Logistic regression 2

Percentage Accurate: 99.3% → 99.4%

Time: 10.1s

Alternatives: 10

Speedup: 1.0×

• could not determine a ground truth

  1. x = 2.001517262950818e+43
  2. y = -1.6380971605512403e-219

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: 99.4% 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 99.2%

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

   1. cancel-sign-sub-inv 99.2%

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

   2. +-commutative 99.2%

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

   3. distribute-lft-neg-out 99.2%

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

   4. distribute-rgt-neg-out 99.2%

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

   5. fma-define 99.2%

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

   6. log1p-define 99.6%

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

3. Simplified 99.6%

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

Alternative 2: 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 99.2%

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

   1. log1p-define 99.6%

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

3. Simplified 99.6%

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

Alternative 3: 99.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -960000000:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;\log 2 + x \cdot \left(\left(0.5 + x \cdot 0.125\right) - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -960000000.0)
   (* y (- x))
   (+ (log 2.0) (* x (- (+ 0.5 (* x 0.125)) y)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -960000000.0) {
		tmp = y * -x;
	} 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 <= (-960000000.0d0)) then
        tmp = y * -x
    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 <= -960000000.0) {
		tmp = y * -x;
	} else {
		tmp = Math.log(2.0) + (x * ((0.5 + (x * 0.125)) - y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -960000000.0:
		tmp = y * -x
	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 <= -960000000.0)
		tmp = Float64(y * Float64(-x));
	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 <= -960000000.0)
		tmp = y * -x;
	else
		tmp = log(2.0) + (x * ((0.5 + (x * 0.125)) - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -960000000.0], N[(y * (-x)), $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 < -9.6e8

   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-rgt-neg-in 100.0%

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

   7. Simplified 100.0%

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

   if -9.6e8 < x

   1. Initial program 98.9%

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

      1. log1p-define 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around 0 99.0%

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

4. Final simplification 99.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -960000000:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;\log 2 + x \cdot \left(\left(0.5 + x \cdot 0.125\right) - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 82.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.9 \cdot 10^{-8}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-100}:\\ \;\;\;\;\log 2 + x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \left(\frac{0.5}{y} + -1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -3.9e-8)
   (* y (- x))
   (if (<= x 5e-100) (+ (log 2.0) (* x 0.5)) (* x (* y (+ (/ 0.5 y) -1.0))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -3.9e-8) {
		tmp = y * -x;
	} else if (x <= 5e-100) {
		tmp = log(2.0) + (x * 0.5);
	} else {
		tmp = x * (y * ((0.5 / y) + -1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-3.9d-8)) then
        tmp = y * -x
    else if (x <= 5d-100) then
        tmp = log(2.0d0) + (x * 0.5d0)
    else
        tmp = x * (y * ((0.5d0 / y) + (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -3.9e-8) {
		tmp = y * -x;
	} else if (x <= 5e-100) {
		tmp = Math.log(2.0) + (x * 0.5);
	} else {
		tmp = x * (y * ((0.5 / y) + -1.0));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -3.9e-8:
		tmp = y * -x
	elif x <= 5e-100:
		tmp = math.log(2.0) + (x * 0.5)
	else:
		tmp = x * (y * ((0.5 / y) + -1.0))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -3.9e-8)
		tmp = Float64(y * Float64(-x));
	elseif (x <= 5e-100)
		tmp = Float64(log(2.0) + Float64(x * 0.5));
	else
		tmp = Float64(x * Float64(y * Float64(Float64(0.5 / y) + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -3.9e-8)
		tmp = y * -x;
	elseif (x <= 5e-100)
		tmp = log(2.0) + (x * 0.5);
	else
		tmp = x * (y * ((0.5 / y) + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -3.9e-8], N[(y * (-x)), $MachinePrecision], If[LessEqual[x, 5e-100], N[(N[Log[2.0], $MachinePrecision] + N[(x * 0.5), $MachinePrecision]), $MachinePrecision], N[(x * N[(y * N[(N[(0.5 / y), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.89999999999999985e-8

   1. Initial program 98.7%

      \[\log \left(1 + e^{x}\right) - x \cdot y \]
   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 98.7%

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

      1. neg-mul-1 98.7%

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

      2. distribute-rgt-neg-in 98.7%

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

   7. Simplified 98.7%

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

   if -3.89999999999999985e-8 < x < 5.0000000000000001e-100

   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 77.8%

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

      1. metadata-eval 77.8%

         \[\leadsto \log \color{blue}{\left(1 + 1\right)} + 0.5 \cdot x \]

      2. log1p-undefine 77.8%

         \[\leadsto \color{blue}{\mathsf{log1p}\left(1\right)} + 0.5 \cdot x \]

      3. +-commutative 77.8%

         \[\leadsto \color{blue}{0.5 \cdot x + \mathsf{log1p}\left(1\right)} \]

      4. *-commutative 77.8%

         \[\leadsto \color{blue}{x \cdot 0.5} + \mathsf{log1p}\left(1\right) \]

      5. log1p-undefine 77.8%

         \[\leadsto x \cdot 0.5 + \color{blue}{\log \left(1 + 1\right)} \]

      6. metadata-eval 77.8%

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

   8. Simplified 77.8%

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

   if 5.0000000000000001e-100 < x

   1. Initial program 97.8%

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

      1. log1p-define 97.8%

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

   3. Simplified 97.8%

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

   5. Taylor expanded in x around 0 97.4%

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

   6. Taylor expanded in y around inf 97.3%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot x + \left(0.5 \cdot \frac{x}{y} + \frac{\log 2}{y}\right)\right)} \]

   7. Taylor expanded in x around inf 72.3%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot \left(0.5 \cdot \frac{1}{y} - 1\right)\right)} \]
   8. Step-by-step derivation

      1. sub-neg 72.3%

         \[\leadsto x \cdot \left(y \cdot \color{blue}{\left(0.5 \cdot \frac{1}{y} + \left(-1\right)\right)}\right) \]

      2. associate-*r/ 72.3%

         \[\leadsto x \cdot \left(y \cdot \left(\color{blue}{\frac{0.5 \cdot 1}{y}} + \left(-1\right)\right)\right) \]

      3. metadata-eval 72.3%

         \[\leadsto x \cdot \left(y \cdot \left(\frac{\color{blue}{0.5}}{y} + \left(-1\right)\right)\right) \]

      4. metadata-eval 72.3%

         \[\leadsto x \cdot \left(y \cdot \left(\frac{0.5}{y} + \color{blue}{-1}\right)\right) \]

   9. Simplified 72.3%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot \left(\frac{0.5}{y} + -1\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.9 \cdot 10^{-8}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-100}:\\ \;\;\;\;\log 2 + x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \left(\frac{0.5}{y} + -1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 82.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.4 \cdot 10^{-8}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{-103}:\\ \;\;\;\;\mathsf{log1p}\left(x + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \left(\frac{0.5}{y} + -1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -4.4e-8)
   (* y (- x))
   (if (<= x 1.45e-103) (log1p (+ x 1.0)) (* x (* y (+ (/ 0.5 y) -1.0))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -4.4e-8) {
		tmp = y * -x;
	} else if (x <= 1.45e-103) {
		tmp = log1p((x + 1.0));
	} else {
		tmp = x * (y * ((0.5 / y) + -1.0));
	}
	return tmp;
}

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -4.4e-8) {
		tmp = y * -x;
	} else if (x <= 1.45e-103) {
		tmp = Math.log1p((x + 1.0));
	} else {
		tmp = x * (y * ((0.5 / y) + -1.0));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -4.4e-8:
		tmp = y * -x
	elif x <= 1.45e-103:
		tmp = math.log1p((x + 1.0))
	else:
		tmp = x * (y * ((0.5 / y) + -1.0))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -4.4e-8)
		tmp = Float64(y * Float64(-x));
	elseif (x <= 1.45e-103)
		tmp = log1p(Float64(x + 1.0));
	else
		tmp = Float64(x * Float64(y * Float64(Float64(0.5 / y) + -1.0)));
	end
	return tmp
end

Wolfram

code[x_, y_] := If[LessEqual[x, -4.4e-8], N[(y * (-x)), $MachinePrecision], If[LessEqual[x, 1.45e-103], N[Log[1 + N[(x + 1.0), $MachinePrecision]], $MachinePrecision], N[(x * N[(y * N[(N[(0.5 / y), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.3999999999999997e-8

   1. Initial program 98.7%

      \[\log \left(1 + e^{x}\right) - x \cdot y \]
   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 98.7%

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

      1. neg-mul-1 98.7%

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

      2. distribute-rgt-neg-in 98.7%

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

   7. Simplified 98.7%

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

   if -4.3999999999999997e-8 < x < 1.4499999999999999e-103

   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 0 77.8%

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

      1. log1p-define 77.8%

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

   7. Simplified 77.8%

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

   8. Taylor expanded in x around 0 77.8%

      \[\leadsto \mathsf{log1p}\left(\color{blue}{1 + x}\right) \]
   9. Step-by-step derivation

      1. +-commutative 77.8%

         \[\leadsto \mathsf{log1p}\left(\color{blue}{x + 1}\right) \]

   10. Simplified 77.8%

       \[\leadsto \mathsf{log1p}\left(\color{blue}{x + 1}\right) \]

   if 1.4499999999999999e-103 < x

   1. Initial program 97.8%

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

      1. log1p-define 97.8%

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

   3. Simplified 97.8%

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

   5. Taylor expanded in x around 0 97.4%

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

   6. Taylor expanded in y around inf 97.3%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot x + \left(0.5 \cdot \frac{x}{y} + \frac{\log 2}{y}\right)\right)} \]

   7. Taylor expanded in x around inf 72.3%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot \left(0.5 \cdot \frac{1}{y} - 1\right)\right)} \]
   8. Step-by-step derivation

      1. sub-neg 72.3%

         \[\leadsto x \cdot \left(y \cdot \color{blue}{\left(0.5 \cdot \frac{1}{y} + \left(-1\right)\right)}\right) \]

      2. associate-*r/ 72.3%

         \[\leadsto x \cdot \left(y \cdot \left(\color{blue}{\frac{0.5 \cdot 1}{y}} + \left(-1\right)\right)\right) \]

      3. metadata-eval 72.3%

         \[\leadsto x \cdot \left(y \cdot \left(\frac{\color{blue}{0.5}}{y} + \left(-1\right)\right)\right) \]

      4. metadata-eval 72.3%

         \[\leadsto x \cdot \left(y \cdot \left(\frac{0.5}{y} + \color{blue}{-1}\right)\right) \]

   9. Simplified 72.3%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot \left(\frac{0.5}{y} + -1\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.4 \cdot 10^{-8}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{-103}:\\ \;\;\;\;\mathsf{log1p}\left(x + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \left(\frac{0.5}{y} + -1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 99.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.36:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;\log 2 + x \cdot \left(0.5 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.36) (* y (- x)) (+ (log 2.0) (* x (- 0.5 y)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.36) {
		tmp = y * -x;
	} 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 <= (-1.36d0)) then
        tmp = y * -x
    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 <= -1.36) {
		tmp = y * -x;
	} else {
		tmp = Math.log(2.0) + (x * (0.5 - y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.36:
		tmp = y * -x
	else:
		tmp = math.log(2.0) + (x * (0.5 - y))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.36)
		tmp = Float64(y * Float64(-x));
	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 <= -1.36)
		tmp = y * -x;
	else
		tmp = log(2.0) + (x * (0.5 - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.36], N[(y * (-x)), $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 < -1.3600000000000001

   1. Initial program 98.6%

      \[\log \left(1 + e^{x}\right) - x \cdot y \]
   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 98.6%

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

      1. neg-mul-1 98.6%

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

      2. distribute-rgt-neg-in 98.6%

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

   7. Simplified 98.6%

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

   if -1.3600000000000001 < x

   1. Initial program 99.4%

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

      1. log1p-define 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around 0 99.3%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.36:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;\log 2 + x \cdot \left(0.5 - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 82.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{-8}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{-101}:\\ \;\;\;\;\log 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \left(\frac{0.5}{y} + -1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2.4e-8)
   (* y (- x))
   (if (<= x 2.2e-101) (log 2.0) (* x (* y (+ (/ 0.5 y) -1.0))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.4e-8) {
		tmp = y * -x;
	} else if (x <= 2.2e-101) {
		tmp = log(2.0);
	} else {
		tmp = x * (y * ((0.5 / y) + -1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-2.4d-8)) then
        tmp = y * -x
    else if (x <= 2.2d-101) then
        tmp = log(2.0d0)
    else
        tmp = x * (y * ((0.5d0 / y) + (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -2.4e-8) {
		tmp = y * -x;
	} else if (x <= 2.2e-101) {
		tmp = Math.log(2.0);
	} else {
		tmp = x * (y * ((0.5 / y) + -1.0));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2.4e-8:
		tmp = y * -x
	elif x <= 2.2e-101:
		tmp = math.log(2.0)
	else:
		tmp = x * (y * ((0.5 / y) + -1.0))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2.4e-8)
		tmp = Float64(y * Float64(-x));
	elseif (x <= 2.2e-101)
		tmp = log(2.0);
	else
		tmp = Float64(x * Float64(y * Float64(Float64(0.5 / y) + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2.4e-8)
		tmp = y * -x;
	elseif (x <= 2.2e-101)
		tmp = log(2.0);
	else
		tmp = x * (y * ((0.5 / y) + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2.4e-8], N[(y * (-x)), $MachinePrecision], If[LessEqual[x, 2.2e-101], N[Log[2.0], $MachinePrecision], N[(x * N[(y * N[(N[(0.5 / y), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.39999999999999998e-8

   1. Initial program 98.7%

      \[\log \left(1 + e^{x}\right) - x \cdot y \]
   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 98.7%

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

      1. neg-mul-1 98.7%

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

      2. distribute-rgt-neg-in 98.7%

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

   7. Simplified 98.7%

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

   if -2.39999999999999998e-8 < x < 2.1999999999999999e-101

   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 77.2%

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

   if 2.1999999999999999e-101 < x

   1. Initial program 97.8%

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

      1. log1p-define 97.8%

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

   3. Simplified 97.8%

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

   5. Taylor expanded in x around 0 97.4%

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

   6. Taylor expanded in y around inf 97.3%

      \[\leadsto \color{blue}{y \cdot \left(-1 \cdot x + \left(0.5 \cdot \frac{x}{y} + \frac{\log 2}{y}\right)\right)} \]

   7. Taylor expanded in x around inf 72.3%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot \left(0.5 \cdot \frac{1}{y} - 1\right)\right)} \]
   8. Step-by-step derivation

      1. sub-neg 72.3%

         \[\leadsto x \cdot \left(y \cdot \color{blue}{\left(0.5 \cdot \frac{1}{y} + \left(-1\right)\right)}\right) \]

      2. associate-*r/ 72.3%

         \[\leadsto x \cdot \left(y \cdot \left(\color{blue}{\frac{0.5 \cdot 1}{y}} + \left(-1\right)\right)\right) \]

      3. metadata-eval 72.3%

         \[\leadsto x \cdot \left(y \cdot \left(\frac{\color{blue}{0.5}}{y} + \left(-1\right)\right)\right) \]

      4. metadata-eval 72.3%

         \[\leadsto x \cdot \left(y \cdot \left(\frac{0.5}{y} + \color{blue}{-1}\right)\right) \]

   9. Simplified 72.3%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot \left(\frac{0.5}{y} + -1\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{-8}:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{-101}:\\ \;\;\;\;\log 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot \left(\frac{0.5}{y} + -1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 98.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -960000000:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{log1p}\left(1\right) - x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -960000000.0) (* y (- x)) (- (log1p 1.0) (* x y))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -960000000.0) {
		tmp = y * -x;
	} else {
		tmp = log1p(1.0) - (x * y);
	}
	return tmp;
}

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -960000000.0) {
		tmp = y * -x;
	} else {
		tmp = Math.log1p(1.0) - (x * y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -960000000.0:
		tmp = y * -x
	else:
		tmp = math.log1p(1.0) - (x * y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -960000000.0)
		tmp = Float64(y * Float64(-x));
	else
		tmp = Float64(log1p(1.0) - Float64(x * y));
	end
	return tmp
end

Wolfram

code[x_, y_] := If[LessEqual[x, -960000000.0], N[(y * (-x)), $MachinePrecision], N[(N[Log[1 + 1.0], $MachinePrecision] - N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -9.6e8

   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-rgt-neg-in 100.0%

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

   7. Simplified 100.0%

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

   if -9.6e8 < x

   1. Initial program 98.9%

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

      1. log1p-define 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around 0 98.1%

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

4. Final simplification 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -960000000:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{log1p}\left(1\right) - x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 54.0% accurate, 51.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.2%

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

   1. log1p-define 99.6%

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

3. Simplified 99.6%

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

5. Taylor expanded in x around inf 54.2%

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

   1. neg-mul-1 54.2%

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

   2. distribute-rgt-neg-in 54.2%

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

7. Simplified 54.2%

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

8. Final simplification 54.2%

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

Alternative 10: 2.2% accurate, 69.0× speedup

Math

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

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 * y)
end

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.2%

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

   1. log1p-define 99.6%

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

3. Simplified 99.6%

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

5. Taylor expanded in x around inf 54.2%

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

   1. neg-mul-1 54.2%

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

   2. distribute-rgt-neg-in 54.2%

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

7. Simplified 54.2%

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

   1. add-sqr-sqrt 25.5%

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

   2. sqrt-unprod 17.4%

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

   3. sqr-neg 17.4%

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

   4. sqrt-unprod 1.1%

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

   5. add-sqr-sqrt 2.2%

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

   6. pow1 2.2%

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

9. Applied egg-rr 2.2%

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

    1. unpow1 2.2%

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

11. Simplified 2.2%

    \[\leadsto \color{blue}{x \cdot y} \]
12. 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 2024182 
(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)))