Details

sample97.0ms

Algorithm

intervals

Results

48.0ms	253×	body	80	valid
3.0ms	4×	body	640	valid
2.0ms	4×	body	320	valid
2.0ms	4×	body	160	valid
1.0ms	1×	body	1280	valid

simplify2.0s

Counts

1 → 1

Iterations

Useful iterations: 4 (134.0ms)

Iter	Nodes	Cost
0	21	29
1	50	29
2	93	29
3	210	29
4	640	28
5	3078	28
done	5000	28

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.5b

localize34.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* K (+ m n)) 2.0)
0.0b	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
0.0b	(* K (+ m n))
37.8b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite1.6s

Algorithm

rewrite-expression-head

Rules

20×	`*-un-lft-identity`
14×	`add-log-exp`
12×	`add-sqr-sqrt`
11×	`add-exp-log` `add-cbrt-cube`
8×	`add-cube-cbrt`
6×	`pow1` `diff-log` `distribute-lft-out--`
4×	`associate-r/` `associate-r*`
3×	`sub-neg` `times-frac` `associate-l` `associate-/r*`
2×	`cbrt-undiv` `cos-sum` `distribute-rgt-neg-in` `flip3-+` `div-exp` `neg-log` `prod-exp` `cbrt-unprod` `flip-+` `associate-/l/` `associate--r+`
1×	`associate--l-` `neg-sub0` `distribute-rgt-in` `cos-diff` `flip3--` `frac-2neg` `distribute-lft-in` `pow-prod-down` `clear-num` `-commutative` `flip--` `div-inv` `distribute-lft-out` `associate-/l` `associate--r-` `difference-of-squares` `unswap-sqr`

Counts

4 → 80

Calls

4 calls:

29.0ms	(/ (* K (+ m n)) 2.0)
1.5s	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
24.0ms	(* K (+ m n))
41.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series475.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(/ (* K (+ m n)) 2.0)
277.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
42.0ms	(* K (+ m n))
79.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify1.4s

Counts

92 → 92

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	170	1279
1	427	1230
2	1761	1100
done	5000	1092

prune581.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.3b

localize22.0ms

Local error

Found 2 expressions with local error:

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

rewrite1.4s

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:

66.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
1.3s	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))

series623.0ms

Counts

2 → 6

Calls

2 calls:

373.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
250.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))

simplify1.9s

Counts

50 → 50

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	122	937
1	312	879
2	833	826
3	3166	809
done	5000	801

prune265.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.3b

localize73.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (cos (- (/ (* K (+ m n)) 2.0) M)))
37.8b	(cos (- (/ (* K (+ m n)) 2.0) M))
37.8b	(cos (- (/ (* K (+ m n)) 2.0) M))
37.8b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite136.0ms

Algorithm

rewrite-expression-head

Rules

6×	`cos-sum`
5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`cbrt-prod` `cos-diff` `sub-neg`
1×	`pow1/3`

Counts

4 → 41

Calls

4 calls:

4.0ms	(cbrt (cos (- (/ (* K (+ m n)) 2.0) M)))
36.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
37.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
58.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series484.0ms

Counts

4 → 12

Calls

4 calls:

221.0ms	(cbrt (cos (- (/ (* K (+ m n)) 2.0) M)))
82.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
93.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
87.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify2.8s

Counts

53 → 53

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	48	853
1	84	812
2	126	730
3	209	727
4	451	727
5	1262	727
6	4297	727
done	5002	687

prune405.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 1.3b

localize45.0ms

Local error

Found 4 expressions with local error:

0.5b	(log (exp (cos (- (/ (* K (+ m n)) 2.0) M))))
37.8b	(cos (- (/ (* K (+ m n)) 2.0) M))
37.8b	(cos (- (/ (* K (+ m n)) 2.0) M))
37.8b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite152.0ms

Algorithm

rewrite-expression-head

Rules

8×	`cos-sum`
6×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
5×	`pow1`
4×	`add-exp-log` `cos-diff` `sub-neg` `log-prod` `log-pow` `add-cbrt-cube` `add-log-exp`
3×	`exp-prod`
2×	`log-div` `exp-diff`
1×	`rem-log-exp` `exp-sum`

Counts

4 → 48

Calls

4 calls:

52.0ms	(log (exp (cos (- (/ (* K (+ m n)) 2.0) M))))
30.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
31.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
37.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series286.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(log (exp (cos (- (/ (* K (+ m n)) 2.0) M))))
65.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
66.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))
63.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify798.0ms

Counts

60 → 60

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	66	1000
1	110	917
2	176	826
3	291	826
4	547	826
5	1314	826
done	5000	826

prune482.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 1.3b

regimes355.0ms

Accuracy

0% (0.2b remaining)

Error of 1.3b against oracle of 1.0b and baseline of 1.3b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	17	20
1	21	18
2	22	18
done	22	18

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.9s	8095×	body	80	valid
101.0ms	149×	body	640	valid
84.0ms	101×	body	1280	valid
41.0ms	90×	body	320	valid
16.0ms	55×	body	160	valid
3.0ms	2×	body	2560	valid