Details

Time bar (total: 8.4m)

sample155.0ms

Algorithm
intervals
Results
58.0ms48×body1280valid
33.0ms147×body80valid
29.0ms36×body640valid
11.0ms15×body320valid
5.0ms10×body160valid

simplify250.0ms

Calls
1 calls:
Slowest
250.0ms
(* (* (* -2 J) (cos (/ K 2))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.5b

localize30.0ms

Local error

Found 4 expressions with local error:

11.0b
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
7.4b
(* (* (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
(* (cos (/ K 2)) J)

rewrite12.9s

Algorithm
rewrite-expression-head
Rules
1276×associate-/r*
1153×associate-*r*
1120×add-sqr-sqrt
784×frac-times
555×*-un-lft-identity
536×associate-*l*
522×add-cube-cbrt
337×unswap-sqr
312×times-frac
175×associate-/l*
145×*-commutative
98×add-cbrt-cube add-exp-log
82×swap-sqr
59×clear-num
58×frac-2neg
49×prod-exp cbrt-unprod
32×associate-*l/
28×associate-*r/
26×pow1
24×cbrt-undiv div-exp
13×sqrt-prod
10×pow-prod-down
4×sqrt-div insert-posit16 div-inv distribute-lft-out add-log-exp
2×flip3-+ un-div-inv flip-+
1×pow2 rem-sqrt-square sqrt-pow1 pow-plus pow1/2 pow-sqr pow-prod-up
Calls
4 calls:
Slowest
11.1s
(* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (* (cos (/ K 2)) J))
1.4s
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
305.0ms
(* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J))))
11.0ms
(* (cos (/ K 2)) J)

series550.0ms

Calls
4 calls:
Slowest
203.0ms
(* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (* (cos (/ K 2)) J))
142.0ms
(* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J))))
137.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
68.0ms
(* (cos (/ K 2)) J)

simplify6.5m

Calls
2076 calls:
Slowest
2.3s
(* (/ (* (* 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)))))
2.2s
(* (/ (* (* 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)))))
2.1s
(* (/ (* (* U U) U) (* (* (* 2 2) 2) (* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* J J) J)))) (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) (/ U (* 2 (* (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 (* (cos (/ K 2)) J)) (* 2 (* (cos (/ K 2)) J))) (* 2 (* (cos (/ K 2)) J)))))
2.0s
(* (/ (* (* 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)))))

prune17.7s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 9.9b

localize68.0ms

Local error

Found 4 expressions with local error:

11.0b
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
11.0b
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
7.4b
(sqrt (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)))
7.4b
(sqrt (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)))

rewrite5.5s

Algorithm
rewrite-expression-head
Rules
38×sqrt-prod
26×*-un-lft-identity
16×add-sqr-sqrt
12×sqrt-div
10×pow1 sqrt-pow1 add-cube-cbrt
8×distribute-lft-out
6×rem-sqrt-square pow1/2
4×flip3-+ add-cbrt-cube associate-*l* add-exp-log flip-+ insert-posit16 add-log-exp
Calls
4 calls:
Slowest
1.4s
(sqrt (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)))
1.4s
(sqrt (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)))
1.4s
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
1.3s
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))

series727.0ms

Calls
4 calls:
Slowest
247.0ms
(sqrt (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)))
243.0ms
(sqrt (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)))
121.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
116.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))

simplify15.0s

Calls
60 calls:
Slowest
488.0ms
(+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)
474.0ms
(sqrt (sqrt (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))))
473.0ms
(exp (* 1/4 (- (+ (log (/ 1/4 (pow (cos (* 1/2 K)) 2))) (* 2 (log (/ -1 J)))) (* 2 (log (/ -1 U))))))
470.0ms
(sqrt (* (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)))))
460.0ms
(+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)

prune1.6s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 9.9b

localize47.0ms

Local error

Found 4 expressions with local error:

11.0b
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
4.8b
(* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (* (cos (/ K 2)) (* (cbrt J) (cbrt J))))
2.8b
(* (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (* (cos (/ K 2)) (* (cbrt J) (cbrt J)))) (cbrt J))
0.6b
(cbrt J)

rewrite57.0s

Algorithm
rewrite-expression-head
Rules
648×add-sqr-sqrt
456×unswap-sqr
170×associate-*l*
166×associate-*r*
153×cbrt-prod
139×add-cbrt-cube
134×cbrt-unprod
57×sqrt-prod
55×pow1
54×add-exp-log
51×*-un-lft-identity
40×swap-sqr
39×add-cube-cbrt
37×pow-prod-down prod-exp
23×*-commutative
10×associate-*l/
6×sqrt-div distribute-lft-out
4×insert-posit16 add-log-exp
3×flip3-+ flip-+
1×rem-sqrt-square sqrt-pow1 pow1/2 pow1/3
Calls
4 calls:
Slowest
44.1s
(* (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (* (cos (/ K 2)) (* (cbrt J) (cbrt J)))) (cbrt J))
11.5s
(* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (* (cos (/ K 2)) (* (cbrt J) (cbrt J))))
1.4s
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))
1.0ms
(cbrt J)

series1.1s

Calls
4 calls:
Slowest
417.0ms
(* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (* (cos (/ K 2)) (* (cbrt J) (cbrt J))))
293.0ms
(cbrt J)
253.0ms
(* (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (* (cos (/ K 2)) (* (cbrt J) (cbrt J)))) (cbrt J))
123.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))