Average Error: 0.0 → 0.0

Time: 13.6s

Precision: binary64

Cost: 60544

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

↓

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

\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 + {\left(e^{\frac{\sqrt[3]{mu - \left(\left(Ec - Vef\right) - EDonor\right)} \cdot \sqrt[3]{mu - \left(\left(Ec - Vef\right) - EDonor\right)}}{\sqrt[3]{KbT} \cdot \sqrt[3]{KbT}}}\right)}^{\left(\frac{\sqrt[3]{mu - \left(\left(Ec - Vef\right) - EDonor\right)}}{\sqrt[3]{KbT}}\right)}}

(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
    (pow
     (exp
      (/
       (*
        (cbrt (- mu (- (- Ec Vef) EDonor)))
        (cbrt (- mu (- (- Ec Vef) EDonor))))
       (* (cbrt KbT) (cbrt KbT))))
     (/ (cbrt (- mu (- (- Ec Vef) EDonor))) (cbrt KbT)))))))

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 + pow(exp((cbrt(mu - ((Ec - Vef) - EDonor)) * cbrt(mu - ((Ec - Vef) - EDonor))) / (cbrt(KbT) * cbrt(KbT))), (cbrt(mu - ((Ec - Vef) - EDonor)) / cbrt(KbT)))));
}

Error

The X axis uses an exponential scale — Bits error versus `NdChar`

Try it out

In
Out

Enter valid numbers for all inputs

Alternatives

Alternative 1
Error	32.8
Cost	53632

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

Alternative 2
Error	0.0
Cost	41344

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

Alternative 3
Error	19.5
Cost	34624

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

Alternative 4
Error	0.1
Cost	27328

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

Alternative 5
Error	36.5
Cost	21824

\[\frac{NdChar}{1 + e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}} + \frac{NaChar}{1 - e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT} \cdot 2}} \cdot \left(1 - e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}\right)\]

Alternative 6
Error	14.3
Cost	21056

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

Alternative 7
Error	34.2
Cost	20288

\[\frac{NdChar}{2} + \frac{NaChar}{1 + \log \left(e^{e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}}\right)}\]

Alternative 8
Error	0.1
Cost	14656

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

Alternative 9
Error	0.0
Cost	14528

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

Alternative 10
Error	5.5
Cost	14528

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

Alternative 11
Error	6.0
Cost	14400

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

Alternative 12
Error	5.4
Cost	14400

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

Alternative 13
Error	20.1
Cost	14272

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

Alternative 14
Error	19.8
Cost	14208

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

Alternative 15
Error	20.1
Cost	14144

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

Alternative 16
Error	19.4
Cost	14144

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

Alternative 17
Error	19.9
Cost	14144

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

Alternative 18
Error	30.1
Cost	8768

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

Alternative 19
Error	30.0
Cost	8640

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

Alternative 20
Error	29.8
Cost	8640

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

Alternative 21
Error	34.1
Cost	7488

\[\frac{NdChar}{1 + e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}} + NaChar \cdot 0.5\]

Alternative 22
Error	34.1
Cost	7488

\[\frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}} + \frac{NdChar}{2}\]

Alternative 23
Error	34.1
Cost	7488

\[\frac{NdChar}{1 + e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}} + \frac{NaChar}{2}\]

Alternative 24
Error	61.8
Cost	64

\[1\]

Alternative 25
Error	50.3
Cost	64

\[0\]

Alternative 26
Error	61.8
Cost	64

\[-1\]

Derivation

Initial program 0.0
\[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}}\]
Simplified0.0
\[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}}}\]
Using strategy rm
Applied add-cube-cbrt_binary64_17710.0
\[\leadsto \frac{NdChar}{1 + e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{\color{blue}{\left(\sqrt[3]{KbT} \cdot \sqrt[3]{KbT}\right) \cdot \sqrt[3]{KbT}}}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}}\]
Applied add-cube-cbrt_binary64_17710.0
\[\leadsto \frac{NdChar}{1 + e^{\frac{\color{blue}{\left(\sqrt[3]{mu - \left(\left(Ec - Vef\right) - EDonor\right)} \cdot \sqrt[3]{mu - \left(\left(Ec - Vef\right) - EDonor\right)}\right) \cdot \sqrt[3]{mu - \left(\left(Ec - Vef\right) - EDonor\right)}}}{\left(\sqrt[3]{KbT} \cdot \sqrt[3]{KbT}\right) \cdot \sqrt[3]{KbT}}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}}\]
Applied times-frac_binary64_17420.0
\[\leadsto \frac{NdChar}{1 + e^{\color{blue}{\frac{\sqrt[3]{mu - \left(\left(Ec - Vef\right) - EDonor\right)} \cdot \sqrt[3]{mu - \left(\left(Ec - Vef\right) - EDonor\right)}}{\sqrt[3]{KbT} \cdot \sqrt[3]{KbT}} \cdot \frac{\sqrt[3]{mu - \left(\left(Ec - Vef\right) - EDonor\right)}}{\sqrt[3]{KbT}}}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}}\]
Applied exp-prod_binary64_17880.0
\[\leadsto \frac{NdChar}{1 + \color{blue}{{\left(e^{\frac{\sqrt[3]{mu - \left(\left(Ec - Vef\right) - EDonor\right)} \cdot \sqrt[3]{mu - \left(\left(Ec - Vef\right) - EDonor\right)}}{\sqrt[3]{KbT} \cdot \sqrt[3]{KbT}}}\right)}^{\left(\frac{\sqrt[3]{mu - \left(\left(Ec - Vef\right) - EDonor\right)}}{\sqrt[3]{KbT}}\right)}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}}\]
Simplified0.0
\[\leadsto \color{blue}{\frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}} + \frac{NdChar}{1 + {\left(e^{\frac{\sqrt[3]{mu - \left(\left(Ec - Vef\right) - EDonor\right)} \cdot \sqrt[3]{mu - \left(\left(Ec - Vef\right) - EDonor\right)}}{\sqrt[3]{KbT} \cdot \sqrt[3]{KbT}}}\right)}^{\left(\frac{\sqrt[3]{mu - \left(\left(Ec - Vef\right) - EDonor\right)}}{\sqrt[3]{KbT}}\right)}}}\]
Final simplification0.0
\[\leadsto \frac{NaChar}{1 + e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}}} + \frac{NdChar}{1 + {\left(e^{\frac{\sqrt[3]{mu - \left(\left(Ec - Vef\right) - EDonor\right)} \cdot \sqrt[3]{mu - \left(\left(Ec - Vef\right) - EDonor\right)}}{\sqrt[3]{KbT} \cdot \sqrt[3]{KbT}}}\right)}^{\left(\frac{\sqrt[3]{mu - \left(\left(Ec - Vef\right) - EDonor\right)}}{\sqrt[3]{KbT}}\right)}}\]

Reproduce

herbie shell --seed 2021042 
(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))))))