Details

simplify13.1m

Calls

8594 calls:

Slowest
1.2s
(* (* (/ 1 2) (pow (/ 1 (/ (* 2 d) (* M D))) 2)) (/ h l))
1.1s
(+ (log (* (/ 1 2) (pow (/ 1 (/ (* 2 d) (* M D))) 2))) (log (/ h l)))
1.1s
(* (* (/ 1 2) (pow (/ 1 (/ (* 2 d) (* M D))) 2)) (/ h l))
1.0s
(* (* l (cos k)) (+ (* (+ 1 (pow (/ k t) 2)) (+ 1 (pow (/ k t) 2))) (- (* 1 1) (* (+ 1 (pow (/ k t) 2)) 1))))
997.0ms
(* (cos k) (+ (* (+ 1 (pow (/ k t) 2)) (+ 1 (pow (/ k t) 2))) (- (* 1 1) (* (+ 1 (pow (/ k t) 2)) 1))))

sample4.3m

Algorithm
56×intervals
Results
1.0m247477×body80valid
50.1s23985×body1280valid
40.4s158365×body80nan
26.7s18193×body640valid
18.9s7170×body2560valid
18.4s8447×body10240exit
15.3s3457×body5120valid
8.2s9008×body320valid
5.3s8748×body160valid
664.0ms609×body1280nan
568.0ms373×body320nan
460.0ms625×body640nan
115.0ms187×body160nan

prune2.6m

series43.0s

Calls

395 calls:

Slowest
1.2s
(sqrt (* (* 2 n) (* U (- (- t (* 2 (/ l (/ Om l)))) (* (* (* n (/ l Om)) (/ l Om)) (- U U*))))))
1.2s
(sqrt (* (* 2 n) (* U (- (- t (* 2 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2)) (- U U*))))))
1.2s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))))
1.1s
(sqrt (* (* 2 n) (* U (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*))))))
850.0ms
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

regimes16.8s

Accuracy

Total 42.3b remaining (23.3%)

9.4b27.1%Toniolo and Linder, Equation (13)
7.1b48.1%Henrywood and Agarwal, Equation (12)
6.7b72%Toniolo and Linder, Equation (7)
6.1b17.1%Toniolo and Linder, Equation (10-)
2.9b0%Henrywood and Agarwal, Equation (13)

bsearch5.8s

rewrite4.1s

Algorithm
105×rewrite-expression-head
Calls

395 calls:

Slowest
255.0ms
(cbrt (* (* (+ (+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4))) (* 4 (* b b))) (+ (+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4))) (* 4 (* b b)))) (+ (+ (pow b 4) (+ (* 2 (* (pow a 2) (pow b 2))) (pow a 4))) (* 4 (* b b)))))
114.0ms
(* (* (* (/ t (/ l t)) (* (/ t l) (sin k))) (tan k)) (+ (+ 1 (pow (/ k t) 2)) 1))
111.0ms
(* (* (* (* -2 J) (* (cbrt (cos (/ K 2))) (log (exp (cbrt (cos (/ K 2))))))) (cbrt (cos (/ K 2)))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))
104.0ms
(* (* (* (* -2 J) (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))) (cbrt (cos (/ K 2)))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))
88.0ms
(* (* (* (/ (* t t) l) (* (/ t l) (sin k))) (tan k)) (+ (+ 1 (pow (/ k t) 2)) 1))
Rules
4016×times-frac
2618×add-sqr-sqrt
2609×*-un-lft-identity
2562×add-cube-cbrt
1341×cbrt-prod
1280×add-exp-log
1273×sqrt-prod
989×add-cbrt-cube
848×associate-*r*
754×pow1
630×associate-*r/
546×associate-/r/
535×associate-*l*
531×cbrt-div
466×add-log-exp
463×frac-times
451×associate-*l/
447×div-inv
412×flip3--
412×flip--
411×prod-exp
297×associate-/l*
287×cbrt-unprod
279×sqrt-div
258×flip3-+
258×flip-+
250×associate-/r*
197×unpow-prod-down
187×pow-prod-down
162×div-exp
153×*-commutative
127×frac-add
124×cbrt-undiv
115×pow-to-exp
104×distribute-lft-in
104×distribute-rgt-in
92×frac-2neg
92×clear-num
83×tan-quot
78×frac-sub
78×sub-neg
71×pow-exp
62×associate-/l/
50×pow-unpow
44×unpow2
41×pow1/3
38×pow1/2
38×rem-sqrt-square
35×pow-pow
34×sum-log
33×associate--l+
21×+-commutative
20×unpow-prod-up
17×distribute-lft-out
17×rec-exp
16×div-sub
11×difference-of-squares
10×pow-prod-up
9×associate-+r+
9×pow-plus
9×pow-sub
7×pow-flip
7×distribute-lft-out--
6×cos-sum
6×difference-of-sqr-1
6×unpow3
6×inv-pow
6×pow2
6×cube-mult
6×diff-log
5×associate-+l+
5×un-div-inv
4×pow3
4×acos-asin
4×associate--r+
3×asin-acos
3×rem-cbrt-cube
3×cos-diff
2×unpow1/3
2×associate-+l-
1×mul0
1×distribute-rgt-out
1×associate--r-
1×sub-div

localize3.3s

end2.0ms