
193.0ms	(/ 1 (exp (- (fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l) (fabs (- m n)))))

simplify1.4s

Counts

105 → 105

Iterations

Iter	Nodes
done	2002
4	2002
3	1998
2	703
1	374
0	192

prune607.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.6b

localize46.0ms

Local error

Found 1 expressions with local error:

0.0b	(fma (- (* (+ m n) 1/2) M) (- (* (+ m n) 1/2) M) (- l (fabs (- m n))))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `fma-udef` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Counts

1 → 11

Calls

1 calls:

0.0ms

(fma (- (* (+ m n) 1/2) M) (- (* (+ m n) 1/2) M) (- l (fabs (- m n))))

series237.0ms

Counts

1 → 3

Calls

1 calls:

237.0ms

(fma (- (* (+ m n) 1/2) M) (- (* (+ m n) 1/2) M) (- l (fabs (- m n))))

simplify1.4s

Counts

14 → 14

Iterations

Iter	Nodes
done	2021
4	2021
3	496
2	148
1	66
0	34

prune177.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.6b

localize52.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma (- (* (+ m n) 1/2) M) (- (* (+ m n) 1/2) M) (- l (fabs (- m n))))
19.8b	(posit16->real (real->posit16 (fma (- (* (+ m n) 1/2) M) (- (* (+ m n) 1/2) M) (- l (fabs (- m n))))))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

2×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`fma-udef` `remove-posit16`

Counts

2 → 22

Calls

2 calls:

0.0ms	(fma (- (* (+ m n) 1/2) M) (- (* (+ m n) 1/2) M) (- l (fabs (- m n))))
1.0ms	(posit16->real (real->posit16 (fma (- (* (+ m n) 1/2) M) (- (* (+ m n) 1/2) M) (- l (fabs (- m n))))))

series424.0ms

Counts

2 → 6

Calls

2 calls:

218.0ms	(fma (- (* (+ m n) 1/2) M) (- (* (+ m n) 1/2) M) (- l (fabs (- m n))))
206.0ms	(posit16->real (real->posit16 (fma (- (* (+ m n) 1/2) M) (- (* (+ m n) 1/2) M) (- l (fabs (- m n))))))

simplify1.3s

Counts

28 → 28

Iterations

Iter	Nodes
done	2016
4	2016
3	507
2	161
1	79
0	45

prune340.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.6b

regimes442.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	16
1	16
0	14

end0.0ms

sample3.9s

Algorithm

intervals

Results

3.0s	8091×	body	80	valid
226.0ms	130×	body	1280	valid
214.0ms	159×	body	640	valid
91.0ms	109×	body	320	valid
29.0ms	50×	body	160	valid
9.0ms	4×	body	2560	valid