Details

simplify22.6m

Calls

10094 calls:

Slowest
2.3s
(/ (* (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d))) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))) (* (* (/ l h) (/ l h)) (/ l h)))
2.0s
(/ (* (* (* (/ 2 k) l) (* (/ 2 k) l)) (* (/ 2 k) l)) (* (* (* (/ (sin k) l) (* t (* k (tan k)))) (* (/ (sin k) l) (* t (* k (tan k))))) (* (/ (sin k) l) (* t (* k (tan k))))))
2.0s
(/ (* (* (* (* (* (/ M d) (/ D 2)) (* (/ M d) (/ D 2))) h) (* (* (* (/ M d) (/ D 2)) (* (/ M d) (/ D 2))) h)) (* (* (* (/ M d) (/ D 2)) (* (/ M d) (/ D 2))) h)) (* (* (* 2 l) (* 2 l)) (* 2 l)))
1.9s
(/ (* (* (* (* (* (/ M d) (/ D 2)) (* (/ M d) (/ D 2))) h) (* (* (* (/ M d) (/ D 2)) (* (/ M d) (/ D 2))) h)) (* (* (* (/ M d) (/ D 2)) (* (/ M d) (/ D 2))) h)) (* (* (* 2 l) (* 2 l)) (* 2 l)))
1.9s
(/ (* (* (* (* (* (/ M d) (/ D 2)) (* (/ M d) (/ D 2))) h) (* (* (* (/ M d) (/ D 2)) (* (/ M d) (/ D 2))) h)) (* (* (* (/ M d) (/ D 2)) (* (/ M d) (/ D 2))) h)) (* (* (* 2 l) (* 2 l)) (* 2 l)))

sample3.8m

Algorithm
53×intervals
Results
50.0s224477×body80valid
45.1s22830×body1280valid
37.8s146412×body80nan
26.1s17906×body640valid
18.4s8087×body10240exit
14.6s5561×body2560valid
8.0s8761×body320valid
7.8s1029×body5120valid
5.4s8539×body160valid
950.0ms622×body1280nan
471.0ms595×body640nan
242.0ms380×body320nan
123.0ms197×body160nan

prune3.0m

series1.2m

Calls

392 calls:

Slowest
3.1s
(sqrt (pow (* (* U (- t (* (/ l Om) (+ (* 2 l) (* n (* (/ l Om) (- U U*))))))) (* 2 n)) 1))
2.4s
(sqrt (pow (pow (* (- t (* (/ l Om) (fma 2 l (* (* n (/ l Om)) (- U U*))))) (* 2 (* n U))) 1) 1))
1.7s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))))
1.3s
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
1.2s
(sqrt (* (* (* (* 2 n) U) 1) (- t (fma (/ l Om) (* l 2) (* (- U U*) (* n (* (/ l Om) (/ l Om))))))))

regimes13.9s

Accuracy

Total 36.5b remaining (29%)

7.6b35.5%Toniolo and Linder, Equation (13)
6.0b40.6%Henrywood and Agarwal, Equation (12)
5.3b54.4%Toniolo and Linder, Equation (7)
4.3b-2.4%Toniolo and Linder, Equation (10-)
4.0b0%Maksimov and Kolovsky, Equation (3)

rewrite5.8s

Algorithm
105×rewrite-expression-head
Calls

392 calls:

Slowest
339.0ms
(exp (- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))))
329.0ms
(exp (- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))))
271.0ms
(* (* (* (* (- 1 (* v v)) (sqrt (fma (* v v) -3 1))) (* (- 1 (* v v)) (sqrt (fma (* v v) -3 1)))) (* (- 1 (* v v)) (sqrt (fma (* v v) -3 1)))) (/ (* 1/2 (sqrt 2)) 16))
262.0ms
(+ (sqrt (- (* (* (/ c0 h) (/ (* (/ d D) (/ d D)) w)) (* (/ c0 h) (/ (* (/ d D) (/ d D)) w))) (* M M))) (* (/ c0 h) (/ (* (/ d D) (/ d D)) w)))
214.0ms
(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
Rules
6763×times-frac
4040×add-sqr-sqrt
4017×*-un-lft-identity
3972×add-cube-cbrt
1457×cbrt-prod
1241×div-inv
1204×associate-*r*
1189×add-exp-log
986×add-cbrt-cube
735×sqrt-prod
692×pow1
598×associate-*l*
543×associate-*l/
531×associate-/l*
460×add-log-exp
399×associate-/r*
394×prod-diff
392×expm1-log1p-u log1p-expm1-u insert-posit16
362×associate-/r/
353×associate-*r/
344×frac-times
280×prod-exp
245×unpow-prod-down
229×flip-- flip3--
220×div-exp
213×cbrt-unprod
183×cbrt-undiv
171×exp-sum
162×distribute-rgt-neg-in
156×distribute-lft-neg-in
137×pow-prod-down
131×*-commutative
121×cbrt-div
114×frac-2neg clear-num
105×associate-/l/
82×sqrt-div
81×fma-neg
74×sub-neg
70×flip-+ flip3-+
67×distribute-rgt-in distribute-lft-in
58×unpow2
54×pow-to-exp
47×pow-exp
45×pow1/3 rem-sqrt-square
44×fma-def pow1/2
40×tan-quot
39×rec-exp
36×pow-unpow
34×div-sub
32×unpow-prod-up
30×exp-prod
28×exp-diff
26×frac-add
24×neg-mul-1
23×associate-+r-
21×pow-pow pow-prod-up
20×diff-log
19×frac-sub pow2
17×pow-sub
16×distribute-lft-out--
15×pow-plus
13×fma-udef
12×sum-log difference-of-squares rem-exp-log
11×pow-flip
10×inv-pow
neg-sub0 +-commutative
associate-+r+ associate--l+
distribute-lft-out difference-of-sqr-1
distribute-frac-neg neg-log sub-div associate--r+ distribute-neg-frac associate--r-
acos-asin
sin-mult associate--l- hypot-udef exp-neg asin-acos un-div-inv
associate-+l+ sqrt-undiv distribute-rgt-out-- cos-sum
mul0 cube-unmult pow3 sqrt-unprod sqr-sin rem-square-sqrt rem-cbrt-cube cos-diff

localize3.1s

bsearch2.4s

end1.0ms