Details

sample100.0ms

Algorithm

intervals

Results

64.0ms	259×	body	80	valid
3.0ms	4×	body	640	valid
3.0ms	4×	body	320	valid
3.0ms	3×	body	1280	valid
1.0ms	2×	body	160	valid

simplify2.4s

Counts

1 → 1

Iterations

Iter	Nodes
done	5052
5	3741
4	818
3	257
2	102
1	51
0	21

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.1b

localize58.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (exp (- (- (fabs (- m n)) (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))) l)) (cos (- (/ (+ m n) (/ 2 K)) M)))
0.0b	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
0.2b	(/ (+ m n) (/ 2 K))
30.5b	(cos (- (/ (+ m n) (/ 2 K)) M))

rewrite486.0ms

Algorithm

rewrite-expression-head

Rules

101×	`*-un-lft-identity` `times-frac`
83×	`add-sqr-sqrt`
59×	`add-cube-cbrt`
14×	`distribute-lft-out`
13×	`pow1` `associate-/r` `add-cbrt-cube` `associate-l*`
12×	`add-exp-log`
9×	`associate-r`
8×	`swap-sqr` `difference-of-squares`
6×	`flip3--` `div-inv` `flip--` `distribute-lft-out--`
5×	`sub-neg`
4×	`frac-times` `exp-sum` `insert-posit16` `associate-/l*` `add-log-exp`
3×	`distribute-rgt-in` `cos-diff` `cbrt-undiv` `distribute-lft-in` `div-exp` `associate-*l/`
2×	`cos-sum` `pow-prod-down` `prod-exp` `associate--l+` `associate-r/` `-commutative` `cbrt-unprod` `unswap-sqr` `associate-/l/`
1×	`pow2` `clear-num` `frac-2neg` `flip3-+` `pow-plus` `exp-diff` `associate-/r/` `pow-sqr` `pow-prod-up` `flip-+`

Counts

4 → 173

Calls

4 calls:

251.0ms	(* (exp (- (- (fabs (- m n)) (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))) l)) (cos (- (/ (+ m n) (/ 2 K)) M)))
173.0ms	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
17.0ms	(/ (+ m n) (/ 2 K))
42.0ms	(cos (- (/ (+ m n) (/ 2 K)) M))

series552.0ms

Counts

4 → 12

Calls

4 calls:

339.0ms	(* (exp (- (- (fabs (- m n)) (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))) l)) (cos (- (/ (+ m n) (/ 2 K)) M)))
104.0ms	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))
40.0ms	(/ (+ m n) (/ 2 K))
69.0ms	(cos (- (/ (+ m n) (/ 2 K)) M))

simplify2.3s

Counts

185 → 185

Iterations

Iter	Nodes
done	5004
2	2919
1	892
0	329

prune1.4s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.7b

localize46.0ms

Local error

Found 3 expressions with local error:

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

rewrite231.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
10×	`pow1` `add-log-exp` `difference-of-squares`
8×	`flip3--` `swap-sqr` `flip--`
7×	`sub-neg` `add-cube-cbrt` `distribute-lft-out--`
6×	`associate-r` `associate-l`
5×	`add-cbrt-cube` `add-exp-log`
4×	`distribute-rgt-in` `frac-times` `distribute-lft-in` `times-frac` `diff-log` `associate--r+`
3×	`insert-posit16`
2×	`associate-l/` `associate--l+` `associate-r/`
1×	`associate--l-` `pow2` `pow-plus` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`

Counts

3 → 86

Calls

3 calls:

28.0ms	(- (- (fabs (- m n)) (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))) l)
13.0ms	(- (fabs (- m n)) (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)))
189.0ms	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))

series458.0ms

Counts

3 → 9

Calls

3 calls:

234.0ms	(- (- (fabs (- m n)) (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))) l)
130.0ms	(- (fabs (- m n)) (* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M)))
94.0ms	(* (- (/ (+ m n) 2) M) (- (/ (+ m n) 2) M))

simplify1.5s

Counts

95 → 95

Iterations

Iter	Nodes
done	5000
2	1349
1	424
0	155

prune599.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.7b

localize72.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (cos (- (/ (+ m n) (/ 2 K)) M)))
30.5b	(cos (- (/ (+ m n) (/ 2 K)) M))
30.5b	(cos (- (/ (+ m n) (/ 2 K)) M))
30.5b	(cos (- (/ (+ m n) (/ 2 K)) M))

rewrite199.0ms

Algorithm

rewrite-expression-head

Rules

6×	`cos-sum`
5×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`cbrt-prod` `cos-diff` `sub-neg`
1×	`pow1/3`

Counts

4 → 45

Calls

4 calls:

4.0ms	(cbrt (cos (- (/ (+ m n) (/ 2 K)) M)))
80.0ms	(cos (- (/ (+ m n) (/ 2 K)) M))
56.0ms	(cos (- (/ (+ m n) (/ 2 K)) M))
58.0ms	(cos (- (/ (+ m n) (/ 2 K)) M))

series425.0ms

Counts

4 → 12

Calls

4 calls:

175.0ms	(cbrt (cos (- (/ (+ m n) (/ 2 K)) M)))
86.0ms	(cos (- (/ (+ m n) (/ 2 K)) M))
88.0ms	(cos (- (/ (+ m n) (/ 2 K)) M))
77.0ms	(cos (- (/ (+ m n) (/ 2 K)) M))

simplify3.7s

Counts

57 → 57

Iterations

Iter	Nodes
done	5009
7	3265
6	1200
5	539
4	293
3	177
2	120
1	82
0	50

prune622.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.7b

localize136.0ms

Local error

Found 4 expressions with local error:

30.5b	(cos (- (/ (+ m n) (/ 2 K)) M))
30.5b	(cos (- (/ (+ m n) (/ 2 K)) M))
30.5b	(cos (- (/ (+ m n) (/ 2 K)) M))
30.5b	(cos (- (/ (+ m n) (/ 2 K)) M))

rewrite301.0ms

Algorithm

rewrite-expression-head

Rules

8×	`cos-sum`
4×	`cos-diff` `add-sqr-sqrt` `pow1` `sub-neg` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `add-log-exp`

Counts

4 → 44

Calls

4 calls:

55.0ms	(cos (- (/ (+ m n) (/ 2 K)) M))
80.0ms	(cos (- (/ (+ m n) (/ 2 K)) M))
80.0ms	(cos (- (/ (+ m n) (/ 2 K)) M))
84.0ms	(cos (- (/ (+ m n) (/ 2 K)) M))

series352.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(cos (- (/ (+ m n) (/ 2 K)) M))
74.0ms	(cos (- (/ (+ m n) (/ 2 K)) M))
92.0ms	(cos (- (/ (+ m n) (/ 2 K)) M))
101.0ms	(cos (- (/ (+ m n) (/ 2 K)) M))

simplify2.5s

Counts

56 → 56

Iterations

Iter	Nodes
done	5000
9	2087
8	746
7	335
6	237
5	184
4	144
3	122
2	93
1	64
0	38

prune673.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.7b

regimes558.0ms

Accuracy

0% (0.2b remaining)

Error of 1.2b against oracle of 1.0b and baseline of 1.2b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	20
1	20
0	16

end0.0ms

sample3.4s

Algorithm

intervals

Results

2.6s	8090×	body	80	valid
201.0ms	147×	body	640	valid
193.0ms	113×	body	1280	valid
119.0ms	102×	body	320	valid
24.0ms	53×	body	160	valid
7.0ms	4×	body	2560	valid