Details

sample99.0ms

Algorithm

intervals

Results

57.0ms	257×	body	80	valid
5.0ms	4×	body	1280	valid
4.0ms	7×	body	320	valid
2.0ms	3×	body	640	valid
2.0ms	5×	body	160	valid

simplify1.1s

Counts

1 → 1

Iterations

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

prune31.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.0b

localize70.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)
0.0b	(- (* K (/ (+ m n) 2)) M)
0.0b	(* K (/ (+ m n) 2))
40.4b	(cos (- (* K (/ (+ m n) 2)) M))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

21×	`*-un-lft-identity`
20×	`add-sqr-sqrt`
16×	`associate-r`
15×	`add-cube-cbrt`
13×	`times-frac`
9×	`add-cbrt-cube` `add-exp-log`
6×	`pow1` `prod-diff` `add-log-exp`
5×	`cos-sum`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-l` `distribute-lft-out`
2×	`sub-neg` `prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`cos-diff` `cbrt-undiv` `flip3--` `fma-neg` `diff-log` `div-exp` `pow-prod-down` `associate-r/` `-commutative` `fma-udef` `div-inv` `flip--`

Counts

4 → 84

Calls

4 calls:

0.0ms	(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)
12.0ms	(- (* K (/ (+ m n) 2)) M)
21.0ms	(* K (/ (+ m n) 2))
44.0ms	(cos (- (* K (/ (+ m n) 2)) M))

series374.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)
70.0ms	(- (* K (/ (+ m n) 2)) M)
54.0ms	(* K (/ (+ m n) 2))
98.0ms	(cos (- (* K (/ (+ m n) 2)) M))

simplify988.0ms

Counts

96 → 96

Iterations

Iter	Nodes
3	3260
2	1058
1	405
0	188

prune1.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.6b

localize28.0ms

Local error

Found 3 expressions with local error:

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

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 175

Calls

3 calls:

41.0ms	(- (/ (+ m n) 2) M)
38.0ms	(- (/ (+ m n) 2) M)
0.0ms	(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)

series242.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(- (/ (+ m n) 2) M)
27.0ms	(- (/ (+ m n) 2) M)
188.0ms	(fma (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M) l)

simplify2.9s

Counts

184 → 184

Iterations

Iter	Nodes
4	6286
3	1706
2	626
1	298
0	145

prune1.4s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.6b

localize77.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ K (sqrt 2)) (/ (+ m n) (sqrt 2)))
0.4b	(/ K (sqrt 2))
0.5b	(/ (+ m n) (sqrt 2))
40.2b	(cos (- (* (/ K (sqrt 2)) (/ (+ m n) (sqrt 2))) M))

rewrite140.0ms

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:

34.0ms	(* (/ K (sqrt 2)) (/ (+ m n) (sqrt 2)))
9.0ms	(/ K (sqrt 2))
25.0ms	(/ (+ m n) (sqrt 2))
67.0ms	(cos (- (* (/ K (sqrt 2)) (/ (+ m n) (sqrt 2))) M))

series813.0ms

Counts

4 → 12

Calls

4 calls:

254.0ms	(* (/ K (sqrt 2)) (/ (+ m n) (sqrt 2)))
78.0ms	(/ K (sqrt 2))
103.0ms	(/ (+ m n) (sqrt 2))
377.0ms	(cos (- (* (/ K (sqrt 2)) (/ (+ m n) (sqrt 2))) M))

simplify4.4s

Counts

203 → 203

Iterations

Iter	Nodes
3	8839
2	1975
1	622
0	256

prune2.5s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.6b

localize50.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ K (sqrt (sqrt 2)))
0.3b	(/ (/ K (sqrt (sqrt 2))) (sqrt (sqrt 2)))
0.5b	(/ (+ m n) (sqrt 2))
40.4b	(cos (- (* (/ (/ K (sqrt (sqrt 2))) (sqrt (sqrt 2))) (/ (+ m n) (sqrt 2))) M))

rewrite128.0ms

Algorithm

rewrite-expression-head

Rules

609×	`sqrt-prod`
600×	`times-frac`
344×	`*-un-lft-identity`
330×	`add-sqr-sqrt` `add-cube-cbrt`
38×	`associate-/l*`
24×	`associate-/r*`
13×	`add-cbrt-cube` `add-exp-log` `div-inv`
7×	`distribute-lft-out`
5×	`cbrt-undiv` `cos-sum` `div-exp`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg` `prod-diff` `associate-/l/`
1×	`cos-diff` `sub-neg` `flip3-+` `flip-+`

Counts

4 → 458

Calls

4 calls:

13.0ms	(/ K (sqrt (sqrt 2)))
18.0ms	(/ (/ K (sqrt (sqrt 2))) (sqrt (sqrt 2)))
18.0ms	(/ (+ m n) (sqrt 2))
59.0ms	(cos (- (* (/ (/ K (sqrt (sqrt 2))) (sqrt (sqrt 2))) (/ (+ m n) (sqrt 2))) M))

series758.0ms

Counts

4 → 12

Calls

4 calls:

202.0ms	(/ K (sqrt (sqrt 2)))
100.0ms	(/ (/ K (sqrt (sqrt 2))) (sqrt (sqrt 2)))
102.0ms	(/ (+ m n) (sqrt 2))
355.0ms	(cos (- (* (/ (/ K (sqrt (sqrt 2))) (sqrt (sqrt 2))) (/ (+ m n) (sqrt 2))) M))

simplify1.1s

Counts

470 → 470

Iterations

Iter	Nodes
2	2340
1	1052
0	515

prune5.2s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 1.6b

regimes570.0ms

Accuracy

0% (0.3b remaining)

Error of 1.5b against oracle of 1.2b and baseline of 1.5b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
2	17
1	17
0	15

end0.0ms

sample3.7s

Algorithm

intervals

Results

2.9s	8131×	body	80	valid
202.0ms	157×	body	640	valid
155.0ms	113×	body	1280	valid
95.0ms	130×	body	320	valid
41.0ms	82×	body	160	valid
10.0ms	5×	body	2560	valid