Details

sample82.0ms

Algorithm

intervals

Results

47.0ms	259×	body	80	valid
3.0ms	6×	body	320	valid
3.0ms	4×	body	640	valid
2.0ms	2×	body	1280	valid
0.0ms	1×	body	160	valid

simplify2.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	5005
5	3184
4	821
3	262
2	104
1	51
0	21

prune24.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.4b

localize92.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ (* K (+ m n)) 2) M)
0.0b	(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
0.0b	(pow (- (/ (+ m n) 2) M) 2)
32.7b	(cos (- (/ (* K (+ m n)) 2) M))

rewrite1.8s

Algorithm

rewrite-expression-head

Rules

217×	`add-sqr-sqrt`
186×	`*-un-lft-identity`
181×	`prod-diff`
96×	`add-cube-cbrt`
78×	`unpow-prod-down`
68×	`distribute-rgt-neg-in`
66×	`distribute-lft-neg-in`
54×	`difference-of-squares`
46×	`distribute-lft-out--`
34×	`times-frac`
33×	`fma-neg`
23×	`cos-sum`
16×	`add-log-exp`
13×	`unpow2` `sqr-pow`
11×	`associate--r+`
7×	`diff-log` `div-inv`
6×	`neg-mul-1`
5×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `sub-neg` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u`
3×	`pow-unpow`
2×	`flip3--` `neg-log` `flip--`
1×	`associate--l-` `neg-sub0` `cos-diff` `pow-to-exp` `pow-pow` `pow-exp` `associate--r-`

Counts

4 → 295

Calls

4 calls:

39.0ms	(- (/ (* K (+ m n)) 2) M)
1.7s	(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
68.0ms	(pow (- (/ (+ m n) 2) M) 2)
37.0ms	(cos (- (/ (* K (+ m n)) 2) M))

series513.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(- (/ (* K (+ m n)) 2) M)
233.0ms	(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
101.0ms	(pow (- (/ (+ m n) 2) M) 2)
91.0ms	(cos (- (/ (* K (+ m n)) 2) M))

simplify2.1s

Counts

307 → 307

Iterations

Iter	Nodes
done	5001
2	1952
1	991
0	460

prune1.7s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.7b

localize45.0ms

Local error

Found 3 expressions with local error:

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

rewrite1.4s

Algorithm

rewrite-expression-head

Rules

195×	`add-sqr-sqrt`
164×	`*-un-lft-identity`
148×	`prod-diff`
78×	`unpow-prod-down`
74×	`add-cube-cbrt`
68×	`distribute-rgt-neg-in`
66×	`distribute-lft-neg-in`
54×	`difference-of-squares`
46×	`distribute-lft-out--`
29×	`fma-neg`
15×	`add-log-exp`
13×	`times-frac` `unpow2` `sqr-pow`
11×	`associate--r+`
7×	`diff-log`
6×	`neg-mul-1`
4×	`pow1` `add-exp-log`
3×	`expm1-log1p-u` `pow-unpow` `sub-neg` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u`
2×	`flip3--` `neg-log` `flip--`
1×	`associate--l-` `neg-sub0` `pow-to-exp` `pow-pow` `pow-exp` `associate--r-`

Counts

3 → 245

Calls

3 calls:

13.0ms	(- l (fabs (- m n)))
1.3s	(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
59.0ms	(pow (- (/ (+ m n) 2) M) 2)

series325.0ms

Counts

3 → 9

Calls

3 calls:

22.0ms	(- l (fabs (- m n)))
193.0ms	(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
110.0ms	(pow (- (/ (+ m n) 2) M) 2)

simplify2.3s

Counts

254 → 254

Iterations

Iter	Nodes
done	5000
3	4400
2	1455
1	697
0	290

prune1.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.7b

localize87.0ms

Local error

Found 4 expressions with local error:

0.0b	(- l (fabs (- m n)))
0.0b	(- (- (posit16->real (real->posit16 (* (- (/ (+ n m) 2) M) (- (/ (+ n m) 2) M))))) (- l (fabs (- m n))))
0.0b	(* (- (/ (+ n m) 2) M) (- (/ (+ n m) 2) M))
25.6b	(posit16->real (real->posit16 (* (- (/ (+ n m) 2) M) (- (/ (+ n m) 2) M))))

rewrite447.0ms

Algorithm

rewrite-expression-head

Rules

211×	`*-un-lft-identity`
175×	`add-sqr-sqrt`
164×	`prod-diff`
129×	`add-cube-cbrt`
76×	`times-frac`
50×	`distribute-rgt-in` `distribute-lft-in`
23×	`distribute-lft-out--`
20×	`distribute-rgt-neg-in` `difference-of-squares`
18×	`distribute-lft-neg-in` `distribute-lft-out`
16×	`add-log-exp`
13×	`fma-neg`
11×	`pow1` `associate--r+`
8×	`flip3--` `swap-sqr` `flip--`
7×	`diff-log`
6×	`neg-mul-1` `add-cbrt-cube` `associate-r` `associate-l` `add-exp-log` `div-inv`
5×	`sub-neg`
4×	`expm1-log1p-u` `frac-times` `insert-posit16` `log1p-expm1-u`
2×	`neg-log` `associate-l/` `associate-r/`
1×	`associate--l-` `pow2` `neg-sub0` `pow-plus` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `remove-posit16` `associate--r-` `unswap-sqr`

Counts

4 → 283

Calls

4 calls:

11.0ms	(- l (fabs (- m n)))
50.0ms	(- (- (posit16->real (real->posit16 (* (- (/ (+ n m) 2) M) (- (/ (+ n m) 2) M))))) (- l (fabs (- m n))))
363.0ms	(* (- (/ (+ n m) 2) M) (- (/ (+ n m) 2) M))
1.0ms	(posit16->real (real->posit16 (* (- (/ (+ n m) 2) M) (- (/ (+ n m) 2) M))))

series388.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(- l (fabs (- m n)))
172.0ms	(- (- (posit16->real (real->posit16 (* (- (/ (+ n m) 2) M) (- (/ (+ n m) 2) M))))) (- l (fabs (- m n))))
95.0ms	(* (- (/ (+ n m) 2) M) (- (/ (+ n m) 2) M))
99.0ms	(posit16->real (real->posit16 (* (- (/ (+ n m) 2) M) (- (/ (+ n m) 2) M))))

simplify2.0s

Counts

295 → 295

Iterations

Iter	Nodes
done	5001
2	2629
1	997
0	424

prune2.4s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 1.7b

localize95.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt 2)
1.0b	(cbrt 2)
1.0b	(cbrt 2)
32.7b	(cos (fma (/ K (* (cbrt 2) (cbrt 2))) (/ (+ m n) (cbrt 2)) (- M)))

rewrite8.0ms

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-sum` `fma-udef`

Counts

4 → 53

Calls

4 calls:

1.0ms	(cbrt 2)
1.0ms	(cbrt 2)
1.0ms	(cbrt 2)
3.0ms	(cos (fma (/ K (* (cbrt 2) (cbrt 2))) (/ (+ m n) (cbrt 2)) (- M)))

series258.0ms

Counts

4 → 6

Calls

4 calls:

0.0ms	(cbrt 2)
0.0ms	(cbrt 2)
0.0ms	(cbrt 2)
257.0ms	(cos (fma (/ K (* (cbrt 2) (cbrt 2))) (/ (+ m n) (cbrt 2)) (- M)))

simplify3.9s

Counts

59 → 59

Iterations

Iter	Nodes
done	5000
6	4829
5	1028
4	398
3	243
2	142
1	81
0	52

prune577.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 1.7b

regimes600.0ms

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	21
1	21
0	17

end0.0ms

sample2.7s

Algorithm

intervals

Results

2.0s	8088×	body	80	valid
111.0ms	121×	body	1280	valid
103.0ms	151×	body	640	valid
57.0ms	62×	body	160	valid
47.0ms	103×	body	320	valid
6.0ms	4×	body	2560	valid