Details

simplify3.8m (43.3%)

series1.6m (18.5%)

Calls

426 calls:

5.2s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))
5.0s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
5.0s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))))
5.0s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
1.5s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))

sample1.4m (16.0%)

Algorithm
61×intervals
Results
15.6s29368×body1280valid
15.5s253795×body80valid
9.6s161044×body80nan
8.7s8782×body2560valid
7.1s20111×body640valid
5.2s3342×body5120valid
2.4s9995×body320valid
1.2s9039×body160valid
465.0ms890×body10240exit
137.0ms609×body1280nan
112.0ms613×body640nan
95.0ms8256×pre80true
47.0ms353×body320nan
18.0ms199×body160nan

prune1.1m (12.2%)

rewrite37.5s (7.1%)

Algorithm
115×rewrite-expression-head
Calls

426 calls:

5.5s
(* (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))))
2.3s
(* (/ (/ (cbrt 1.0) (/ (sqrt (fabs (cbrt k))) (cbrt 1.0))) (sqrt (sqrt k))) (/ (cbrt 1.0) (sqrt (sqrt (cbrt k)))))
880.0ms
(* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
864.0ms
(cbrt (pow (/ NdChar (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT)))) 3))
853.0ms
(/ NdChar (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))))
Rules
33070×add-exp-log
23248×prod-exp
13639×times-frac
12272×pow-exp
9656×div-exp
9481×add-sqr-sqrt
7423×*-un-lft-identity
6785×add-cube-cbrt
5986×sqrt-prod
5609×pow-to-exp
3055×associate-*l*
2893×cbrt-prod
2434×add-cbrt-cube
1667×associate-*r*
1527×unpow-prod-down
1389×1-exp rec-exp
1097×pow1
940×cbrt-unprod
639×unswap-sqr
523×add-log-exp
468×cbrt-undiv
453×sqr-pow
425×associate-/l*
415×associate-*r/
369×div-inv
359×associate-/r*
325×pow-unpow
324×pow-prod-down
314×associate-/r/
308×sqrt-div
270×associate-*l/
218×distribute-lft-out--
196×flip-+ flip3-+
190×frac-times
182×flip3-- flip--
177×exp-prod
176×difference-of-squares
144×*-commutative
139×distribute-lft-out
137×distribute-lft-neg-in distribute-rgt-neg-in
108×sqrt-pow1
106×tan-quot
90×clear-num frac-2neg
82×distribute-rgt-in distribute-lft-in
78×cube-prod
73×pow1/2
70×rem-sqrt-square
68×sub-neg
62×unpow2
55×log-pow pow1/3
46×associate-/l/ pow-pow
35×frac-sub
34×sum-log
33×cbrt-div
27×div-sub
23×+-commutative
20×pow-sub
19×pow-flip
18×frac-add swap-sqr associate--l+
17×neg-mul-1 log-prod
16×diff-log neg-sub0
14×pow-neg
12×associate-+r+
11×exp-sum
exp-diff
pow-prod-up pow-sqr
unpow3 rem-exp-log inv-pow cube-mult distribute-frac-neg
cos-sum rem-cube-cbrt
un-div-inv exp-neg
pow-plus pow2 sum-cubes distribute-neg-frac rem-log-exp
cube-div associate-+l+ cos-diff acos-asin asin-acos rem-cbrt-cube associate--r+
log-div
sub-div associate--r- mul0

regimes11.5s (2.2%)

Accuracy

Total 45.5b remaining (20.8%)

Threshold costs 5.1b (2.3%)

8.9b13.4%Toniolo and Linder, Equation (13)
6.7b-2%Toniolo and Linder, Equation (10+)
5.4b56%Henrywood and Agarwal, Equation (3)
5.3b26.8%Toniolo and Linder, Equation (10-)
5.2b10.2%Henrywood and Agarwal, Equation (12)

bsearch2.5s (0.5%)

localize2.2s (0.4%)

end1.0ms (0.0%)