Details

Time bar (total: 5.8m)

sample163.0ms

Algorithm
intervals
Results
69.0ms48×body1280valid
34.0ms43×body640valid
26.0ms133×body80valid
12.0ms22×body320valid
4.0ms12×body160valid

simplify206.0ms

Calls
1 calls:
Slowest
206.0ms
(* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.7b

localize37.0ms

Local error

Found 4 expressions with local error:

8.0b
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
4.6b
(* (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))))
0.2b
(/ U (* 2 (* (cos (/ K 2)) J)))

rewrite110.0ms

Algorithm
rewrite-expression-head
Rules
11×pow1
10×add-sqr-sqrt associate-*l*
9×*-un-lft-identity add-cube-cbrt
8×add-cbrt-cube add-exp-log
6×sqrt-prod
5×associate-*r*
4×sqrt-div insert-posit16 add-log-exp
3×associate-*l/ div-inv
2×flip3-+ pow-prod-down prod-exp *-commutative cbrt-unprod flip-+
1×pow2 frac-times rem-sqrt-square clear-num associate-/r* frac-2neg pow-plus pow1/2 associate-*r/ pow-prod-up
Calls
4 calls:
Slowest
53.0ms
(* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) (* -2 (* (cos (/ K 2)) J)))
24.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
24.0ms
(* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J))))
7.0ms
(/ U (* 2 (* (cos (/ K 2)) J)))

series452.0ms

Calls
4 calls:
Slowest
154.0ms
(* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) (* -2 (* (cos (/ K 2)) J)))
114.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
96.0ms
(* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J))))
88.0ms
(/ U (* 2 (* (cos (/ K 2)) J)))

simplify9.3s

Calls
46 calls:
Slowest
809.0ms
(+ (log (/ U (* 2 (* (cos (/ K 2)) J)))) (log (/ U (* 2 (* (cos (/ K 2)) J)))))
516.0ms
(+ (log (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))) (log (* -2 (* (cos (/ K 2)) J))))
501.0ms
(* (cbrt (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))) (cbrt (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))))
469.0ms
(* (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) (/ U (* 2 (* (cos (/ K 2)) J)))) (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) (/ U (* 2 (* (cos (/ K 2)) J)))))
458.0ms
(* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) (* -2 (* (cos (/ K 2)) J)))

prune1.1s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 4.5b

localize15.0ms

Local error

Found 4 expressions with local error:

8.0b
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
8.0b
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
8.0b
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
4.6b
(* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) (* -2 (* (cos (/ K 2)) J)))

rewrite99.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
9×*-un-lft-identity add-cube-cbrt
8×sqrt-div
6×pow1 add-cbrt-cube associate-*l* add-exp-log
4×flip3-+ flip-+ insert-posit16 add-log-exp
3×rem-sqrt-square pow1/2
2×associate-*l/
1×associate-*r* pow-prod-down prod-exp *-commutative cbrt-unprod
Calls
4 calls:
Slowest
41.0ms
(* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) (* -2 (* (cos (/ K 2)) J)))
27.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
17.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
13.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))

series458.0ms

Calls
4 calls:
Slowest
187.0ms
(* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) (* -2 (* (cos (/ K 2)) J)))
95.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
93.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
82.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))

simplify8.9s

Calls
41 calls:
Slowest
452.0ms
(* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) (* -2 (* (cos (/ K 2)) J)))
445.0ms
(sqrt (* (cbrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) (cbrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))))
418.0ms
(sqrt (* (cbrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) (cbrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))))
415.0ms
(sqrt (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)))
409.0ms
(sqrt (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)))

prune1.3s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 4.5b

localize92.0ms

Local error

Found 4 expressions with local error:

16.5b
(/ (* (sqrt (+ 1 (* (* (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J)) (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J))) (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J))))) (* (* -2 J) (cos (/ K 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)))))
10.6b
(+ (* (* (/ 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)))
6.8b
(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))))
4.2b
(sqrt (+ 1 (* (* (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J)) (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J))) (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J)))))

rewrite278.0ms

Algorithm
rewrite-expression-head
Rules
102×frac-times
90×frac-add
68×sqrt-div associate-*l/
66×associate-*r/
45×flip3-- flip--
32×associate-/r/
13×add-cbrt-cube add-exp-log
12×add-sqr-sqrt sqrt-prod
10×*-un-lft-identity add-cube-cbrt
9×add-log-exp
6×associate-/r* times-frac
5×flip3-+ flip-+
4×pow1 insert-posit16
3×cbrt-undiv div-exp prod-exp cbrt-unprod
2×rem-sqrt-square associate-+r+ sum-log pow1/2 associate-/l/
1×+-commutative clear-num associate-+r- sub-neg frac-2neg diff-log div-inv associate-/l*
Calls
4 calls:
Slowest
109.0ms
(/ (* (sqrt (+ 1 (* (* (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J)) (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J))) (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J))))) (* (* -2 J) (cos (/ K 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)))))
98.0ms
(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))))
63.0ms
(+ (* (* (/ 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)))
1.0ms
(sqrt (+ 1 (* (* (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J)) (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J))) (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J)))))

series785.0ms

Calls
4 calls:
Slowest
340.0ms
(/ (* (sqrt (+ 1 (* (* (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J)) (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J))) (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J))))) (* (* -2 J) (cos (/ K 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)))))
212.0ms
(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))))
127.0ms
(+ (* (* (/ 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)))
105.0ms
(sqrt (+ 1 (* (* (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J)) (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J))) (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J)))))

simplify2.0m

Calls
178 calls:
Slowest
1.8s
(/ (* (* (* (sqrt (+ 1 (* (* (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J)) (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J))) (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J))))) (* (* -2 J) (cos (/ K 2)))) (* (sqrt (+ 1 (* (* (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J)) (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J))) (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J))))) (* (* -2 J) (cos (/ K 2))))) (* (sqrt (+ 1 (* (* (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J)) (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J))) (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J))))) (* (* -2 J) (cos (/ K 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 (+ (* (* (/ 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 (+ (* (* (/ 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
(sqrt (+ (* (* (* U (/ U (* 2 (* (cos (/ K 2)) J)))) (* (/ U (* 2 (* (cos (/ K 2)) J))) U)) (+ (* (* 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)))))
1.4s
(sqrt (+ (* (* (* (/ U (* 2 (* (cos (/ K 2)) J))) U) (* (/ U (* 2 (* (cos (/ K 2)) J))) U)) (+ (* (* 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)))))
1.3s
(+ (* (* (* U U) (* U U)) (+ (* (* 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)) (* 2 (* (cos (/ K 2)) J)))) (- (pow (* 1 1) 3) (pow (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1) 3))))
1.3s
(+ (* (* (* (/ U (* 2 (* (cos (/ K 2)) J))) U) (* (/ U (* 2 (* (cos (/ K 2)) J))) U)) (+ (* (* 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))))

prune4.4s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 4.5b

localize62.0ms

Local error

Found 4 expressions with local error:

14.7b
(* (/ (sqrt (+ 1 (* (* (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J)) (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J))) (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J))))) (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 J) (cos (/ K 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)))))))
10.6b
(+ (* (* (/ 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)))
10.6b
(+ (* (* (/ 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)))
8.5b
(/ (sqrt (+ 1 (* (* (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J)) (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J))) (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J))))) (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))))))

rewrite550.0ms

Algorithm
rewrite-expression-head
Rules
194×sqrt-div
183×sqrt-prod
171×frac-times
150×frac-add
117×times-frac
111×associate-*l/ associate-*r/
96×associate-/r/
90×associate-*l*
86×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
75×flip3-- flip--
45×associate-*r*
27×add-cbrt-cube add-exp-log
14×add-log-exp
9×associate-/r*
8×cbrt-undiv div-exp prod-exp cbrt-unprod
6×pow1 flip3-+ flip-+ associate-/l*
4×associate-+r+ sum-log insert-posit16
3×div-inv
2×+-commutative associate-+r- sub-neg diff-log associate-/l/
1×sqrt-undiv clear-num frac-2neg pow-prod-down *-commutative
Calls
4 calls:
Slowest
306.0ms
(* (/ (sqrt (+ 1 (* (* (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J)) (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J))) (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J))))) (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 J) (cos (/ K 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)))))))
128.0ms
(/ (sqrt (+ 1 (* (* (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J)) (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J))) (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J))))) (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))))))
52.0ms
(+ (* (* (/ 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)))
47.0ms
(+ (* (* (/ 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)))

series994.0ms

Calls
4 calls:
Slowest
407.0ms
(/ (sqrt (+ 1 (* (* (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J)) (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J))) (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J))))) (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))))))
361.0ms
(* (/ (sqrt (+ 1 (* (* (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J)) (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J))) (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J))))) (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 J) (cos (/ K 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)))))))
120.0ms
(+ (* (* (/ 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)))
106.0ms
(+ (* (* (/ 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)))

simplify3.2m

Calls
452 calls:
Slowest
1.6s
(/ (sqrt (+ 1 (* (* (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J)) (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J))) (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J))))) (sqrt (sqrt (+ (* (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) (* (/ U (* 2 (* (cos (/ K 2)) J))) U)) (+ (* (* 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)))))))
1.5s
(/ (sqrt (+ 1 (* (* (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J)) (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J))) (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J))))) (sqrt (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)))))))
1.4s
(* (* (* (/ (sqrt (+ 1 (* (* (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J)) (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J))) (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J))))) (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 (+ 1 (* (* (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J)) (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J))) (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J))))) (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 (+ 1 (* (* (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J)) (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J))) (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J))))) (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 J) (cos (/ K 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)))))) (/ (* (* -2 J) (cos (/ K 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))))))) (/ (* (* -2 J) (cos (/ K 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))))))))
1.3s
(sqrt (sqrt (* (* (* 2 (* (cos (/ K 2)) J)) (* (* 2 (* (cos (/ K 2)) J)) (* 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)))))))
1.2s
(/ (sqrt (+ 1 (* (* (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J)) (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J))) (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J))))) (sqrt (sqrt (+ (* (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ 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)) (- (pow (* 1 1) 3) (pow (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1) 3)))))))

prune7.1s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 4.5b

regimes417.0ms

Accuracy

12.2% (7.5b remaining)

Error of 15.6b against oracle of 8.1b and baseline of 16.6b

bsearch233.0ms

end0.0ms

sample4.3s

Algorithm
intervals
Results
1.7s1514×body1280valid
1.2s1296×body640valid
783.0ms4296×body80valid
362.0ms588×body320valid
96.0ms309×body160valid