Details

Time bar (total: 14.7s)

sample79.0ms

Algorithm
intervals
Results
22.0ms140×body80valid
19.0ms41×body1280valid
13.0ms39×body640valid
7.0ms25×body320valid
2.0ms11×body160valid

simplify4.2s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
017636
134636
268636
3112636
4165636
5277636
6720636
72651636
done5042636

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.4b

localize46.0ms

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)
7.5b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
8.7b
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

rewrite255.0ms

Algorithm
rewrite-expression-head
Rules
28×add-exp-log
20×pow1
18×add-cbrt-cube
15×*-un-lft-identity
12×add-sqr-sqrt prod-exp
11×add-cube-cbrt
10×associate-*r*
9×pow-prod-down cbrt-unprod
8×sqrt-prod
7×unpow-prod-down
4×sqrt-div pow-exp add-log-exp
3×pow-unpow times-frac div-exp
2×flip3-+ associate-*l* associate-*r/ *-commutative flip-+ distribute-lft-out
1×pow-to-exp rem-sqrt-square pow-pow sqrt-pow1 pow1/2 div-inv sqr-pow
Counts
4 → 85
Calls
4 calls:
22.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
17.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
70.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
142.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

series695.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(* (* -2.0 J) (cos (/ K 2.0)))
147.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
212.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
267.0ms
(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

simplify2.4s

Counts
97 → 97
Iterations

Useful iterations: done (2.4s)

IterNodesCost
019249466
149646775
2152346535
done500046295

prune720.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 12.2b

localize42.0ms

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)
7.5b
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
8.8b
(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))

rewrite309.0ms

Algorithm
rewrite-expression-head
Rules
31×add-exp-log
23×pow1
21×add-cbrt-cube
14×prod-exp
11×*-un-lft-identity pow-prod-down cbrt-unprod
10×add-sqr-sqrt
9×add-cube-cbrt
7×unpow-prod-down
4×sqrt-div associate-*r* pow-exp associate-*r/ sqrt-prod add-log-exp
3×pow-unpow times-frac div-exp
2×flip3-+ associate-*l* *-commutative flip-+
1×pow-to-exp rem-sqrt-square pow-pow sqrt-pow1 pow1/2 div-inv distribute-lft-out sqr-pow
Counts
4 → 82
Calls
4 calls:
27.0ms
(* (* 2.0 J) (cos (/ K 2.0)))
32.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
92.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
155.0ms
(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))

series725.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(* (* 2.0 J) (cos (/ K 2.0)))
203.0ms
(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
209.0ms
(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
253.0ms
(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))

simplify2.7s

Counts
94 → 94
Iterations

Useful iterations: done (2.7s)

IterNodesCost
019948414
152745706
2168844986
done500144826

prune603.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 12.2b

localize80.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (cos (/ K 2.0)))
0.3b
(cbrt (cos (/ K 2.0)))
7.5b
(sqrt (+ 1.0 (pow (/ U (* (* (* 2.0 J) (* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0))))) (cbrt (cos (/ K 2.0))))) 2.0)))
8.8b
(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* (* (* 2.0 J) (* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0))))) (cbrt (cos (/ K 2.0))))) 2.0)))))

rewrite611.0ms

Algorithm
rewrite-expression-head
Rules
17×pow1
16×add-cbrt-cube add-exp-log
9×*-un-lft-identity
8×add-sqr-sqrt pow-prod-down prod-exp cbrt-unprod
7×add-cube-cbrt
6×cbrt-prod
4×sqrt-div associate-*r/ sqrt-prod add-log-exp
2×flip3-+ pow1/3 flip-+
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-*r* associate-*l* *-commutative distribute-lft-out
Counts
4 → 62
Calls
4 calls:
2.0ms
(cbrt (cos (/ K 2.0)))
2.0ms
(cbrt (cos (/ K 2.0)))
264.0ms
(sqrt (+ 1.0 (pow (/ U (* (* (* 2.0 J) (* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0))))) (cbrt (cos (/ K 2.0))))) 2.0)))
340.0ms
(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* (* (* 2.0 J) (* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0))))) (cbrt (cos (/ K 2.0))))) 2.0)))))

series970.0ms

Counts
4 → 12
Calls
4 calls:
212.0ms
(cbrt (cos (/ K 2.0)))
230.0ms
(cbrt (cos (/ K 2.0)))
226.0ms
(sqrt (+ 1.0 (pow (/ U (* (* (* 2.0 J) (* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0))))) (cbrt (cos (/ K 2.0))))) 2.0)))
301.0ms
(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* (* (* 2.0 J) (* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0))))) (cbrt (cos (/ K 2.0))))) 2.0)))))

simplify189.0ms

Iterations

Useful iterations: 0 (46.0ms)

IterNodesCost
012343112