Details

simplify46.5m

Calls

18083 calls:

Slowest
4.3s
(/ (/ (* (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* d 2) (* d 2)) (* d 2))) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* d 2) (* d 2)) (* d 2)))) (* (* 2 2) 2)) (* (* l l) l))
3.0s
(/ (/ (* (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* d d) d) (* (* 2 2) 2))) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* d d) d) (* (* 2 2) 2)))) (* (* 2 2) 2)) (* (* l l) l))
3.0s
(/ (* (/ (* (* (* d d) d) (* (* c0 c0) c0)) (* (* (* w D) (* w D)) (* w D))) (/ (* (* (* d d) d) (* (* c0 c0) c0)) (* (* (* w D) (* w D)) (* w D)))) (* (* h h) h))
2.9s
(/ (* (/ (* (* (* d c0) (* d c0)) (* d c0)) (* (* (* w w) w) (* (* D D) D))) (/ (* (* (* d c0) (* d c0)) (* d c0)) (* (* (* w w) w) (* (* D D) D)))) (* (* h h) h))
2.9s
(/ (* (/ (* (* (* d d) d) (* (* c0 c0) c0)) (* (* (* w w) w) (* (* D D) D))) (/ (* (* (* d d) d) (* (* c0 c0) c0)) (* (* (* w w) w) (* (* D D) D)))) (* (* h h) h))

prune4.6m

sample3.6m

Algorithm
58×intervals
Results
57.5s250107×body80valid
40.9s160569×body80nan
32.9s21702×body1280valid
20.6s15235×body640valid
19.4s8484×body10240exit
9.0s5745×body2560valid
5.6s7523×body320valid
5.4s2412×body5120valid
4.4s8084×body160valid
823.0ms8256×pre80true
634.0ms584×body1280nan
521.0ms636×body640nan
181.0ms320×body320nan
98.0ms188×body160nan

series1.3m

Calls

448 calls:

Slowest
1.7s
(sqrt (+ (* t (* (* (* 2 n) U) 1)) (* (* (* (* (/ l Om) n) U) (- (* l -2) (* (* (/ l Om) n) (- U U*)))) 2)))
1.7s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))))
1.7s
(* (* (/ (- (- Ec (+ (+ Vef mu) EDonor))) KbT) (/ (- (- Ec (+ (+ Vef mu) EDonor))) KbT)) (/ (- (- Ec (+ (+ Vef mu) EDonor))) KbT))
1.6s
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (* (fabs (/ (cbrt d) (cbrt l))) (pow (/ (cbrt d) (cbrt l)) (/ 1 2)))) (- 1 (pow (* (/ (/ (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) 2) l) h) 1)))
1.6s
(sqrt (* (* (* (* 2 n) U) 1) (- t (* (/ l Om) (- (* l 2) (- (* (- U U*) (* (/ l Om) n))))))))

rewrite28.8s

Algorithm
116×rewrite-expression-head
Calls

448 calls:

Slowest
1.2s
(/ NdChar (+ (exp (/ (- (- Ec (+ (+ Vef mu) EDonor))) KbT)) 1))
1.1s
(* (* (/ (- (- Ec (+ (+ Vef mu) EDonor))) KbT) (/ (- (- Ec (+ (+ Vef mu) EDonor))) KbT)) (/ (- (- Ec (+ (+ Vef mu) EDonor))) KbT))
799.0ms
(cbrt (* (* (/ (- (- Ec (+ (+ Vef mu) EDonor))) KbT) (/ (- (- Ec (+ (+ Vef mu) EDonor))) KbT)) (/ (- (- Ec (+ (+ Vef mu) EDonor))) KbT)))
733.0ms
(* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (* (cos (/ K 2)) J))
704.0ms
(* (/ (- (- Ec (+ (+ Vef mu) EDonor))) KbT) (/ (- (- Ec (+ (+ Vef mu) EDonor))) KbT))
Rules
38509×times-frac
18744×*-un-lft-identity
17878×add-sqr-sqrt
16576×add-cube-cbrt
9231×add-exp-log
6641×add-cbrt-cube
5453×sqrt-prod
4028×prod-exp
3190×div-exp
3070×cbrt-prod
2683×cbrt-unprod
2491×cbrt-undiv
1895×pow1
1443×associate-*r*
1440×div-inv
1314×associate-/r/
1029×associate-/l*
976×associate-*l*
852×sqrt-div
739×associate-/r*
678×distribute-lft-out
569×pow-prod-down
565×associate-*r/
536×difference-of-squares
531×add-log-exp
501×flip-+ flip3-+
489×distribute-lft-out--
453×associate-*l/
449×frac-times
448×insert-posit16
430×pow-exp
366×swap-sqr
285×distribute-rgt-neg-in
282×pow-to-exp
274×unswap-sqr
261×distribute-lft-neg-in
241×flip3-- flip--
211×pow-unpow
198×unpow-prod-down
195×sqrt-pow1
190×pow-prod-up
181×*-commutative
149×1-exp
134×rec-exp
132×pow1/2
114×tan-quot
109×frac-2neg clear-num
103×pow-sqr
101×pow-plus
98×frac-add
96×div-sub
90×associate-/l/
88×exp-prod
84×log-pow
77×pow-sub
70×sqr-pow
69×rem-sqrt-square
67×pow2
65×distribute-rgt-in distribute-lft-in
62×sin-mult
60×sub-neg
49×distribute-rgt-out--
40×frac-sub
36×cbrt-div
29×pow1/3
27×neg-mul-1
25×log-prod
23×sum-log
21×pow-pow
20×pow-flip diff-log
15×+-commutative
14×sqr-sin
11×inv-pow
10×exp-sum distribute-frac-neg cube-prod rem-exp-log
associate-+r- difference-of-sqr-1 un-div-inv asin-acos
associate-+l+
associate-+r+ cube-unmult associate--l+ pow-div distribute-neg-frac cos-sum cube-div
exp-diff
distribute-lft-neg-out sqrt-unprod sub-div associate--r+ rem-log-exp rem-square-sqrt associate--r-
neg-sub0 distribute-rgt-neg-out unpow2 cos-diff
pow3 associate-+l- log-div
remove-posit16 sqrt-undiv unpow3 sqrt-pow2 sqr-neg rem-cbrt-cube cube-mult acos-asin

regimes17.6s

Accuracy

Total 51.0b remaining (32%)

16.0b-1.1%Henrywood and Agarwal, Equation (13)
9.7b-4.4%Toniolo and Linder, Equation (13)
7.6b7%Maksimov and Kolovsky, Equation (3)
5.6b76.6%Toniolo and Linder, Equation (7)
3.7b0%Henrywood and Agarwal, Equation (12)

localize6.2s

bsearch3.5s

end1.0ms