Details

sample66.0ms

Algorithm

intervals

Results

41.0ms	266×	body	80	valid
1.0ms	2×	body	1280	valid
1.0ms	4×	body	160	valid
0.0ms	1×	body	320	valid

simplify771.0ms

Counts: 1 → 1

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.6b

localize56.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ (* K (+ m n)) 2.0) M)
0.0b	(pow (- (/ (+ m n) 2.0) M) 2.0)
0.0b	(* K (+ m n))
37.2b	(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite194.0ms

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:

32.0ms	(- (/ (* K (+ m n)) 2.0) M)
78.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
20.0ms	(* K (+ m n))
63.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

series586.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(- (/ (* K (+ m n)) 2.0) M)
377.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)
42.0ms	(* K (+ m n))
84.0ms	(cos (- (/ (* K (+ m n)) 2.0) M))

simplify624.0ms

Counts: 79 → 79

prune517.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize21.0ms

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)

rewrite1.6s

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:

1.5s	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
76.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

series672.0ms

Counts

2 → 6

Calls

2 calls:

322.0ms	(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
349.0ms	(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify1.3s

Counts: 50 → 50

prune227.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

localize37.0ms

Local error

Found 4 expressions with local error:

0.0b	(* K (+ m n))
1.9b	(exp (log (* K (+ m n))))
9.0b	(log (* K (+ m n)))
17.9b	(cos (- (/ (exp (log (* K (+ m n)))) 2.0) M))

rewrite248.0ms

Algorithm

rewrite-expression-head

Rules

12×	`pow1`
9×	`add-exp-log` `add-sqr-sqrt` `*-un-lft-identity`
7×	`add-cube-cbrt`
6×	`associate-*r/` `add-cbrt-cube`
5×	`exp-prod`
4×	`log-div` `associate-r` `log-pow` `add-log-exp`
3×	`flip3-+` `associate-l` `pow-prod-down` `flip-+`
2×	`cos-sum` `log-prod` `exp-diff` `rem-log-exp` `prod-exp`
1×	`distribute-rgt-in` `cos-diff` `sub-neg` `distribute-lft-in` `exp-sum` `*-commutative` `cbrt-unprod` `rem-exp-log` `distribute-lft-out` `unswap-sqr`

Counts

4 → 63

Calls

4 calls:

27.0ms	(* K (+ m n))
25.0ms	(exp (log (* K (+ m n))))
9.0ms	(log (* K (+ m n)))
184.0ms	(cos (- (/ (exp (log (* K (+ m n)))) 2.0) M))

series297.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* K (+ m n))
49.0ms	(exp (log (* K (+ m n))))
106.0ms	(log (* K (+ m n)))
96.0ms	(cos (- (/ (exp (log (* K (+ m n)))) 2.0) M))

simplify1.2s

Counts: 75 → 75

prune514.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

localize88.0ms

Local error

Found 4 expressions with local error:

1.4b	(pow (exp (sqrt (log (* K (+ m n))))) (sqrt (log (* K (+ m n)))))
9.0b	(log (* K (+ m n)))
9.0b	(log (* K (+ m n)))
18.0b	(cos (- (/ (pow (exp (sqrt (log (* K (+ m n))))) (sqrt (log (* K (+ m n))))) 2.0) M))

rewrite356.0ms

Algorithm

rewrite-expression-head

Rules

17×	`pow1`
10×	`add-exp-log` `sqrt-prod`
9×	`add-sqr-sqrt` `add-cube-cbrt` `pow-pow` `*-un-lft-identity`
8×	`pow-unpow` `exp-prod` `log-pow`
4×	`log-div` `associate-*r/` `rem-log-exp` `pow-prod-down` `add-cbrt-cube` `add-log-exp`
3×	`unpow-prod-down`
2×	`cos-sum` `log-prod` `flip3-+` `prod-exp` `flip-+`
1×	`cos-diff` `pow-to-exp` `sub-neg` `pow-exp` `sqr-pow`

Counts

4 → 68

Calls

4 calls:

48.0ms	(pow (exp (sqrt (log (* K (+ m n))))) (sqrt (log (* K (+ m n)))))
10.0ms	(log (* K (+ m n)))
9.0ms	(log (* K (+ m n)))
287.0ms	(cos (- (/ (pow (exp (sqrt (log (* K (+ m n))))) (sqrt (log (* K (+ m n))))) 2.0) M))

series808.0ms

Counts

4 → 12

Calls

4 calls:

233.0ms	(pow (exp (sqrt (log (* K (+ m n))))) (sqrt (log (* K (+ m n)))))
76.0ms	(log (* K (+ m n)))
80.0ms	(log (* K (+ m n)))
418.0ms	(cos (- (/ (pow (exp (sqrt (log (* K (+ m n))))) (sqrt (log (* K (+ m n))))) 2.0) M))

simplify911.0ms

Counts: 80 → 80

prune663.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

regimes269.0ms

Accuracy

0% (0.1b remaining)

Error of 1.4b against oracle of 1.3b and baseline of 1.4b

bsearch0.0ms

simplify852.0ms

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.9s	8071×	body	80	valid
241.0ms	126×	body	1280	valid
128.0ms	143×	body	640	valid
90.0ms	108×	body	320	valid
22.0ms	68×	body	160	valid
7.0ms	5×	body	2560	valid