Details

Time bar (total: 12.0s)

sample87.0ms

Algorithm
intervals
Results
45.0ms262×body80valid
5.0ms4×body1280valid
1.0ms3×body160valid
1.0ms1×body640valid
1.0ms1×body320valid

simplify58.0ms

Counts
1 → 1

prune31.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.4b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b
(- l (fabs (- m n)))
0.0b
(* K (+ m n))
0.0b
(pow (- (/ (+ m n) 2.0) M) 2.0)
32.7b
(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite173.0ms

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:
7.0ms
(- l (fabs (- m n)))
25.0ms
(* K (+ m n))
104.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
32.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))

series546.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(- l (fabs (- m n)))
48.0ms
(* K (+ m n))
396.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
87.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))

simplify64.0ms

Counts
79 → 79

prune482.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize34.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ 1 (exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))))
0.0b
(- l (fabs (- m n)))
0.0b
(pow (- (/ (+ m n) 2.0) M) 2.0)

rewrite2.6s

Algorithm
rewrite-expression-head
Rules
24×*-un-lft-identity
22×add-sqr-sqrt
15×add-cube-cbrt
13×times-frac
6×unpow-prod-down pow-flip
5×pow1 add-exp-log exp-prod add-cbrt-cube add-log-exp
4×exp-sum associate-/r*
3×pow-unpow associate-/l* distribute-lft-out-- difference-of-squares
2×div-exp distribute-lft-out
1×cbrt-undiv pow-to-exp associate-+r- sub-neg rec-exp flip3-- pow-pow frac-2neg exp-diff diff-log 1-exp pow-exp clear-num associate-/r/ flip-- div-inv inv-pow sqr-pow
Counts
3 → 75
Calls
3 calls:
2.5s
(/ 1 (exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))))
6.0ms
(- l (fabs (- m n)))
107.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)

series663.0ms

Counts
3 → 9
Calls
3 calls:
238.0ms
(/ 1 (exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n))))))
14.0ms
(- l (fabs (- m n)))
410.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify118.0ms

Counts
84 → 84

prune357.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.4b

localize70.0ms

Local error

Found 4 expressions with local error:

0.0b
(pow (- (/ (+ m n) 2.0) M) 2.0)
0.1b
(exp (cos (- (/ (* K (+ m n)) 2.0) M)))
0.6b
(log (exp (cos (- (/ (* K (+ m n)) 2.0) M))))
32.7b
(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite255.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
11×*-un-lft-identity
9×add-cube-cbrt
6×pow1 unpow-prod-down cos-sum exp-prod
5×add-exp-log add-log-exp
4×log-prod exp-diff log-pow add-cbrt-cube
3×cos-diff sub-neg pow-unpow
2×log-div exp-sum difference-of-squares
1×pow-to-exp pow-pow times-frac rem-log-exp pow-exp rem-exp-log distribute-lft-out-- sqr-pow
Counts
4 → 62
Calls
4 calls:
83.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
44.0ms
(exp (cos (- (/ (* K (+ m n)) 2.0) M)))
84.0ms
(log (exp (cos (- (/ (* K (+ m n)) 2.0) M))))
40.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))

series712.0ms

Counts
4 → 12
Calls
4 calls:
411.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
124.0ms
(exp (cos (- (/ (* K (+ m n)) 2.0) M)))
80.0ms
(log (exp (cos (- (/ (* K (+ m n)) 2.0) M))))
96.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))

simplify68.0ms

Counts
74 → 74

prune477.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.4b

localize47.0ms

Local error

Found 4 expressions with local error:

0.6b
(log (* (sqrt (exp (cos (- (/ (* K (+ m n)) 2.0) M)))) (sqrt (exp (cos (- (/ (* K (+ m n)) 2.0) M))))))
0.6b
(* (sqrt (exp (cos (- (/ (* K (+ m n)) 2.0) M)))) (sqrt (exp (cos (- (/ (* K (+ m n)) 2.0) M)))))
32.7b
(cos (- (/ (* K (+ m n)) 2.0) M))
32.7b
(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite717.0ms

Algorithm
rewrite-expression-head
Rules
52×sqrt-pow1
36×add-sqr-sqrt exp-prod
35×pow1
28×cos-sum
24×add-cube-cbrt *-un-lft-identity exp-diff sqrt-div
23×log-pow
22×sqrt-prod
16×pow1/2 pow-prod-up
14×sub-neg
12×pow-prod-down pow-sqr
9×add-exp-log swap-sqr
8×frac-times log-div
7×associate-*r* associate-*l*
6×cos-diff add-cbrt-cube
4×associate-*r/ exp-sum associate-*l/ add-log-exp unswap-sqr
2×pow2 pow-plus rem-log-exp prod-exp
1×log-prod sqrt-unprod rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 130
Calls
4 calls:
362.0ms
(log (* (sqrt (exp (cos (- (/ (* K (+ m n)) 2.0) M)))) (sqrt (exp (cos (- (/ (* K (+ m n)) 2.0) M))))))
269.0ms
(* (sqrt (exp (cos (- (/ (* K (+ m n)) 2.0) M)))) (sqrt (exp (cos (- (/ (* K (+ m n)) 2.0) M)))))
43.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))
30.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))

series368.0ms

Counts
4 → 12
Calls
4 calls:
83.0ms
(log (* (sqrt (exp (cos (- (/ (* K (+ m n)) 2.0) M)))) (sqrt (exp (cos (- (/ (* K (+ m n)) 2.0) M))))))
120.0ms
(* (sqrt (exp (cos (- (/ (* K (+ m n)) 2.0) M)))) (sqrt (exp (cos (- (/ (* K (+ m n)) 2.0) M)))))
79.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))
86.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))

simplify55.0ms

Counts
142 → 142

prune795.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.4b

regimes172.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify98.0ms

end0.0ms

sample3.0s

Algorithm
intervals
Results
2.1s8079×body80valid
137.0ms122×body1280valid
89.0ms152×body640valid
46.0ms105×body320valid
18.0ms62×body160valid
4.0ms3×body2560valid