Average Error: 0.0 → 0.1
Time: 21.6s
Precision: binary64
Cost: 21056
\[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}\]
↓
\[\frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}} + \frac{NdChar}{1 + \sqrt[3]{e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT} \cdot 3}}}\]
\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}
↓
\frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}} + \frac{NdChar}{1 + \sqrt[3]{e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT} \cdot 3}}}
(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (+
  (/ NdChar (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))))
  (/ NaChar (+ 1.0 (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT))))))
↓
(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (+
  (/ NaChar (+ 1.0 (exp (/ (- (+ (+ Vef Ev) EAccept) mu) KbT))))
  (/
   NdChar
   (+ 1.0 (cbrt (exp (* (/ (- mu (- (- Ec Vef) EDonor)) KbT) 3.0)))))))
double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	return (NdChar / (1.0 + exp(-(((Ec - Vef) - EDonor) - mu) / KbT))) + (NaChar / (1.0 + exp((((Ev + Vef) + EAccept) + -mu) / KbT)));
}
↓
double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	return (NaChar / (1.0 + exp((((Vef + Ev) + EAccept) - mu) / KbT))) + (NdChar / (1.0 + cbrt(exp(((mu - ((Ec - Vef) - EDonor)) / KbT) * 3.0))));
}

Error

Bits error versus NdChar

Bits error versus Ec

Bits error versus Vef

Bits error versus EDonor

Bits error versus mu

Bits error versus KbT

Bits error versus NaChar

Bits error versus Ev

Bits error versus EAccept

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Alternatives

Alternative 1
Error0.0
Cost14528
\[\frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}}\]
Alternative 2
Error2.4
Cost14728
\[\begin{array}{l} \mathbf{if}\;mu \leq -2.8328638319249255 \cdot 10^{+30} \lor \neg \left(mu \leq 1.0245339146462255 \cdot 10^{-47}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor + \left(Vef + mu\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(Vef + EDonor\right) - Ec}{KbT}}}\\ \end{array}\]
Alternative 3
Error4.6
Cost14721
\[\begin{array}{l} \mathbf{if}\;Ec \leq 4.088554872931449 \cdot 10^{+153}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor + \left(Vef + mu\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}} + \frac{NdChar}{1 + e^{-\frac{Ec}{KbT}}}\\ \end{array}\]
Alternative 4
Error14.1
Cost16776
\[\begin{array}{l} \mathbf{if}\;Vef \leq -1.4053948343147115 \cdot 10^{+59}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}} + \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{elif}\;Vef \leq -3.0599551530578095 \cdot 10^{-145}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{elif}\;Vef \leq -3.294752565815866 \cdot 10^{-211}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}} + \frac{NdChar}{1 + e^{-\frac{Ec}{KbT}}}\\ \mathbf{elif}\;Vef \leq 1.391225305711632 \cdot 10^{-277}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{elif}\;Vef \leq 2.838117375807998 \cdot 10^{-107}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}} + \frac{NdChar}{1 + e^{-\frac{Ec}{KbT}}}\\ \mathbf{elif}\;Vef \leq 2.9511845217658305 \cdot 10^{-107}:\\ \;\;\;\;0\\ \mathbf{elif}\;Vef \leq 1.7886890628643488 \cdot 10^{+53}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{elif}\;Vef \leq 6.191549155749893 \cdot 10^{+173}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}} + \frac{NdChar}{1 + e^{-\frac{Ec}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}} + \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \end{array}\]
Alternative 5
Error14.8
Cost14472
\[\begin{array}{l} \mathbf{if}\;EDonor \leq -1.1746929784487831 \cdot 10^{+20} \lor \neg \left(EDonor \leq 9.378150138278924 \cdot 10^{+139}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \end{array}\]
Alternative 6
Error14.8
Cost14472
\[\begin{array}{l} \mathbf{if}\;EDonor \leq -3.744693307284445 \cdot 10^{+37} \lor \neg \left(EDonor \leq 1.5902483586030957 \cdot 10^{-14}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}} + \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \end{array}\]
Alternative 7
Error18.4
Cost14472
\[\begin{array}{l} \mathbf{if}\;NaChar \leq -1.621080494661621 \cdot 10^{-157} \lor \neg \left(NaChar \leq 2.832745812653842 \cdot 10^{-205}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}} + \frac{NaChar}{1 + \left(\left(\frac{EAccept}{KbT} + \left(\frac{Ev}{KbT} + \left(1 + \frac{Vef}{KbT}\right)\right)\right) - \frac{mu}{KbT}\right)}\\ \end{array}\]
Alternative 8
Error30.3
Cost11850
\[\begin{array}{l} \mathbf{if}\;Vef \leq -8.629595721620021 \cdot 10^{+256}:\\ \;\;\;\;0\\ \mathbf{elif}\;Vef \leq -2.5536374021517217 \cdot 10^{+183}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{elif}\;Vef \leq -3.3021256759429486 \cdot 10^{-104}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}} + \frac{NdChar}{1 + \left(\left(\frac{EDonor}{KbT} + \left(\frac{mu}{KbT} + \left(1 + \frac{Vef}{KbT}\right)\right)\right) - \frac{Ec}{KbT}\right)}\\ \mathbf{elif}\;Vef \leq -7.506021632030447 \cdot 10^{-261}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}} + \frac{NaChar}{1 + \left(\left(\frac{EAccept}{KbT} + \left(\frac{Ev}{KbT} + \left(1 + \frac{Vef}{KbT}\right)\right)\right) - \frac{mu}{KbT}\right)}\\ \mathbf{elif}\;Vef \leq 4.6559696032877494 \cdot 10^{-185}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}} + \frac{NdChar}{1 + \left(\left(\frac{EDonor}{KbT} + \left(\frac{mu}{KbT} + \left(1 + \frac{Vef}{KbT}\right)\right)\right) - \frac{Ec}{KbT}\right)}\\ \mathbf{elif}\;Vef \leq 1.956551918064716 \cdot 10^{+61}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}} + \frac{NaChar}{1 + \left(\left(\frac{EAccept}{KbT} + \left(\frac{Ev}{KbT} + \left(1 + \frac{Vef}{KbT}\right)\right)\right) - \frac{mu}{KbT}\right)}\\ \mathbf{elif}\;Vef \leq 1.410485124626147 \cdot 10^{+124}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{elif}\;Vef \leq 3.9344520676382454 \cdot 10^{+158}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{elif}\;Vef \leq 3.1632004568170373 \cdot 10^{+206}:\\ \;\;\;\;0\\ \mathbf{elif}\;Vef \leq 1.8264694626504873 \cdot 10^{+224}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}} + \frac{NaChar}{1 + \left(\left(\frac{EAccept}{KbT} + \left(\frac{Ev}{KbT} + \left(1 + \frac{Vef}{KbT}\right)\right)\right) - \frac{mu}{KbT}\right)}\\ \end{array}\]
Alternative 9
Error25.9
Cost10245
\[\begin{array}{l} \mathbf{if}\;NaChar \leq -7.88926300056861 \cdot 10^{+128}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{elif}\;NaChar \leq -7.736866173255707 \cdot 10^{-124}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}} + \frac{NaChar}{1 + \left(\left(\frac{EAccept}{KbT} + \left(\frac{Ev}{KbT} + \left(1 + \frac{Vef}{KbT}\right)\right)\right) - \frac{mu}{KbT}\right)}\\ \mathbf{elif}\;NaChar \leq -5.8212049171576495 \cdot 10^{-155}:\\ \;\;\;\;0\\ \mathbf{elif}\;NaChar \leq -5.6365748428798625 \cdot 10^{-188}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{elif}\;NaChar \leq 1.2670654023436142 \cdot 10^{+20}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}} + \frac{NaChar}{1 + \left(\left(\frac{EAccept}{KbT} + \left(\frac{Ev}{KbT} + \left(1 + \frac{Vef}{KbT}\right)\right)\right) - \frac{mu}{KbT}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}} + NdChar \cdot 0.5\\ \end{array}\]
Alternative 10
Error28.7
Cost8772
\[\begin{array}{l} \mathbf{if}\;NaChar \leq -6.659465260608525 \cdot 10^{-31}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{elif}\;NaChar \leq 4.07230268981671 \cdot 10^{-152}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{elif}\;NaChar \leq 6.038784831490222 \cdot 10^{-95}:\\ \;\;\;\;0\\ \mathbf{elif}\;NaChar \leq 1.3771840565544393 \cdot 10^{+20}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}} + NdChar \cdot 0.5\\ \end{array}\]
Alternative 11
Error34.5
Cost7816
\[\begin{array}{l} \mathbf{if}\;Ec \leq 4.297478264229415 \cdot 10^{+76} \lor \neg \left(Ec \leq 3.007228432256223 \cdot 10^{+112}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]
Alternative 12
Error50.3
Cost64
\[0\]
Alternative 13
Error61.9
Cost64
\[1\]

Error

Derivation

  1. Initial program 0.0

    \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}}}\]
  3. Using strategy rm

  4. Applied add-cbrt-cube_binary64_14780.1

    \[\leadsto \frac{NdChar}{1 + \color{blue}{\sqrt[3]{\left(e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}} \cdot e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}\right) \cdot e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}}\]

  5. Simplified0.1

    \[\leadsto \frac{NdChar}{1 + \sqrt[3]{\color{blue}{{\left(e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}\right)}^{3}}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}}\]
  6. Using strategy rm

  7. Applied pow-to-exp_binary64_15110.1

    \[\leadsto \frac{NdChar}{1 + \sqrt[3]{\color{blue}{e^{\log \left(e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}\right) \cdot 3}}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}}\]

  8. Simplified0.1

    \[\leadsto \frac{NdChar}{1 + \sqrt[3]{e^{\color{blue}{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT} \cdot 3}}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}}\]

  9. Simplified0.1

    \[\leadsto \color{blue}{\frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}} + \frac{NdChar}{1 + \sqrt[3]{e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT} \cdot 3}}}}\]

  10. Final simplification0.1

    \[\leadsto \frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}} + \frac{NdChar}{1 + \sqrt[3]{e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT} \cdot 3}}}\]

Reproduce

herbie shell --seed 2021044 
(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
  :name "Bulmash initializePoisson"
  :precision binary64
  (+ (/ NdChar (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT)))) (/ NaChar (+ 1.0 (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT))))))