Logistic regression 2

Percentage Accurate: 99.1% → 99.2%

Time: 12.2s

Alternatives: 11

Speedup: 1.0×

• could not determine a ground truth

  1. x = 3.965558043119397e+63
  2. y = -2.3039404847152117e-144

• Rival profile vector overflowed, profile may not be complete

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: 99.1% 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: 99.2% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 98.8%

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

   1. cancel-sign-sub-inv 98.8%

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

   2. +-commutative 98.8%

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

   3. distribute-lft-neg-out 98.8%

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

   4. distribute-rgt-neg-out 98.8%

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

   5. fma-define 98.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, -y, \log \left(1 + e^{x}\right)\right)} \]

   6. log1p-define 98.8%

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

3. Simplified 98.8%

   \[\leadsto \color{blue}{\mathsf{fma}\left(x, -y, \mathsf{log1p}\left(e^{x}\right)\right)} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 2: 99.2% 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-define 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. Add Preprocessing
5. Add Preprocessing

Alternative 3: 98.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -236000:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;\log 2 + \left(x \cdot 0.5 + x \cdot \left(x \cdot 0.125 - y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -236000.0)
   (* x (- y))
   (+ (log 2.0) (+ (* x 0.5) (* x (- (* x 0.125) y))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -236000.0) {
		tmp = x * -y;
	} else {
		tmp = log(2.0) + ((x * 0.5) + (x * ((x * 0.125) - 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 <= (-236000.0d0)) then
        tmp = x * -y
    else
        tmp = log(2.0d0) + ((x * 0.5d0) + (x * ((x * 0.125d0) - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -236000.0) {
		tmp = x * -y;
	} else {
		tmp = Math.log(2.0) + ((x * 0.5) + (x * ((x * 0.125) - y)));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -236000.0:
		tmp = x * -y
	else:
		tmp = math.log(2.0) + ((x * 0.5) + (x * ((x * 0.125) - y)))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -236000.0)
		tmp = Float64(x * Float64(-y));
	else
		tmp = Float64(log(2.0) + Float64(Float64(x * 0.5) + Float64(x * Float64(Float64(x * 0.125) - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -236000.0)
		tmp = x * -y;
	else
		tmp = log(2.0) + ((x * 0.5) + (x * ((x * 0.125) - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -236000.0], N[(x * (-y)), $MachinePrecision], N[(N[Log[2.0], $MachinePrecision] + N[(N[(x * 0.5), $MachinePrecision] + N[(x * N[(N[(x * 0.125), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -236000

   1. Initial program 100.0%

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

      1. log1p-define 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. Add Preprocessing

   5. Taylor expanded in x around inf 100.0%

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

      1. neg-mul-1 100.0%

         \[\leadsto \color{blue}{-x \cdot y} \]

      2. distribute-lft-neg-in 100.0%

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

      3. *-commutative 100.0%

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

   7. Simplified 100.0%

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

   if -236000 < x

   1. Initial program 98.3%

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

      1. log1p-define 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. Add Preprocessing

   5. Taylor expanded in x around 0 98.2%

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

      1. associate--l+ 98.2%

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

      2. distribute-lft-in 98.2%

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

      3. *-commutative 98.2%

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

   7. Applied egg-rr 98.2%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -236000:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;\log 2 + \left(x \cdot 0.5 + x \cdot \left(x \cdot 0.125 - y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -236000:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;\log 2 + x \cdot \left(\left(0.5 + x \cdot 0.125\right) - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -236000.0)
   (* x (- y))
   (+ (log 2.0) (* x (- (+ 0.5 (* x 0.125)) y)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -236000.0) {
		tmp = x * -y;
	} else {
		tmp = log(2.0) + (x * ((0.5 + (x * 0.125)) - 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 <= (-236000.0d0)) then
        tmp = x * -y
    else
        tmp = log(2.0d0) + (x * ((0.5d0 + (x * 0.125d0)) - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -236000.0) {
		tmp = x * -y;
	} else {
		tmp = Math.log(2.0) + (x * ((0.5 + (x * 0.125)) - y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -236000.0:
		tmp = x * -y
	else:
		tmp = math.log(2.0) + (x * ((0.5 + (x * 0.125)) - y))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -236000.0)
		tmp = Float64(x * Float64(-y));
	else
		tmp = Float64(log(2.0) + Float64(x * Float64(Float64(0.5 + Float64(x * 0.125)) - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -236000.0)
		tmp = x * -y;
	else
		tmp = log(2.0) + (x * ((0.5 + (x * 0.125)) - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -236000.0], N[(x * (-y)), $MachinePrecision], N[(N[Log[2.0], $MachinePrecision] + N[(x * N[(N[(0.5 + N[(x * 0.125), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -236000

   1. Initial program 100.0%

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

      1. log1p-define 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. Add Preprocessing

   5. Taylor expanded in x around inf 100.0%

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

      1. neg-mul-1 100.0%

         \[\leadsto \color{blue}{-x \cdot y} \]

      2. distribute-lft-neg-in 100.0%

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

      3. *-commutative 100.0%

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

   7. Simplified 100.0%

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

   if -236000 < x

   1. Initial program 98.3%

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

      1. log1p-define 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. Add Preprocessing

   5. Taylor expanded in x around 0 98.2%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -236000:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;\log 2 + x \cdot \left(\left(0.5 + x \cdot 0.125\right) - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 80.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{-7}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-126}:\\ \;\;\;\;\log 2 + x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(0.5 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.1e-7)
   (* x (- y))
   (if (<= x 2.4e-126) (+ (log 2.0) (* x 0.5)) (* x (- 0.5 y)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.1e-7) {
		tmp = x * -y;
	} else if (x <= 2.4e-126) {
		tmp = log(2.0) + (x * 0.5);
	} 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) :: tmp
    if (x <= (-1.1d-7)) then
        tmp = x * -y
    else if (x <= 2.4d-126) then
        tmp = log(2.0d0) + (x * 0.5d0)
    else
        tmp = x * (0.5d0 - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -1.1e-7) {
		tmp = x * -y;
	} else if (x <= 2.4e-126) {
		tmp = Math.log(2.0) + (x * 0.5);
	} else {
		tmp = x * (0.5 - y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.1e-7:
		tmp = x * -y
	elif x <= 2.4e-126:
		tmp = math.log(2.0) + (x * 0.5)
	else:
		tmp = x * (0.5 - y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.1e-7)
		tmp = Float64(x * Float64(-y));
	elseif (x <= 2.4e-126)
		tmp = Float64(log(2.0) + Float64(x * 0.5));
	else
		tmp = Float64(x * Float64(0.5 - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.1e-7)
		tmp = x * -y;
	elseif (x <= 2.4e-126)
		tmp = log(2.0) + (x * 0.5);
	else
		tmp = x * (0.5 - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.1e-7], N[(x * (-y)), $MachinePrecision], If[LessEqual[x, 2.4e-126], N[(N[Log[2.0], $MachinePrecision] + N[(x * 0.5), $MachinePrecision]), $MachinePrecision], N[(x * N[(0.5 - y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.1000000000000001e-7

   1. Initial program 100.0%

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

      1. log1p-define 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. Add Preprocessing

   5. Taylor expanded in x around inf 98.9%

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

      1. neg-mul-1 98.9%

         \[\leadsto \color{blue}{-x \cdot y} \]

      2. distribute-lft-neg-in 98.9%

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

      3. *-commutative 98.9%

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

   7. Simplified 98.9%

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

   if -1.1000000000000001e-7 < x < 2.40000000000000007e-126

   1. Initial program 100.0%

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

      1. log1p-define 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. Add Preprocessing

   5. Taylor expanded in x around 0 100.0%

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

   6. Taylor expanded in y around 0 83.3%

      \[\leadsto \log 2 + \color{blue}{0.5 \cdot x} \]
   7. Step-by-step derivation

      1. *-commutative 83.3%

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

   8. Simplified 83.3%

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

   if 2.40000000000000007e-126 < x

   1. Initial program 93.1%

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

      1. log1p-define 93.1%

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

   3. Simplified 93.1%

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

   5. Taylor expanded in x around 0 91.6%

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

   6. Taylor expanded in x around inf 91.5%

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

   7. Taylor expanded in x around inf 65.3%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{-7}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-126}:\\ \;\;\;\;\log 2 + x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(0.5 - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 80.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{-9}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-126}:\\ \;\;\;\;\log \left(x + 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(0.5 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.15e-9)
   (* x (- y))
   (if (<= x 2.4e-126) (log (+ x 2.0)) (* x (- 0.5 y)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.15e-9) {
		tmp = x * -y;
	} else if (x <= 2.4e-126) {
		tmp = log((x + 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) :: tmp
    if (x <= (-1.15d-9)) then
        tmp = x * -y
    else if (x <= 2.4d-126) then
        tmp = log((x + 2.0d0))
    else
        tmp = x * (0.5d0 - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -1.15e-9) {
		tmp = x * -y;
	} else if (x <= 2.4e-126) {
		tmp = Math.log((x + 2.0));
	} else {
		tmp = x * (0.5 - y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.15e-9:
		tmp = x * -y
	elif x <= 2.4e-126:
		tmp = math.log((x + 2.0))
	else:
		tmp = x * (0.5 - y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.15e-9)
		tmp = Float64(x * Float64(-y));
	elseif (x <= 2.4e-126)
		tmp = log(Float64(x + 2.0));
	else
		tmp = Float64(x * Float64(0.5 - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.15e-9)
		tmp = x * -y;
	elseif (x <= 2.4e-126)
		tmp = log((x + 2.0));
	else
		tmp = x * (0.5 - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.15e-9], N[(x * (-y)), $MachinePrecision], If[LessEqual[x, 2.4e-126], N[Log[N[(x + 2.0), $MachinePrecision]], $MachinePrecision], N[(x * N[(0.5 - y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.15e-9

   1. Initial program 100.0%

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

      1. log1p-define 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. Add Preprocessing

   5. Taylor expanded in x around inf 98.9%

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

      1. neg-mul-1 98.9%

         \[\leadsto \color{blue}{-x \cdot y} \]

      2. distribute-lft-neg-in 98.9%

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

      3. *-commutative 98.9%

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

   7. Simplified 98.9%

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

   if -1.15e-9 < x < 2.40000000000000007e-126

   1. Initial program 100.0%

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

      1. log1p-define 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. Add Preprocessing

   5. Taylor expanded in y around inf 99.9%

      \[\leadsto \color{blue}{y \cdot \left(\frac{\log \left(1 + e^{x}\right)}{y} - x\right)} \]
   6. Step-by-step derivation

      1. log1p-define 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in y around 0 83.3%

      \[\leadsto \color{blue}{\log \left(1 + e^{x}\right)} \]

   9. Taylor expanded in x around 0 83.3%

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

   if 2.40000000000000007e-126 < x

   1. Initial program 93.1%

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

      1. log1p-define 93.1%

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

   3. Simplified 93.1%

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

   5. Taylor expanded in x around 0 91.6%

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

   6. Taylor expanded in x around inf 91.5%

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

   7. Taylor expanded in x around inf 65.3%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{-9}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-126}:\\ \;\;\;\;\log \left(x + 2\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(0.5 - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 98.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -236000:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;\log 2 + x \cdot \left(0.5 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -236000.0) (* x (- y)) (+ (log 2.0) (* x (- 0.5 y)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -236000.0) {
		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 <= (-236000.0d0)) 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 <= -236000.0) {
		tmp = x * -y;
	} else {
		tmp = Math.log(2.0) + (x * (0.5 - y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -236000.0:
		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 <= -236000.0)
		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 <= -236000.0)
		tmp = x * -y;
	else
		tmp = log(2.0) + (x * (0.5 - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -236000.0], 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 < -236000

   1. Initial program 100.0%

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

      1. log1p-define 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. Add Preprocessing

   5. Taylor expanded in x around inf 100.0%

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

      1. neg-mul-1 100.0%

         \[\leadsto \color{blue}{-x \cdot y} \]

      2. distribute-lft-neg-in 100.0%

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

      3. *-commutative 100.0%

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

   7. Simplified 100.0%

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

   if -236000 < x

   1. Initial program 98.3%

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

      1. log1p-define 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. Add Preprocessing

   5. Taylor expanded in x around 0 97.9%

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

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -236000:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;\log 2 + x \cdot \left(0.5 - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 80.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.7 \cdot 10^{-11}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-126}:\\ \;\;\;\;\log 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(0.5 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -5.7e-11)
   (* x (- y))
   (if (<= x 1.05e-126) (log 2.0) (* x (- 0.5 y)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -5.7e-11) {
		tmp = x * -y;
	} else if (x <= 1.05e-126) {
		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) :: tmp
    if (x <= (-5.7d-11)) then
        tmp = x * -y
    else if (x <= 1.05d-126) 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 tmp;
	if (x <= -5.7e-11) {
		tmp = x * -y;
	} else if (x <= 1.05e-126) {
		tmp = Math.log(2.0);
	} else {
		tmp = x * (0.5 - y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -5.7e-11:
		tmp = x * -y
	elif x <= 1.05e-126:
		tmp = math.log(2.0)
	else:
		tmp = x * (0.5 - y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -5.7e-11)
		tmp = Float64(x * Float64(-y));
	elseif (x <= 1.05e-126)
		tmp = log(2.0);
	else
		tmp = Float64(x * Float64(0.5 - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -5.7e-11)
		tmp = x * -y;
	elseif (x <= 1.05e-126)
		tmp = log(2.0);
	else
		tmp = x * (0.5 - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -5.7e-11], N[(x * (-y)), $MachinePrecision], If[LessEqual[x, 1.05e-126], N[Log[2.0], $MachinePrecision], N[(x * N[(0.5 - y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.6999999999999997e-11

   1. Initial program 100.0%

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

      1. log1p-define 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. Add Preprocessing

   5. Taylor expanded in x around inf 98.9%

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

      1. neg-mul-1 98.9%

         \[\leadsto \color{blue}{-x \cdot y} \]

      2. distribute-lft-neg-in 98.9%

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

      3. *-commutative 98.9%

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

   7. Simplified 98.9%

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

   if -5.6999999999999997e-11 < x < 1.0499999999999999e-126

   1. Initial program 100.0%

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

      1. log1p-define 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. Add Preprocessing

   5. Taylor expanded in y around inf 99.9%

      \[\leadsto \color{blue}{y \cdot \left(\frac{\log \left(1 + e^{x}\right)}{y} - x\right)} \]
   6. Step-by-step derivation

      1. log1p-define 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in x around 0 83.1%

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

   if 1.0499999999999999e-126 < x

   1. Initial program 93.1%

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

      1. log1p-define 93.1%

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

   3. Simplified 93.1%

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

   5. Taylor expanded in x around 0 91.6%

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

   6. Taylor expanded in x around inf 91.5%

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

   7. Taylor expanded in x around inf 65.3%

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

4. Final simplification 85.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.7 \cdot 10^{-11}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-126}:\\ \;\;\;\;\log 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(0.5 - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 98.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -236000:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{log1p}\left(1\right) - x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -236000.0) (* x (- y)) (- (log1p 1.0) (* x y))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -236000.0) {
		tmp = x * -y;
	} else {
		tmp = log1p(1.0) - (x * y);
	}
	return tmp;
}

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -236000.0) {
		tmp = x * -y;
	} else {
		tmp = Math.log1p(1.0) - (x * y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -236000.0:
		tmp = x * -y
	else:
		tmp = math.log1p(1.0) - (x * y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -236000.0)
		tmp = Float64(x * Float64(-y));
	else
		tmp = Float64(log1p(1.0) - Float64(x * y));
	end
	return tmp
end

Wolfram

code[x_, y_] := If[LessEqual[x, -236000.0], N[(x * (-y)), $MachinePrecision], N[(N[Log[1 + 1.0], $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -236000

   1. Initial program 100.0%

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

      1. log1p-define 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. Add Preprocessing

   5. Taylor expanded in x around inf 100.0%

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

      1. neg-mul-1 100.0%

         \[\leadsto \color{blue}{-x \cdot y} \]

      2. distribute-lft-neg-in 100.0%

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

      3. *-commutative 100.0%

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

   7. Simplified 100.0%

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

   if -236000 < x

   1. Initial program 98.3%

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

      1. log1p-define 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. Add Preprocessing

   5. Taylor expanded in x around 0 97.3%

      \[\leadsto \mathsf{log1p}\left(\color{blue}{1}\right) - x \cdot y \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -236000:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{log1p}\left(1\right) - x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 51.9% 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-define 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. Add Preprocessing

5. Taylor expanded in x around inf 52.6%

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

   1. neg-mul-1 52.6%

      \[\leadsto \color{blue}{-x \cdot y} \]

   2. distribute-lft-neg-in 52.6%

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

   3. *-commutative 52.6%

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

7. Simplified 52.6%

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

8. Final simplification 52.6%

   \[\leadsto x \cdot \left(-y\right) \]
9. Add Preprocessing

Alternative 11: 3.5% 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-define 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. Add Preprocessing

5. Taylor expanded in x around 0 86.5%

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

6. Taylor expanded in x around inf 86.4%

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

7. Taylor expanded in x around inf 40.8%

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

8. Taylor expanded in y around 0 3.4%

   \[\leadsto \color{blue}{0.5 \cdot x} \]
9. Step-by-step derivation

   1. *-commutative 48.3%

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

10. Simplified 3.4%

    \[\leadsto \color{blue}{x \cdot 0.5} \]
11. Add Preprocessing

Developer Target 1: 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 2024155 
(FPCore (x y)
  :name "Logistic regression 2"
  :precision binary64

  :alt
  (! :herbie-platform default (if (<= x 0) (- (log (+ 1 (exp x))) (* x y)) (- (log (+ 1 (exp (- x)))) (* (- x) (- 1 y)))))

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