Details

sample88.0ms

Algorithm

intervals

Results

56.0ms	257×	body	80	valid
6.0ms	9×	body	640	valid
4.0ms	5×	body	1280	valid
2.0ms	4×	body	320	valid
1.0ms	4×	body	160	valid

simplify874.0ms

Counts

1 → 1

Iterations

Iter	Nodes
5	3132
4	821
3	260
2	102
1	51
0	21

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.5b

localize74.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ (+ m n) 2) M)
0.0b	(- (/ (+ m n) 2) M)
0.0b	(* K (/ (+ m n) 2))
35.9b	(cos (- (* K (/ (+ m n) 2)) M))

rewrite530.0ms

Algorithm

rewrite-expression-head

Rules

168×	`*-un-lft-identity`
125×	`add-sqr-sqrt`
111×	`times-frac`
110×	`add-cube-cbrt`
99×	`prod-diff`
32×	`fma-neg`
27×	`distribute-lft-out`
16×	`associate-r`
9×	`add-cbrt-cube` `add-exp-log` `div-inv`
8×	`add-log-exp`
6×	`pow1`
5×	`cos-sum`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `difference-of-squares`
3×	`sub-neg` `associate-l`
2×	`flip3--` `diff-log` `prod-exp` `cbrt-unprod` `flip--` `distribute-lft-out--` `unswap-sqr`
1×	`cos-diff` `cbrt-undiv` `div-exp` `pow-prod-down` `associate-r/` `-commutative`

Counts

4 → 218

Calls

4 calls:

61.0ms	(- (/ (+ m n) 2) M)
394.0ms	(- (/ (+ m n) 2) M)
19.0ms	(* K (/ (+ m n) 2))
50.0ms	(cos (- (* K (/ (+ m n) 2)) M))

series228.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(- (/ (+ m n) 2) M)
37.0ms	(- (/ (+ m n) 2) M)
76.0ms	(* K (/ (+ m n) 2))
81.0ms	(cos (- (* K (/ (+ m n) 2)) M))

simplify1.5s

Counts

230 → 230

Iterations

Iter	Nodes
3	3807
2	1207
1	471
0	219

prune4.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.5b

localize54.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (/ (+ m n) 2) M)
0.0b	(- (/ (+ m n) 2) M)

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

150×	`*-un-lft-identity`
108×	`add-sqr-sqrt`
98×	`times-frac` `add-cube-cbrt`
96×	`prod-diff`
32×	`fma-neg`
24×	`distribute-lft-out`
8×	`div-inv`
6×	`add-log-exp`
4×	`difference-of-squares`
2×	`expm1-log1p-u` `pow1` `sub-neg` `flip3--` `add-cbrt-cube` `diff-log` `add-exp-log` `insert-posit16` `log1p-expm1-u` `flip--` `distribute-lft-out--`

Counts

2 → 164

Calls

2 calls:

52.0ms	(- (/ (+ m n) 2) M)
52.0ms	(- (/ (+ m n) 2) M)

series76.0ms

Counts

2 → 6

Calls

2 calls:

37.0ms	(- (/ (+ m n) 2) M)
39.0ms	(- (/ (+ m n) 2) M)

simplify2.6s

Counts

170 → 170

Iterations

Iter	Nodes
4	5235
3	1478
2	526
1	248
0	121

prune2.7s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.5b

localize57.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ K (sqrt 2)) (/ (+ m n) (sqrt 2)))
0.4b	(/ (+ m n) (sqrt 2))
0.5b	(/ K (sqrt 2))
35.6b	(cos (- (* (/ K (sqrt 2)) (/ (+ m n) (sqrt 2))) M))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

96×	`times-frac`
95×	`add-sqr-sqrt`
91×	`*-un-lft-identity`
65×	`add-cube-cbrt`
54×	`sqrt-prod`
28×	`associate-r`
22×	`associate-l`
20×	`add-cbrt-cube` `add-exp-log`
13×	`distribute-lft-out`
12×	`associate-/r*`
9×	`unswap-sqr`
7×	`associate-/l*`
6×	`pow1` `cbrt-undiv` `div-exp`
5×	`cos-sum`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`prod-diff`
2×	`clear-num` `frac-2neg` `associate-/l/`
1×	`cos-diff` `frac-times` `sub-neg` `flip3-+` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `flip-+`

Counts

4 → 191

Calls

4 calls:

43.0ms	(* (/ K (sqrt 2)) (/ (+ m n) (sqrt 2)))
17.0ms	(/ (+ m n) (sqrt 2))
7.0ms	(/ K (sqrt 2))
33.0ms	(cos (- (* (/ K (sqrt 2)) (/ (+ m n) (sqrt 2))) M))

series878.0ms

Counts

4 → 12

Calls

4 calls:

218.0ms	(* (/ K (sqrt 2)) (/ (+ m n) (sqrt 2)))
139.0ms	(/ (+ m n) (sqrt 2))
71.0ms	(/ K (sqrt 2))
450.0ms	(cos (- (* (/ K (sqrt 2)) (/ (+ m n) (sqrt 2))) M))

simplify4.6s

Counts

203 → 203

Iterations

Iter	Nodes
3	8317
2	1917
1	622
0	256

prune4.0s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 1.5b

localize125.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (+ m n) (sqrt 2))
0.5b	(/ K (sqrt 2))
35.6b	(cos (- (* (/ K (sqrt 2)) (posit16->real (real->posit16 (/ (+ m n) (sqrt 2))))) M))
60.2b	(posit16->real (real->posit16 (/ (+ m n) (sqrt 2))))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

51×	`*-un-lft-identity`
42×	`times-frac`
37×	`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*`
5×	`cos-sum`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`prod-diff`
2×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv` `associate-/l/`
1×	`cos-diff` `sub-neg` `flip3-+` `flip-+` `remove-posit16`

Counts

4 → 120

Calls

4 calls:

33.0ms	(/ (+ m n) (sqrt 2))
5.0ms	(/ K (sqrt 2))
31.0ms	(cos (- (* (/ K (sqrt 2)) (posit16->real (real->posit16 (/ (+ m n) (sqrt 2))))) M))
1.0ms	(posit16->real (real->posit16 (/ (+ m n) (sqrt 2))))

series781.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(/ (+ m n) (sqrt 2))
105.0ms	(/ K (sqrt 2))
393.0ms	(cos (- (* (/ K (sqrt 2)) (posit16->real (real->posit16 (/ (+ m n) (sqrt 2))))) M))
158.0ms	(posit16->real (real->posit16 (/ (+ m n) (sqrt 2))))

simplify2.6s

Counts

132 → 132

Iterations

Iter	Nodes
4	4649
3	1664
2	685
1	359
0	209

prune4.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 1.4b

regimes658.0ms

Accuracy

0% (0.8b remaining)

Error of 1.9b against oracle of 1.1b and baseline of 1.9b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
2	28
1	28
0	25

end0.0ms

sample4.1s

Algorithm

intervals

Results

3.1s	8092×	body	80	valid
285.0ms	162×	body	640	valid
149.0ms	101×	body	1280	valid
89.0ms	112×	body	320	valid
26.0ms	48×	body	160	valid
3.0ms	2×	body	2560	valid