Average Error: 0.0 → 0.0
Time: 36.7s
Precision: binary64
Cost: 27456
\[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]
↓
\[\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + {\left({\left(e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}\right)}^{3}\right)}^{0.3333333333333333}} \]
(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
 (+
  (/ NdChar (+ 1.0 (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT))))
  (/
   NaChar
   (+
    1.0
    (pow
     (pow (exp (/ (+ Vef (+ Ev (- EAccept mu))) KbT)) 3.0)
     0.3333333333333333)))))
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 (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / (1.0 + pow(pow(exp(((Vef + (Ev + (EAccept - mu))) / KbT)), 3.0), 0.3333333333333333)));
}

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    code = (ndchar / (1.0d0 + exp((-(((ec - vef) - edonor) - mu) / kbt)))) + (nachar / (1.0d0 + exp(((((ev + vef) + eaccept) + -mu) / kbt))))
end function
↓
real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    code = (ndchar / (1.0d0 + exp(((mu + (edonor + (vef - ec))) / kbt)))) + (nachar / (1.0d0 + ((exp(((vef + (ev + (eaccept - mu))) / kbt)) ** 3.0d0) ** 0.3333333333333333d0)))
end function

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	return (NdChar / (1.0 + Math.exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + (NaChar / (1.0 + Math.exp(((((Ev + Vef) + EAccept) + -mu) / KbT))));
}
↓
public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	return (NdChar / (1.0 + Math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / (1.0 + Math.pow(Math.pow(Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)), 3.0), 0.3333333333333333)));
}

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	return (NdChar / (1.0 + math.exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + (NaChar / (1.0 + math.exp(((((Ev + Vef) + EAccept) + -mu) / KbT))))
↓
def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	return (NdChar / (1.0 + math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / (1.0 + math.pow(math.pow(math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)), 3.0), 0.3333333333333333)))

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	return Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(-Float64(Float64(Float64(Ec - Vef) - EDonor) - mu)) / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(Float64(Ev + Vef) + EAccept) + Float64(-mu)) / KbT)))))
end
↓
function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	return Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(mu + Float64(EDonor + Float64(Vef - Ec))) / KbT)))) + Float64(NaChar / Float64(1.0 + ((exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT)) ^ 3.0) ^ 0.3333333333333333))))
end

function tmp = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = (NdChar / (1.0 + exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + (NaChar / (1.0 + exp(((((Ev + Vef) + EAccept) + -mu) / KbT))));
end
↓
function tmp = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / (1.0 + ((exp(((Vef + (Ev + (EAccept - mu))) / KbT)) ^ 3.0) ^ 0.3333333333333333)));
end

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := N[(N[(NdChar / N[(1.0 + N[Exp[N[((-N[(N[(N[(Ec - Vef), $MachinePrecision] - EDonor), $MachinePrecision] - mu), $MachinePrecision]) / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(N[(Ev + Vef), $MachinePrecision] + EAccept), $MachinePrecision] + (-mu)), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
↓
code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Power[N[Power[N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision], 3.0], $MachinePrecision], 0.3333333333333333], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

\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{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + {\left({\left(e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}\right)}^{3}\right)}^{0.3333333333333333}}

Error

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

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

    \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) + \left(EAccept - mu\right)}{KbT}}}} \]
    Proof
    (+.f64 (/.f64 NdChar (+.f64 1 (exp.f64 (/.f64 (-.f64 mu (-.f64 (-.f64 Ec Vef) EDonor)) KbT)))) (/.f64 NaChar (+.f64 1 (exp.f64 (/.f64 (+.f64 (+.f64 Vef Ev) (-.f64 EAccept mu)) KbT))))): 0 points increase in error, 0 points decrease in error
    (+.f64 (/.f64 NdChar (+.f64 1 (exp.f64 (/.f64 (Rewrite=> sub-neg_binary64 (+.f64 mu (neg.f64 (-.f64 (-.f64 Ec Vef) EDonor)))) KbT)))) (/.f64 NaChar (+.f64 1 (exp.f64 (/.f64 (+.f64 (+.f64 Vef Ev) (-.f64 EAccept mu)) KbT))))): 0 points increase in error, 0 points decrease in error
    (+.f64 (/.f64 NdChar (+.f64 1 (exp.f64 (/.f64 (+.f64 (Rewrite<= remove-double-neg_binary64 (neg.f64 (neg.f64 mu))) (neg.f64 (-.f64 (-.f64 Ec Vef) EDonor))) KbT)))) (/.f64 NaChar (+.f64 1 (exp.f64 (/.f64 (+.f64 (+.f64 Vef Ev) (-.f64 EAccept mu)) KbT))))): 0 points increase in error, 0 points decrease in error
    (+.f64 (/.f64 NdChar (+.f64 1 (exp.f64 (/.f64 (Rewrite<= +-commutative_binary64 (+.f64 (neg.f64 (-.f64 (-.f64 Ec Vef) EDonor)) (neg.f64 (neg.f64 mu)))) KbT)))) (/.f64 NaChar (+.f64 1 (exp.f64 (/.f64 (+.f64 (+.f64 Vef Ev) (-.f64 EAccept mu)) KbT))))): 0 points increase in error, 0 points decrease in error
    (+.f64 (/.f64 NdChar (+.f64 1 (exp.f64 (/.f64 (Rewrite<= distribute-neg-in_binary64 (neg.f64 (+.f64 (-.f64 (-.f64 Ec Vef) EDonor) (neg.f64 mu)))) KbT)))) (/.f64 NaChar (+.f64 1 (exp.f64 (/.f64 (+.f64 (+.f64 Vef Ev) (-.f64 EAccept mu)) KbT))))): 0 points increase in error, 0 points decrease in error
    (+.f64 (/.f64 NdChar (+.f64 1 (exp.f64 (/.f64 (neg.f64 (Rewrite<= sub-neg_binary64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu))) KbT)))) (/.f64 NaChar (+.f64 1 (exp.f64 (/.f64 (+.f64 (+.f64 Vef Ev) (-.f64 EAccept mu)) KbT))))): 0 points increase in error, 0 points decrease in error
    (+.f64 (/.f64 NdChar (+.f64 1 (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 1 (exp.f64 (/.f64 (+.f64 (Rewrite<= +-commutative_binary64 (+.f64 Ev Vef)) (-.f64 EAccept mu)) KbT))))): 0 points increase in error, 0 points decrease in error
    (+.f64 (/.f64 NdChar (+.f64 1 (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 1 (exp.f64 (/.f64 (Rewrite<= associate--l+_binary64 (-.f64 (+.f64 (+.f64 Ev Vef) EAccept) mu)) KbT))))): 0 points increase in error, 0 points decrease in error
    (+.f64 (/.f64 NdChar (+.f64 1 (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 1 (exp.f64 (/.f64 (Rewrite<= unsub-neg_binary64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu))) KbT))))): 0 points increase in error, 0 points decrease in error

  3. Applied egg-rr0.0

    \[\leadsto \frac{NdChar}{1 + e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}} + \frac{NaChar}{1 + \color{blue}{{\left({\left(e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}\right)}^{3}\right)}^{0.3333333333333333}}} \]

  4. Final simplification0.0

    \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + {\left({\left(e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}\right)}^{3}\right)}^{0.3333333333333333}} \]

Alternatives

Alternative 1
Error0.0
Cost20928
\[\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + {e}^{\left(\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}\right)}} \]
Alternative 2
Error17.0
Cost15332
\[\begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{\left(EAccept - mu\right) + \left(Vef + Ev\right)}{KbT}}}\\ t_1 := t_0 + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ t_2 := t_0 + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ t_3 := \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}}\\ t_4 := t_3 + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{if}\;EDonor \leq -2.65 \cdot 10^{+75}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;EDonor \leq -2.8 \cdot 10^{-46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;EDonor \leq -7.5 \cdot 10^{-100}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;EDonor \leq -4.8 \cdot 10^{-279}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{elif}\;EDonor \leq 3.4 \cdot 10^{-253}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;EDonor \leq 7.7 \cdot 10^{-168}:\\ \;\;\;\;NdChar + t_0\\ \mathbf{elif}\;EDonor \leq 6.7 \cdot 10^{-105}:\\ \;\;\;\;t_3 + \frac{NaChar}{1 + \left(1 + -0.3333333333333333 \cdot \frac{\left(\left(Vef + \left(Ev + EAccept\right)\right) - mu\right) \cdot -3}{KbT}\right)}\\ \mathbf{elif}\;EDonor \leq 3.2 \cdot 10^{-7}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;EDonor \leq 2 \cdot 10^{+201}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
Alternative 3
Error21.1
Cost15276
\[\begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{-mu}{KbT}}}\\ t_2 := \left(Vef + \left(Ev + EAccept\right)\right) - mu\\ t_3 := \frac{NaChar}{1 + e^{\frac{t_2}{KbT}}}\\ t_4 := t_0 + \frac{NaChar}{1 + \left(1 + -0.3333333333333333 \cdot \frac{t_2 \cdot -3}{KbT}\right)}\\ t_5 := \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}}\\ t_6 := NdChar + \frac{NaChar}{1 + e^{\frac{\left(EAccept - mu\right) + \left(Vef + Ev\right)}{KbT}}}\\ \mathbf{if}\;mu \leq -2.3 \cdot 10^{+169}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;mu \leq -5.8 \cdot 10^{-304}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;mu \leq 1.2 \cdot 10^{-189}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;mu \leq 5.8 \cdot 10^{-140}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;mu \leq 2.7 \cdot 10^{-92}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;mu \leq 26.5:\\ \;\;\;\;t_5\\ \mathbf{elif}\;mu \leq 1.25 \cdot 10^{+67}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;mu \leq 1.75 \cdot 10^{+131}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;mu \leq 1.35 \cdot 10^{+145}:\\ \;\;\;\;t_0 + \frac{NaChar}{1 + \left(1 + \frac{Vef}{KbT}\right)}\\ \mathbf{elif}\;mu \leq 1.14 \cdot 10^{+179}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;mu \leq 5.5 \cdot 10^{+249}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 4
Error16.4
Cost15069
\[\begin{array}{l} t_0 := \left(Vef + \left(Ev + EAccept\right)\right) - mu\\ t_1 := \frac{NaChar}{1 + e^{\frac{\left(EAccept - mu\right) + \left(Vef + Ev\right)}{KbT}}}\\ t_2 := t_1 + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ t_3 := t_1 + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{if}\;EDonor \leq -3.05 \cdot 10^{+74}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;EDonor \leq -4.8 \cdot 10^{-50}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;EDonor \leq -1.15 \cdot 10^{-106}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{t_0}{KbT}}}\\ \mathbf{elif}\;EDonor \leq 8.2 \cdot 10^{-72}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{elif}\;EDonor \leq 3.4 \cdot 10^{-9}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;EDonor \leq 4.5 \cdot 10^{+57} \lor \neg \left(EDonor \leq 8.8 \cdot 10^{+133}\right):\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + \left(1 + -0.3333333333333333 \cdot \frac{t_0 \cdot -3}{KbT}\right)}\\ \end{array} \]
Alternative 5
Error22.5
Cost15068
\[\begin{array}{l} t_0 := \left(Vef + \left(Ev + EAccept\right)\right) - mu\\ t_1 := \frac{NaChar}{1 + e^{\frac{t_0}{KbT}}}\\ t_2 := \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + \left(1 + -0.3333333333333333 \cdot \frac{t_0 \cdot -3}{KbT}\right)}\\ t_3 := \frac{NaChar}{1 + e^{\frac{\left(EAccept - mu\right) + \left(Vef + Ev\right)}{KbT}}}\\ t_4 := t_3 + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ t_5 := NdChar + t_3\\ \mathbf{if}\;Ec \leq -3.8 \cdot 10^{+188}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;Ec \leq -1.1 \cdot 10^{+125}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;Ec \leq -2.15 \cdot 10^{-118}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;Ec \leq -1.25 \cdot 10^{-160}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;Ec \leq -3.5 \cdot 10^{-213}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;Ec \leq 3.1 \cdot 10^{-155}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;Ec \leq 2.7 \cdot 10^{+156}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
Alternative 6
Error0.0
Cost14528
\[\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(EAccept - mu\right) + \left(Vef + Ev\right)}{KbT}}} \]
Alternative 7
Error20.6
Cost9436
\[\begin{array}{l} t_0 := \left(Vef + \left(Ev + EAccept\right)\right) - mu\\ t_1 := NdChar + \frac{NaChar}{1 + e^{\frac{\left(EAccept - mu\right) + \left(Vef + Ev\right)}{KbT}}}\\ t_2 := \frac{NaChar}{1 + e^{\frac{t_0}{KbT}}}\\ t_3 := \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + \left(1 + -0.3333333333333333 \cdot \frac{t_0 \cdot -3}{KbT}\right)}\\ \mathbf{if}\;NdChar \leq -8 \cdot 10^{+140}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;NdChar \leq -3.6 \cdot 10^{+108}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;NdChar \leq -1.65 \cdot 10^{-50}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;NdChar \leq -1.8 \cdot 10^{-89}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;NdChar \leq -9.5 \cdot 10^{-128}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;NdChar \leq -6 \cdot 10^{-143}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;NdChar \leq 9 \cdot 10^{+16}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]
Alternative 8
Error29.2
Cost8818
\[\begin{array}{l} t_0 := \frac{NaChar}{2} + \frac{NdChar}{1 + e^{\frac{-Ec}{KbT}}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{\left(Vef + \left(Ev + EAccept\right)\right) - mu}{KbT}}}\\ t_2 := \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{if}\;Vef \leq -2.2 \cdot 10^{+98}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;Vef \leq -1.46 \cdot 10^{+35}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;Vef \leq -3.5 \cdot 10^{+17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;Vef \leq -1.35 \cdot 10^{-12}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;Vef \leq -1.1 \cdot 10^{-115}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;Vef \leq -1.25 \cdot 10^{-219}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;Vef \leq 2.35 \cdot 10^{-299}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;Vef \leq 2.35 \cdot 10^{-200}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{elif}\;Vef \leq 10^{-24} \lor \neg \left(Vef \leq 390000\right) \land \left(Vef \leq 5.8 \cdot 10^{+102} \lor \neg \left(Vef \leq 2.5 \cdot 10^{+137}\right)\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 9
Error21.8
Cost8532
\[\begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{\left(Vef + \left(Ev + EAccept\right)\right) - mu}{KbT}}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + \left(1 + \frac{Vef}{KbT}\right)}\\ t_2 := NdChar + \frac{NaChar}{1 + e^{\frac{\left(EAccept - mu\right) + \left(Vef + Ev\right)}{KbT}}}\\ \mathbf{if}\;NdChar \leq -4.2 \cdot 10^{+141}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;NdChar \leq -4.1 \cdot 10^{+102}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;NdChar \leq -5.4 \cdot 10^{-19}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;NdChar \leq -1.8 \cdot 10^{-89}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;NdChar \leq 2.65 \cdot 10^{+16}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 10
Error25.3
Cost8288
\[\begin{array}{l} t_0 := NdChar + \frac{NaChar}{1 + e^{\frac{\left(EAccept - mu\right) + \left(Vef + Ev\right)}{KbT}}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{\left(Vef + \left(Ev + EAccept\right)\right) - mu}{KbT}}}\\ \mathbf{if}\;NdChar \leq -3.1 \cdot 10^{+237}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{elif}\;NdChar \leq -6 \cdot 10^{+168}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;NdChar \leq -5 \cdot 10^{+140}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;NdChar \leq -3 \cdot 10^{+102}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;NdChar \leq -7.2 \cdot 10^{-19}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;NdChar \leq -1.35 \cdot 10^{-89}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;NdChar \leq 2.4 \cdot 10^{+223}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;NdChar \leq 4.9 \cdot 10^{+264}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{2} + \frac{NdChar}{1 + e^{\frac{-Ec}{KbT}}}\\ \end{array} \]
Alternative 11
Error23.9
Cost8284
\[\begin{array}{l} t_0 := NdChar + \frac{NaChar}{1 + e^{\frac{\left(EAccept - mu\right) + \left(Vef + Ev\right)}{KbT}}}\\ t_1 := \frac{NaChar}{2} + \frac{NdChar}{1 + e^{\frac{\left(Vef + EDonor\right) - Ec}{KbT}}}\\ t_2 := \frac{NaChar}{1 + e^{\frac{\left(Vef + \left(Ev + EAccept\right)\right) - mu}{KbT}}}\\ \mathbf{if}\;NdChar \leq -1.35 \cdot 10^{+195}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;NdChar \leq -1.45 \cdot 10^{+171}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;NdChar \leq -3.4 \cdot 10^{+142}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;NdChar \leq -5.4 \cdot 10^{+102}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;NdChar \leq -4.4 \cdot 10^{-17}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;NdChar \leq -1.8 \cdot 10^{-89}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;NdChar \leq 1.1 \cdot 10^{+68}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 12
Error23.5
Cost8284
\[\begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{\left(Vef + \left(Ev + EAccept\right)\right) - mu}{KbT}}}\\ t_1 := NdChar + \frac{NaChar}{1 + e^{\frac{\left(EAccept - mu\right) + \left(Vef + Ev\right)}{KbT}}}\\ t_2 := \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{if}\;NdChar \leq -5.2 \cdot 10^{+194}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;NdChar \leq -2.05 \cdot 10^{+170}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;NdChar \leq -3.6 \cdot 10^{+143}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;NdChar \leq -3.7 \cdot 10^{+102}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;NdChar \leq -3.3 \cdot 10^{-19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;NdChar \leq -1.8 \cdot 10^{-89}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;NdChar \leq 1.85 \cdot 10^{+67}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{2} + \frac{NdChar}{1 + e^{\frac{\left(Vef + EDonor\right) - Ec}{KbT}}}\\ \end{array} \]
Alternative 13
Error41.6
Cost7896
\[\begin{array}{l} t_0 := \frac{KbT}{\frac{Vef}{NdChar}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{if}\;KbT \leq -2.9 \cdot 10^{-111}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;KbT \leq -3.8 \cdot 10^{-255}:\\ \;\;\;\;t_0 + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{elif}\;KbT \leq 2.25 \cdot 10^{-292}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;KbT \leq 1.8 \cdot 10^{-60}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + t_0\\ \mathbf{elif}\;KbT \leq 2.2 \cdot 10^{+15}:\\ \;\;\;\;\frac{NdChar}{1 - \frac{Ec}{KbT}} + \frac{NaChar}{1 + \left(\left(\frac{Ev}{KbT} + \left(\left(1 + \frac{Vef}{KbT}\right) + \frac{EAccept}{KbT}\right)\right) - \frac{mu}{KbT}\right)}\\ \mathbf{elif}\;KbT \leq 2.6 \cdot 10^{+81}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 14
Error46.9
Cost7761
\[\begin{array}{l} \mathbf{if}\;EAccept \leq 3.1 \cdot 10^{+63}:\\ \;\;\;\;\frac{NaChar}{2} + \frac{NdChar}{2}\\ \mathbf{elif}\;EAccept \leq 1.9 \cdot 10^{+195} \lor \neg \left(EAccept \leq 3.4 \cdot 10^{+230}\right) \land EAccept \leq 6.2 \cdot 10^{+274}:\\ \;\;\;\;\frac{NdChar}{1 - \frac{Ec}{KbT}} + \frac{NaChar}{1 + \left(\left(\frac{Ev}{KbT} + \left(\left(1 + \frac{Vef}{KbT}\right) + \frac{EAccept}{KbT}\right)\right) - \frac{mu}{KbT}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{KbT}{\frac{Vef}{NdChar}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \end{array} \]
Alternative 15
Error41.4
Cost7761
\[\begin{array}{l} t_0 := \frac{KbT}{\frac{Vef}{NdChar}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{if}\;KbT \leq -5.2 \cdot 10^{-111}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;KbT \leq -2.1 \cdot 10^{-255}:\\ \;\;\;\;t_0 + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{elif}\;KbT \leq 2.25 \cdot 10^{-292} \lor \neg \left(KbT \leq 8.8 \cdot 10^{-62}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + t_0\\ \end{array} \]
Alternative 16
Error25.7
Cost7760
\[\begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{\left(Vef + \left(Ev + EAccept\right)\right) - mu}{KbT}}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{if}\;KbT \leq -2.1 \cdot 10^{+122}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;KbT \leq 4.8 \cdot 10^{-20}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;KbT \leq 3.5 \cdot 10^{+33}:\\ \;\;\;\;\frac{NdChar}{1 - \frac{Ec}{KbT}} + \frac{NaChar}{1 + \left(\left(\frac{Ev}{KbT} + \left(\left(1 + \frac{Vef}{KbT}\right) + \frac{EAccept}{KbT}\right)\right) - \frac{mu}{KbT}\right)}\\ \mathbf{elif}\;KbT \leq 1.65 \cdot 10^{+226}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 17
Error45.1
Cost7628
\[\begin{array}{l} t_0 := \frac{KbT}{\frac{Vef}{NdChar}}\\ \mathbf{if}\;KbT \leq -2.65 \cdot 10^{+36}:\\ \;\;\;\;\frac{NaChar}{2} + \frac{NdChar}{2}\\ \mathbf{elif}\;KbT \leq 6.4 \cdot 10^{-273}:\\ \;\;\;\;t_0 + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{elif}\;KbT \leq 7.4 \cdot 10^{-60}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 - \frac{Ec}{KbT}} + \frac{NaChar}{1 + \left(\left(\frac{Ev}{KbT} + \left(\left(1 + \frac{Vef}{KbT}\right) + \frac{EAccept}{KbT}\right)\right) - \frac{mu}{KbT}\right)}\\ \end{array} \]
Alternative 18
Error46.1
Cost2252
\[\begin{array}{l} t_0 := \frac{NdChar}{1 - \frac{Ec}{KbT}}\\ \mathbf{if}\;KbT \leq -2.6 \cdot 10^{+123}:\\ \;\;\;\;\frac{NaChar}{2} + \frac{NdChar}{2}\\ \mathbf{elif}\;KbT \leq -5.8 \cdot 10^{-163}:\\ \;\;\;\;t_0 + NaChar \cdot 0.5\\ \mathbf{elif}\;KbT \leq 1.5 \cdot 10^{-95}:\\ \;\;\;\;\frac{NdChar}{\frac{Vef}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;t_0 + \frac{NaChar}{1 + \left(\left(\frac{Ev}{KbT} + \left(\left(1 + \frac{Vef}{KbT}\right) + \frac{EAccept}{KbT}\right)\right) - \frac{mu}{KbT}\right)}\\ \end{array} \]
Alternative 19
Error45.9
Cost1101
\[\begin{array}{l} \mathbf{if}\;KbT \leq -4 \cdot 10^{+123}:\\ \;\;\;\;\frac{NaChar}{2} + \frac{NdChar}{2}\\ \mathbf{elif}\;KbT \leq -1.55 \cdot 10^{-171} \lor \neg \left(KbT \leq 8 \cdot 10^{-113}\right):\\ \;\;\;\;\frac{NdChar}{1 - \frac{Ec}{KbT}} + NaChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{\frac{Vef}{KbT}}\\ \end{array} \]
Alternative 20
Error45.5
Cost713
\[\begin{array}{l} \mathbf{if}\;KbT \leq -4.6 \cdot 10^{-174} \lor \neg \left(KbT \leq 1.35 \cdot 10^{-113}\right):\\ \;\;\;\;\frac{NaChar}{2} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{\frac{Vef}{KbT}}\\ \end{array} \]
Alternative 21
Error51.2
Cost585
\[\begin{array}{l} \mathbf{if}\;KbT \leq -2.95 \cdot 10^{-164} \lor \neg \left(KbT \leq 3.95 \cdot 10^{-115}\right):\\ \;\;\;\;NaChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{\frac{Vef}{KbT}}\\ \end{array} \]
Alternative 22
Error52.6
Cost192
\[NaChar \cdot 0.5 \]

Error

Reproduce

herbie shell --seed 2022343 
(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))))))