Details

Time bar (total: 2.8s)

sample41.0ms

Algorithm
intervals
Results
20.0ms259×body80valid
2.0msbody640valid
1.0msbody2560valid
1.0msbody320valid
0.0msbody1280valid

simplify916.0ms

Counts
1 → 1
Iterations

Useful iterations: 4 (63.0ms)

IterNodesCost
02129
15029
29229
320229
446228
5152728
done500028

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.6b

localize22.0ms

Local error

Found 3 expressions with local error:

0.0b
(- (/ (* K (+ m n)) 2.0) M)
0.0b
(pow (- (/ (+ m n) 2.0) M) 2.0)
35.4b
(cos (- (/ (* K (+ m n)) 2.0) M))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
*-un-lft-identity
unpow-prod-down
add-cube-cbrt add-log-exp
pow1 add-exp-log
pow-unpow add-cbrt-cube difference-of-squares
sub-neg cos-sum distribute-lft-out--
cos-diff pow-to-exp flip3-- pow-pow times-frac diff-log pow-exp flip-- sqr-pow
Counts
3 → 44
Calls
3 calls:
9.0ms
(- (/ (* K (+ m n)) 2.0) M)
34.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
15.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))

series384.0ms

Counts
3 → 9
Calls
3 calls:
55.0ms
(- (/ (* K (+ m n)) 2.0) M)
272.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)
57.0ms
(cos (- (/ (* K (+ m n)) 2.0) M))

simplify539.0ms

Counts
53 → 53
Iterations

Useful iterations: 3 (169.0ms)

IterNodesCost
0130801
1275757
2580706
31455699
done5000699

prune230.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 1.0b

localize19.0ms

Local error

Found 1 expressions with local error:

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

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
add-sqr-sqrt
unpow-prod-down
*-un-lft-identity
add-cube-cbrt pow-unpow
pow1 add-exp-log difference-of-squares
pow-to-exp pow-pow times-frac pow-exp add-cbrt-cube distribute-lft-out-- add-log-exp sqr-pow
Counts
1 → 20
Calls
1 calls:
31.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)

series270.0ms

Counts
1 → 3
Calls
1 calls:
270.0ms
(pow (- (/ (+ m n) 2.0) M) 2.0)

simplify244.0ms

Iterations

Useful iterations: 3 (92.0ms)

IterNodesCost
074337
1159318
2322305
3718304