Numeric.SpecFunctions.Extra:bd0 from math-functions-0.1.5.2

Percentage Accurate: 77.4% → 99.4%

Time: 8.9s

Alternatives: 9

Speedup: 0.5×

Specification

Math

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

FPCore

(FPCore (x y z) :precision binary64 (- (* x (log (/ x y))) z))

C

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

Fortran

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

Java

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

Python

def code(x, y, z):
	return (x * math.log((x / y))) - z

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 77.4% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z) :precision binary64 (- (* x (log (/ x y))) z))

C

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

Fortran

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

Java

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

Python

def code(x, y, z):
	return (x * math.log((x / y))) - z

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-310}:\\ \;\;\;\;x \cdot \left(\log \left({\left(\sqrt[3]{y}\right)}^{-2}\right) + \left(\log \left(-x\right) - \log \left(-\sqrt[3]{y}\right)\right)\right) - z\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \log x - x \cdot \log y\right) - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -5e-310)
   (- (* x (+ (log (pow (cbrt y) -2.0)) (- (log (- x)) (log (- (cbrt y)))))) z)
   (- (- (* x (log x)) (* x (log y))) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -5e-310) {
		tmp = (x * (log(pow(cbrt(y), -2.0)) + (log(-x) - log(-cbrt(y))))) - z;
	} else {
		tmp = ((x * log(x)) - (x * log(y))) - z;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -5e-310) {
		tmp = (x * (Math.log(Math.pow(Math.cbrt(y), -2.0)) + (Math.log(-x) - Math.log(-Math.cbrt(y))))) - z;
	} else {
		tmp = ((x * Math.log(x)) - (x * Math.log(y))) - z;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -5e-310)
		tmp = Float64(Float64(x * Float64(log((cbrt(y) ^ -2.0)) + Float64(log(Float64(-x)) - log(Float64(-cbrt(y)))))) - z);
	else
		tmp = Float64(Float64(Float64(x * log(x)) - Float64(x * log(y))) - z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -5e-310], N[(N[(x * N[(N[Log[N[Power[N[Power[y, 1/3], $MachinePrecision], -2.0], $MachinePrecision]], $MachinePrecision] + N[(N[Log[(-x)], $MachinePrecision] - N[Log[(-N[Power[y, 1/3], $MachinePrecision])], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision], N[(N[(N[(x * N[Log[x], $MachinePrecision]), $MachinePrecision] - N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.999999999999985e-310

   1. Initial program 73.5%

      \[x \cdot \log \left(\frac{x}{y}\right) - z \]
   2. Step-by-step derivation

      1. *-un-lft-identity 73.5%

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

      2. add-cube-cbrt 73.5%

         \[\leadsto x \cdot \log \left(\frac{1 \cdot x}{\color{blue}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}}}\right) - z \]

      3. times-frac 73.5%

         \[\leadsto x \cdot \log \color{blue}{\left(\frac{1}{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \frac{x}{\sqrt[3]{y}}\right)} - z \]

      4. log-prod 89.1%

         \[\leadsto x \cdot \color{blue}{\left(\log \left(\frac{1}{\sqrt[3]{y} \cdot \sqrt[3]{y}}\right) + \log \left(\frac{x}{\sqrt[3]{y}}\right)\right)} - z \]

      5. pow2 89.1%

         \[\leadsto x \cdot \left(\log \left(\frac{1}{\color{blue}{{\left(\sqrt[3]{y}\right)}^{2}}}\right) + \log \left(\frac{x}{\sqrt[3]{y}}\right)\right) - z \]

      6. metadata-eval 89.1%

         \[\leadsto x \cdot \left(\log \left(\frac{1}{{\left(\sqrt[3]{y}\right)}^{\color{blue}{\left(1 + 1\right)}}}\right) + \log \left(\frac{x}{\sqrt[3]{y}}\right)\right) - z \]

      7. pow-flip 89.1%

         \[\leadsto x \cdot \left(\log \color{blue}{\left({\left(\sqrt[3]{y}\right)}^{\left(-\left(1 + 1\right)\right)}\right)} + \log \left(\frac{x}{\sqrt[3]{y}}\right)\right) - z \]

      8. metadata-eval 89.1%

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

      9. metadata-eval 89.1%

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

   3. Applied egg-rr 89.1%

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

      1. frac-2neg 89.1%

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

      2. log-div 99.5%

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

   5. Applied egg-rr 99.5%

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

   if -4.999999999999985e-310 < y

   1. Initial program 78.4%

      \[x \cdot \log \left(\frac{x}{y}\right) - z \]
   2. Step-by-step derivation

      1. log-div 99.5%

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

   3. Applied egg-rr 99.5%

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

      1. sub-neg 99.5%

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

      2. distribute-rgt-in 99.6%

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

   5. Applied egg-rr 99.6%

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

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-310}:\\ \;\;\;\;x \cdot \left(\log \left({\left(\sqrt[3]{y}\right)}^{-2}\right) + \left(\log \left(-x\right) - \log \left(-\sqrt[3]{y}\right)\right)\right) - z\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \log x - x \cdot \log y\right) - z\\ \end{array} \]

Alternative 2: 87.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \log \left(\frac{x}{y}\right)\\ \mathbf{if}\;t_0 \leq -\infty:\\ \;\;\;\;-z\\ \mathbf{elif}\;t_0 \leq 10^{+306}:\\ \;\;\;\;t_0 - z\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (log (/ x y)))))
   (if (<= t_0 (- INFINITY)) (- z) (if (<= t_0 1e+306) (- t_0 z) (- z)))))

C

double code(double x, double y, double z) {
	double t_0 = x * log((x / y));
	double tmp;
	if (t_0 <= -((double) INFINITY)) {
		tmp = -z;
	} else if (t_0 <= 1e+306) {
		tmp = t_0 - z;
	} else {
		tmp = -z;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z) {
	double t_0 = x * Math.log((x / y));
	double tmp;
	if (t_0 <= -Double.POSITIVE_INFINITY) {
		tmp = -z;
	} else if (t_0 <= 1e+306) {
		tmp = t_0 - z;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * math.log((x / y))
	tmp = 0
	if t_0 <= -math.inf:
		tmp = -z
	elif t_0 <= 1e+306:
		tmp = t_0 - z
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * log(Float64(x / y)))
	tmp = 0.0
	if (t_0 <= Float64(-Inf))
		tmp = Float64(-z);
	elseif (t_0 <= 1e+306)
		tmp = Float64(t_0 - z);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * log((x / y));
	tmp = 0.0;
	if (t_0 <= -Inf)
		tmp = -z;
	elseif (t_0 <= 1e+306)
		tmp = t_0 - z;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[Log[N[(x / y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, (-Infinity)], (-z), If[LessEqual[t$95$0, 1e+306], N[(t$95$0 - z), $MachinePrecision], (-z)]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x (log.f64 (/.f64 x y))) < -inf.0 or 1.00000000000000002e306 < (*.f64 x (log.f64 (/.f64 x y)))

   1. Initial program 4.6%

      \[x \cdot \log \left(\frac{x}{y}\right) - z \]

   2. Taylor expanded in x around 0 53.9%

      \[\leadsto \color{blue}{-1 \cdot z} \]
   3. Step-by-step derivation

      1. neg-mul-1 53.9%

         \[\leadsto \color{blue}{-z} \]

   4. Simplified 53.9%

      \[\leadsto \color{blue}{-z} \]

   if -inf.0 < (*.f64 x (log.f64 (/.f64 x y))) < 1.00000000000000002e306

   1. Initial program 99.8%

      \[x \cdot \log \left(\frac{x}{y}\right) - z \]
3. Recombined 2 regimes into one program.

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \log \left(\frac{x}{y}\right) \leq -\infty:\\ \;\;\;\;-z\\ \mathbf{elif}\;x \cdot \log \left(\frac{x}{y}\right) \leq 10^{+306}:\\ \;\;\;\;x \cdot \log \left(\frac{x}{y}\right) - z\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 3: 99.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-310}:\\ \;\;\;\;\mathsf{fma}\left(\log \left(-x\right) + \log \left(\frac{-1}{y}\right), x, -z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \log x - x \cdot \log y\right) - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -5e-310)
   (fma (+ (log (- x)) (log (/ -1.0 y))) x (- z))
   (- (- (* x (log x)) (* x (log y))) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -5e-310) {
		tmp = fma((log(-x) + log((-1.0 / y))), x, -z);
	} else {
		tmp = ((x * log(x)) - (x * log(y))) - z;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -5e-310)
		tmp = fma(Float64(log(Float64(-x)) + log(Float64(-1.0 / y))), x, Float64(-z));
	else
		tmp = Float64(Float64(Float64(x * log(x)) - Float64(x * log(y))) - z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -5e-310], N[(N[(N[Log[(-x)], $MachinePrecision] + N[Log[N[(-1.0 / y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * x + (-z)), $MachinePrecision], N[(N[(N[(x * N[Log[x], $MachinePrecision]), $MachinePrecision] - N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.999999999999985e-310

   1. Initial program 73.5%

      \[x \cdot \log \left(\frac{x}{y}\right) - z \]
   2. Step-by-step derivation

      1. *-commutative 73.5%

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

      2. add-sqr-sqrt 0.0%

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

      3. associate-*r* 0.0%

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

      4. fma-neg 0.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\log \left(\frac{x}{y}\right) \cdot \sqrt{x}, \sqrt{x}, -z\right)} \]

   3. Applied egg-rr 0.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\log \left(\frac{x}{y}\right) \cdot \sqrt{x}, \sqrt{x}, -z\right)} \]

   4. Taylor expanded in y around -inf 99.5%

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

      1. fma-neg 99.5%

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

      2. neg-mul-1 99.5%

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

   6. Simplified 99.5%

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

   if -4.999999999999985e-310 < y

   1. Initial program 78.4%

      \[x \cdot \log \left(\frac{x}{y}\right) - z \]
   2. Step-by-step derivation

      1. log-div 99.5%

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

   3. Applied egg-rr 99.5%

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

      1. sub-neg 99.5%

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

      2. distribute-rgt-in 99.6%

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

   5. Applied egg-rr 99.6%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-310}:\\ \;\;\;\;\mathsf{fma}\left(\log \left(-x\right) + \log \left(\frac{-1}{y}\right), x, -z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \log x - x \cdot \log y\right) - z\\ \end{array} \]

Alternative 4: 93.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{+223}:\\ \;\;\;\;x \cdot \left(\log \left(-x\right) - \log \left(-y\right)\right)\\ \mathbf{elif}\;x \leq -1 \cdot 10^{-214}:\\ \;\;\;\;\left(-z\right) - x \cdot \log \left(\frac{y}{x}\right)\\ \mathbf{elif}\;x \leq -1 \cdot 10^{-308}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x - \log y\right) - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.05e+223)
   (* x (- (log (- x)) (log (- y))))
   (if (<= x -1e-214)
     (- (- z) (* x (log (/ y x))))
     (if (<= x -1e-308) (- z) (- (* x (- (log x) (log y))) z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.05e+223) {
		tmp = x * (log(-x) - log(-y));
	} else if (x <= -1e-214) {
		tmp = -z - (x * log((y / x)));
	} else if (x <= -1e-308) {
		tmp = -z;
	} else {
		tmp = (x * (log(x) - log(y))) - z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-1.05d+223)) then
        tmp = x * (log(-x) - log(-y))
    else if (x <= (-1d-214)) then
        tmp = -z - (x * log((y / x)))
    else if (x <= (-1d-308)) then
        tmp = -z
    else
        tmp = (x * (log(x) - log(y))) - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.05e+223) {
		tmp = x * (Math.log(-x) - Math.log(-y));
	} else if (x <= -1e-214) {
		tmp = -z - (x * Math.log((y / x)));
	} else if (x <= -1e-308) {
		tmp = -z;
	} else {
		tmp = (x * (Math.log(x) - Math.log(y))) - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.05e+223:
		tmp = x * (math.log(-x) - math.log(-y))
	elif x <= -1e-214:
		tmp = -z - (x * math.log((y / x)))
	elif x <= -1e-308:
		tmp = -z
	else:
		tmp = (x * (math.log(x) - math.log(y))) - z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.05e+223)
		tmp = Float64(x * Float64(log(Float64(-x)) - log(Float64(-y))));
	elseif (x <= -1e-214)
		tmp = Float64(Float64(-z) - Float64(x * log(Float64(y / x))));
	elseif (x <= -1e-308)
		tmp = Float64(-z);
	else
		tmp = Float64(Float64(x * Float64(log(x) - log(y))) - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.05e+223)
		tmp = x * (log(-x) - log(-y));
	elseif (x <= -1e-214)
		tmp = -z - (x * log((y / x)));
	elseif (x <= -1e-308)
		tmp = -z;
	else
		tmp = (x * (log(x) - log(y))) - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.05e+223], N[(x * N[(N[Log[(-x)], $MachinePrecision] - N[Log[(-y)], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1e-214], N[((-z) - N[(x * N[Log[N[(y / x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1e-308], (-z), N[(N[(x * N[(N[Log[x], $MachinePrecision] - N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.04999999999999995e223

   1. Initial program 40.3%

      \[x \cdot \log \left(\frac{x}{y}\right) - z \]

   2. Taylor expanded in z around 0 40.3%

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

      1. frac-2neg 40.3%

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

      2. log-div 93.4%

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

   4. Applied egg-rr 93.4%

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

   if -1.04999999999999995e223 < x < -9.99999999999999913e-215

   1. Initial program 85.7%

      \[x \cdot \log \left(\frac{x}{y}\right) - z \]
   2. Step-by-step derivation

      1. clear-num 45.7%

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

      2. neg-log 47.4%

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

   3. Applied egg-rr 87.4%

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

   if -9.99999999999999913e-215 < x < -9.9999999999999991e-309

   1. Initial program 55.6%

      \[x \cdot \log \left(\frac{x}{y}\right) - z \]

   2. Taylor expanded in x around 0 97.1%

      \[\leadsto \color{blue}{-1 \cdot z} \]
   3. Step-by-step derivation

      1. neg-mul-1 97.1%

         \[\leadsto \color{blue}{-z} \]

   4. Simplified 97.1%

      \[\leadsto \color{blue}{-z} \]

   if -9.9999999999999991e-309 < x

   1. Initial program 78.4%

      \[x \cdot \log \left(\frac{x}{y}\right) - z \]
   2. Step-by-step derivation

      1. log-div 99.5%

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

   3. Applied egg-rr 99.5%

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

4. Final simplification 94.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{+223}:\\ \;\;\;\;x \cdot \left(\log \left(-x\right) - \log \left(-y\right)\right)\\ \mathbf{elif}\;x \leq -1 \cdot 10^{-214}:\\ \;\;\;\;\left(-z\right) - x \cdot \log \left(\frac{y}{x}\right)\\ \mathbf{elif}\;x \leq -1 \cdot 10^{-308}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x - \log y\right) - z\\ \end{array} \]

Alternative 5: 99.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-310}:\\ \;\;\;\;x \cdot \left(\log \left(-x\right) - \log \left(-y\right)\right) - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x - \log y\right) - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -5e-310)
   (- (* x (- (log (- x)) (log (- y)))) z)
   (- (* x (- (log x) (log y))) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -5e-310) {
		tmp = (x * (log(-x) - log(-y))) - z;
	} else {
		tmp = (x * (log(x) - log(y))) - z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-5d-310)) then
        tmp = (x * (log(-x) - log(-y))) - z
    else
        tmp = (x * (log(x) - log(y))) - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -5e-310) {
		tmp = (x * (Math.log(-x) - Math.log(-y))) - z;
	} else {
		tmp = (x * (Math.log(x) - Math.log(y))) - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -5e-310:
		tmp = (x * (math.log(-x) - math.log(-y))) - z
	else:
		tmp = (x * (math.log(x) - math.log(y))) - z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -5e-310)
		tmp = Float64(Float64(x * Float64(log(Float64(-x)) - log(Float64(-y)))) - z);
	else
		tmp = Float64(Float64(x * Float64(log(x) - log(y))) - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -5e-310)
		tmp = (x * (log(-x) - log(-y))) - z;
	else
		tmp = (x * (log(x) - log(y))) - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -5e-310], N[(N[(x * N[(N[Log[(-x)], $MachinePrecision] - N[Log[(-y)], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision], N[(N[(x * N[(N[Log[x], $MachinePrecision] - N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.999999999999985e-310

   1. Initial program 73.5%

      \[x \cdot \log \left(\frac{x}{y}\right) - z \]
   2. Step-by-step derivation

      1. frac-2neg 35.9%

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

      2. log-div 46.2%

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

   3. Applied egg-rr 99.5%

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

   if -4.999999999999985e-310 < y

   1. Initial program 78.4%

      \[x \cdot \log \left(\frac{x}{y}\right) - z \]
   2. Step-by-step derivation

      1. log-div 99.5%

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

   3. Applied egg-rr 99.5%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-310}:\\ \;\;\;\;x \cdot \left(\log \left(-x\right) - \log \left(-y\right)\right) - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x - \log y\right) - z\\ \end{array} \]

Alternative 6: 99.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-310}:\\ \;\;\;\;x \cdot \left(\log \left(-x\right) - \log \left(-y\right)\right) - z\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \log x - x \cdot \log y\right) - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -5e-310)
   (- (* x (- (log (- x)) (log (- y)))) z)
   (- (- (* x (log x)) (* x (log y))) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -5e-310) {
		tmp = (x * (log(-x) - log(-y))) - z;
	} else {
		tmp = ((x * log(x)) - (x * log(y))) - z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-5d-310)) then
        tmp = (x * (log(-x) - log(-y))) - z
    else
        tmp = ((x * log(x)) - (x * log(y))) - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -5e-310) {
		tmp = (x * (Math.log(-x) - Math.log(-y))) - z;
	} else {
		tmp = ((x * Math.log(x)) - (x * Math.log(y))) - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -5e-310:
		tmp = (x * (math.log(-x) - math.log(-y))) - z
	else:
		tmp = ((x * math.log(x)) - (x * math.log(y))) - z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -5e-310)
		tmp = Float64(Float64(x * Float64(log(Float64(-x)) - log(Float64(-y)))) - z);
	else
		tmp = Float64(Float64(Float64(x * log(x)) - Float64(x * log(y))) - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -5e-310)
		tmp = (x * (log(-x) - log(-y))) - z;
	else
		tmp = ((x * log(x)) - (x * log(y))) - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -5e-310], N[(N[(x * N[(N[Log[(-x)], $MachinePrecision] - N[Log[(-y)], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision], N[(N[(N[(x * N[Log[x], $MachinePrecision]), $MachinePrecision] - N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.999999999999985e-310

   1. Initial program 73.5%

      \[x \cdot \log \left(\frac{x}{y}\right) - z \]
   2. Step-by-step derivation

      1. frac-2neg 35.9%

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

      2. log-div 46.2%

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

   3. Applied egg-rr 99.5%

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

   if -4.999999999999985e-310 < y

   1. Initial program 78.4%

      \[x \cdot \log \left(\frac{x}{y}\right) - z \]
   2. Step-by-step derivation

      1. log-div 99.5%

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

   3. Applied egg-rr 99.5%

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

      1. sub-neg 99.5%

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

      2. distribute-rgt-in 99.6%

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

   5. Applied egg-rr 99.6%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-310}:\\ \;\;\;\;x \cdot \left(\log \left(-x\right) - \log \left(-y\right)\right) - z\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \log x - x \cdot \log y\right) - z\\ \end{array} \]

Alternative 7: 66.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+100}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{+68}:\\ \;\;\;\;x \cdot \log \left(\frac{x}{y}\right)\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-26}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-22}:\\ \;\;\;\;\left(-x\right) \cdot \log \left(\frac{y}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.1e+100)
   (- z)
   (if (<= z -1.4e+68)
     (* x (log (/ x y)))
     (if (<= z -5.5e-26)
       (- z)
       (if (<= z 2.3e-22) (* (- x) (log (/ y x))) (- z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.1e+100) {
		tmp = -z;
	} else if (z <= -1.4e+68) {
		tmp = x * log((x / y));
	} else if (z <= -5.5e-26) {
		tmp = -z;
	} else if (z <= 2.3e-22) {
		tmp = -x * log((y / x));
	} else {
		tmp = -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-1.1d+100)) then
        tmp = -z
    else if (z <= (-1.4d+68)) then
        tmp = x * log((x / y))
    else if (z <= (-5.5d-26)) then
        tmp = -z
    else if (z <= 2.3d-22) then
        tmp = -x * log((y / x))
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.1e+100) {
		tmp = -z;
	} else if (z <= -1.4e+68) {
		tmp = x * Math.log((x / y));
	} else if (z <= -5.5e-26) {
		tmp = -z;
	} else if (z <= 2.3e-22) {
		tmp = -x * Math.log((y / x));
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.1e+100:
		tmp = -z
	elif z <= -1.4e+68:
		tmp = x * math.log((x / y))
	elif z <= -5.5e-26:
		tmp = -z
	elif z <= 2.3e-22:
		tmp = -x * math.log((y / x))
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.1e+100)
		tmp = Float64(-z);
	elseif (z <= -1.4e+68)
		tmp = Float64(x * log(Float64(x / y)));
	elseif (z <= -5.5e-26)
		tmp = Float64(-z);
	elseif (z <= 2.3e-22)
		tmp = Float64(Float64(-x) * log(Float64(y / x)));
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.1e+100)
		tmp = -z;
	elseif (z <= -1.4e+68)
		tmp = x * log((x / y));
	elseif (z <= -5.5e-26)
		tmp = -z;
	elseif (z <= 2.3e-22)
		tmp = -x * log((y / x));
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.1e+100], (-z), If[LessEqual[z, -1.4e+68], N[(x * N[Log[N[(x / y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5.5e-26], (-z), If[LessEqual[z, 2.3e-22], N[((-x) * N[Log[N[(y / x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], (-z)]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.1e100 or -1.4e68 < z < -5.5000000000000005e-26 or 2.2999999999999998e-22 < z

   1. Initial program 75.1%

      \[x \cdot \log \left(\frac{x}{y}\right) - z \]

   2. Taylor expanded in x around 0 82.5%

      \[\leadsto \color{blue}{-1 \cdot z} \]
   3. Step-by-step derivation

      1. neg-mul-1 82.5%

         \[\leadsto \color{blue}{-z} \]

   4. Simplified 82.5%

      \[\leadsto \color{blue}{-z} \]

   if -1.1e100 < z < -1.4e68

   1. Initial program 83.9%

      \[x \cdot \log \left(\frac{x}{y}\right) - z \]

   2. Taylor expanded in z around 0 83.9%

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

   if -5.5000000000000005e-26 < z < 2.2999999999999998e-22

   1. Initial program 75.9%

      \[x \cdot \log \left(\frac{x}{y}\right) - z \]

   2. Taylor expanded in z around 0 63.5%

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

      1. clear-num 63.5%

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

      2. neg-log 65.1%

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

   4. Applied egg-rr 65.1%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+100}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{+68}:\\ \;\;\;\;x \cdot \log \left(\frac{x}{y}\right)\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-26}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-22}:\\ \;\;\;\;\left(-x\right) \cdot \log \left(\frac{y}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 8: 66.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+100}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{+72} \lor \neg \left(z \leq -5.2 \cdot 10^{-26}\right) \land z \leq 1.7 \cdot 10^{-22}:\\ \;\;\;\;x \cdot \log \left(\frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.1e+100)
   (- z)
   (if (or (<= z -1.1e+72) (and (not (<= z -5.2e-26)) (<= z 1.7e-22)))
     (* x (log (/ x y)))
     (- z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.1e+100) {
		tmp = -z;
	} else if ((z <= -1.1e+72) || (!(z <= -5.2e-26) && (z <= 1.7e-22))) {
		tmp = x * log((x / y));
	} else {
		tmp = -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-1.1d+100)) then
        tmp = -z
    else if ((z <= (-1.1d+72)) .or. (.not. (z <= (-5.2d-26))) .and. (z <= 1.7d-22)) then
        tmp = x * log((x / y))
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.1e+100) {
		tmp = -z;
	} else if ((z <= -1.1e+72) || (!(z <= -5.2e-26) && (z <= 1.7e-22))) {
		tmp = x * Math.log((x / y));
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.1e+100:
		tmp = -z
	elif (z <= -1.1e+72) or (not (z <= -5.2e-26) and (z <= 1.7e-22)):
		tmp = x * math.log((x / y))
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.1e+100)
		tmp = Float64(-z);
	elseif ((z <= -1.1e+72) || (!(z <= -5.2e-26) && (z <= 1.7e-22)))
		tmp = Float64(x * log(Float64(x / y)));
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.1e+100)
		tmp = -z;
	elseif ((z <= -1.1e+72) || (~((z <= -5.2e-26)) && (z <= 1.7e-22)))
		tmp = x * log((x / y));
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.1e+100], (-z), If[Or[LessEqual[z, -1.1e+72], And[N[Not[LessEqual[z, -5.2e-26]], $MachinePrecision], LessEqual[z, 1.7e-22]]], N[(x * N[Log[N[(x / y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], (-z)]]

Derivation

1. Split input into 2 regimes

2. if z < -1.1e100 or -1.1e72 < z < -5.2000000000000002e-26 or 1.6999999999999999e-22 < z

   1. Initial program 75.1%

      \[x \cdot \log \left(\frac{x}{y}\right) - z \]

   2. Taylor expanded in x around 0 82.5%

      \[\leadsto \color{blue}{-1 \cdot z} \]
   3. Step-by-step derivation

      1. neg-mul-1 82.5%

         \[\leadsto \color{blue}{-z} \]

   4. Simplified 82.5%

      \[\leadsto \color{blue}{-z} \]

   if -1.1e100 < z < -1.1e72 or -5.2000000000000002e-26 < z < 1.6999999999999999e-22

   1. Initial program 76.3%

      \[x \cdot \log \left(\frac{x}{y}\right) - z \]

   2. Taylor expanded in z around 0 64.5%

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

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+100}:\\ \;\;\;\;-z\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{+72} \lor \neg \left(z \leq -5.2 \cdot 10^{-26}\right) \land z \leq 1.7 \cdot 10^{-22}:\\ \;\;\;\;x \cdot \log \left(\frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]

Alternative 9: 50.3% accurate, 53.5× speedup

Math

\[\begin{array}{l} \\ -z \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := (-z)

Derivation

1. Initial program 75.6%

   \[x \cdot \log \left(\frac{x}{y}\right) - z \]

2. Taylor expanded in x around 0 53.9%

   \[\leadsto \color{blue}{-1 \cdot z} \]
3. Step-by-step derivation

   1. neg-mul-1 53.9%

      \[\leadsto \color{blue}{-z} \]

4. Simplified 53.9%

   \[\leadsto \color{blue}{-z} \]

5. Final simplification 53.9%

   \[\leadsto -z \]

Developer target: 88.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y < 7.595077799083773 \cdot 10^{-308}:\\ \;\;\;\;x \cdot \log \left(\frac{x}{y}\right) - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x - \log y\right) - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (< y 7.595077799083773e-308)
   (- (* x (log (/ x y))) z)
   (- (* x (- (log x) (log y))) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y < 7.595077799083773e-308) {
		tmp = (x * log((x / y))) - z;
	} else {
		tmp = (x * (log(x) - log(y))) - z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y < 7.595077799083773d-308) then
        tmp = (x * log((x / y))) - z
    else
        tmp = (x * (log(x) - log(y))) - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y < 7.595077799083773e-308) {
		tmp = (x * Math.log((x / y))) - z;
	} else {
		tmp = (x * (Math.log(x) - Math.log(y))) - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y < 7.595077799083773e-308:
		tmp = (x * math.log((x / y))) - z
	else:
		tmp = (x * (math.log(x) - math.log(y))) - z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y < 7.595077799083773e-308)
		tmp = Float64(Float64(x * log(Float64(x / y))) - z);
	else
		tmp = Float64(Float64(x * Float64(log(x) - log(y))) - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y < 7.595077799083773e-308)
		tmp = (x * log((x / y))) - z;
	else
		tmp = (x * (log(x) - log(y))) - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Less[y, 7.595077799083773e-308], N[(N[(x * N[Log[N[(x / y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision], N[(N[(x * N[(N[Log[x], $MachinePrecision] - N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]]

Reproduce

herbie shell --seed 2023224 
(FPCore (x y z)
  :name "Numeric.SpecFunctions.Extra:bd0 from math-functions-0.1.5.2"
  :precision binary64

  :herbie-target
  (if (< y 7.595077799083773e-308) (- (* x (log (/ x y))) z) (- (* x (- (log x) (log y))) z))

  (- (* x (log (/ x y))) z))