Details

sample142.0ms

Algorithm

intervals

Results

86.0ms	250×	body	80	valid
9.0ms	6×	body	1280	valid
8.0ms	7×	body	640	valid
4.0ms	5×	body	320	valid
2.0ms	1×	body	2560	valid
2.0ms	4×	body	160	valid

simplify547.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	2000
4	821
3	262
2	104
1	51
0	21

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 19.3b

localize60.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* K (+ m n)) 2)
0.0b	(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
0.0b	(pow (- (/ (+ m n) 2) M) 2)
36.8b	(cos (- (/ (* K (+ m n)) 2) M))

rewrite1.0s

Algorithm

rewrite-expression-head

Rules

202×	`add-sqr-sqrt`
171×	`*-un-lft-identity`
160×	`prod-diff`
83×	`add-cube-cbrt`
78×	`unpow-prod-down`
68×	`distribute-rgt-neg-in`
66×	`distribute-lft-neg-in`
53×	`difference-of-squares`
45×	`distribute-lft-out--`
26×	`fma-neg`
25×	`times-frac`
23×	`cos-sum`
14×	`add-log-exp`
13×	`unpow2` `sqr-pow`
11×	`associate--r+`
10×	`add-exp-log`
9×	`add-cbrt-cube`
6×	`neg-mul-1` `diff-log`
5×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `div-inv`
3×	`pow-unpow` `associate-/r*` `sub-neg`
2×	`cbrt-undiv` `div-exp` `neg-log` `associate-*r/` `associate-/l/`
1×	`associate--l-` `neg-sub0` `cos-diff` `pow-to-exp` `clear-num` `pow-pow` `frac-2neg` `flip3-+` `flip3--` `pow-exp` `prod-exp` `cbrt-unprod` `flip-+` `flip--` `associate-/l*` `associate--r-`

Counts

4 → 276

Calls

4 calls:

18.0ms	(/ (* K (+ m n)) 2)
891.0ms	(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
56.0ms	(pow (- (/ (+ m n) 2) M) 2)
36.0ms	(cos (- (/ (* K (+ m n)) 2) M))

series417.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(/ (* K (+ m n)) 2)
209.0ms	(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
84.0ms	(pow (- (/ (+ m n) 2) M) 2)
66.0ms	(cos (- (/ (* K (+ m n)) 2) M))

simplify796.0ms

Counts

288 → 288

Iterations

Iter	Nodes
done	2000
1	1059
0	473

prune1.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.7b

localize32.0ms

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)

rewrite838.0ms

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:

8.0ms	(- l (fabs (- m n)))
785.0ms	(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
36.0ms	(pow (- (/ (+ m n) 2) M) 2)

series331.0ms

Counts

3 → 9

Calls

3 calls:

19.0ms	(- l (fabs (- m n)))
206.0ms	(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
107.0ms	(pow (- (/ (+ m n) 2) M) 2)

simplify835.0ms

Counts

254 → 254

Iterations

Iter	Nodes
done	2002
2	1455
1	697
0	290

prune1.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 2.7b

localize57.0ms

Local error

Found 4 expressions with local error:

0.0b	(- l (fabs (- m n)))
0.0b	(- (- (pow (- (/ (+ m n) 2) M) 2)) (posit16->real (real->posit16 (- l (fabs (- m n))))))
0.0b	(pow (- (/ (+ m n) 2) M) 2)
60.3b	(posit16->real (real->posit16 (- l (fabs (- m n)))))

rewrite858.0ms

Algorithm

rewrite-expression-head

Rules

108×	`add-sqr-sqrt`
87×	`prod-diff`
83×	`*-un-lft-identity`
59×	`add-cube-cbrt`
54×	`unpow-prod-down`
45×	`distribute-rgt-neg-in`
44×	`distribute-lft-neg-in`
29×	`fma-neg`
20×	`difference-of-squares`
12×	`distribute-lft-out--`
10×	`add-log-exp`
9×	`times-frac` `unpow2` `sqr-pow`
5×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `neg-mul-1` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u`
3×	`pow-unpow` `diff-log`
2×	`sub-neg` `flip3--` `flip--`
1×	`associate--l-` `neg-sub0` `pow-to-exp` `pow-pow` `neg-log` `pow-exp` `remove-posit16`

Counts

4 → 188

Calls

4 calls:

5.0ms	(- l (fabs (- m n)))
798.0ms	(- (- (pow (- (/ (+ m n) 2) M) 2)) (posit16->real (real->posit16 (- l (fabs (- m n))))))
51.0ms	(pow (- (/ (+ m n) 2) M) 2)
0.0ms	(posit16->real (real->posit16 (- l (fabs (- m n)))))

series334.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(- l (fabs (- m n)))
198.0ms	(- (- (pow (- (/ (+ m n) 2) M) 2)) (posit16->real (real->posit16 (- l (fabs (- m n))))))
107.0ms	(pow (- (/ (+ m n) 2) M) 2)
15.0ms	(posit16->real (real->posit16 (- l (fabs (- m n)))))

simplify1.0s

Counts

200 → 200

Iterations

Iter	Nodes
done	2008
2	1309
1	616
0	262

prune1.3s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 2.7b

localize59.0ms

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))
22.5b	(posit16->real (real->posit16 (* (- (/ (+ n m) 2) M) (- (/ (+ n m) 2) M))))

rewrite210.0ms

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:

5.0ms	(- l (fabs (- m n)))
18.0ms	(- (- (posit16->real (real->posit16 (* (- (/ (+ n m) 2) M) (- (/ (+ n m) 2) M))))) (- l (fabs (- m n))))
181.0ms	(* (- (/ (+ n m) 2) M) (- (/ (+ n m) 2) M))
0.0ms	(posit16->real (real->posit16 (* (- (/ (+ n m) 2) M) (- (/ (+ n m) 2) M))))

series435.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(- l (fabs (- m n)))
201.0ms	(- (- (posit16->real (real->posit16 (* (- (/ (+ n m) 2) M) (- (/ (+ n m) 2) M))))) (- l (fabs (- m n))))
120.0ms	(* (- (/ (+ n m) 2) M) (- (/ (+ n m) 2) M))
92.0ms	(posit16->real (real->posit16 (* (- (/ (+ n m) 2) M) (- (/ (+ n m) 2) M))))

simplify780.0ms

Counts

295 → 295

Iterations

Iter	Nodes
done	2001
1	997
0	424

prune2.8s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 2.7b

regimes701.0ms

Accuracy

31.4% (0.9b remaining)

Error of 2.0b against oracle of 1.1b and baseline of 2.4b

bsearch372.0ms

Steps

Iters	Range		Point
7	520296.8443274253	43300588.52716438	4874821.850288491
8	-2.6248144306860336e+85	-4.022166283273843e+82	-4.0776803569038904e+82

simplify8.0ms

Iterations

Iter	Nodes
done	46
1	46
0	36

end0.0ms

sample3.7s

Algorithm

intervals

Results

2.8s	8119×	body	80	valid
252.0ms	137×	body	1280	valid
167.0ms	139×	body	640	valid
77.0ms	104×	body	320	valid
27.0ms	54×	body	160	valid
6.0ms	3×	body	2560	valid