Details

simplify36.4m

Calls

13866 calls:

Slowest
3.1s
(/ (* (* (* (* v v) (* (* v v) 7/2)) (* (* v v) (* (* v v) 7/2))) (* (* v v) (* (* v v) 7/2))) (* (* (* (* (sqrt 2) PI) (* (sqrt 2) PI)) (* (sqrt 2) PI)) (* (* t t) t)))
2.7s
(* (* (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 d) (* 2 d)) (* 2 d))) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))) (* (* (/ h l) (/ h l)) (/ h l)))
2.7s
(* (* (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 2) 2) (* (* d d) d))) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 2) 2) (* (* d d) d)))) (/ (* (* h h) h) (* (* l l) l)))
2.7s
(* (* (* (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 2) 2) (* (* d d) d))) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 2) 2) (* (* d d) d)))) (* (* h h) h)) (* (* (/ 1 l) (/ 1 l)) (/ 1 l)))
2.4s
(* (* (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 2) 2) (* (* d d) d))) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 2) 2) (* (* d d) d)))) (* (* (/ h l) (/ h l)) (/ h l)))

prune3.9m

sample3.3m

Algorithm
54×intervals
Results
56.0s239338×body80valid
37.8s159684×body80nan
30.1s17567×body1280valid
19.2s13961×body640valid
18.2s8277×body10240exit
8.4s4981×body2560valid
6.8s7249×body320valid
5.2s2452×body5120valid
4.0s7923×body160valid
1.1s620×body1280nan
518.0ms652×body640nan
214.0ms359×body320nan
57.0ms174×body160nan

series1.2m

Calls

402 calls:

Slowest
1.7s
(sqrt (* (* (* (* 2 n) U) 1) (- t (* (/ l Om) (- (* l 2) (- (* (- U U*) (* (/ l Om) n))))))))
1.7s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))))
1.5s
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (pow (/ d l) (/ 1 2))) (- 1 (* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ (* (cbrt h) (cbrt h)) 1)) (/ (cbrt h) l))))
1.4s
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
1.4s
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (* (sqrt (/ 1 (* (cbrt l) (cbrt l)))) (pow (/ d (cbrt l)) (/ 1 2)))) (- 1 (* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ (* (cbrt h) (cbrt h)) 1)) (/ (cbrt h) l))))

rewrite36.1s

Algorithm
103×rewrite-expression-head
Calls

402 calls:

Slowest
5.8s
(cbrt (* (* (* (* (sqrt (sqrt (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))) (sqrt (sqrt (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))))) (* (sqrt (sqrt (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))) (sqrt (sqrt (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))))) (* (* (sqrt (sqrt (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))) (sqrt (sqrt (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))))) (* (sqrt (sqrt (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))) (sqrt (sqrt (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))))))) (* (* (sqrt (sqrt (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))) (sqrt (sqrt (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))))) (* (sqrt (sqrt (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1))))) (sqrt (sqrt (acos (/ (- 1 (* 5 (* v v))) (- (* v v) 1)))))))))
2.5s
(* NaChar (/ 1 (log (* E (exp (exp (/ (+ (- (+ Ev Vef) mu) EAccept) KbT)))))))
935.0ms
(* E (exp (exp (/ (+ (- (+ Ev Vef) mu) EAccept) KbT))))
678.0ms
(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
666.0ms
(* (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) h) (/ 1 l))
Rules
89922×times-frac
33140×add-sqr-sqrt
32908×*-un-lft-identity
32174×add-cube-cbrt
11635×add-exp-log
5728×prod-exp
5300×add-cbrt-cube
5203×div-inv
4104×div-exp
3053×associate-/r/
2698×pow1
2045×cbrt-unprod
1931×sqrt-pow1
1855×cbrt-undiv
1246×flip-+ flip3-+
1133×sqrt-prod
1037×pow-prod-up
1001×pow1/2
991×associate-/l*
781×associate-*r*
757×associate-*l*
712×pow-prod-down
711×pow-exp
652×associate-*r/
616×1-exp
526×associate-*l/
520×frac-times
492×add-log-exp
473×pow-unpow
441×associate-/r*
439×pow-sqr
422×sqrt-div
404×difference-of-squares
402×insert-posit16
281×rec-exp
248×frac-add
230×unswap-sqr
206×flip3-- flip--
201×cbrt-prod
190×pow-to-exp
178×distribute-lft-out--
160×swap-sqr
158×*-commutative unpow-prod-down
149×distribute-lft-out
134×frac-sub
116×tan-quot
105×pow-plus
87×distribute-rgt-neg-in
85×distribute-lft-neg-in
78×frac-2neg clear-num
72×pow2
66×rem-sqrt-square
54×sub-neg
50×distribute-rgt-in sqr-pow distribute-lft-in
49×pow1/3
47×pow-pow
46×cbrt-div
35×associate-/l/
32×sin-mult
26×diff-log
23×sum-log
22×sqrt-unprod sub-div
21×div-sub
17×+-commutative
13×neg-mul-1
11×distribute-rgt-out--
10×unpow2 cube-prod
pow-flip inv-pow
associate-+l+ associate--r+
associate--l+ pow-sub
distribute-neg-frac rem-square-sqrt cos-sum log-pow cube-div
un-div-inv
neg-sub0 associate-+r+
associate-+r- distribute-frac-neg cube-unmult sqr-sin cos-diff associate--r-
exp-sum pow3 neg-log asin-acos acos-asin
sqrt-undiv distribute-rgt-neg-out unpow3 associate--l- sqrt-pow2 associate-+l- cube-mult rem-cbrt-cube e-exp-1 distribute-rgt-out

regimes14.5s

Accuracy

Total 54.4b remaining (37.6%)

11.4b-0.6%Henrywood and Agarwal, Equation (13)
9.1b33.6%Henrywood and Agarwal, Equation (3)
9.1b0%Toniolo and Linder, Equation (13)
7.5b7.9%Maksimov and Kolovsky, Equation (3)
5.9b75.3%Toniolo and Linder, Equation (7)

localize6.1s

bsearch3.3s

end1.0ms