Details

sample98.0ms

Algorithm

intervals

Results

55.0ms	257×	body	80	valid
11.0ms	9×	body	640	valid
5.0ms	5×	body	1280	valid
2.0ms	4×	body	320	valid
1.0ms	4×	body	160	valid

simplify1.3s

Counts

1 → 1

Iterations

Iter	Nodes
5	2910
4	776
3	248
2	100
1	51
0	21

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.5b

localize66.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ (+ m n) 2) M)
0.0b	(* K (+ m n))
0.0b	(pow (- (/ (+ m n) 2) M) 2)
35.9b	(cos (- (/ (* K (+ m n)) 2) M))

rewrite184.0ms

Algorithm

rewrite-expression-head

Rules

20×	`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` `insert-posit16` `difference-of-squares`
3×	`pow-unpow` `associate-l`
2×	`cos-sum` `sub-neg` `times-frac` `associate-*r/` `distribute-lft-out--`
1×	`distribute-rgt-in` `cos-diff` `pow-to-exp` `pow-pow` `distribute-lft-in` `flip3-+` `flip3--` `diff-log` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `flip--` `distribute-lft-out` `unpow2` `unswap-sqr` `sqr-pow`

Counts

4 → 73

Calls

4 calls:

58.0ms	(- (/ (+ m n) 2) M)
26.0ms	(* K (+ m n))
71.0ms	(pow (- (/ (+ m n) 2) M) 2)
27.0ms	(cos (- (/ (* K (+ m n)) 2) M))

series266.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (/ (+ m n) 2) M)
49.0ms	(* K (+ m n))
103.0ms	(pow (- (/ (+ m n) 2) M) 2)
81.0ms	(cos (- (/ (* K (+ m n)) 2) M))

simplify1.0s

Counts

85 → 85

Iterations

Iter	Nodes
3	2759
2	937
1	370
0	152

prune1.8s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.5b

localize42.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (/ (+ m n) 2) M)
0.0b	(pow (- (/ (+ m n) 2) M) 2)

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
8×	`*-un-lft-identity`
6×	`unpow-prod-down`
4×	`add-cube-cbrt` `add-log-exp` `difference-of-squares`
3×	`pow1` `pow-unpow` `add-exp-log`
2×	`times-frac` `add-cbrt-cube` `insert-posit16` `distribute-lft-out--`
1×	`pow-to-exp` `sub-neg` `pow-pow` `flip3--` `diff-log` `pow-exp` `flip--` `unpow2` `sqr-pow`

Counts

2 → 38

Calls

2 calls:

60.0ms	(- (/ (+ m n) 2) M)
53.0ms	(pow (- (/ (+ m n) 2) M) 2)

series106.0ms

Counts

2 → 6

Calls

2 calls:

28.0ms	(- (/ (+ m n) 2) M)
78.0ms	(pow (- (/ (+ m n) 2) M) 2)

simplify1.3s

Counts

44 → 44

Iterations

Iter	Nodes
4	2854
3	1098
2	486
1	209
0	85

prune671.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.5b

localize90.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (+ m n))
0.6b	(cbrt (+ m n))
0.6b	(cbrt (+ m n))
36.1b	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2) M))

rewrite274.0ms

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-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out`
2×	`cos-sum`
1×	`cos-diff` `sub-neg`

Counts

4 → 56

Calls

4 calls:

5.0ms	(cbrt (+ m n))
5.0ms	(cbrt (+ m n))
5.0ms	(cbrt (+ m n))
257.0ms	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2) M))

series630.0ms

Counts

4 → 12

Calls

4 calls:

178.0ms	(cbrt (+ m n))
156.0ms	(cbrt (+ m n))
143.0ms	(cbrt (+ m n))
152.0ms	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) 2) M))

simplify795.0ms

Counts

68 → 68

Iterations

Iter	Nodes
4	2041
3	879
2	391
1	187
0	92

prune1.7s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.5b

localize87.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (cbrt (+ m n)))
0.6b	(cbrt (cbrt (+ m n)))
0.6b	(cbrt (cbrt (+ m n)))
35.8b	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (* (* (cbrt (cbrt (+ m n))) (cbrt (cbrt (+ m n)))) (cbrt (cbrt (+ m n))))) 2) M))

rewrite419.0ms

Algorithm

rewrite-expression-head

Rules

33×	`cbrt-prod`
16×	`*-un-lft-identity`
12×	`cbrt-div`
10×	`add-sqr-sqrt` `add-cube-cbrt`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out`
2×	`cos-sum`
1×	`cos-diff` `sub-neg`

Counts

4 → 65

Calls

4 calls:

3.0ms	(cbrt (cbrt (+ m n)))
3.0ms	(cbrt (cbrt (+ m n)))
3.0ms	(cbrt (cbrt (+ m n)))
410.0ms	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (* (* (cbrt (cbrt (+ m n))) (cbrt (cbrt (+ m n)))) (cbrt (cbrt (+ m n))))) 2) M))

series1.0s

Counts

4 → 12

Calls

4 calls:

267.0ms	(cbrt (cbrt (+ m n)))
302.0ms	(cbrt (cbrt (+ m n)))
341.0ms	(cbrt (cbrt (+ m n)))
128.0ms	(cos (- (/ (* (* K (* (cbrt (+ m n)) (cbrt (+ m n)))) (* (* (cbrt (cbrt (+ m n))) (cbrt (cbrt (+ m n)))) (cbrt (cbrt (+ m n))))) 2) M))

simplify1.1s

Counts

77 → 77

Iterations

Iter	Nodes
4	2793
3	1110
2	455
1	209
0	107

prune1.8s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 1.5b

regimes741.0ms

Accuracy

0% (0.3b remaining)

Error of 1.4b against oracle of 1.1b and baseline of 1.4b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
2	19
1	19
0	17

end0.0ms

sample3.5s

Algorithm

intervals

Results

2.8s	8092×	body	80	valid
169.0ms	101×	body	1280	valid
166.0ms	162×	body	640	valid
81.0ms	112×	body	320	valid
21.0ms	48×	body	160	valid
3.0ms	2×	body	2560	valid