Logistic regression 2

Percentage Accurate: 99.3% → 99.1%

Time: 11.1s

Alternatives: 9

Speedup: 1.0×

• could not determine a ground truth

  1. x = 2.401560084894005e+140
  2. y = 4.8059772214763046e-70

Specification

Math

\[\begin{array}{l} \\ \log \left(1 + e^{x}\right) - x \cdot y \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (- (log (+ 1.0 (exp x))) (* x y)))

C

double code(double x, double y) {
	return log((1.0 + exp(x))) - (x * y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = log((1.0d0 + exp(x))) - (x * y)
end function

Java

public static double code(double x, double y) {
	return Math.log((1.0 + Math.exp(x))) - (x * y);
}

Python

def code(x, y):
	return math.log((1.0 + math.exp(x))) - (x * y)

Julia

function code(x, y)
	return Float64(log(Float64(1.0 + exp(x))) - Float64(x * y))
end

MATLAB

function tmp = code(x, y)
	tmp = log((1.0 + exp(x))) - (x * y);
end

Wolfram

code[x_, y_] := N[(N[Log[N[(1.0 + N[Exp[x], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \log \left(1 + e^{x}\right) - x \cdot y \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (- (log (+ 1.0 (exp x))) (* x y)))

C

double code(double x, double y) {
	return log((1.0 + exp(x))) - (x * y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = log((1.0d0 + exp(x))) - (x * y)
end function

Java

public static double code(double x, double y) {
	return Math.log((1.0 + Math.exp(x))) - (x * y);
}

Python

def code(x, y):
	return math.log((1.0 + math.exp(x))) - (x * y)

Julia

function code(x, y)
	return Float64(log(Float64(1.0 + exp(x))) - Float64(x * y))
end

MATLAB

function tmp = code(x, y)
	tmp = log((1.0 + exp(x))) - (x * y);
end

Wolfram

code[x_, y_] := N[(N[Log[N[(1.0 + N[Exp[x], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1150000:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;\log 2 + x \cdot \left(x \cdot 0.125 + \left(0.5 - y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1150000.0)
   (* x (- y))
   (+ (log 2.0) (* x (+ (* x 0.125) (- 0.5 y))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1150000.0) {
		tmp = x * -y;
	} else {
		tmp = log(2.0) + (x * ((x * 0.125) + (0.5 - y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-1150000.0d0)) then
        tmp = x * -y
    else
        tmp = log(2.0d0) + (x * ((x * 0.125d0) + (0.5d0 - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -1150000.0) {
		tmp = x * -y;
	} else {
		tmp = Math.log(2.0) + (x * ((x * 0.125) + (0.5 - y)));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1150000.0:
		tmp = x * -y
	else:
		tmp = math.log(2.0) + (x * ((x * 0.125) + (0.5 - y)))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1150000.0)
		tmp = Float64(x * Float64(-y));
	else
		tmp = Float64(log(2.0) + Float64(x * Float64(Float64(x * 0.125) + Float64(0.5 - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1150000.0)
		tmp = x * -y;
	else
		tmp = log(2.0) + (x * ((x * 0.125) + (0.5 - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1150000.0], N[(x * (-y)), $MachinePrecision], N[(N[Log[2.0], $MachinePrecision] + N[(x * N[(N[(x * 0.125), $MachinePrecision] + N[(0.5 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.15e6

   1. Initial program 100.0%

      \[\log \left(1 + e^{x}\right) - x \cdot y \]
   2. Step-by-step derivation

      1. log1p-def 100.0%

         \[\leadsto \color{blue}{\mathsf{log1p}\left(e^{x}\right)} - x \cdot y \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{log1p}\left(e^{x}\right) - x \cdot y} \]

   4. Taylor expanded in x around inf 100.0%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot y\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 100.0%

         \[\leadsto \color{blue}{\left(-1 \cdot x\right) \cdot y} \]

      2. neg-mul-1 100.0%

         \[\leadsto \color{blue}{\left(-x\right)} \cdot y \]

      3. *-commutative 100.0%

         \[\leadsto \color{blue}{y \cdot \left(-x\right)} \]

   6. Simplified 100.0%

      \[\leadsto \color{blue}{y \cdot \left(-x\right)} \]

   if -1.15e6 < x

   1. Initial program 98.2%

      \[\log \left(1 + e^{x}\right) - x \cdot y \]
   2. Step-by-step derivation

      1. log1p-def 98.3%

         \[\leadsto \color{blue}{\mathsf{log1p}\left(e^{x}\right)} - x \cdot y \]

   3. Simplified 98.3%

      \[\leadsto \color{blue}{\mathsf{log1p}\left(e^{x}\right) - x \cdot y} \]

   4. Taylor expanded in x around 0 98.8%

      \[\leadsto \color{blue}{\log 2 + \left(0.125 \cdot {x}^{2} + x \cdot \left(0.5 - y\right)\right)} \]
   5. Step-by-step derivation

      1. *-commutative 98.8%

         \[\leadsto \log 2 + \left(\color{blue}{{x}^{2} \cdot 0.125} + x \cdot \left(0.5 - y\right)\right) \]

      2. unpow2 98.8%

         \[\leadsto \log 2 + \left(\color{blue}{\left(x \cdot x\right)} \cdot 0.125 + x \cdot \left(0.5 - y\right)\right) \]

      3. associate-*l* 98.8%

         \[\leadsto \log 2 + \left(\color{blue}{x \cdot \left(x \cdot 0.125\right)} + x \cdot \left(0.5 - y\right)\right) \]

      4. distribute-lft-out 98.8%

         \[\leadsto \log 2 + \color{blue}{x \cdot \left(x \cdot 0.125 + \left(0.5 - y\right)\right)} \]

   6. Simplified 98.8%

      \[\leadsto \color{blue}{\log 2 + x \cdot \left(x \cdot 0.125 + \left(0.5 - y\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1150000:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;\log 2 + x \cdot \left(x \cdot 0.125 + \left(0.5 - y\right)\right)\\ \end{array} \]

Alternative 2: 99.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ e^{\log \left(\mathsf{log1p}\left(e^{x}\right)\right)} - x \cdot y \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (- (exp (log (log1p (exp x)))) (* x y)))

C

double code(double x, double y) {
	return exp(log(log1p(exp(x)))) - (x * y);
}

Java

public static double code(double x, double y) {
	return Math.exp(Math.log(Math.log1p(Math.exp(x)))) - (x * y);
}

Python

def code(x, y):
	return math.exp(math.log(math.log1p(math.exp(x)))) - (x * y)

Julia

function code(x, y)
	return Float64(exp(log(log1p(exp(x)))) - Float64(x * y))
end

Wolfram

code[x_, y_] := N[(N[Exp[N[Log[N[Log[1 + N[Exp[x], $MachinePrecision]], $MachinePrecision]], $MachinePrecision]], $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 98.8%

   \[\log \left(1 + e^{x}\right) - x \cdot y \]
2. Step-by-step derivation

   1. log1p-def 98.8%

      \[\leadsto \color{blue}{\mathsf{log1p}\left(e^{x}\right)} - x \cdot y \]

3. Simplified 98.8%

   \[\leadsto \color{blue}{\mathsf{log1p}\left(e^{x}\right) - x \cdot y} \]
4. Step-by-step derivation

   1. add-exp-log 98.8%

      \[\leadsto \color{blue}{e^{\log \left(\mathsf{log1p}\left(e^{x}\right)\right)}} - x \cdot y \]

5. Applied egg-rr 98.8%

   \[\leadsto \color{blue}{e^{\log \left(\mathsf{log1p}\left(e^{x}\right)\right)}} - x \cdot y \]

6. Final simplification 98.8%

   \[\leadsto e^{\log \left(\mathsf{log1p}\left(e^{x}\right)\right)} - x \cdot y \]

Alternative 3: 99.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \mathsf{log1p}\left(e^{x}\right) - x \cdot y \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (- (log1p (exp x)) (* x y)))

C

double code(double x, double y) {
	return log1p(exp(x)) - (x * y);
}

Java

public static double code(double x, double y) {
	return Math.log1p(Math.exp(x)) - (x * y);
}

Python

def code(x, y):
	return math.log1p(math.exp(x)) - (x * y)

Julia

function code(x, y)
	return Float64(log1p(exp(x)) - Float64(x * y))
end

Wolfram

code[x_, y_] := N[(N[Log[1 + N[Exp[x], $MachinePrecision]], $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 98.8%

   \[\log \left(1 + e^{x}\right) - x \cdot y \]
2. Step-by-step derivation

   1. log1p-def 98.8%

      \[\leadsto \color{blue}{\mathsf{log1p}\left(e^{x}\right)} - x \cdot y \]

3. Simplified 98.8%

   \[\leadsto \color{blue}{\mathsf{log1p}\left(e^{x}\right) - x \cdot y} \]

4. Final simplification 98.8%

   \[\leadsto \mathsf{log1p}\left(e^{x}\right) - x \cdot y \]

Alternative 4: 80.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-y\right)\\ \mathbf{if}\;x \leq -9.2 \cdot 10^{-12}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -3 \cdot 10^{-31}:\\ \;\;\;\;\log 2\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{-74}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -8.6 \cdot 10^{-105}:\\ \;\;\;\;\log 2\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{-140}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-60}:\\ \;\;\;\;\log 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(0.5 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* x (- y))))
   (if (<= x -9.2e-12)
     t_0
     (if (<= x -3e-31)
       (log 2.0)
       (if (<= x -1.5e-74)
         t_0
         (if (<= x -8.6e-105)
           (log 2.0)
           (if (<= x -3.8e-140)
             t_0
             (if (<= x 1.4e-60) (log 2.0) (* x (- 0.5 y))))))))))

C

double code(double x, double y) {
	double t_0 = x * -y;
	double tmp;
	if (x <= -9.2e-12) {
		tmp = t_0;
	} else if (x <= -3e-31) {
		tmp = log(2.0);
	} else if (x <= -1.5e-74) {
		tmp = t_0;
	} else if (x <= -8.6e-105) {
		tmp = log(2.0);
	} else if (x <= -3.8e-140) {
		tmp = t_0;
	} else if (x <= 1.4e-60) {
		tmp = log(2.0);
	} else {
		tmp = x * (0.5 - y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * -y
    if (x <= (-9.2d-12)) then
        tmp = t_0
    else if (x <= (-3d-31)) then
        tmp = log(2.0d0)
    else if (x <= (-1.5d-74)) then
        tmp = t_0
    else if (x <= (-8.6d-105)) then
        tmp = log(2.0d0)
    else if (x <= (-3.8d-140)) then
        tmp = t_0
    else if (x <= 1.4d-60) then
        tmp = log(2.0d0)
    else
        tmp = x * (0.5d0 - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x * -y;
	double tmp;
	if (x <= -9.2e-12) {
		tmp = t_0;
	} else if (x <= -3e-31) {
		tmp = Math.log(2.0);
	} else if (x <= -1.5e-74) {
		tmp = t_0;
	} else if (x <= -8.6e-105) {
		tmp = Math.log(2.0);
	} else if (x <= -3.8e-140) {
		tmp = t_0;
	} else if (x <= 1.4e-60) {
		tmp = Math.log(2.0);
	} else {
		tmp = x * (0.5 - y);
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x * -y
	tmp = 0
	if x <= -9.2e-12:
		tmp = t_0
	elif x <= -3e-31:
		tmp = math.log(2.0)
	elif x <= -1.5e-74:
		tmp = t_0
	elif x <= -8.6e-105:
		tmp = math.log(2.0)
	elif x <= -3.8e-140:
		tmp = t_0
	elif x <= 1.4e-60:
		tmp = math.log(2.0)
	else:
		tmp = x * (0.5 - y)
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x * Float64(-y))
	tmp = 0.0
	if (x <= -9.2e-12)
		tmp = t_0;
	elseif (x <= -3e-31)
		tmp = log(2.0);
	elseif (x <= -1.5e-74)
		tmp = t_0;
	elseif (x <= -8.6e-105)
		tmp = log(2.0);
	elseif (x <= -3.8e-140)
		tmp = t_0;
	elseif (x <= 1.4e-60)
		tmp = log(2.0);
	else
		tmp = Float64(x * Float64(0.5 - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x * -y;
	tmp = 0.0;
	if (x <= -9.2e-12)
		tmp = t_0;
	elseif (x <= -3e-31)
		tmp = log(2.0);
	elseif (x <= -1.5e-74)
		tmp = t_0;
	elseif (x <= -8.6e-105)
		tmp = log(2.0);
	elseif (x <= -3.8e-140)
		tmp = t_0;
	elseif (x <= 1.4e-60)
		tmp = log(2.0);
	else
		tmp = x * (0.5 - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x * (-y)), $MachinePrecision]}, If[LessEqual[x, -9.2e-12], t$95$0, If[LessEqual[x, -3e-31], N[Log[2.0], $MachinePrecision], If[LessEqual[x, -1.5e-74], t$95$0, If[LessEqual[x, -8.6e-105], N[Log[2.0], $MachinePrecision], If[LessEqual[x, -3.8e-140], t$95$0, If[LessEqual[x, 1.4e-60], N[Log[2.0], $MachinePrecision], N[(x * N[(0.5 - y), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -9.19999999999999957e-12 or -2.99999999999999981e-31 < x < -1.50000000000000003e-74 or -8.59999999999999928e-105 < x < -3.79999999999999998e-140

   1. Initial program 99.8%

      \[\log \left(1 + e^{x}\right) - x \cdot y \]
   2. Step-by-step derivation

      1. log1p-def 100.0%

         \[\leadsto \color{blue}{\mathsf{log1p}\left(e^{x}\right)} - x \cdot y \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{log1p}\left(e^{x}\right) - x \cdot y} \]

   4. Taylor expanded in x around inf 92.2%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot y\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 92.2%

         \[\leadsto \color{blue}{\left(-1 \cdot x\right) \cdot y} \]

      2. neg-mul-1 92.2%

         \[\leadsto \color{blue}{\left(-x\right)} \cdot y \]

      3. *-commutative 92.2%

         \[\leadsto \color{blue}{y \cdot \left(-x\right)} \]

   6. Simplified 92.2%

      \[\leadsto \color{blue}{y \cdot \left(-x\right)} \]

   if -9.19999999999999957e-12 < x < -2.99999999999999981e-31 or -1.50000000000000003e-74 < x < -8.59999999999999928e-105 or -3.79999999999999998e-140 < x < 1.4000000000000001e-60

   1. Initial program 100.0%

      \[\log \left(1 + e^{x}\right) - x \cdot y \]
   2. Step-by-step derivation

      1. log1p-def 100.0%

         \[\leadsto \color{blue}{\mathsf{log1p}\left(e^{x}\right)} - x \cdot y \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{log1p}\left(e^{x}\right) - x \cdot y} \]

   4. Taylor expanded in x around 0 100.0%

      \[\leadsto \color{blue}{\log 2 + x \cdot \left(0.5 - y\right)} \]
   5. Step-by-step derivation

      1. add-cbrt-cube 96.1%

         \[\leadsto \color{blue}{\sqrt[3]{\left(\left(\log 2 + x \cdot \left(0.5 - y\right)\right) \cdot \left(\log 2 + x \cdot \left(0.5 - y\right)\right)\right) \cdot \left(\log 2 + x \cdot \left(0.5 - y\right)\right)}} \]

      2. pow3 96.1%

         \[\leadsto \sqrt[3]{\color{blue}{{\left(\log 2 + x \cdot \left(0.5 - y\right)\right)}^{3}}} \]

      3. +-commutative 96.1%

         \[\leadsto \sqrt[3]{{\color{blue}{\left(x \cdot \left(0.5 - y\right) + \log 2\right)}}^{3}} \]

      4. fma-def 96.1%

         \[\leadsto \sqrt[3]{{\color{blue}{\left(\mathsf{fma}\left(x, 0.5 - y, \log 2\right)\right)}}^{3}} \]

   6. Applied egg-rr 96.1%

      \[\leadsto \color{blue}{\sqrt[3]{{\left(\mathsf{fma}\left(x, 0.5 - y, \log 2\right)\right)}^{3}}} \]

   7. Taylor expanded in y around 0 85.8%

      \[\leadsto \sqrt[3]{\color{blue}{{\left(\log 2 + 0.5 \cdot x\right)}^{3}}} \]

   8. Taylor expanded in x around 0 85.4%

      \[\leadsto \color{blue}{\log 2} \]

   if 1.4000000000000001e-60 < x

   1. Initial program 87.3%

      \[\log \left(1 + e^{x}\right) - x \cdot y \]
   2. Step-by-step derivation

      1. log1p-def 87.3%

         \[\leadsto \color{blue}{\mathsf{log1p}\left(e^{x}\right)} - x \cdot y \]

   3. Simplified 87.3%

      \[\leadsto \color{blue}{\mathsf{log1p}\left(e^{x}\right) - x \cdot y} \]

   4. Taylor expanded in x around 0 96.5%

      \[\leadsto \color{blue}{\log 2 + x \cdot \left(0.5 - y\right)} \]

   5. Taylor expanded in x around inf 69.4%

      \[\leadsto \color{blue}{x \cdot \left(0.5 - y\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 86.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.2 \cdot 10^{-12}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;x \leq -3 \cdot 10^{-31}:\\ \;\;\;\;\log 2\\ \mathbf{elif}\;x \leq -1.5 \cdot 10^{-74}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;x \leq -8.6 \cdot 10^{-105}:\\ \;\;\;\;\log 2\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{-140}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{-60}:\\ \;\;\;\;\log 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(0.5 - y\right)\\ \end{array} \]

Alternative 5: 80.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-y\right)\\ \mathbf{if}\;x \leq -3.1 \cdot 10^{-11}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -8 \cdot 10^{-29}:\\ \;\;\;\;\log 2 + x \cdot 0.5\\ \mathbf{elif}\;x \leq -1.35 \cdot 10^{-74}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -8.6 \cdot 10^{-105}:\\ \;\;\;\;\log 2\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{-143}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{-59}:\\ \;\;\;\;\log 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(0.5 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* x (- y))))
   (if (<= x -3.1e-11)
     t_0
     (if (<= x -8e-29)
       (+ (log 2.0) (* x 0.5))
       (if (<= x -1.35e-74)
         t_0
         (if (<= x -8.6e-105)
           (log 2.0)
           (if (<= x -2.8e-143)
             t_0
             (if (<= x 1.75e-59) (log 2.0) (* x (- 0.5 y))))))))))

C

double code(double x, double y) {
	double t_0 = x * -y;
	double tmp;
	if (x <= -3.1e-11) {
		tmp = t_0;
	} else if (x <= -8e-29) {
		tmp = log(2.0) + (x * 0.5);
	} else if (x <= -1.35e-74) {
		tmp = t_0;
	} else if (x <= -8.6e-105) {
		tmp = log(2.0);
	} else if (x <= -2.8e-143) {
		tmp = t_0;
	} else if (x <= 1.75e-59) {
		tmp = log(2.0);
	} else {
		tmp = x * (0.5 - y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * -y
    if (x <= (-3.1d-11)) then
        tmp = t_0
    else if (x <= (-8d-29)) then
        tmp = log(2.0d0) + (x * 0.5d0)
    else if (x <= (-1.35d-74)) then
        tmp = t_0
    else if (x <= (-8.6d-105)) then
        tmp = log(2.0d0)
    else if (x <= (-2.8d-143)) then
        tmp = t_0
    else if (x <= 1.75d-59) then
        tmp = log(2.0d0)
    else
        tmp = x * (0.5d0 - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x * -y;
	double tmp;
	if (x <= -3.1e-11) {
		tmp = t_0;
	} else if (x <= -8e-29) {
		tmp = Math.log(2.0) + (x * 0.5);
	} else if (x <= -1.35e-74) {
		tmp = t_0;
	} else if (x <= -8.6e-105) {
		tmp = Math.log(2.0);
	} else if (x <= -2.8e-143) {
		tmp = t_0;
	} else if (x <= 1.75e-59) {
		tmp = Math.log(2.0);
	} else {
		tmp = x * (0.5 - y);
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x * -y
	tmp = 0
	if x <= -3.1e-11:
		tmp = t_0
	elif x <= -8e-29:
		tmp = math.log(2.0) + (x * 0.5)
	elif x <= -1.35e-74:
		tmp = t_0
	elif x <= -8.6e-105:
		tmp = math.log(2.0)
	elif x <= -2.8e-143:
		tmp = t_0
	elif x <= 1.75e-59:
		tmp = math.log(2.0)
	else:
		tmp = x * (0.5 - y)
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x * Float64(-y))
	tmp = 0.0
	if (x <= -3.1e-11)
		tmp = t_0;
	elseif (x <= -8e-29)
		tmp = Float64(log(2.0) + Float64(x * 0.5));
	elseif (x <= -1.35e-74)
		tmp = t_0;
	elseif (x <= -8.6e-105)
		tmp = log(2.0);
	elseif (x <= -2.8e-143)
		tmp = t_0;
	elseif (x <= 1.75e-59)
		tmp = log(2.0);
	else
		tmp = Float64(x * Float64(0.5 - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x * -y;
	tmp = 0.0;
	if (x <= -3.1e-11)
		tmp = t_0;
	elseif (x <= -8e-29)
		tmp = log(2.0) + (x * 0.5);
	elseif (x <= -1.35e-74)
		tmp = t_0;
	elseif (x <= -8.6e-105)
		tmp = log(2.0);
	elseif (x <= -2.8e-143)
		tmp = t_0;
	elseif (x <= 1.75e-59)
		tmp = log(2.0);
	else
		tmp = x * (0.5 - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x * (-y)), $MachinePrecision]}, If[LessEqual[x, -3.1e-11], t$95$0, If[LessEqual[x, -8e-29], N[(N[Log[2.0], $MachinePrecision] + N[(x * 0.5), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.35e-74], t$95$0, If[LessEqual[x, -8.6e-105], N[Log[2.0], $MachinePrecision], If[LessEqual[x, -2.8e-143], t$95$0, If[LessEqual[x, 1.75e-59], N[Log[2.0], $MachinePrecision], N[(x * N[(0.5 - y), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -3.10000000000000028e-11 or -7.99999999999999955e-29 < x < -1.35000000000000009e-74 or -8.59999999999999928e-105 < x < -2.7999999999999999e-143

   1. Initial program 99.8%

      \[\log \left(1 + e^{x}\right) - x \cdot y \]
   2. Step-by-step derivation

      1. log1p-def 100.0%

         \[\leadsto \color{blue}{\mathsf{log1p}\left(e^{x}\right)} - x \cdot y \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{log1p}\left(e^{x}\right) - x \cdot y} \]

   4. Taylor expanded in x around inf 92.2%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot y\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 92.2%

         \[\leadsto \color{blue}{\left(-1 \cdot x\right) \cdot y} \]

      2. neg-mul-1 92.2%

         \[\leadsto \color{blue}{\left(-x\right)} \cdot y \]

      3. *-commutative 92.2%

         \[\leadsto \color{blue}{y \cdot \left(-x\right)} \]

   6. Simplified 92.2%

      \[\leadsto \color{blue}{y \cdot \left(-x\right)} \]

   if -3.10000000000000028e-11 < x < -7.99999999999999955e-29

   1. Initial program 99.6%

      \[\log \left(1 + e^{x}\right) - x \cdot y \]
   2. Step-by-step derivation

      1. log1p-def 99.8%

         \[\leadsto \color{blue}{\mathsf{log1p}\left(e^{x}\right)} - x \cdot y \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\mathsf{log1p}\left(e^{x}\right) - x \cdot y} \]

   4. Taylor expanded in x around 0 100.0%

      \[\leadsto \color{blue}{\log 2 + x \cdot \left(0.5 - y\right)} \]
   5. Step-by-step derivation

      1. add-cbrt-cube 99.6%

         \[\leadsto \color{blue}{\sqrt[3]{\left(\left(\log 2 + x \cdot \left(0.5 - y\right)\right) \cdot \left(\log 2 + x \cdot \left(0.5 - y\right)\right)\right) \cdot \left(\log 2 + x \cdot \left(0.5 - y\right)\right)}} \]

      2. pow3 99.8%

         \[\leadsto \sqrt[3]{\color{blue}{{\left(\log 2 + x \cdot \left(0.5 - y\right)\right)}^{3}}} \]

      3. +-commutative 99.8%

         \[\leadsto \sqrt[3]{{\color{blue}{\left(x \cdot \left(0.5 - y\right) + \log 2\right)}}^{3}} \]

      4. fma-def 99.8%

         \[\leadsto \sqrt[3]{{\color{blue}{\left(\mathsf{fma}\left(x, 0.5 - y, \log 2\right)\right)}}^{3}} \]

   6. Applied egg-rr 99.8%

      \[\leadsto \color{blue}{\sqrt[3]{{\left(\mathsf{fma}\left(x, 0.5 - y, \log 2\right)\right)}^{3}}} \]

   7. Taylor expanded in y around 0 99.8%

      \[\leadsto \sqrt[3]{\color{blue}{{\left(\log 2 + 0.5 \cdot x\right)}^{3}}} \]
   8. Step-by-step derivation

      1. rem-cbrt-cube 100.0%

         \[\leadsto \color{blue}{\log 2 + 0.5 \cdot x} \]

      2. +-commutative 100.0%

         \[\leadsto \color{blue}{0.5 \cdot x + \log 2} \]

   9. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{0.5 \cdot x + \log 2} \]

   if -1.35000000000000009e-74 < x < -8.59999999999999928e-105 or -2.7999999999999999e-143 < x < 1.75e-59

   1. Initial program 100.0%

      \[\log \left(1 + e^{x}\right) - x \cdot y \]
   2. Step-by-step derivation

      1. log1p-def 100.0%

         \[\leadsto \color{blue}{\mathsf{log1p}\left(e^{x}\right)} - x \cdot y \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{log1p}\left(e^{x}\right) - x \cdot y} \]

   4. Taylor expanded in x around 0 100.0%

      \[\leadsto \color{blue}{\log 2 + x \cdot \left(0.5 - y\right)} \]
   5. Step-by-step derivation

      1. add-cbrt-cube 95.9%

         \[\leadsto \color{blue}{\sqrt[3]{\left(\left(\log 2 + x \cdot \left(0.5 - y\right)\right) \cdot \left(\log 2 + x \cdot \left(0.5 - y\right)\right)\right) \cdot \left(\log 2 + x \cdot \left(0.5 - y\right)\right)}} \]

      2. pow3 95.9%

         \[\leadsto \sqrt[3]{\color{blue}{{\left(\log 2 + x \cdot \left(0.5 - y\right)\right)}^{3}}} \]

      3. +-commutative 95.9%

         \[\leadsto \sqrt[3]{{\color{blue}{\left(x \cdot \left(0.5 - y\right) + \log 2\right)}}^{3}} \]

      4. fma-def 95.9%

         \[\leadsto \sqrt[3]{{\color{blue}{\left(\mathsf{fma}\left(x, 0.5 - y, \log 2\right)\right)}}^{3}} \]

   6. Applied egg-rr 95.9%

      \[\leadsto \color{blue}{\sqrt[3]{{\left(\mathsf{fma}\left(x, 0.5 - y, \log 2\right)\right)}^{3}}} \]

   7. Taylor expanded in y around 0 85.0%

      \[\leadsto \sqrt[3]{\color{blue}{{\left(\log 2 + 0.5 \cdot x\right)}^{3}}} \]

   8. Taylor expanded in x around 0 85.0%

      \[\leadsto \color{blue}{\log 2} \]

   if 1.75e-59 < x

   1. Initial program 87.3%

      \[\log \left(1 + e^{x}\right) - x \cdot y \]
   2. Step-by-step derivation

      1. log1p-def 87.3%

         \[\leadsto \color{blue}{\mathsf{log1p}\left(e^{x}\right)} - x \cdot y \]

   3. Simplified 87.3%

      \[\leadsto \color{blue}{\mathsf{log1p}\left(e^{x}\right) - x \cdot y} \]

   4. Taylor expanded in x around 0 96.5%

      \[\leadsto \color{blue}{\log 2 + x \cdot \left(0.5 - y\right)} \]

   5. Taylor expanded in x around inf 69.4%

      \[\leadsto \color{blue}{x \cdot \left(0.5 - y\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.1 \cdot 10^{-11}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;x \leq -8 \cdot 10^{-29}:\\ \;\;\;\;\log 2 + x \cdot 0.5\\ \mathbf{elif}\;x \leq -1.35 \cdot 10^{-74}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;x \leq -8.6 \cdot 10^{-105}:\\ \;\;\;\;\log 2\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{-143}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{-59}:\\ \;\;\;\;\log 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(0.5 - y\right)\\ \end{array} \]

Alternative 6: 99.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.4:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;\log 2 + x \cdot \left(0.5 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.4) (* x (- y)) (+ (log 2.0) (* x (- 0.5 y)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.4) {
		tmp = x * -y;
	} else {
		tmp = log(2.0) + (x * (0.5 - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-1.4d0)) then
        tmp = x * -y
    else
        tmp = log(2.0d0) + (x * (0.5d0 - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -1.4) {
		tmp = x * -y;
	} else {
		tmp = Math.log(2.0) + (x * (0.5 - y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.4:
		tmp = x * -y
	else:
		tmp = math.log(2.0) + (x * (0.5 - y))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.4)
		tmp = Float64(x * Float64(-y));
	else
		tmp = Float64(log(2.0) + Float64(x * Float64(0.5 - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.4)
		tmp = x * -y;
	else
		tmp = log(2.0) + (x * (0.5 - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.4], N[(x * (-y)), $MachinePrecision], N[(N[Log[2.0], $MachinePrecision] + N[(x * N[(0.5 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.3999999999999999

   1. Initial program 99.8%

      \[\log \left(1 + e^{x}\right) - x \cdot y \]
   2. Step-by-step derivation

      1. log1p-def 100.0%

         \[\leadsto \color{blue}{\mathsf{log1p}\left(e^{x}\right)} - x \cdot y \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{log1p}\left(e^{x}\right) - x \cdot y} \]

   4. Taylor expanded in x around inf 98.8%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot y\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 98.8%

         \[\leadsto \color{blue}{\left(-1 \cdot x\right) \cdot y} \]

      2. neg-mul-1 98.8%

         \[\leadsto \color{blue}{\left(-x\right)} \cdot y \]

      3. *-commutative 98.8%

         \[\leadsto \color{blue}{y \cdot \left(-x\right)} \]

   6. Simplified 98.8%

      \[\leadsto \color{blue}{y \cdot \left(-x\right)} \]

   if -1.3999999999999999 < x

   1. Initial program 98.3%

      \[\log \left(1 + e^{x}\right) - x \cdot y \]
   2. Step-by-step derivation

      1. log1p-def 98.3%

         \[\leadsto \color{blue}{\mathsf{log1p}\left(e^{x}\right)} - x \cdot y \]

   3. Simplified 98.3%

      \[\leadsto \color{blue}{\mathsf{log1p}\left(e^{x}\right) - x \cdot y} \]

   4. Taylor expanded in x around 0 99.2%

      \[\leadsto \color{blue}{\log 2 + x \cdot \left(0.5 - y\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.4:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;\log 2 + x \cdot \left(0.5 - y\right)\\ \end{array} \]

Alternative 7: 98.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1150000:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;\log 2 - x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1150000.0) (* x (- y)) (- (log 2.0) (* x y))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1150000.0) {
		tmp = x * -y;
	} else {
		tmp = log(2.0) - (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-1150000.0d0)) then
        tmp = x * -y
    else
        tmp = log(2.0d0) - (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -1150000.0) {
		tmp = x * -y;
	} else {
		tmp = Math.log(2.0) - (x * y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1150000.0:
		tmp = x * -y
	else:
		tmp = math.log(2.0) - (x * y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1150000.0)
		tmp = Float64(x * Float64(-y));
	else
		tmp = Float64(log(2.0) - Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1150000.0)
		tmp = x * -y;
	else
		tmp = log(2.0) - (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1150000.0], N[(x * (-y)), $MachinePrecision], N[(N[Log[2.0], $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.15e6

   1. Initial program 100.0%

      \[\log \left(1 + e^{x}\right) - x \cdot y \]
   2. Step-by-step derivation

      1. log1p-def 100.0%

         \[\leadsto \color{blue}{\mathsf{log1p}\left(e^{x}\right)} - x \cdot y \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{log1p}\left(e^{x}\right) - x \cdot y} \]

   4. Taylor expanded in x around inf 100.0%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot y\right)} \]
   5. Step-by-step derivation

      1. associate-*r* 100.0%

         \[\leadsto \color{blue}{\left(-1 \cdot x\right) \cdot y} \]

      2. neg-mul-1 100.0%

         \[\leadsto \color{blue}{\left(-x\right)} \cdot y \]

      3. *-commutative 100.0%

         \[\leadsto \color{blue}{y \cdot \left(-x\right)} \]

   6. Simplified 100.0%

      \[\leadsto \color{blue}{y \cdot \left(-x\right)} \]

   if -1.15e6 < x

   1. Initial program 98.2%

      \[\log \left(1 + e^{x}\right) - x \cdot y \]
   2. Step-by-step derivation

      1. log1p-def 98.3%

         \[\leadsto \color{blue}{\mathsf{log1p}\left(e^{x}\right)} - x \cdot y \]

   3. Simplified 98.3%

      \[\leadsto \color{blue}{\mathsf{log1p}\left(e^{x}\right) - x \cdot y} \]

   4. Taylor expanded in x around 0 98.1%

      \[\leadsto \color{blue}{\log 2} - x \cdot y \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1150000:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;\log 2 - x \cdot y\\ \end{array} \]

Alternative 8: 53.2% accurate, 51.8× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(-y\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* x (- y)))

C

double code(double x, double y) {
	return x * -y;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x * -y
end function

Java

public static double code(double x, double y) {
	return x * -y;
}

Python

def code(x, y):
	return x * -y

Julia

function code(x, y)
	return Float64(x * Float64(-y))
end

MATLAB

function tmp = code(x, y)
	tmp = x * -y;
end

Wolfram

code[x_, y_] := N[(x * (-y)), $MachinePrecision]

Derivation

1. Initial program 98.8%

   \[\log \left(1 + e^{x}\right) - x \cdot y \]
2. Step-by-step derivation

   1. log1p-def 98.8%

      \[\leadsto \color{blue}{\mathsf{log1p}\left(e^{x}\right)} - x \cdot y \]

3. Simplified 98.8%

   \[\leadsto \color{blue}{\mathsf{log1p}\left(e^{x}\right) - x \cdot y} \]

4. Taylor expanded in x around inf 52.6%

   \[\leadsto \color{blue}{-1 \cdot \left(x \cdot y\right)} \]
5. Step-by-step derivation

   1. associate-*r* 52.6%

      \[\leadsto \color{blue}{\left(-1 \cdot x\right) \cdot y} \]

   2. neg-mul-1 52.6%

      \[\leadsto \color{blue}{\left(-x\right)} \cdot y \]

   3. *-commutative 52.6%

      \[\leadsto \color{blue}{y \cdot \left(-x\right)} \]

6. Simplified 52.6%

   \[\leadsto \color{blue}{y \cdot \left(-x\right)} \]

7. Final simplification 52.6%

   \[\leadsto x \cdot \left(-y\right) \]

Alternative 9: 3.6% accurate, 69.0× speedup

Math

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

FPCore

(FPCore (x y) :precision binary64 (* x 0.5))

C

double code(double x, double y) {
	return x * 0.5;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x * 0.5d0
end function

Java

public static double code(double x, double y) {
	return x * 0.5;
}

Python

def code(x, y):
	return x * 0.5

Julia

function code(x, y)
	return Float64(x * 0.5)
end

MATLAB

function tmp = code(x, y)
	tmp = x * 0.5;
end

Wolfram

code[x_, y_] := N[(x * 0.5), $MachinePrecision]

Derivation

1. Initial program 98.8%

   \[\log \left(1 + e^{x}\right) - x \cdot y \]
2. Step-by-step derivation

   1. log1p-def 98.8%

      \[\leadsto \color{blue}{\mathsf{log1p}\left(e^{x}\right)} - x \cdot y \]

3. Simplified 98.8%

   \[\leadsto \color{blue}{\mathsf{log1p}\left(e^{x}\right) - x \cdot y} \]

4. Taylor expanded in x around 0 86.9%

   \[\leadsto \color{blue}{\log 2 + x \cdot \left(0.5 - y\right)} \]

5. Taylor expanded in x around inf 40.7%

   \[\leadsto \color{blue}{x \cdot \left(0.5 - y\right)} \]

6. Taylor expanded in y around 0 3.8%

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

7. Final simplification 3.8%

   \[\leadsto x \cdot 0.5 \]

Developer target: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 0:\\ \;\;\;\;\log \left(1 + e^{x}\right) - x \cdot y\\ \mathbf{else}:\\ \;\;\;\;\log \left(1 + e^{-x}\right) - \left(-x\right) \cdot \left(1 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 0.0)
   (- (log (+ 1.0 (exp x))) (* x y))
   (- (log (+ 1.0 (exp (- x)))) (* (- x) (- 1.0 y)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 0.0) {
		tmp = log((1.0 + exp(x))) - (x * y);
	} else {
		tmp = log((1.0 + exp(-x))) - (-x * (1.0 - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= 0.0d0) then
        tmp = log((1.0d0 + exp(x))) - (x * y)
    else
        tmp = log((1.0d0 + exp(-x))) - (-x * (1.0d0 - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 0.0) {
		tmp = Math.log((1.0 + Math.exp(x))) - (x * y);
	} else {
		tmp = Math.log((1.0 + Math.exp(-x))) - (-x * (1.0 - y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 0.0:
		tmp = math.log((1.0 + math.exp(x))) - (x * y)
	else:
		tmp = math.log((1.0 + math.exp(-x))) - (-x * (1.0 - y))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 0.0)
		tmp = Float64(log(Float64(1.0 + exp(x))) - Float64(x * y));
	else
		tmp = Float64(log(Float64(1.0 + exp(Float64(-x)))) - Float64(Float64(-x) * Float64(1.0 - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 0.0)
		tmp = log((1.0 + exp(x))) - (x * y);
	else
		tmp = log((1.0 + exp(-x))) - (-x * (1.0 - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 0.0], N[(N[Log[N[(1.0 + N[Exp[x], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision], N[(N[Log[N[(1.0 + N[Exp[(-x)], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - N[((-x) * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Reproduce

herbie shell --seed 2023275 
(FPCore (x y)
  :name "Logistic regression 2"
  :precision binary64

  :herbie-target
  (if (<= x 0.0) (- (log (+ 1.0 (exp x))) (* x y)) (- (log (+ 1.0 (exp (- x)))) (* (- x) (- 1.0 y))))

  (- (log (+ 1.0 (exp x))) (* x y)))