Details

sample130.0ms

Algorithm

intervals

Results

49.0ms	249×	body	80	valid
30.0ms	9×	body	1280	valid
5.0ms	6×	body	640	valid
2.0ms	3×	body	320	valid
1.0ms	3×	body	160	valid

simplify4.9s

Counts

1 → 1

Iterations

Useful iterations: 4 (125.0ms)

Iter	Nodes	Cost
0	21	29
1	50	29
2	93	29
3	197	29
4	465	28
5	1141	28
6	4709	28
done	5000	28

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.3b

localize62.0ms

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))

rewrite1.8s

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:

1.6s	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
103.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
25.0ms	(* K (+ m n))
71.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series854.0ms

Counts

4 → 12

Calls

4 calls:

306.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
379.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
49.0ms	(* K (+ m n))
118.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify2.2s

Counts

89 → 89

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	189	1340
1	430	1261
2	1075	1168
3	3410	1149
done	5000	1141

prune588.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 1.7b

localize28.0ms

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)

rewrite1.7s

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:

1.6s	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
97.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series704.0ms

Counts

2 → 6

Calls

2 calls:

310.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
395.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify1.5s

Counts

50 → 50

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	122	937
1	273	879
2	634	826
3	2008	807
done	5000	799

prune241.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 1.7b

localize45.0ms

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))

rewrite433.0ms

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:

9.0ms	(cbrt (+ m n))
9.0ms	(cbrt (+ m n))
7.0ms	(cbrt (+ m n))
405.0ms	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

series770.0ms

Counts

4 → 12

Calls

4 calls:

208.0ms	(cbrt (+ m n))
202.0ms	(cbrt (+ m n))
200.0ms	(cbrt (+ m n))
160.0ms	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

simplify2.6s

Counts

64 → 64

Iterations

Useful iterations: 4 (739.0ms)

Iter	Nodes	Cost
0	91	868
1	189	835
2	370	653
3	731	602
4	1762	596
done	5001	596

prune555.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 1.7b

localize54.0ms

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))

rewrite778.0ms

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:

8.0ms	(cbrt (+ m n))
8.0ms	(cbrt (+ m n))
261.0ms	(* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (* (cbrt (- m)) (cbrt -1)))
495.0ms	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (* (cbrt (- m)) (cbrt -1))) 2.0) M))

series1.2s

Counts

4 → 12

Calls

4 calls:

175.0ms	(cbrt (+ m n))
219.0ms	(cbrt (+ m n))
237.0ms	(* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (* (cbrt (- m)) (cbrt -1)))
537.0ms	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (* (cbrt (- m)) (cbrt -1))) 2.0) M))

simplify1.5s

Counts

86 → 86

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	191	1700
1	491	1651
2	1673	1417
done	5001	1383

prune693.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 1.7b

regimes305.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 1 (3.0ms)

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

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.9s	8070×	body	80	valid
113.0ms	123×	body	1280	valid
82.0ms	133×	body	640	valid
57.0ms	65×	body	160	valid
42.0ms	102×	body	320	valid
6.0ms	5×	body	2560	valid