Details

sample99.0ms

Algorithm

intervals

Results

49.0ms	259×	body	80	valid
4.0ms	5×	body	640	valid
4.0ms	3×	body	1280	valid
1.0ms	2×	body	160	valid
1.0ms	1×	body	320	valid

simplify4.8s

Counts

1 → 1

Iterations

Useful iterations: 4 (201.0ms)

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

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.3b

localize49.0ms

Local error

Found 4 expressions with local error:

0.0b	(* K (+ m n))
0.0b	(- (/ (* K (+ m n)) 2.0) M)
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
30.4b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite221.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 67

Calls

4 calls:

42.0ms	(* K (+ m n))
37.0ms	(- (/ (* K (+ m n)) 2.0) M)
75.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
63.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series659.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* K (+ m n))
90.0ms	(- (/ (* K (+ m n)) 2.0) M)
413.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
115.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify1.8s

Counts

79 → 79

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	167	995
1	379	940
2	921	869
3	2845	862
done	5000	854

prune483.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 1.0b

localize34.0ms

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)

rewrite374.0ms

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))
104.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series647.0ms

Counts

2 → 6

Calls

2 calls:

290.0ms	(- (- (fabs (- m n)) l) (pow (- (/ (+ m n) 2.0) M) 2.0))
357.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify1.4s

Counts

47 → 47

Iterations

Useful iterations: done (1.4s)

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

prune190.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 1.0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (+ m n))
0.5b	(cbrt (+ m n))
0.5b	(cbrt (+ m n))
30.4b	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

rewrite427.0ms

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:

7.0ms	(cbrt (+ m n))
7.0ms	(cbrt (+ m n))
7.0ms	(cbrt (+ m n))
404.0ms	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

series813.0ms

Counts

4 → 12

Calls

4 calls:

205.0ms	(cbrt (+ m n))
239.0ms	(cbrt (+ m n))
209.0ms	(cbrt (+ m n))
159.0ms	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2.0) M))

simplify2.9s

Counts

64 → 64

Iterations

Useful iterations: 4 (645.0ms)

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

prune523.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 1.0b

localize51.0ms

Local error

Found 4 expressions with local error:

13.8b	(cbrt (* K (+ m n)))
13.8b	(cbrt (* K (+ m n)))
13.8b	(cbrt (* K (+ m n)))
30.5b	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))

rewrite139.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 43

Calls

4 calls:

14.0ms	(cbrt (* K (+ m n)))
18.0ms	(cbrt (* K (+ m n)))
14.0ms	(cbrt (* K (+ m n)))
91.0ms	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))

series535.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(cbrt (* K (+ m n)))
144.0ms	(cbrt (* K (+ m n)))
155.0ms	(cbrt (* K (+ m n)))
94.0ms	(cos (- (/ (* (* (cbrt (* K (+ m n))) (cbrt (* K (+ m n)))) (cbrt (* K (+ m n)))) 2.0) M))

simplify2.4s

Counts

55 → 55

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	86	881
1	186	859
2	355	602
3	714	545
4	1391	521
5	3182	506
done	5001	500

prune416.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 1.0b

regimes268.0ms

Accuracy

0% (0.2b remaining)

Error of 1.4b against oracle of 1.2b and baseline of 1.4b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	16	19
1	20	17
done	20	17

end0.0ms

sample3.0s

Algorithm

intervals

Results

2.1s	8098×	body	80	valid
113.0ms	129×	body	1280	valid
91.0ms	153×	body	640	valid
41.0ms	94×	body	320	valid
17.0ms	56×	body	160	valid
3.0ms	2×	body	2560	valid