Quotient of sum of exps

Percentage Accurate: 98.8% → 98.8%

Time: 4.5s

Alternatives: 8

Speedup: 1.0×

• could not determine a ground truth

  1. a = -2.00000000000000007e154
  2. b = -2.00000000000000007e154

Specification

Math

\[\begin{array}{l} \\ \frac{e^{a}}{e^{a} + e^{b}} \end{array} \]

FPCore

(FPCore (a b) :precision binary64 (/ (exp a) (+ (exp a) (exp b))))

C

double code(double a, double b) {
	return exp(a) / (exp(a) + exp(b));
}

Fortran

real(8) function code(a, b)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = exp(a) / (exp(a) + exp(b))
end function

Java

public static double code(double a, double b) {
	return Math.exp(a) / (Math.exp(a) + Math.exp(b));
}

Python

def code(a, b):
	return math.exp(a) / (math.exp(a) + math.exp(b))

Julia

function code(a, b)
	return Float64(exp(a) / Float64(exp(a) + exp(b)))
end

MATLAB

function tmp = code(a, b)
	tmp = exp(a) / (exp(a) + exp(b));
end

Wolfram

code[a_, b_] := N[(N[Exp[a], $MachinePrecision] / N[(N[Exp[a], $MachinePrecision] + N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 98.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{e^{a}}{e^{a} + e^{b}} \end{array} \]

FPCore

(FPCore (a b) :precision binary64 (/ (exp a) (+ (exp a) (exp b))))

C

double code(double a, double b) {
	return exp(a) / (exp(a) + exp(b));
}

Fortran

real(8) function code(a, b)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = exp(a) / (exp(a) + exp(b))
end function

Java

public static double code(double a, double b) {
	return Math.exp(a) / (Math.exp(a) + Math.exp(b));
}

Python

def code(a, b):
	return math.exp(a) / (math.exp(a) + math.exp(b))

Julia

function code(a, b)
	return Float64(exp(a) / Float64(exp(a) + exp(b)))
end

MATLAB

function tmp = code(a, b)
	tmp = exp(a) / (exp(a) + exp(b));
end

Wolfram

code[a_, b_] := N[(N[Exp[a], $MachinePrecision] / N[(N[Exp[a], $MachinePrecision] + N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 98.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{e^{a}}{e^{a} + e^{b}} \end{array} \]

FPCore

(FPCore (a b) :precision binary64 (/ (exp a) (+ (exp a) (exp b))))

C

double code(double a, double b) {
	return exp(a) / (exp(a) + exp(b));
}

Fortran

real(8) function code(a, b)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = exp(a) / (exp(a) + exp(b))
end function

Java

public static double code(double a, double b) {
	return Math.exp(a) / (Math.exp(a) + Math.exp(b));
}

Python

def code(a, b):
	return math.exp(a) / (math.exp(a) + math.exp(b))

Julia

function code(a, b)
	return Float64(exp(a) / Float64(exp(a) + exp(b)))
end

MATLAB

function tmp = code(a, b)
	tmp = exp(a) / (exp(a) + exp(b));
end

Wolfram

code[a_, b_] := N[(N[Exp[a], $MachinePrecision] / N[(N[Exp[a], $MachinePrecision] + N[Exp[b], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.6%

   \[\frac{e^{a}}{e^{a} + e^{b}} \]

2. Final simplification 99.6%

   \[\leadsto \frac{e^{a}}{e^{a} + e^{b}} \]

Alternative 2: 97.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;e^{a} \leq 0.999999999995:\\ \;\;\;\;\frac{e^{a}}{e^{a} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{e^{b} + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b)
 :precision binary64
 (if (<= (exp a) 0.999999999995)
   (/ (exp a) (+ (exp a) 1.0))
   (/ 1.0 (+ (exp b) 1.0))))

C

double code(double a, double b) {
	double tmp;
	if (exp(a) <= 0.999999999995) {
		tmp = exp(a) / (exp(a) + 1.0);
	} else {
		tmp = 1.0 / (exp(b) + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(a, b)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (exp(a) <= 0.999999999995d0) then
        tmp = exp(a) / (exp(a) + 1.0d0)
    else
        tmp = 1.0d0 / (exp(b) + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double a, double b) {
	double tmp;
	if (Math.exp(a) <= 0.999999999995) {
		tmp = Math.exp(a) / (Math.exp(a) + 1.0);
	} else {
		tmp = 1.0 / (Math.exp(b) + 1.0);
	}
	return tmp;
}

Python

def code(a, b):
	tmp = 0
	if math.exp(a) <= 0.999999999995:
		tmp = math.exp(a) / (math.exp(a) + 1.0)
	else:
		tmp = 1.0 / (math.exp(b) + 1.0)
	return tmp

Julia

function code(a, b)
	tmp = 0.0
	if (exp(a) <= 0.999999999995)
		tmp = Float64(exp(a) / Float64(exp(a) + 1.0));
	else
		tmp = Float64(1.0 / Float64(exp(b) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b)
	tmp = 0.0;
	if (exp(a) <= 0.999999999995)
		tmp = exp(a) / (exp(a) + 1.0);
	else
		tmp = 1.0 / (exp(b) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_] := If[LessEqual[N[Exp[a], $MachinePrecision], 0.999999999995], N[(N[Exp[a], $MachinePrecision] / N[(N[Exp[a], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(N[Exp[b], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (exp.f64 a) < 0.999999999995

   1. Initial program 98.6%

      \[\frac{e^{a}}{e^{a} + e^{b}} \]

   2. Taylor expanded in b around 0 97.4%

      \[\leadsto \color{blue}{\frac{e^{a}}{1 + e^{a}}} \]

   if 0.999999999995 < (exp.f64 a)

   1. Initial program 100.0%

      \[\frac{e^{a}}{e^{a} + e^{b}} \]

   2. Taylor expanded in a around 0 98.9%

      \[\leadsto \color{blue}{\frac{1}{1 + e^{b}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;e^{a} \leq 0.999999999995:\\ \;\;\;\;\frac{e^{a}}{e^{a} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{e^{b} + 1}\\ \end{array} \]

Alternative 3: 97.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;e^{a} \leq 0.999999999995:\\ \;\;\;\;e^{a} \cdot \left(0.5 + a \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{e^{b} + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b)
 :precision binary64
 (if (<= (exp a) 0.999999999995)
   (* (exp a) (+ 0.5 (* a -0.25)))
   (/ 1.0 (+ (exp b) 1.0))))

C

double code(double a, double b) {
	double tmp;
	if (exp(a) <= 0.999999999995) {
		tmp = exp(a) * (0.5 + (a * -0.25));
	} else {
		tmp = 1.0 / (exp(b) + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(a, b)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (exp(a) <= 0.999999999995d0) then
        tmp = exp(a) * (0.5d0 + (a * (-0.25d0)))
    else
        tmp = 1.0d0 / (exp(b) + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double a, double b) {
	double tmp;
	if (Math.exp(a) <= 0.999999999995) {
		tmp = Math.exp(a) * (0.5 + (a * -0.25));
	} else {
		tmp = 1.0 / (Math.exp(b) + 1.0);
	}
	return tmp;
}

Python

def code(a, b):
	tmp = 0
	if math.exp(a) <= 0.999999999995:
		tmp = math.exp(a) * (0.5 + (a * -0.25))
	else:
		tmp = 1.0 / (math.exp(b) + 1.0)
	return tmp

Julia

function code(a, b)
	tmp = 0.0
	if (exp(a) <= 0.999999999995)
		tmp = Float64(exp(a) * Float64(0.5 + Float64(a * -0.25)));
	else
		tmp = Float64(1.0 / Float64(exp(b) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b)
	tmp = 0.0;
	if (exp(a) <= 0.999999999995)
		tmp = exp(a) * (0.5 + (a * -0.25));
	else
		tmp = 1.0 / (exp(b) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_] := If[LessEqual[N[Exp[a], $MachinePrecision], 0.999999999995], N[(N[Exp[a], $MachinePrecision] * N[(0.5 + N[(a * -0.25), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(N[Exp[b], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (exp.f64 a) < 0.999999999995

   1. Initial program 98.6%

      \[\frac{e^{a}}{e^{a} + e^{b}} \]
   2. Step-by-step derivation

      1. clear-num 98.6%

         \[\leadsto \color{blue}{\frac{1}{\frac{e^{a} + e^{b}}{e^{a}}}} \]

      2. associate-/r/ 98.6%

         \[\leadsto \color{blue}{\frac{1}{e^{a} + e^{b}} \cdot e^{a}} \]

   3. Applied egg-rr 98.6%

      \[\leadsto \color{blue}{\frac{1}{e^{a} + e^{b}} \cdot e^{a}} \]

   4. Taylor expanded in b around 0 97.4%

      \[\leadsto \color{blue}{\frac{1}{1 + e^{a}}} \cdot e^{a} \]

   5. Taylor expanded in a around 0 94.3%

      \[\leadsto \color{blue}{\left(0.5 + -0.25 \cdot a\right)} \cdot e^{a} \]
   6. Step-by-step derivation

      1. *-commutative 94.3%

         \[\leadsto \left(0.5 + \color{blue}{a \cdot -0.25}\right) \cdot e^{a} \]

   7. Simplified 94.3%

      \[\leadsto \color{blue}{\left(0.5 + a \cdot -0.25\right)} \cdot e^{a} \]

   if 0.999999999995 < (exp.f64 a)

   1. Initial program 100.0%

      \[\frac{e^{a}}{e^{a} + e^{b}} \]

   2. Taylor expanded in a around 0 98.9%

      \[\leadsto \color{blue}{\frac{1}{1 + e^{b}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 97.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;e^{a} \leq 0.999999999995:\\ \;\;\;\;e^{a} \cdot \left(0.5 + a \cdot -0.25\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{e^{b} + 1}\\ \end{array} \]

Alternative 4: 98.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;e^{a} \leq 0.1:\\ \;\;\;\;\frac{e^{a}}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{e^{b} + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b)
 :precision binary64
 (if (<= (exp a) 0.1) (/ (exp a) 2.0) (/ 1.0 (+ (exp b) 1.0))))

C

double code(double a, double b) {
	double tmp;
	if (exp(a) <= 0.1) {
		tmp = exp(a) / 2.0;
	} else {
		tmp = 1.0 / (exp(b) + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(a, b)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (exp(a) <= 0.1d0) then
        tmp = exp(a) / 2.0d0
    else
        tmp = 1.0d0 / (exp(b) + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double a, double b) {
	double tmp;
	if (Math.exp(a) <= 0.1) {
		tmp = Math.exp(a) / 2.0;
	} else {
		tmp = 1.0 / (Math.exp(b) + 1.0);
	}
	return tmp;
}

Python

def code(a, b):
	tmp = 0
	if math.exp(a) <= 0.1:
		tmp = math.exp(a) / 2.0
	else:
		tmp = 1.0 / (math.exp(b) + 1.0)
	return tmp

Julia

function code(a, b)
	tmp = 0.0
	if (exp(a) <= 0.1)
		tmp = Float64(exp(a) / 2.0);
	else
		tmp = Float64(1.0 / Float64(exp(b) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b)
	tmp = 0.0;
	if (exp(a) <= 0.1)
		tmp = exp(a) / 2.0;
	else
		tmp = 1.0 / (exp(b) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_] := If[LessEqual[N[Exp[a], $MachinePrecision], 0.1], N[(N[Exp[a], $MachinePrecision] / 2.0), $MachinePrecision], N[(1.0 / N[(N[Exp[b], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (exp.f64 a) < 0.10000000000000001

   1. Initial program 98.6%

      \[\frac{e^{a}}{e^{a} + e^{b}} \]

   2. Taylor expanded in b around 0 98.6%

      \[\leadsto \color{blue}{\frac{e^{a}}{1 + e^{a}}} \]

   3. Taylor expanded in a around 0 96.2%

      \[\leadsto \frac{e^{a}}{\color{blue}{2}} \]

   if 0.10000000000000001 < (exp.f64 a)

   1. Initial program 100.0%

      \[\frac{e^{a}}{e^{a} + e^{b}} \]

   2. Taylor expanded in a around 0 97.5%

      \[\leadsto \color{blue}{\frac{1}{1 + e^{b}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 97.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;e^{a} \leq 0.1:\\ \;\;\;\;\frac{e^{a}}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{e^{b} + 1}\\ \end{array} \]

Alternative 5: 67.5% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 1.7 \cdot 10^{+19}:\\ \;\;\;\;\frac{e^{a}}{2}\\ \mathbf{else}:\\ \;\;\;\;-0.020833333333333332 \cdot {a}^{3}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b)
 :precision binary64
 (if (<= b 1.7e+19) (/ (exp a) 2.0) (* -0.020833333333333332 (pow a 3.0))))

C

double code(double a, double b) {
	double tmp;
	if (b <= 1.7e+19) {
		tmp = exp(a) / 2.0;
	} else {
		tmp = -0.020833333333333332 * pow(a, 3.0);
	}
	return tmp;
}

Fortran

real(8) function code(a, b)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 1.7d+19) then
        tmp = exp(a) / 2.0d0
    else
        tmp = (-0.020833333333333332d0) * (a ** 3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double a, double b) {
	double tmp;
	if (b <= 1.7e+19) {
		tmp = Math.exp(a) / 2.0;
	} else {
		tmp = -0.020833333333333332 * Math.pow(a, 3.0);
	}
	return tmp;
}

Python

def code(a, b):
	tmp = 0
	if b <= 1.7e+19:
		tmp = math.exp(a) / 2.0
	else:
		tmp = -0.020833333333333332 * math.pow(a, 3.0)
	return tmp

Julia

function code(a, b)
	tmp = 0.0
	if (b <= 1.7e+19)
		tmp = Float64(exp(a) / 2.0);
	else
		tmp = Float64(-0.020833333333333332 * (a ^ 3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b)
	tmp = 0.0;
	if (b <= 1.7e+19)
		tmp = exp(a) / 2.0;
	else
		tmp = -0.020833333333333332 * (a ^ 3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_] := If[LessEqual[b, 1.7e+19], N[(N[Exp[a], $MachinePrecision] / 2.0), $MachinePrecision], N[(-0.020833333333333332 * N[Power[a, 3.0], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 1.7e19

   1. Initial program 99.4%

      \[\frac{e^{a}}{e^{a} + e^{b}} \]

   2. Taylor expanded in b around 0 79.3%

      \[\leadsto \color{blue}{\frac{e^{a}}{1 + e^{a}}} \]

   3. Taylor expanded in a around 0 76.1%

      \[\leadsto \frac{e^{a}}{\color{blue}{2}} \]

   if 1.7e19 < b

   1. Initial program 100.0%

      \[\frac{e^{a}}{e^{a} + e^{b}} \]

   2. Taylor expanded in b around 0 34.4%

      \[\leadsto \color{blue}{\frac{e^{a}}{1 + e^{a}}} \]

   3. Taylor expanded in a around 0 2.7%

      \[\leadsto \color{blue}{-0.020833333333333332 \cdot {a}^{3} + \left(0.5 + 0.25 \cdot a\right)} \]

   4. Taylor expanded in a around inf 45.0%

      \[\leadsto \color{blue}{-0.020833333333333332 \cdot {a}^{3}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 1.7 \cdot 10^{+19}:\\ \;\;\;\;\frac{e^{a}}{2}\\ \mathbf{else}:\\ \;\;\;\;-0.020833333333333332 \cdot {a}^{3}\\ \end{array} \]

Alternative 6: 64.3% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \frac{e^{a}}{2} \end{array} \]

FPCore

(FPCore (a b) :precision binary64 (/ (exp a) 2.0))

C

double code(double a, double b) {
	return exp(a) / 2.0;
}

Fortran

real(8) function code(a, b)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = exp(a) / 2.0d0
end function

Java

public static double code(double a, double b) {
	return Math.exp(a) / 2.0;
}

Python

def code(a, b):
	return math.exp(a) / 2.0

Julia

function code(a, b)
	return Float64(exp(a) / 2.0)
end

MATLAB

function tmp = code(a, b)
	tmp = exp(a) / 2.0;
end

Wolfram

code[a_, b_] := N[(N[Exp[a], $MachinePrecision] / 2.0), $MachinePrecision]

Derivation

1. Initial program 99.6%

   \[\frac{e^{a}}{e^{a} + e^{b}} \]

2. Taylor expanded in b around 0 68.5%

   \[\leadsto \color{blue}{\frac{e^{a}}{1 + e^{a}}} \]

3. Taylor expanded in a around 0 66.0%

   \[\leadsto \frac{e^{a}}{\color{blue}{2}} \]

4. Final simplification 66.0%

   \[\leadsto \frac{e^{a}}{2} \]

Alternative 7: 38.7% accurate, 61.0× speedup

Math

\[\begin{array}{l} \\ 0.5 + a \cdot 0.25 \end{array} \]

FPCore

(FPCore (a b) :precision binary64 (+ 0.5 (* a 0.25)))

C

double code(double a, double b) {
	return 0.5 + (a * 0.25);
}

Fortran

real(8) function code(a, b)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = 0.5d0 + (a * 0.25d0)
end function

Java

public static double code(double a, double b) {
	return 0.5 + (a * 0.25);
}

Python

def code(a, b):
	return 0.5 + (a * 0.25)

Julia

function code(a, b)
	return Float64(0.5 + Float64(a * 0.25))
end

MATLAB

function tmp = code(a, b)
	tmp = 0.5 + (a * 0.25);
end

Wolfram

code[a_, b_] := N[(0.5 + N[(a * 0.25), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.6%

   \[\frac{e^{a}}{e^{a} + e^{b}} \]

2. Taylor expanded in b around 0 68.5%

   \[\leadsto \color{blue}{\frac{e^{a}}{1 + e^{a}}} \]

3. Taylor expanded in a around 0 42.1%

   \[\leadsto \color{blue}{0.5 + 0.25 \cdot a} \]
4. Step-by-step derivation

   1. *-commutative 42.1%

      \[\leadsto 0.5 + \color{blue}{a \cdot 0.25} \]

5. Simplified 42.1%

   \[\leadsto \color{blue}{0.5 + a \cdot 0.25} \]

6. Final simplification 42.1%

   \[\leadsto 0.5 + a \cdot 0.25 \]

Alternative 8: 38.5% accurate, 305.0× speedup

Math

\[\begin{array}{l} \\ 0.5 \end{array} \]

FPCore

(FPCore (a b) :precision binary64 0.5)

C

double code(double a, double b) {
	return 0.5;
}

Fortran

real(8) function code(a, b)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = 0.5d0
end function

Java

public static double code(double a, double b) {
	return 0.5;
}

Python

def code(a, b):
	return 0.5

Julia

function code(a, b)
	return 0.5
end

MATLAB

function tmp = code(a, b)
	tmp = 0.5;
end

Wolfram

code[a_, b_] := 0.5

Derivation

1. Initial program 99.6%

   \[\frac{e^{a}}{e^{a} + e^{b}} \]

2. Taylor expanded in a around 0 80.8%

   \[\leadsto \color{blue}{\frac{1}{1 + e^{b}}} \]

3. Taylor expanded in b around 0 41.0%

   \[\leadsto \color{blue}{0.5} \]

4. Final simplification 41.0%

   \[\leadsto 0.5 \]

Developer target: 100.0% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \frac{1}{1 + e^{b - a}} \end{array} \]

FPCore

(FPCore (a b) :precision binary64 (/ 1.0 (+ 1.0 (exp (- b a)))))

C

double code(double a, double b) {
	return 1.0 / (1.0 + exp((b - a)));
}

Fortran

real(8) function code(a, b)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = 1.0d0 / (1.0d0 + exp((b - a)))
end function

Java

public static double code(double a, double b) {
	return 1.0 / (1.0 + Math.exp((b - a)));
}

Python

def code(a, b):
	return 1.0 / (1.0 + math.exp((b - a)))

Julia

function code(a, b)
	return Float64(1.0 / Float64(1.0 + exp(Float64(b - a))))
end

MATLAB

function tmp = code(a, b)
	tmp = 1.0 / (1.0 + exp((b - a)));
end

Wolfram

code[a_, b_] := N[(1.0 / N[(1.0 + N[Exp[N[(b - a), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2023250 
(FPCore (a b)
  :name "Quotient of sum of exps"
  :precision binary64

  :herbie-target
  (/ 1.0 (+ 1.0 (exp (- b a))))

  (/ (exp a) (+ (exp a) (exp b))))