Details

simplify6.2m (38.7%)

sample3.3m (20.5%)

Algorithm
61×intervals
Results
45.4s253560×body80valid
40.2s29210×body1280valid
24.9s160234×body80nan
22.1s20401×body640valid
19.0s8958×body2560valid
11.9s3343×body5120valid
7.6s10108×body320valid
3.2s8732×body160valid
835.0ms658×body10240exit
459.0ms586×body1280nan
358.0ms662×body640nan
209.0ms8256×pre80true
114.0ms381×body320nan
30.0ms155×body160nan

series2.4m (15.1%)

Calls

450 calls:

7.4s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))))
7.4s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))
7.3s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
6.6s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
2.5s
(pow (exp (sqrt (/ (- (+ (+ Ev Vef) EAccept) mu) KbT))) (sqrt (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT)))

prune2.4m (14.9%)

rewrite1.3m (8.3%)

Algorithm
118×rewrite-expression-head
Calls

450 calls:

25.1s
(* (/ NaChar (+ (pow (exp (/ (- (+ (+ Ev Vef) EAccept) mu) KbT)) 3) (pow 1.0 3))) (+ (* 1.0 1.0) (- (* (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT)) (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT))) (* 1.0 (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT))))))
3.4s
(- (* (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT)) (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT))) (* 1.0 (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT))))
2.1s
(* (* (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0))) (* (pow (/ 1 (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (* (pow (/ 1 (cbrt (* (cbrt l) (cbrt l)))) (/ 1.0 2.0)) (pow (/ d (cbrt (cbrt l))) (/ 1.0 2.0))))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l))))
1.7s
(* (* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
1.5s
(/ (- (pow 1.0 3) (pow (* 5.0 (* v v)) 3)) (* (* (* PI (* t (sqrt (* 2.0 (- 1.0 (* 3.0 (* v v))))))) (- 1.0 (* v v))) (+ (* 1.0 1.0) (* (* 5.0 (pow v 2)) (+ 1.0 (* 5.0 (* v v)))))))
Rules
90472×add-exp-log
67971×prod-exp
40059×pow-exp
26869×div-exp
15625×pow-to-exp
10758×times-frac
7452×add-sqr-sqrt
7326×*-un-lft-identity
6296×add-cube-cbrt
6215×sqrt-prod
4627×rec-exp 1-exp
2641×add-cbrt-cube
2082×unpow-prod-down
1986×associate-*l*
1378×associate-*r/
1171×pow1
1069×cbrt-unprod
821×associate-*r*
734×associate-/r*
623×frac-times
576×sqr-pow
554×add-log-exp
538×cbrt-prod
467×pow-unpow
461×associate-*l/
459×cbrt-undiv
436×associate-/l*
426×unswap-sqr
407×flip3-- flip--
362×pow-prod-down
360×distribute-lft-out
356×div-inv
335×sqrt-div
326×frac-add
315×flip-+ flip3-+
261×associate-/r/
251×distribute-lft-out--
203×div-sub
172×difference-of-squares
163×exp-diff
159×*-commutative
145×distribute-rgt-neg-in exp-prod
110×tan-quot
102×unpow2 sqrt-pow1
98×pow-pow
97×distribute-lft-neg-in
95×distribute-rgt-in distribute-lft-in
92×clear-num frac-2neg
89×frac-sub
81×pow1/2
78×sub-neg
71×cube-prod
69×rem-sqrt-square
68×log-prod
60×neg-sub0
54×associate-+r- unsub-neg
46×associate-/l/
43×pow1/3
34×sum-log
27×pow-sub swap-sqr associate--l+
23×+-commutative
20×sub-div diff-log
16×associate-+r+
14×pow-prod-up associate--r+
13×neg-mul-1
10×cos-sum cbrt-div
pow-sqr exp-sum
log-pow
cube-div sum-cubes unpow3 cube-mult distribute-neg-frac
difference-cubes pow-plus inv-pow cos-diff pow-flip log-div
rem-cube-cbrt pow-neg rem-exp-log pow2 rem-log-exp
un-div-inv sqrt-unprod distribute-frac-neg acos-asin
associate--l- asin-acos
associate-+l+ distribute-rgt-out-- rem-square-sqrt mul0 exp-to-pow

regimes16.8s (1.8%)

Accuracy

Total 43.9b remaining (20.5%)

Threshold costs 4.7b (2.2%)

8.0b14.9%Toniolo and Linder, Equation (13)
6.4b73.3%Toniolo and Linder, Equation (7)
5.4b0%Henrywood and Agarwal, Equation (12)
4.3b31.8%Toniolo and Linder, Equation (10-)
3.7b51.3%Toniolo and Linder, Equation (10+)

bsearch4.1s (0.4%)

localize3.9s (0.4%)

end0.0ms (0.0%)