Details

prune10.1m (41.0%)

simplify7.5m (30.8%)

sample4.2m (17.3%)

Algorithm
61×intervals
Results
1.0m252736×body80valid
50.5s29428×body1280valid
42.8s159195×body80nan
25.9s20197×body640valid
20.0s8725×body2560valid
11.8s3555×body5120valid
10.8s9981×body320valid
5.8s9165×body160valid
2.1s623×body10240exit
737.0ms644×body1280nan
507.0ms637×body640nan
288.0ms8256×pre80true
183.0ms321×body320nan
66.0ms197×body160nan

series1.4m (5.9%)

Calls

460 calls:

2.9s
(sqrt (* 2 (* (* (cbrt (* U (* n (- t (* (/ l Om) (- (* 2 l) (* (/ l Om) (* n (- U* U))))))))) (cbrt (* U (* n (- t (* (/ l Om) (- (* 2 l) (* (/ l Om) (* n (- U* U)))))))))) (* (cbrt U) (cbrt (* n (- t (* (/ l Om) (- (* 2 l) (* (/ l Om) (* n (- U* U))))))))))))
2.2s
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))) (* (sqrt (/ (/ 1 (cbrt l)) (cbrt l))) (sqrt (/ d (cbrt l))))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
2.1s
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))) (* (sqrt (/ (/ 1 (cbrt l)) (cbrt l))) (sqrt (/ d (cbrt l))))) (- 1 (* (/ (/ (* (/ M (/ (* d 2) D)) (/ M (/ (* d 2) D))) 2) (* (cbrt l) (cbrt l))) (/ h (cbrt l)))))
2.0s
(sqrt (* 2 (* (* (cbrt (* U (* n (- t (* (/ l Om) (- (* 2 l) (* (/ l Om) (* n (- U* U))))))))) (cbrt (* U (* n (- t (* (/ l Om) (- (* 2 l) (* (/ l Om) (* n (- U* U)))))))))) (cbrt (* U (* n (- t (* (/ l Om) (- (* 2 l) (* (/ l Om) (* n (- U* U))))))))))))
1.9s
(sqrt (* 2 (* U (* n (- t (* (/ l Om) (- (* 2 l) (* (/ l Om) (* n (- U* U))))))))))

rewrite43.2s (2.9%)

Algorithm
118×rewrite-expression-head
Calls

460 calls:

13.9s
(sqrt (- 1 (/ (/ (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))) (/ (/ d (/ (* M D) 2)) (/ (cbrt h) (cbrt l)))) (/ d (/ (* M D) 2)))))
962.0ms
(/ (+ (exp (/ (- EDonor (- Ec (+ Vef mu))) KbT)) 1) NdChar)
631.0ms
(* (/ (* (sqrt (+ 1 (* -3 (* v v)))) (sqrt 2)) 4) (* (/ (* (sqrt (+ 1 (* -3 (* v v)))) (sqrt 2)) 4) (* (- 1 (* v v)) (* (- 1 (* v v)) (- 1 (* v v))))))
598.0ms
(sqrt (- 1 (/ (/ (/ h l) (/ d (/ (* M D) 2))) (/ d (/ (* M D) 2)))))
568.0ms
(/ 1 (/ (+ (exp (/ (- EDonor (- Ec (+ Vef mu))) KbT)) 1) NdChar))
Rules
197552×times-frac
77067×add-sqr-sqrt
76111×*-un-lft-identity
75224×add-cube-cbrt
30811×cbrt-prod
10849×sqrt-prod
9924×add-exp-log
9330×div-inv
5623×add-cbrt-cube
5045×div-exp
4651×associate-/l*
2985×prod-exp
2798×cbrt-undiv
2009×associate-*l*
1865×unpow-prod-down
1805×associate-/r*
1802×cbrt-unprod
1797×pow1
1434×associate-/r/
1048×associate-*r/
1003×associate-*r*
725×frac-times
661×sqr-pow
548×add-log-exp
533×pow-prod-down
519×sqrt-div
460×insert-posit16
456×1-exp
417×associate-*l/
347×distribute-lft-out
341×unswap-sqr
323×flip3-- flip--
271×flip-+ flip3-+
247×difference-of-squares
221×pow-exp
214×rec-exp
204×distribute-rgt-neg-in distribute-lft-neg-in
191×sqrt-pow1
182×swap-sqr
156×cbrt-div *-commutative
155×pow-prod-up
142×distribute-rgt-in distribute-lft-in
137×sub-neg
131×pow1/2
124×pow-unpow
112×unpow-prod-up
109×frac-2neg clear-num
92×tan-quot
88×distribute-lft-out--
87×pow-to-exp
86×pow-plus
85×associate-/l/ pow-sqr
72×rem-sqrt-square
68×neg-mul-1
55×frac-add
51×pow2
43×pow1/3
41×distribute-rgt-out
40×sin-mult
34×pow-pow
25×sum-log
21×log-pow
20×+-commutative diff-log
19×log-prod exp-prod
17×distribute-lft1-in div-sub
16×pow-flip cos-sum
12×exp-sum count-2 distribute-rgt1-in
10×cube-prod inv-pow cos-diff
pow-sub
associate--l+
associate-+l+
pow3 unpow2 cube-div
difference-of-sqr--1 difference-of-sqr-1 acos-asin
associate--r+ rem-log-exp
sqrt-unprod associate-+l- rem-square-sqrt
remove-posit16 associate-+r- frac-sub cube-unmult sqr-sin un-div-inv distribute-neg-frac asin-acos rem-exp-log
neg-sub0 exp-diff distribute-rgt-out-- unpow3 associate--l- sub-div sqrt-pow2 exp-to-pow rem-cbrt-cube cube-mult

regimes21.1s (1.4%)

Accuracy

Total 41.8b remaining (22.9%)

Threshold costs 3.3b (1.8%)

8.4b43.7%Henrywood and Agarwal, Equation (3)
6.8b18.2%Henrywood and Agarwal, Equation (13)
6.2b74.3%Toniolo and Linder, Equation (7)
5.1b45.2%Toniolo and Linder, Equation (13)
4.2b22.4%Henrywood and Agarwal, Equation (12)

localize7.5s (0.5%)

bsearch3.5s (0.2%)

end1.0ms (0.0%)