Details

sample90.0ms

Algorithm

intervals

Results

35.0ms	259×	body	80	valid
2.0ms	6×	body	320	valid
2.0ms	4×	body	640	valid
2.0ms	2×	body	1280	valid
0.0ms	1×	body	160	valid

simplify4.4s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
5	1428
4	534
3	208
2	93
1	50
0	21

prune40.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.6b

localize151.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (- (fabs (- m n)) l) (pow (- (/ (+ m n) 2.0) M) 2.0))
0.0b	(- (/ (* (+ m n) K) 2.0) M)
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
32.7b	(cos (- (/ (* (+ m n) K) 2.0) M))

rewrite842.0ms

Algorithm

rewrite-expression-head

Rules

120×	`add-sqr-sqrt`
102×	`*-un-lft-identity`
101×	`prod-diff`
61×	`add-cube-cbrt`
37×	`unpow-prod-down`
27×	`times-frac` `difference-of-squares`
23×	`cos-sum`
21×	`distribute-lft-out--`
12×	`fma-neg`
11×	`associate--l+` `add-log-exp`
7×	`div-inv` `sqr-pow`
5×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `sub-neg` `add-cbrt-cube` `diff-log` `insert-posit16` `log1p-expm1-u`
3×	`pow-unpow`
2×	`flip3--` `flip--`
1×	`associate--l-` `cos-diff` `pow-to-exp` `pow-pow` `pow-exp`

Counts

4 → 190

Calls

4 calls:

548.0ms	(- (- (fabs (- m n)) l) (pow (- (/ (+ m n) 2.0) M) 2.0))
49.0ms	(- (/ (* (+ m n) K) 2.0) M)
133.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
82.0ms	(cos (- (/ (* (+ m n) K) 2.0) M))

series1.1s

Counts

4 → 12

Calls

4 calls:

371.0ms	(- (- (fabs (- m n)) l) (pow (- (/ (+ m n) 2.0) M) 2.0))
88.0ms	(- (/ (* (+ m n) K) 2.0) M)
530.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
150.0ms	(cos (- (/ (* (+ m n) K) 2.0) M))

simplify4.2s

Counts

202 → 202

Iterations

Iter	Nodes
done	5001
2	1806
1	857
0	411

prune3.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.7b

localize86.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (fabs (- m n)) l)
0.0b	(- (- (fabs (- m n)) l) (pow (- (/ (+ m n) 2.0) M) 2.0))
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)

rewrite563.0ms

Algorithm

rewrite-expression-head

Rules

98×	`add-sqr-sqrt`
80×	`*-un-lft-identity`
68×	`prod-diff`
39×	`add-cube-cbrt`
37×	`unpow-prod-down`
27×	`difference-of-squares`
21×	`distribute-lft-out--`
11×	`associate--l+`
10×	`add-log-exp`
8×	`fma-neg`
7×	`sqr-pow`
6×	`times-frac`
4×	`pow1` `diff-log` `add-exp-log`
3×	`expm1-log1p-u` `pow-unpow` `sub-neg` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u`
2×	`flip3--` `flip--`
1×	`associate--l-` `pow-to-exp` `pow-pow` `pow-exp`

Counts

3 → 140

Calls

3 calls:

10.0ms	(- (fabs (- m n)) l)
438.0ms	(- (- (fabs (- m n)) l) (pow (- (/ (+ m n) 2.0) M) 2.0))
101.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series1.0s

Counts

3 → 9

Calls

3 calls:

67.0ms	(- (fabs (- m n)) l)
393.0ms	(- (- (fabs (- m n)) l) (pow (- (/ (+ m n) 2.0) M) 2.0))
587.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify6.0s

Counts

149 → 149

Iterations

Iter	Nodes
done	5000
3	3969
2	1281
1	573
0	244

prune2.5s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.7b

localize96.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (fabs (- m n)) l)
0.0b	(- (- (fabs (- m n)) l) (posit16->real (real->posit16 (pow (- (/ (+ m n) 2.0) M) 2.0))))
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
25.6b	(posit16->real (real->posit16 (pow (- (/ (+ m n) 2.0) M) 2.0)))

rewrite238.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-sqr-sqrt` `*-un-lft-identity`
33×	`prod-diff`
28×	`add-cube-cbrt`
11×	`associate--l+` `add-log-exp`
9×	`distribute-lft-out--`
8×	`fma-neg` `difference-of-squares`
6×	`unpow-prod-down`
5×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `diff-log` `insert-posit16` `log1p-expm1-u`
3×	`pow-unpow` `sub-neg`
2×	`flip3--` `flip--`
1×	`associate--l-` `pow-to-exp` `pow-pow` `times-frac` `pow-exp` `remove-posit16` `sqr-pow`

Counts

4 → 114

Calls

4 calls:

14.0ms	(- (fabs (- m n)) l)
71.0ms	(- (- (fabs (- m n)) l) (posit16->real (real->posit16 (pow (- (/ (+ m n) 2.0) M) 2.0))))
143.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
2.0ms	(posit16->real (real->posit16 (pow (- (/ (+ m n) 2.0) M) 2.0)))

series1.5s

Counts

4 → 12

Calls

4 calls:

40.0ms	(- (fabs (- m n)) l)
392.0ms	(- (- (fabs (- m n)) l) (posit16->real (real->posit16 (pow (- (/ (+ m n) 2.0) M) 2.0))))
557.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
533.0ms	(posit16->real (real->posit16 (pow (- (/ (+ m n) 2.0) M) 2.0)))

simplify5.6s

Counts

126 → 126

Iterations

Iter	Nodes
done	5001
3	2979
2	984
1	463
0	204

prune2.7s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.7b

localize177.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt 2.0)
1.0b	(cbrt 2.0)
1.0b	(cbrt 2.0)
32.9b	(cos (+ (- (/ (* (/ (+ m n) (cbrt 2.0)) (/ K (cbrt 2.0))) (cbrt 2.0)) M) (fma M -1 M)))

rewrite487.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`cos-diff` `cos-sum` `associate-+l-`

Counts

4 → 54

Calls

4 calls:

3.0ms	(cbrt 2.0)
3.0ms	(cbrt 2.0)
3.0ms	(cbrt 2.0)
474.0ms	(cos (+ (- (/ (* (/ (+ m n) (cbrt 2.0)) (/ K (cbrt 2.0))) (cbrt 2.0)) M) (fma M -1 M)))

series432.0ms

Counts

4 → 6

Calls

4 calls:

0.0ms	(cbrt 2.0)
0.0ms	(cbrt 2.0)
0.0ms	(cbrt 2.0)
432.0ms	(cos (+ (- (/ (* (/ (+ m n) (cbrt 2.0)) (/ K (cbrt 2.0))) (cbrt 2.0)) M) (fma M -1 M)))

simplify5.7s

Counts

60 → 60

Iterations

Iter	Nodes
done	5002
5	2618
4	1253
3	591
2	250
1	131
0	73

prune1.2s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 1.7b

regimes1.8s

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify11.0ms

Iterations

Iter	Nodes
done	20
1	20
0	16

end0.0ms

sample3.1s

Algorithm

intervals

Results

2.1s	8088×	body	80	valid
131.0ms	151×	body	640	valid
112.0ms	121×	body	1280	valid
109.0ms	103×	body	320	valid
20.0ms	62×	body	160	valid
5.0ms	4×	body	2560	valid