Details

sample62.0ms

Algorithm

intervals

Results

32.0ms	263×	body	80	valid
3.0ms	4×	body	1280	valid
1.0ms	2×	body	320	valid
0.0ms	1×	body	160	valid

simplify2.4s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
5	3032
4	640
3	210
2	93
1	50
0	21

prune26.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.0b

localize40.0ms

Local error

Found 4 expressions with local error:

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

rewrite177.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
18×	`*-un-lft-identity`
14×	`add-cube-cbrt`
13×	`associate-l`
11×	`times-frac`
10×	`add-exp-log`
9×	`add-cbrt-cube`
7×	`pow1`
6×	`unpow-prod-down` `add-log-exp`
4×	`cos-sum` `associate-r` `associate--l+`
3×	`distribute-rgt-in` `pow-unpow` `distribute-lft-in`
2×	`frac-times` `sub-neg` `flip3-+` `prod-exp` `associate-*r/` `cbrt-unprod` `flip-+` `difference-of-squares` `unswap-sqr`
1×	`cos-diff` `pow-to-exp` `cbrt-undiv` `pow-pow` `flip3--` `diff-log` `div-exp` `pow-prod-down` `associate-l/` `pow-exp` `-commutative` `div-inv` `flip--` `distribute-lft-out` `distribute-lft-out--` `sqr-pow`

Counts

4 → 85

Calls

4 calls:

12.0ms	(- (* (/ K 2.0) (+ m n)) M)
47.0ms	(* (/ K 2.0) (+ m n))
70.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
45.0ms	(cos (- (* (/ K 2.0) (+ m n)) M))

series631.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(- (* (/ K 2.0) (+ m n)) M)
70.0ms	(* (/ K 2.0) (+ m n))
376.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
99.0ms	(cos (- (* (/ K 2.0) (+ m n)) M))

simplify1.5s

Counts

97 → 97

Iterations

Iter	Nodes
done	5002
2	2289
1	614
0	214

prune966.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize42.0ms

Local error

Found 2 expressions with local error:

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

rewrite255.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
8×	`*-un-lft-identity`
7×	`unpow-prod-down`
5×	`difference-of-squares`
4×	`add-cube-cbrt` `add-log-exp`
3×	`pow1` `pow-unpow` `add-exp-log`
2×	`add-cbrt-cube` `distribute-lft-out--` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `pow-pow` `times-frac` `flip3--` `diff-log` `pow-exp` `flip--`

Counts

2 → 36

Calls

2 calls:

168.0ms	(- (fabs (- m n)) (pow (- (/ (+ m n) 2.0) M) 2.0))
86.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series561.0ms

Counts

2 → 6

Calls

2 calls:

191.0ms	(- (fabs (- m n)) (pow (- (/ (+ m n) 2.0) M) 2.0))
370.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify1.6s

Counts

42 → 42

Iterations

Iter	Nodes
done	5000
3	2373
2	712
1	284
0	113

prune391.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.4b

localize86.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt 2.0)
1.0b	(cbrt 2.0)
1.0b	(cbrt 2.0)
35.1b	(cos (- (* (/ (* (cbrt K) (cbrt K)) (* (cbrt 2.0) (cbrt 2.0))) (* (/ (cbrt K) (cbrt 2.0)) (+ m n))) M))

rewrite174.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`cos-sum`
4×	`distribute-rgt-in` `pow1` `distribute-lft-in` `add-cbrt-cube` `associate--l+` `add-exp-log` `add-log-exp`
3×	`pow1/3`
1×	`cos-diff` `sub-neg`

Counts

4 → 47

Calls

4 calls:

1.0ms	(cbrt 2.0)
1.0ms	(cbrt 2.0)
1.0ms	(cbrt 2.0)
171.0ms	(cos (- (* (/ (* (cbrt K) (cbrt K)) (* (cbrt 2.0) (cbrt 2.0))) (* (/ (cbrt K) (cbrt 2.0)) (+ m n))) M))

series352.0ms

Counts

4 → 6

Calls

4 calls:

0.0ms	(cbrt 2.0)
0.0ms	(cbrt 2.0)
0.0ms	(cbrt 2.0)
351.0ms	(cos (- (* (/ (* (cbrt K) (cbrt K)) (* (cbrt 2.0) (cbrt 2.0))) (* (/ (cbrt K) (cbrt 2.0)) (+ m n))) M))

simplify2.9s

Counts

53 → 53

Iterations

Iter	Nodes
done	5000
4	3523
3	1278
2	432
1	184
0	93

prune589.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.4b

localize207.0ms

Local error

Found 4 expressions with local error:

1.0b	(cbrt 2.0)
35.1b	(cos (- (* (/ (* (cbrt K) (cbrt K)) (* (cbrt 2.0) (cbrt 2.0))) (* (/ (cbrt K) (cbrt 2.0)) (+ m n))) M))
35.1b	(cos (- (* (/ (* (cbrt K) (cbrt K)) (* (cbrt 2.0) (cbrt 2.0))) (* (/ (cbrt K) (cbrt 2.0)) (+ m n))) M))
35.1b	(cos (- (* (/ (* (cbrt K) (cbrt K)) (* (cbrt 2.0) (cbrt 2.0))) (* (/ (cbrt K) (cbrt 2.0)) (+ m n))) M))

rewrite838.0ms

Algorithm

rewrite-expression-head

Rules

18×	`cos-sum`
12×	`distribute-rgt-in` `distribute-lft-in` `associate--l+`
5×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`cbrt-prod` `cos-diff` `sub-neg`
1×	`pow1/3`

Counts

4 → 53

Calls

4 calls:

1.0ms	(cbrt 2.0)
316.0ms	(cos (- (* (/ (* (cbrt K) (cbrt K)) (* (cbrt 2.0) (cbrt 2.0))) (* (/ (cbrt K) (cbrt 2.0)) (+ m n))) M))
238.0ms	(cos (- (* (/ (* (cbrt K) (cbrt K)) (* (cbrt 2.0) (cbrt 2.0))) (* (/ (cbrt K) (cbrt 2.0)) (+ m n))) M))
279.0ms	(cos (- (* (/ (* (cbrt K) (cbrt K)) (* (cbrt 2.0) (cbrt 2.0))) (* (/ (cbrt K) (cbrt 2.0)) (+ m n))) M))

series1.2s

Counts

4 → 10

Calls

4 calls:

0.0ms	(cbrt 2.0)
443.0ms	(cos (- (* (/ (* (cbrt K) (cbrt K)) (* (cbrt 2.0) (cbrt 2.0))) (* (/ (cbrt K) (cbrt 2.0)) (+ m n))) M))
340.0ms	(cos (- (* (/ (* (cbrt K) (cbrt K)) (* (cbrt 2.0) (cbrt 2.0))) (* (/ (cbrt K) (cbrt 2.0)) (+ m n))) M))
373.0ms	(cos (- (* (/ (* (cbrt K) (cbrt K)) (* (cbrt 2.0) (cbrt 2.0))) (* (/ (cbrt K) (cbrt 2.0)) (+ m n))) M))

simplify2.9s

Counts

63 → 63

Iterations

Iter	Nodes
done	5000
4	3523
3	1278
2	432
1	184
0	93

prune890.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.4b

regimes411.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	21
2	21
1	20
0	16

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.5s	8064×	body	80	valid
507.0ms	112×	body	320	valid
191.0ms	165×	body	640	valid
114.0ms	118×	body	1280	valid
15.0ms	49×	body	160	valid
2.0ms	2×	body	2560	valid