Details

sample103.0ms

Algorithm

intervals

Results

48.0ms	249×	body	80	valid
10.0ms	9×	body	1280	valid
5.0ms	6×	body	640	valid
2.0ms	3×	body	320	valid
1.0ms	3×	body	160	valid

simplify13.2s

Counts

1 → 1

Iterations

Useful iterations: done (13.2s)

Iter	Nodes	Cost
0	21	29
1	73	29
2	431	29
done	5000	28

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.3b

localize42.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
0.0b	(* K (+ m n))
33.8b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite1.7s

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
17×	`add-sqr-sqrt`
14×	`add-log-exp`
8×	`add-cube-cbrt`
7×	`pow1` `add-exp-log` `distribute-lft-out--`
6×	`unpow-prod-down` `diff-log` `add-cbrt-cube`
4×	`associate-r`
3×	`sub-neg` `pow-unpow` `associate-l` `difference-of-squares`
2×	`cos-sum` `distribute-rgt-neg-in` `associate-*r/` `neg-log` `associate--r+`
1×	`associate--l-` `neg-sub0` `distribute-rgt-in` `cos-diff` `pow-to-exp` `flip3--` `pow-pow` `distribute-lft-in` `flip3-+` `times-frac` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `flip-+` `distribute-lft-out` `associate--r-` `unswap-sqr` `sqr-pow`

Counts

4 → 77

Calls

4 calls:

1.5s	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
99.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
20.0ms	(* K (+ m n))
56.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series751.0ms

Counts

4 → 12

Calls

4 calls:

250.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
384.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
35.0ms	(* K (+ m n))
83.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify1.5s

Counts

89 → 89

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	189	1340
1	854	1261
done	5000	1169

prune590.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 1.7b

localize31.0ms

Local error

Found 2 expressions with local error:

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

rewrite1.6s

Algorithm

rewrite-expression-head

Rules

16×	`*-un-lft-identity`
12×	`add-log-exp`
11×	`add-sqr-sqrt`
7×	`distribute-lft-out--`
6×	`unpow-prod-down` `diff-log`
4×	`add-cube-cbrt`
3×	`pow1` `add-exp-log` `pow-unpow` `difference-of-squares`
2×	`sub-neg` `distribute-rgt-neg-in` `neg-log` `add-cbrt-cube` `associate--r+`
1×	`associate--l-` `neg-sub0` `pow-to-exp` `flip3--` `pow-pow` `times-frac` `pow-exp` `flip--` `associate--r-` `sqr-pow`

Counts

2 → 44

Calls

2 calls:

1.5s	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
82.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series699.0ms

Counts

2 → 6

Calls

2 calls:

248.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
451.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify1.3s

Counts

50 → 50

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	122	937
1	513	879
done	5000	827

prune267.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 1.7b

localize51.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (+ m n))
0.6b	(cbrt (+ m n))
0.6b	(cbrt (+ m n))
33.4b	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

rewrite401.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
12×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`cbrt-div`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out`
2×	`cos-sum`
1×	`cos-diff` `sub-neg`

Counts

4 → 52

Calls

4 calls:

8.0ms	(cbrt (+ m n))
8.0ms	(cbrt (+ m n))
8.0ms	(cbrt (+ m n))
374.0ms	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

series700.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(cbrt (+ m n))
200.0ms	(cbrt (+ m n))
177.0ms	(cbrt (+ m n))
170.0ms	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

simplify1.7s

Counts

64 → 64

Iterations

Useful iterations: 2 (257.0ms)

Iter	Nodes	Cost
0	91	868
1	268	835
2	1351	602
done	5001	602

prune459.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 1.7b

localize48.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (+ m n))
0.6b	(cbrt (+ m n))
1.2b	(* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (* (cbrt (- m)) (cbrt -1)))
30.0b	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (* (cbrt (- m)) (cbrt -1))) 2.0) M))

rewrite742.0ms

Algorithm

rewrite-expression-head

Rules

25×	`pow1` `add-exp-log`
16×	`cbrt-div`
15×	`pow-prod-down` `prod-exp` `add-cbrt-cube` `cbrt-unprod`
10×	`-un-lft-identity` `associate-r/` `associate-*l/`
8×	`cbrt-prod` `flip3-+` `flip-+`
6×	`add-sqr-sqrt` `add-cube-cbrt`
4×	`frac-times` `add-log-exp`
2×	`cos-sum` `pow1/3` `distribute-lft-out`
1×	`cos-diff` `sub-neg` `associate-r` `associate-l` `*-commutative`

Counts

4 → 74

Calls

4 calls:

4.0ms	(cbrt (+ m n))
4.0ms	(cbrt (+ m n))
263.0ms	(* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (* (cbrt (- m)) (cbrt -1)))
467.0ms	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (* (cbrt (- m)) (cbrt -1))) 2.0) M))

series1.1s

Counts

4 → 12

Calls

4 calls:

174.0ms	(cbrt (+ m n))
207.0ms	(cbrt (+ m n))
214.0ms	(* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (* (cbrt (- m)) (cbrt -1)))
531.0ms	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (* (cbrt (- m)) (cbrt -1))) 2.0) M))

simplify2.0s

Counts

86 → 86

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	191	1700
1	852	1651
done	5000	1409

prune758.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 1.7b

regimes735.0ms

Accuracy

0% (0.2b remaining)

Error of 1.3b against oracle of 1.1b and baseline of 1.3b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	17	20
1	21	18
done	21	18

end0.0ms

sample3.0s

Algorithm

intervals

Results

2.0s	8070×	body	80	valid
135.0ms	133×	body	640	valid
107.0ms	123×	body	1280	valid
89.0ms	102×	body	320	valid
44.0ms	65×	body	160	valid
12.0ms	5×	body	2560	valid