Details

sample73.0ms

Algorithm

intervals

Results

31.0ms	249×	body	80	valid
6.0ms	9×	body	1280	valid
4.0ms	6×	body	640	valid
1.0ms	3×	body	320	valid
1.0ms	3×	body	160	valid

simplify4.8s

Counts

1 → 1

Iterations

Useful iterations: 4 (176.0ms)

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.3b

localize31.0ms

Local error

Found 4 expressions with local error:

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

rewrite488.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
9×	`add-log-exp`
8×	`add-cube-cbrt`
7×	`pow1` `add-exp-log` `unpow-prod-down`
6×	`add-cbrt-cube`
5×	`difference-of-squares`
4×	`associate-r` `distribute-lft-out--`
3×	`sub-neg` `pow-unpow` `diff-log` `associate-l`
2×	`cos-sum` `associate-*r/` `associate--l+` `sqr-pow`
1×	`associate--l-` `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` `unswap-sqr`

Counts

4 → 74

Calls

4 calls:

282.0ms	(- (- (fabs (- m n)) l) (pow (- (/ (+ m n) 2.0) M) 2.0))
94.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
38.0ms	(* K (+ m n))
69.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series803.0ms

Counts

4 → 12

Calls

4 calls:

267.0ms	(- (- (fabs (- m n)) l) (pow (- (/ (+ m n) 2.0) M) 2.0))
407.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
40.0ms	(* K (+ m n))
89.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify1.9s

Counts

86 → 86

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	187	1305
1	418	1230
2	997	1151
3	2981	1145
done	5000	1137

prune502.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 1.7b

localize24.0ms

Local error

Found 2 expressions with local error:

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

rewrite338.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 41

Calls

2 calls:

267.0ms	(- (- (fabs (- m n)) l) (pow (- (/ (+ m n) 2.0) M) 2.0))
69.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series647.0ms

Counts

2 → 6

Calls

2 calls:

271.0ms	(- (- (fabs (- m n)) l) (pow (- (/ (+ m n) 2.0) M) 2.0))
376.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify1.8s

Counts

47 → 47

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	120	902
1	261	848
2	556	809
3	1585	803
done	5001	791

prune233.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 1.7b

localize35.0ms

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))

rewrite423.0ms

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:

4.0ms	(cbrt (+ m n))
5.0ms	(cbrt (+ m n))
10.0ms	(cbrt (+ m n))
401.0ms	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

series700.0ms

Counts

4 → 12

Calls

4 calls:

179.0ms	(cbrt (+ m n))
173.0ms	(cbrt (+ m n))
189.0ms	(cbrt (+ m n))
159.0ms	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

simplify2.7s

Counts

64 → 64

Iterations

Useful iterations: 4 (711.0ms)

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

prune513.0ms

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))

rewrite632.0ms

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))
227.0ms	(* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (* (cbrt (- m)) (cbrt -1)))
384.0ms	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (* (cbrt (- m)) (cbrt -1))) 2.0) M))

series1.1s

Counts

4 → 12

Calls

4 calls:

198.0ms	(cbrt (+ m n))
224.0ms	(cbrt (+ m n))
235.0ms	(* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (* (cbrt (- m)) (cbrt -1)))
472.0ms	(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

prune675.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 1.7b

regimes323.0ms

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	16	19
1	20	17
done	20	17

end0.0ms

sample3.0s

Algorithm

intervals

Results

2.1s	8070×	body	80	valid
125.0ms	133×	body	640	valid
107.0ms	123×	body	1280	valid
80.0ms	102×	body	320	valid
22.0ms	65×	body	160	valid
7.0ms	5×	body	2560	valid