Details

sample64.0ms

Algorithm

intervals

Results

35.0ms	263×	body	80	valid
4.0ms	4×	body	1280	valid
1.0ms	2×	body	320	valid
0.0ms	1×	body	160	valid

simplify2.8s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	3247
4	684
3	220
2	95
1	50
0	21

prune25.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.0b

localize52.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* K (+ m n)) 2.0)
0.0b	(* K (+ m n))
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
35.2b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite164.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
23×	`cos-sum` `add-cube-cbrt`
21×	`prod-diff`
13×	`times-frac`
12×	`add-exp-log`
11×	`add-cbrt-cube`
7×	`pow1`
6×	`unpow-prod-down`
4×	`expm1-log1p-u` `associate-r` `associate-*r/` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`pow-unpow` `associate-/r` `associate-l*`
2×	`cbrt-undiv` `flip3-+` `div-exp` `prod-exp` `cbrt-unprod` `flip-+` `difference-of-squares` `associate-/l/`
1×	`distribute-rgt-in` `cos-diff` `pow-to-exp` `clear-num` `sub-neg` `pow-pow` `frac-2neg` `distribute-lft-in` `pow-prod-down` `pow-exp` `-commutative` `distribute-lft-out` `associate-/l` `distribute-lft-out--` `unswap-sqr` `sqr-pow`

Counts

4 → 105

Calls

4 calls:

11.0ms	(/ (* K (+ m n)) 2.0)
31.0ms	(* K (+ m n))
55.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
63.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series581.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(/ (* K (+ m n)) 2.0)
46.0ms	(* K (+ m n))
401.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
70.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify1.2s

Counts

117 → 117

Iterations

Iter	Nodes
done	5000
2	2221
1	692
0	306

prune1.3s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize22.0ms

Local error

Found 1 expressions with local error:

0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`unpow-prod-down`
5×	`*-un-lft-identity`
3×	`pow-unpow` `add-cube-cbrt`
2×	`pow1` `add-exp-log` `difference-of-squares`
1×	`expm1-log1p-u` `pow-to-exp` `pow-pow` `times-frac` `add-cbrt-cube` `pow-exp` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp` `sqr-pow`

Counts

1 → 22

Calls

1 calls:

73.0ms

(pow (- (/ (+ m n) 2.0) M) 2.0)

series359.0ms

Counts

1 → 3

Calls

1 calls:

359.0ms

(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify1.3s

Counts

25 → 25

Iterations

Iter	Nodes
done	5000
3	1246
2	455
1	194
0	76

prune188.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.4b

localize54.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt 2.0)
1.0b	(cbrt 2.0)
1.0b	(cbrt 2.0)
35.2b	(cos (- (/ (/ (* K (+ m n)) (* (cbrt 2.0) (cbrt 2.0))) (cbrt 2.0)) M))

rewrite118.0ms

Algorithm

rewrite-expression-head

Rules

108×	`times-frac`
104×	`cos-sum`
102×	`prod-diff`
92×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
54×	`cbrt-prod`
21×	`div-inv`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`cos-diff` `sub-neg`

Counts

4 → 153

Calls

4 calls:

1.0ms	(cbrt 2.0)
1.0ms	(cbrt 2.0)
1.0ms	(cbrt 2.0)
100.0ms	(cos (- (/ (/ (* K (+ m n)) (* (cbrt 2.0) (cbrt 2.0))) (cbrt 2.0)) M))

series262.0ms

Counts

4 → 6

Calls

4 calls:

0.0ms	(cbrt 2.0)
0.0ms	(cbrt 2.0)
0.0ms	(cbrt 2.0)
262.0ms	(cos (- (/ (/ (* K (+ m n)) (* (cbrt 2.0) (cbrt 2.0))) (cbrt 2.0)) M))

simplify1.6s

Counts

159 → 159

Iterations

Iter	Nodes
done	5001
2	2179
1	1099
0	641

prune2.3s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.4b

localize144.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt 2.0)
35.2b	(cos (- (/ (/ (* K (+ m n)) (* (cbrt 2.0) (cbrt 2.0))) (cbrt 2.0)) M))
35.2b	(cos (- (/ (/ (* K (+ m n)) (* (cbrt 2.0) (cbrt 2.0))) (cbrt 2.0)) M))
35.2b	(cos (- (/ (/ (* K (+ m n)) (* (cbrt 2.0) (cbrt 2.0))) (cbrt 2.0)) M))

rewrite459.0ms

Algorithm

rewrite-expression-head

Rules

324×	`times-frac`
312×	`cos-sum`
306×	`prod-diff`
260×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
138×	`cbrt-prod`
63×	`div-inv`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
3×	`cos-diff` `sub-neg`
1×	`pow1/3`

Counts

4 → 355

Calls

4 calls:

1.0ms	(cbrt 2.0)
149.0ms	(cos (- (/ (/ (* K (+ m n)) (* (cbrt 2.0) (cbrt 2.0))) (cbrt 2.0)) M))
125.0ms	(cos (- (/ (/ (* K (+ m n)) (* (cbrt 2.0) (cbrt 2.0))) (cbrt 2.0)) M))
143.0ms	(cos (- (/ (/ (* K (+ m n)) (* (cbrt 2.0) (cbrt 2.0))) (cbrt 2.0)) M))

series946.0ms

Counts

4 → 10

Calls

4 calls:

0.0ms	(cbrt 2.0)
319.0ms	(cos (- (/ (/ (* K (+ m n)) (* (cbrt 2.0) (cbrt 2.0))) (cbrt 2.0)) M))
321.0ms	(cos (- (/ (/ (* K (+ m n)) (* (cbrt 2.0) (cbrt 2.0))) (cbrt 2.0)) M))
305.0ms	(cos (- (/ (/ (* K (+ m n)) (* (cbrt 2.0) (cbrt 2.0))) (cbrt 2.0)) M))

simplify1.8s

Counts

365 → 365

Iterations

Iter	Nodes
done	5001
2	2179
1	1099
0	641

prune7.9s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.4b

regimes441.0ms

Accuracy

0% (0.2b remaining)

Error of 1.3b against oracle of 1.2b and baseline of 1.3b

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	22
2	22
1	21
0	17

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.8s	8064×	body	80	valid
226.0ms	165×	body	640	valid
112.0ms	118×	body	1280	valid
47.0ms	112×	body	320	valid
15.0ms	49×	body	160	valid
2.0ms	2×	body	2560	valid