Details

Time bar (total: 3.5s)

sample121.0ms

Algorithm
intervals
Results
35.0ms129×body80valid
35.0ms53×body1280valid
18.0ms37×body640valid
10.0ms31×body320valid
1.0msbody160valid

simplify2.8s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01724
13424
27224
313324
419424
531524
675424
7253924
done500124

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.7b

localize50.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* -2.0 J) (cos (/ K 2.0)))
0.2b
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
6.2b
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
11.3b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite447.0ms

Algorithm
rewrite-expression-head
Rules
28×add-exp-log
20×pow1
18×add-cbrt-cube
17×add-sqr-sqrt
15×*-un-lft-identity
12×prod-exp
11×add-cube-cbrt
10×associate-*r*
pow-prod-down cbrt-unprod
unpow-prod-down sqrt-prod
expm1-log1p-u sqrt-div pow-exp log1p-expm1-u add-log-exp
pow-unpow times-frac div-exp hypot-def
flip3-+ associate-*r/ associate-*l* *-commutative flip-+ distribute-lft-out sqr-pow
pow-to-exp rem-sqrt-square pow-pow sqrt-pow1 pow1/2 div-inv
Counts
4 → 96
Calls
4 calls:
27.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
44.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
284.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
89.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series1.0ms