Details

Time bar (total: 4.7m)

sample161.0ms

Algorithm
intervals
Results
48.0ms40×body1280valid
43.0ms146×body80valid
34.0ms42×body640valid
11.0ms13×body320valid
6.0ms15×body160valid

simplify576.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
576.0ms
(* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))

prune24.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.6b

localize52.0ms

Local error

Found 4 expressions with local error:

10.8b
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
7.6b
(* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (* (cos (/ K 2)) J))
0.2b
(* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J))))
0.1b
(/ U (* 2 (* (cos (/ K 2)) J)))

rewrite685.0ms

Algorithm
rewrite-expression-head
Rules
105×add-cbrt-cube add-exp-log
51×prod-exp cbrt-unprod
27×cbrt-undiv div-exp
24×pow1
18×add-sqr-sqrt
15×*-un-lft-identity times-frac add-cube-cbrt
9×pow-prod-down
8×associate-*r* associate-*l*
7×swap-sqr
5×associate-*l/ div-inv
4×sqrt-div insert-posit16 add-log-exp
3×sqrt-prod associate-/l*
2×flip3-+ *-commutative flip-+
1×pow2 frac-times rem-sqrt-square clear-num associate-/r* frac-2neg sqrt-pow1 pow-plus pow1/2 associate-*r/ pow-sqr pow-prod-up unswap-sqr
Counts
4 → 136
Calls
4 calls:
Slowest
378.0ms
(* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (* (cos (/ K 2)) J))
157.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
132.0ms
(* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J))))
14.0ms
(/ U (* 2 (* (cos (/ K 2)) J)))

series543.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
186.0ms
(* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (* (cos (/ K 2)) J))
132.0ms
(* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J))))
118.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
107.0ms
(/ U (* 2 (* (cos (/ K 2)) J)))

simplify1.0m

Counts
161 → 148
Calls
161 calls:
Slowest
2.2s
(* (/ (* (* U U) U) (* (* (* 2 2) 2) (* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* J J) J)))) (/ (* (* U U) U) (* (* (* 2 2) 2) (* (* (* (cos (/ K 2)) J) (* (cos (/ K 2)) J)) (* (cos (/ K 2)) J)))))
2.0s
(* (/ (* (* U U) U) (* (* (* 2 2) 2) (* (* (* (cos (/ K 2)) J) (* (cos (/ K 2)) J)) (* (cos (/ K 2)) J)))) (/ (* (* U U) U) (* (* (* 2 2) 2) (* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* J J) J)))))
2.0s
(* (/ (* (* U U) U) (* (* (* 2 2) 2) (* (* (* (cos (/ K 2)) J) (* (cos (/ K 2)) J)) (* (cos (/ K 2)) J)))) (/ (* (* U U) U) (* (* (* 2 (* (cos (/ K 2)) J)) (* 2 (* (cos (/ K 2)) J))) (* 2 (* (cos (/ K 2)) J)))))
1.9s
(* (/ (* (* U U) U) (* (* (* 2 (* (cos (/ K 2)) J)) (* 2 (* (cos (/ K 2)) J))) (* 2 (* (cos (/ K 2)) J)))) (/ (* (* U U) U) (* (* (* 2 2) 2) (* (* (* (cos (/ K 2)) J) (* (cos (/ K 2)) J)) (* (cos (/ K 2)) J)))))
1.7s
(* (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) (/ U (* 2 (* (cos (/ K 2)) J)))) (/ (* (* U U) U) (* (* (* 2 2) 2) (* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* J J) J)))))

prune2.0s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 9.0b

localize89.0ms

Local error

Found 4 expressions with local error:

10.8b
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
10.8b
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
10.8b
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
7.6b
(* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (* (cos (/ K 2)) J))

rewrite860.0ms

Algorithm
rewrite-expression-head
Rules
19×pow1
16×add-cbrt-cube add-exp-log
10×add-sqr-sqrt
9×sqrt-prod
8×sqrt-div pow-prod-down prod-exp cbrt-unprod
7×*-un-lft-identity add-cube-cbrt
4×flip3-+ associate-*l/ flip-+ insert-posit16 add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
1×associate-*r* associate-*l* *-commutative
Counts
4 → 73
Calls
4 calls:
Slowest
326.0ms
(* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (* (cos (/ K 2)) J))
194.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
184.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
154.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))

series656.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
224.0ms
(* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (* (cos (/ K 2)) J))
154.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
147.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
131.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))

simplify29.8s

Counts
93 → 85
Calls
93 calls:
Slowest
782.0ms
(sqrt (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)))
631.0ms
(* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))) (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)))
623.0ms
(* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))) (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)))
573.0ms
(* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))) (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)))
510.0ms
(* (* (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (* (cos (/ K 2)) J)) (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (* (cos (/ K 2)) J))) (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (* (cos (/ K 2)) J)))

prune1.9s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 9.0b

localize98.0ms

Local error

Found 4 expressions with local error:

22.4b
(/ (* (* (sqrt (+ 1 (* (* (* (/ U (* (* (cos (/ K 2)) J) 2)) (/ U (* (* (cos (/ K 2)) J) 2))) (* (/ U (* (* (cos (/ K 2)) J) 2)) (/ U (* (* (cos (/ K 2)) J) 2)))) (* (/ U (* (* (cos (/ K 2)) J) 2)) (/ U (* (* (cos (/ K 2)) J) 2)))))) (* (cos (/ K 2)) J)) -2) (sqrt (+ (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J))))) (- (* 1 1) (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)))))
15.6b
(+ (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J))))) (- (* 1 1) (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)))
5.4b
(sqrt (+ (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J))))) (- (* 1 1) (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))))
3.3b
(* (sqrt (+ 1 (* (* (* (/ U (* (* (cos (/ K 2)) J) 2)) (/ U (* (* (cos (/ K 2)) J) 2))) (* (/ U (* (* (cos (/ K 2)) J) 2)) (/ U (* (* (cos (/ K 2)) J) 2)))) (* (/ U (* (* (cos (/ K 2)) J) 2)) (/ U (* (* (cos (/ K 2)) J) 2)))))) (* (cos (/ K 2)) J))

rewrite7.6s

Algorithm
rewrite-expression-head
Rules
102×frac-times
90×frac-add
72×associate-*l/
68×sqrt-div
66×associate-*r/
45×flip3-- flip--
32×associate-/r/
23×add-cbrt-cube add-exp-log
12×add-sqr-sqrt sqrt-prod
11×*-un-lft-identity add-cube-cbrt
10×pow1
9×prod-exp cbrt-unprod add-log-exp
6×associate-/r* times-frac associate-*l*
5×flip3-+ flip-+
4×cbrt-undiv div-exp insert-posit16
3×pow-prod-down
2×associate-+r+ sum-log associate-/l/
1×+-commutative rem-sqrt-square clear-num associate-+r- sub-neg frac-2neg sqrt-pow1 pow1/2 diff-log associate-*r* *-commutative div-inv associate-/l*
Counts
4 → 182
Calls
4 calls:
Slowest
3.1s
(/ (* (* (sqrt (+ 1 (* (* (* (/ U (* (* (cos (/ K 2)) J) 2)) (/ U (* (* (cos (/ K 2)) J) 2))) (* (/ U (* (* (cos (/ K 2)) J) 2)) (/ U (* (* (cos (/ K 2)) J) 2)))) (* (/ U (* (* (cos (/ K 2)) J) 2)) (/ U (* (* (cos (/ K 2)) J) 2)))))) (* (cos (/ K 2)) J)) -2) (sqrt (+ (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J))))) (- (* 1 1) (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)))))
2.9s
(sqrt (+ (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J))))) (- (* 1 1) (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))))
1.5s
(+ (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J))))) (- (* 1 1) (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)))
50.0ms
(* (sqrt (+ 1 (* (* (* (/ U (* (* (cos (/ K 2)) J) 2)) (/ U (* (* (cos (/ K 2)) J) 2))) (* (/ U (* (* (cos (/ K 2)) J) 2)) (/ U (* (* (cos (/ K 2)) J) 2)))) (* (/ U (* (* (cos (/ K 2)) J) 2)) (/ U (* (* (cos (/ K 2)) J) 2)))))) (* (cos (/ K 2)) J))

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
440.0ms
(/ (* (* (sqrt (+ 1 (* (* (* (/ U (* (* (cos (/ K 2)) J) 2)) (/ U (* (* (cos (/ K 2)) J) 2))) (* (/ U (* (* (cos (/ K 2)) J) 2)) (/ U (* (* (cos (/ K 2)) J) 2)))) (* (/ U (* (* (cos (/ K 2)) J) 2)) (/ U (* (* (cos (/ K 2)) J) 2)))))) (* (cos (/ K 2)) J)) -2) (sqrt (+ (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J))))) (- (* 1 1) (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)))))
324.0ms
(* (sqrt (+ 1 (* (* (* (/ U (* (* (cos (/ K 2)) J) 2)) (/ U (* (* (cos (/ K 2)) J) 2))) (* (/ U (* (* (cos (/ K 2)) J) 2)) (/ U (* (* (cos (/ K 2)) J) 2)))) (* (/ U (* (* (cos (/ K 2)) J) 2)) (/ U (* (* (cos (/ K 2)) J) 2)))))) (* (cos (/ K 2)) J))
244.0ms
(sqrt (+ (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J))))) (- (* 1 1) (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))))
160.0ms
(+ (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J))))) (- (* 1 1) (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)))

simplify2.6m

Counts
264 → 194
Calls
264 calls:
Slowest
1.7s
(sqrt (+ (* (* (* U (/ U (* 2 (* (cos (/ K 2)) J)))) (* U (/ U (* 2 (* (cos (/ K 2)) J))))) (+ (* (* 1 1) (* 1 1)) (+ (* (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1) (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) (* (* 1 1) (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))))) (* (* (* 2 (* (cos (/ K 2)) J)) (* 2 (* (cos (/ K 2)) J))) (- (pow (* 1 1) 3) (pow (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1) 3)))))
1.5s
(sqrt (+ (* (* (* U U) (* U (/ U (* 2 (* (cos (/ K 2)) J))))) (+ (* (* 1 1) (* 1 1)) (+ (* (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1) (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) (* (* 1 1) (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))))) (* (* (* (* 2 (* (cos (/ K 2)) J)) (* 2 (* (cos (/ K 2)) J))) (* 2 (* (cos (/ K 2)) J))) (- (pow (* 1 1) 3) (pow (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1) 3)))))
1.5s
(* (* (/ (* (* (sqrt (+ 1 (* (* (* (/ U (* (* (cos (/ K 2)) J) 2)) (/ U (* (* (cos (/ K 2)) J) 2))) (* (/ U (* (* (cos (/ K 2)) J) 2)) (/ U (* (* (cos (/ K 2)) J) 2)))) (* (/ U (* (* (cos (/ K 2)) J) 2)) (/ U (* (* (cos (/ K 2)) J) 2)))))) (* (cos (/ K 2)) J)) -2) (sqrt (+ (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J))))) (- (* 1 1) (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))))) (/ (* (* (sqrt (+ 1 (* (* (* (/ U (* (* (cos (/ K 2)) J) 2)) (/ U (* (* (cos (/ K 2)) J) 2))) (* (/ U (* (* (cos (/ K 2)) J) 2)) (/ U (* (* (cos (/ K 2)) J) 2)))) (* (/ U (* (* (cos (/ K 2)) J) 2)) (/ U (* (* (cos (/ K 2)) J) 2)))))) (* (cos (/ K 2)) J)) -2) (sqrt (+ (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J))))) (- (* 1 1) (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)))))) (/ (* (* (sqrt (+ 1 (* (* (* (/ U (* (* (cos (/ K 2)) J) 2)) (/ U (* (* (cos (/ K 2)) J) 2))) (* (/ U (* (* (cos (/ K 2)) J) 2)) (/ U (* (* (cos (/ K 2)) J) 2)))) (* (/ U (* (* (cos (/ K 2)) J) 2)) (/ U (* (* (cos (/ K 2)) J) 2)))))) (* (cos (/ K 2)) J)) -2) (sqrt (+ (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J))))) (- (* 1 1) (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))))))
1.5s
(* (sqrt (+ (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J))))) (- (* 1 1) (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)))) (sqrt (+ (* 1 1) (- (* (* (* (* (/ U (* (* (cos (/ K 2)) J) 2)) (/ U (* (* (cos (/ K 2)) J) 2))) (* (/ U (* (* (cos (/ K 2)) J) 2)) (/ U (* (* (cos (/ K 2)) J) 2)))) (* (/ U (* (* (cos (/ K 2)) J) 2)) (/ U (* (* (cos (/ K 2)) J) 2)))) (* (* (* (/ U (* (* (cos (/ K 2)) J) 2)) (/ U (* (* (cos (/ K 2)) J) 2))) (* (/ U (* (* (cos (/ K 2)) J) 2)) (/ U (* (* (cos (/ K 2)) J) 2)))) (* (/ U (* (* (cos (/ K 2)) J) 2)) (/ U (* (* (cos (/ K 2)) J) 2))))) (* 1 (* (* (* (/ U (* (* (cos (/ K 2)) J) 2)) (/ U (* (* (cos (/ K 2)) J) 2))) (* (/ U (* (* (cos (/ K 2)) J) 2)) (/ U (* (* (cos (/ K 2)) J) 2)))) (* (/ U (* (* (cos (/ K 2)) J) 2)) (/ U (* (* (cos (/ K 2)) J) 2)))))))))
1.4s
(sqrt (+ (* (* (* (/ U (* 2 (* (cos (/ K 2)) J))) U) (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J))))) (+ (* (* 1 1) (* 1 1)) (+ (* (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1) (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) (* (* 1 1) (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))))) (* (* 2 (* (cos (/ K 2)) J)) (- (pow (* 1 1) 3) (pow (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1) 3)))))

prune4.4s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 9.0b

localize143.0ms

Local error

Found 4 expressions with local error:

22.4b
(/ (* (* (sqrt (+ 1 (* (* (* (/ U (* (* (cos (/ K 2)) J) 2)) (/ U (* (* (cos (/ K 2)) J) 2))) (* (/ U (* (* (cos (/ K 2)) J) 2)) (/ U (* (* (cos (/ K 2)) J) 2)))) (* (/ U (* (* (cos (/ K 2)) J) 2)) (/ U (* (* (cos (/ K 2)) J) 2)))))) (* (cos (/ K 2)) J)) -2) (* (sqrt (sqrt (+ (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J))))) (- (* 1 1) (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))))) (sqrt (sqrt (+ (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J))))) (- (* 1 1) (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)))))))
15.6b
(+ (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J))))) (- (* 1 1) (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)))
15.6b
(+ (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J))))) (- (* 1 1) (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)))
10.8b
(sqrt (sqrt (+ (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J))))) (- (* 1 1) (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)))))

rewrite8.7s

Algorithm
rewrite-expression-head
Rules
4290×sqrt-div
3370×frac-times
2070×frac-add
1554×associate-*l/
1550×associate-*r/
1088×associate-/r/
1035×flip3-- flip--
70×flip3-+ flip-+
36×add-cbrt-cube add-exp-log
16×prod-exp cbrt-unprod
14×add-log-exp
10×sqrt-prod
8×add-sqr-sqrt cbrt-undiv div-exp
6×pow1 *-un-lft-identity add-cube-cbrt
4×associate-+r+ sum-log sqrt-pow1 insert-posit16
2×+-commutative rem-sqrt-square associate-+r- sub-neg pow1/2 diff-log associate-/l/
1×clear-num associate-/r* frac-2neg times-frac div-inv associate-/l*
Counts
4 → 1264
Calls
4 calls:
Slowest
2.9s
(/ (* (* (sqrt (+ 1 (* (* (* (/ U (* (* (cos (/ K 2)) J) 2)) (/ U (* (* (cos (/ K 2)) J) 2))) (* (/ U (* (* (cos (/ K 2)) J) 2)) (/ U (* (* (cos (/ K 2)) J) 2)))) (* (/ U (* (* (cos (/ K 2)) J) 2)) (/ U (* (* (cos (/ K 2)) J) 2)))))) (* (cos (/ K 2)) J)) -2) (* (sqrt (sqrt (+ (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J))))) (- (* 1 1) (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))))) (sqrt (sqrt (+ (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J))))) (- (* 1 1) (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)))))))
2.8s
(sqrt (sqrt (+ (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J))))) (- (* 1 1) (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)))))
1.5s
(+ (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J))))) (- (* 1 1) (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)))
1.4s
(+ (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J))))) (- (* 1 1) (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
475.0ms
(/ (* (* (sqrt (+ 1 (* (* (* (/ U (* (* (cos (/ K 2)) J) 2)) (/ U (* (* (cos (/ K 2)) J) 2))) (* (/ U (* (* (cos (/ K 2)) J) 2)) (/ U (* (* (cos (/ K 2)) J) 2)))) (* (/ U (* (* (cos (/ K 2)) J) 2)) (/ U (* (* (cos (/ K 2)) J) 2)))))) (* (cos (/ K 2)) J)) -2) (* (sqrt (sqrt (+ (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J))))) (- (* 1 1) (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))))) (sqrt (sqrt (+ (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J))))) (- (* 1 1) (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)))))))
290.0ms
(sqrt (sqrt (+ (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J))))) (- (* 1 1) (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)))))
144.0ms
(+ (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J))))) (- (* 1 1) (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)))
141.0ms
(+ (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J))))) (- (* 1 1) (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)))