Details

sample108.0ms

Algorithm

intervals

Results

66.0ms	260×	body	80	valid
6.0ms	4×	body	1280	valid
4.0ms	3×	body	640	valid
2.0ms	2×	body	320	valid

simplify2.3s

Counts

1 → 1

Iterations

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

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.0b

localize51.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
0.0b	(pow (- (/ (+ m n) 2) M) 2)
0.0b	(- (/ (* K (+ m n)) 2) M)
33.3b	(cos (- (/ (* K (+ m n)) 2) M))

rewrite966.0ms

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:

869.0ms	(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
53.0ms	(pow (- (/ (+ m n) 2) M) 2)
14.0ms	(- (/ (* K (+ m n)) 2) M)
22.0ms	(cos (- (/ (* K (+ m n)) 2) M))

series492.0ms

Counts

4 → 12

Calls

4 calls:

226.0ms	(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
101.0ms	(pow (- (/ (+ m n) 2) M) 2)
81.0ms	(- (/ (* K (+ m n)) 2) M)
84.0ms	(cos (- (/ (* K (+ m n)) 2) M))

simplify1.9s

Counts

307 → 307

Iterations

Iter	Nodes
done	5000
2	2052
1	994
0	460

prune1.5s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.8b

localize44.0ms

Local error

Found 3 expressions with local error:

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

rewrite988.0ms

Algorithm

rewrite-expression-head

Rules

239×	`add-sqr-sqrt`
229×	`*-un-lft-identity`
187×	`prod-diff`
115×	`add-cube-cbrt`
78×	`unpow-prod-down`
68×	`distribute-rgt-neg-in`
66×	`distribute-lft-neg-in`
62×	`times-frac`
55×	`difference-of-squares`
46×	`distribute-lft-out--`
42×	`fma-neg`
15×	`add-log-exp`
13×	`unpow2` `sqr-pow`
12×	`distribute-lft-out`
11×	`associate--r+`
7×	`diff-log`
6×	`neg-mul-1`
4×	`pow1` `add-exp-log` `div-inv`
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 → 298

Calls

3 calls:

55.0ms	(- (/ (+ m n) 2) M)
872.0ms	(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
51.0ms	(pow (- (/ (+ m n) 2) M) 2)

series356.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(- (/ (+ m n) 2) M)
217.0ms	(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
105.0ms	(pow (- (/ (+ m n) 2) M) 2)

simplify1.6s

Counts

307 → 307

Iterations

Iter	Nodes
done	5001
2	1816
1	870
0	365

prune1.2s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.8b

localize51.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ (+ n m) 2) M)
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))
22.6b	(posit16->real (real->posit16 (* (- (/ (+ n m) 2) M) (- (/ (+ n m) 2) M))))

rewrite296.0ms

Algorithm

rewrite-expression-head

Rules

276×	`*-un-lft-identity`
219×	`add-sqr-sqrt`
203×	`prod-diff`
170×	`add-cube-cbrt`
125×	`times-frac`
50×	`distribute-rgt-in` `distribute-lft-in`
30×	`distribute-lft-out`
26×	`fma-neg`
23×	`distribute-lft-out--`
21×	`difference-of-squares`
20×	`distribute-rgt-neg-in`
18×	`distribute-lft-neg-in`
16×	`add-log-exp`
11×	`pow1` `associate--r+`
10×	`div-inv`
8×	`flip3--` `swap-sqr` `flip--`
7×	`diff-log`
6×	`neg-mul-1` `add-cbrt-cube` `associate-r` `associate-l` `add-exp-log`
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 → 336

Calls

4 calls:

72.0ms	(- (/ (+ n m) 2) M)
35.0ms	(- (- (posit16->real (real->posit16 (* (- (/ (+ n m) 2) M) (- (/ (+ n m) 2) M))))) (- l (fabs (- m n))))
173.0ms	(* (- (/ (+ n m) 2) M) (- (/ (+ n m) 2) M))
0.0ms	(posit16->real (real->posit16 (* (- (/ (+ n m) 2) M) (- (/ (+ n m) 2) M))))

series422.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(- (/ (+ n m) 2) M)
181.0ms	(- (- (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))
109.0ms	(posit16->real (real->posit16 (* (- (/ (+ n m) 2) M) (- (/ (+ n m) 2) M))))

simplify2.0s

Counts

348 → 348

Iterations

Iter	Nodes
done	5002
2	2547
1	964
0	414

prune2.9s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.8b

localize54.0ms

Local error

Found 4 expressions with local error:

0.2b	(fma (/ K (sqrt 2)) (/ (+ m n) (sqrt 2)) (- M))
0.5b	(/ (+ m n) (sqrt 2))
0.5b	(/ K (sqrt 2))
33.2b	(cos (fma (/ K (sqrt 2)) (/ (+ m n) (sqrt 2)) (- M)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

50×	`*-un-lft-identity`
42×	`times-frac`
36×	`add-sqr-sqrt` `add-cube-cbrt`
27×	`sqrt-prod`
12×	`associate-/r*`
8×	`add-cbrt-cube` `add-exp-log`
7×	`distribute-lft-out` `associate-/l*`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `fma-udef` `div-inv` `associate-/l/`
1×	`cos-sum` `flip3-+` `flip-+`

Counts

4 → 115

Calls

4 calls:

0.0ms	(fma (/ K (sqrt 2)) (/ (+ m n) (sqrt 2)) (- M))
23.0ms	(/ (+ m n) (sqrt 2))
9.0ms	(/ K (sqrt 2))
5.0ms	(cos (fma (/ K (sqrt 2)) (/ (+ m n) (sqrt 2)) (- M)))

series688.0ms

Counts

4 → 12

Calls

4 calls:

276.0ms	(fma (/ K (sqrt 2)) (/ (+ m n) (sqrt 2)) (- M))
92.0ms	(/ (+ m n) (sqrt 2))
61.0ms	(/ K (sqrt 2))
259.0ms	(cos (fma (/ K (sqrt 2)) (/ (+ m n) (sqrt 2)) (- M)))

simplify1.5s

Counts

127 → 127

Iterations

Iter	Nodes
done	5001
3	2083
2	741
1	321
0	172

prune1.1s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.8b

regimes437.0ms

Accuracy

0% (1.4b remaining)

Error of 2.6b against oracle of 1.3b and baseline of 2.6b

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	27
1	27
0	25

end0.0ms

sample3.7s

Algorithm

intervals

Results

2.8s	8117×	body	80	valid
233.0ms	121×	body	1280	valid
172.0ms	127×	body	640	valid
86.0ms	116×	body	320	valid
26.0ms	55×	body	160	valid
6.0ms	3×	body	2560	valid