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

Percentage Accurate: 76.4% → 99.7%

Time: 10.6s

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: 76.4% 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: 99.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(\log \left(\frac{\sqrt[3]{x}}{\sqrt[3]{y}}\right) \cdot 3\right) - z \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (- (* x (* (log (/ (cbrt x) (cbrt y))) 3.0)) z))

C

double code(double x, double y, double z) {
	return (x * (log((cbrt(x) / cbrt(y))) * 3.0)) - z;
}

Java

public static double code(double x, double y, double z) {
	return (x * (Math.log((Math.cbrt(x) / Math.cbrt(y))) * 3.0)) - z;
}

Julia

function code(x, y, z)
	return Float64(Float64(x * Float64(log(Float64(cbrt(x) / cbrt(y))) * 3.0)) - z)
end

Wolfram

code[x_, y_, z_] := N[(N[(x * N[(N[Log[N[(N[Power[x, 1/3], $MachinePrecision] / N[Power[y, 1/3], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * 3.0), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]

Derivation

1. Initial program 80.1%

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

   1. add-cube-cbrt 80.1%

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

   2. log-prod 80.0%

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

   3. pow2 80.0%

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

3. Applied egg-rr 80.0%

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

   1. log-pow 80.0%

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

   2. *-lft-identity 80.0%

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

   3. distribute-rgt-out 80.0%

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

   4. metadata-eval 80.0%

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

5. Simplified 80.0%

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

   1. cbrt-div 99.7%

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

   2. div-inv 99.7%

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

7. Applied egg-rr 99.7%

   \[\leadsto x \cdot \left(\log \color{blue}{\left(\sqrt[3]{x} \cdot \frac{1}{\sqrt[3]{y}}\right)} \cdot 3\right) - z \]
8. Step-by-step derivation

   1. associate-*r/ 99.7%

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

   2. *-rgt-identity 99.7%

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

9. Simplified 99.7%

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

10. Final simplification 99.7%

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

Alternative 2: 86.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \log \left(\frac{x}{y}\right)\\ \mathbf{if}\;t_0 \leq -\infty:\\ \;\;\;\;x \cdot \log \left(x \cdot y\right) - z\\ \mathbf{elif}\;t_0 \leq 2 \cdot 10^{+306}:\\ \;\;\;\;t_0 - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log x - x \cdot \log y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (log (/ x y)))))
   (if (<= t_0 (- INFINITY))
     (- (* x (log (* x y))) z)
     (if (<= t_0 2e+306) (- t_0 z) (- (* x (log x)) (* x (log y)))))))

C

double code(double x, double y, double z) {
	double t_0 = x * log((x / y));
	double tmp;
	if (t_0 <= -((double) INFINITY)) {
		tmp = (x * log((x * y))) - z;
	} else if (t_0 <= 2e+306) {
		tmp = t_0 - z;
	} else {
		tmp = (x * log(x)) - (x * log(y));
	}
	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 = (x * Math.log((x * y))) - z;
	} else if (t_0 <= 2e+306) {
		tmp = t_0 - z;
	} else {
		tmp = (x * Math.log(x)) - (x * Math.log(y));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * math.log((x / y))
	tmp = 0
	if t_0 <= -math.inf:
		tmp = (x * math.log((x * y))) - z
	elif t_0 <= 2e+306:
		tmp = t_0 - z
	else:
		tmp = (x * math.log(x)) - (x * math.log(y))
	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(Float64(x * log(Float64(x * y))) - z);
	elseif (t_0 <= 2e+306)
		tmp = Float64(t_0 - z);
	else
		tmp = Float64(Float64(x * log(x)) - Float64(x * log(y)));
	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 = (x * log((x * y))) - z;
	elseif (t_0 <= 2e+306)
		tmp = t_0 - z;
	else
		tmp = (x * log(x)) - (x * log(y));
	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)], N[(N[(x * N[Log[N[(x * y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision], If[LessEqual[t$95$0, 2e+306], N[(t$95$0 - z), $MachinePrecision], N[(N[(x * N[Log[x], $MachinePrecision]), $MachinePrecision] - N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 7.9%

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

      1. log-div 51.6%

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

      2. sub-neg 51.6%

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

      3. distribute-lft-in 51.6%

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

   3. Applied egg-rr 51.6%

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

      1. distribute-lft-out 51.6%

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

      2. *-commutative 51.6%

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

      3. add-sqr-sqrt 0.0%

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

      4. sqrt-unprod 48.5%

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

      5. sqr-neg 48.5%

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

      6. sqrt-unprod 48.5%

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

      7. add-sqr-sqrt 48.5%

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

      8. log-prod 64.0%

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

   5. Applied egg-rr 64.0%

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

   if -inf.0 < (*.f64 x (log.f64 (/.f64 x y))) < 2.00000000000000003e306

   1. Initial program 99.3%

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

   if 2.00000000000000003e306 < (*.f64 x (log.f64 (/.f64 x y)))

   1. Initial program 5.0%

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

      1. add-cube-cbrt 5.0%

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

      2. log-prod 5.0%

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

      3. pow2 5.0%

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

   3. Applied egg-rr 5.0%

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

      1. log-pow 5.0%

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

      2. *-lft-identity 5.0%

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

      3. distribute-rgt-out 5.0%

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

      4. metadata-eval 5.0%

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

   5. Simplified 5.0%

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

   7. Applied egg-rr 58.5%

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

   8. Taylor expanded in z around 0 56.8%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \log \left(\frac{x}{y}\right) \leq -\infty:\\ \;\;\;\;x \cdot \log \left(x \cdot y\right) - z\\ \mathbf{elif}\;x \cdot \log \left(\frac{x}{y}\right) \leq 2 \cdot 10^{+306}:\\ \;\;\;\;x \cdot \log \left(\frac{x}{y}\right) - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log x - x \cdot \log y\\ \end{array} \]

Alternative 3: 86.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \log \left(\frac{x}{y}\right)\\ \mathbf{if}\;t_0 \leq -\infty \lor \neg \left(t_0 \leq 2 \cdot 10^{+306}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;t_0 - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (log (/ x y)))))
   (if (or (<= t_0 (- INFINITY)) (not (<= t_0 2e+306))) (- z) (- t_0 z))))

C

double code(double x, double y, double z) {
	double t_0 = x * log((x / y));
	double tmp;
	if ((t_0 <= -((double) INFINITY)) || !(t_0 <= 2e+306)) {
		tmp = -z;
	} else {
		tmp = t_0 - 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) || !(t_0 <= 2e+306)) {
		tmp = -z;
	} else {
		tmp = t_0 - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * math.log((x / y))
	tmp = 0
	if (t_0 <= -math.inf) or not (t_0 <= 2e+306):
		tmp = -z
	else:
		tmp = t_0 - 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)) || !(t_0 <= 2e+306))
		tmp = Float64(-z);
	else
		tmp = Float64(t_0 - 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) || ~((t_0 <= 2e+306)))
		tmp = -z;
	else
		tmp = t_0 - 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[Or[LessEqual[t$95$0, (-Infinity)], N[Not[LessEqual[t$95$0, 2e+306]], $MachinePrecision]], (-z), N[(t$95$0 - z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x (log.f64 (/.f64 x y))) < -inf.0 or 2.00000000000000003e306 < (*.f64 x (log.f64 (/.f64 x y)))

   1. Initial program 6.7%

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

      1. sub-neg 6.7%

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

      2. +-commutative 6.7%

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

      3. neg-sub0 6.7%

         \[\leadsto \color{blue}{\left(0 - z\right)} + x \cdot \log \left(\frac{x}{y}\right) \]

      4. associate-+l- 6.7%

         \[\leadsto \color{blue}{0 - \left(z - x \cdot \log \left(\frac{x}{y}\right)\right)} \]

      5. sub0-neg 6.7%

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

      6. cancel-sign-sub-inv 6.7%

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

      7. +-commutative 6.7%

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

      8. remove-double-neg 6.7%

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

      9. sub-neg 6.7%

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

      10. distribute-lft-neg-in 6.7%

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

      11. distribute-rgt-neg-in 6.7%

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

      12. log-div 54.5%

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

      13. sub-neg 54.5%

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

      14. distribute-neg-in 54.5%

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

      15. remove-double-neg 54.5%

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

      16. +-commutative 54.5%

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

      17. sub-neg 54.5%

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

      18. log-div 8.4%

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

      19. fma-neg 8.4%

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

      20. remove-double-neg 8.4%

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

   3. Simplified 8.4%

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

   4. Taylor expanded in x around 0 49.5%

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

   if -inf.0 < (*.f64 x (log.f64 (/.f64 x y))) < 2.00000000000000003e306

   1. Initial program 99.3%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \log \left(\frac{x}{y}\right) \leq -\infty \lor \neg \left(x \cdot \log \left(\frac{x}{y}\right) \leq 2 \cdot 10^{+306}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log \left(\frac{x}{y}\right) - z\\ \end{array} \]

Alternative 4: 87.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \log \left(\frac{x}{y}\right)\\ \mathbf{if}\;t_0 \leq -\infty \lor \neg \left(t_0 \leq 2 \cdot 10^{+306}\right):\\ \;\;\;\;x \cdot \log \left(x \cdot y\right) - z\\ \mathbf{else}:\\ \;\;\;\;t_0 - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (log (/ x y)))))
   (if (or (<= t_0 (- INFINITY)) (not (<= t_0 2e+306)))
     (- (* x (log (* x y))) z)
     (- t_0 z))))

C

double code(double x, double y, double z) {
	double t_0 = x * log((x / y));
	double tmp;
	if ((t_0 <= -((double) INFINITY)) || !(t_0 <= 2e+306)) {
		tmp = (x * log((x * y))) - z;
	} else {
		tmp = t_0 - 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) || !(t_0 <= 2e+306)) {
		tmp = (x * Math.log((x * y))) - z;
	} else {
		tmp = t_0 - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * math.log((x / y))
	tmp = 0
	if (t_0 <= -math.inf) or not (t_0 <= 2e+306):
		tmp = (x * math.log((x * y))) - z
	else:
		tmp = t_0 - 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)) || !(t_0 <= 2e+306))
		tmp = Float64(Float64(x * log(Float64(x * y))) - z);
	else
		tmp = Float64(t_0 - 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) || ~((t_0 <= 2e+306)))
		tmp = (x * log((x * y))) - z;
	else
		tmp = t_0 - 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[Or[LessEqual[t$95$0, (-Infinity)], N[Not[LessEqual[t$95$0, 2e+306]], $MachinePrecision]], N[(N[(x * N[Log[N[(x * y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision], N[(t$95$0 - z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x (log.f64 (/.f64 x y))) < -inf.0 or 2.00000000000000003e306 < (*.f64 x (log.f64 (/.f64 x y)))

   1. Initial program 6.7%

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

      1. log-div 54.5%

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

      2. sub-neg 54.5%

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

      3. distribute-lft-in 54.5%

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

   3. Applied egg-rr 54.5%

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

      1. distribute-lft-out 54.5%

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

      2. *-commutative 54.5%

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

      3. add-sqr-sqrt 24.4%

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

      4. sqrt-unprod 52.7%

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

      5. sqr-neg 52.7%

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

      6. sqrt-unprod 28.3%

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

      7. add-sqr-sqrt 31.0%

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

      8. log-prod 53.7%

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

   5. Applied egg-rr 53.7%

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

   if -inf.0 < (*.f64 x (log.f64 (/.f64 x y))) < 2.00000000000000003e306

   1. Initial program 99.3%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \log \left(\frac{x}{y}\right) \leq -\infty \lor \neg \left(x \cdot \log \left(\frac{x}{y}\right) \leq 2 \cdot 10^{+306}\right):\\ \;\;\;\;x \cdot \log \left(x \cdot y\right) - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log \left(\frac{x}{y}\right) - z\\ \end{array} \]

Alternative 5: 90.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{-128}:\\ \;\;\;\;-\mathsf{fma}\left(x, \log \left(\frac{y}{x}\right), z\right)\\ \mathbf{elif}\;x \leq -1 \cdot 10^{-307}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x - \log y\right) - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.8e-128)
   (- (fma x (log (/ y x)) z))
   (if (<= x -1e-307) (- z) (- (* x (- (log x) (log y))) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.8e-128) {
		tmp = -fma(x, log((y / x)), z);
	} else if (x <= -1e-307) {
		tmp = -z;
	} else {
		tmp = (x * (log(x) - log(y))) - z;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.8e-128)
		tmp = Float64(-fma(x, log(Float64(y / x)), z));
	elseif (x <= -1e-307)
		tmp = Float64(-z);
	else
		tmp = Float64(Float64(x * Float64(log(x) - log(y))) - z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.8e-128], (-N[(x * N[Log[N[(y / x), $MachinePrecision]], $MachinePrecision] + z), $MachinePrecision]), If[LessEqual[x, -1e-307], (-z), N[(N[(x * N[(N[Log[x], $MachinePrecision] - N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.80000000000000012e-128

   1. Initial program 82.6%

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

      1. sub-neg 82.6%

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

      2. +-commutative 82.6%

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

      3. neg-sub0 82.6%

         \[\leadsto \color{blue}{\left(0 - z\right)} + x \cdot \log \left(\frac{x}{y}\right) \]

      4. associate-+l- 82.6%

         \[\leadsto \color{blue}{0 - \left(z - x \cdot \log \left(\frac{x}{y}\right)\right)} \]

      5. sub0-neg 82.6%

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

      6. cancel-sign-sub-inv 82.6%

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

      7. +-commutative 82.6%

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

      8. remove-double-neg 82.6%

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

      9. sub-neg 82.6%

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

      10. distribute-lft-neg-in 82.6%

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

      11. distribute-rgt-neg-in 82.6%

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

      12. log-div 0.0%

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

      13. sub-neg 0.0%

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

      14. distribute-neg-in 0.0%

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

      15. remove-double-neg 0.0%

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

      16. +-commutative 0.0%

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

      17. sub-neg 0.0%

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

      18. log-div 83.8%

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

      19. fma-neg 83.8%

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

      20. remove-double-neg 83.8%

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

   3. Simplified 83.8%

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

   if -1.80000000000000012e-128 < x < -9.99999999999999909e-308

   1. Initial program 75.5%

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

      1. sub-neg 75.5%

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

      2. +-commutative 75.5%

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

      3. neg-sub0 75.5%

         \[\leadsto \color{blue}{\left(0 - z\right)} + x \cdot \log \left(\frac{x}{y}\right) \]

      4. associate-+l- 75.5%

         \[\leadsto \color{blue}{0 - \left(z - x \cdot \log \left(\frac{x}{y}\right)\right)} \]

      5. sub0-neg 75.5%

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

      6. cancel-sign-sub-inv 75.5%

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

      7. +-commutative 75.5%

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

      8. remove-double-neg 75.5%

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

      9. sub-neg 75.5%

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

      10. distribute-lft-neg-in 75.5%

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

      11. distribute-rgt-neg-in 75.5%

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

      12. log-div 0.0%

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

      13. sub-neg 0.0%

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

      14. distribute-neg-in 0.0%

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

      15. remove-double-neg 0.0%

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

      16. +-commutative 0.0%

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

      17. sub-neg 0.0%

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

      18. log-div 68.5%

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

      19. fma-neg 68.5%

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

      20. remove-double-neg 68.5%

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

   3. Simplified 68.5%

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

   4. Taylor expanded in x around 0 86.3%

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

   if -9.99999999999999909e-308 < x

   1. Initial program 79.8%

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

      1. log-div 99.4%

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

   3. Applied egg-rr 99.4%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{-128}:\\ \;\;\;\;-\mathsf{fma}\left(x, \log \left(\frac{y}{x}\right), z\right)\\ \mathbf{elif}\;x \leq -1 \cdot 10^{-307}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x - \log y\right) - z\\ \end{array} \]

Alternative 6: 99.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-310}:\\ \;\;\;\;x \cdot \left(\log \left(-x\right) - \log \left(-y\right)\right) - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x - \log y\right) - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -4e-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 <= -4e-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 <= (-4d-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 <= -4e-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 <= -4e-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 <= -4e-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 <= -4e-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, -4e-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 < -3.999999999999988e-310

   1. Initial program 80.5%

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

      1. clear-num 78.4%

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

      2. log-div 79.2%

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

      3. metadata-eval 79.2%

         \[\leadsto x \cdot \left(\color{blue}{0} - \log \left(\frac{y}{x}\right)\right) - z \]

      4. frac-2neg 79.2%

         \[\leadsto x \cdot \left(0 - \log \color{blue}{\left(\frac{-y}{-x}\right)}\right) - z \]

      5. log-div 99.5%

         \[\leadsto x \cdot \left(0 - \color{blue}{\left(\log \left(-y\right) - \log \left(-x\right)\right)}\right) - z \]

      6. associate--r- 99.5%

         \[\leadsto x \cdot \color{blue}{\left(\left(0 - \log \left(-y\right)\right) + \log \left(-x\right)\right)} - z \]

   3. Applied egg-rr 99.5%

      \[\leadsto x \cdot \color{blue}{\left(\left(0 - \log \left(-y\right)\right) + \log \left(-x\right)\right)} - z \]
   4. Step-by-step derivation

      1. +-commutative 99.5%

         \[\leadsto x \cdot \color{blue}{\left(\log \left(-x\right) + \left(0 - \log \left(-y\right)\right)\right)} - z \]

      2. sub0-neg 99.5%

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

      3. sub-neg 99.5%

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

   5. Simplified 99.5%

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

   if -3.999999999999988e-310 < y

   1. Initial program 79.8%

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

      1. log-div 99.4%

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

   3. Applied egg-rr 99.4%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-310}:\\ \;\;\;\;x \cdot \left(\log \left(-x\right) - \log \left(-y\right)\right) - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x - \log y\right) - z\\ \end{array} \]

Alternative 7: 67.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.55 \cdot 10^{-14} \lor \neg \left(z \leq 4.1 \cdot 10^{-37}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;\left(-x\right) \cdot \log \left(\frac{y}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.55e-14) (not (<= z 4.1e-37))) (- z) (* (- x) (log (/ y x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.55e-14) || !(z <= 4.1e-37)) {
		tmp = -z;
	} else {
		tmp = -x * log((y / x));
	}
	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 <= (-2.55d-14)) .or. (.not. (z <= 4.1d-37))) then
        tmp = -z
    else
        tmp = -x * log((y / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.55e-14) || !(z <= 4.1e-37)) {
		tmp = -z;
	} else {
		tmp = -x * Math.log((y / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.55e-14) or not (z <= 4.1e-37):
		tmp = -z
	else:
		tmp = -x * math.log((y / x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.55e-14) || !(z <= 4.1e-37))
		tmp = Float64(-z);
	else
		tmp = Float64(Float64(-x) * log(Float64(y / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -2.55e-14) || ~((z <= 4.1e-37)))
		tmp = -z;
	else
		tmp = -x * log((y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.55e-14], N[Not[LessEqual[z, 4.1e-37]], $MachinePrecision]], (-z), N[((-x) * N[Log[N[(y / x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.5499999999999999e-14 or 4.0999999999999998e-37 < z

   1. Initial program 79.6%

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

      1. sub-neg 79.6%

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

      2. +-commutative 79.6%

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

      3. neg-sub0 79.6%

         \[\leadsto \color{blue}{\left(0 - z\right)} + x \cdot \log \left(\frac{x}{y}\right) \]

      4. associate-+l- 79.6%

         \[\leadsto \color{blue}{0 - \left(z - x \cdot \log \left(\frac{x}{y}\right)\right)} \]

      5. sub0-neg 79.6%

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

      6. cancel-sign-sub-inv 79.6%

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

      7. +-commutative 79.6%

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

      8. remove-double-neg 79.6%

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

      9. sub-neg 79.6%

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

      10. distribute-lft-neg-in 79.6%

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

      11. distribute-rgt-neg-in 79.6%

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

      12. log-div 50.7%

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

      13. sub-neg 50.7%

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

      14. distribute-neg-in 50.7%

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

      15. remove-double-neg 50.7%

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

      16. +-commutative 50.7%

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

      17. sub-neg 50.7%

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

      18. log-div 78.3%

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

      19. fma-neg 78.3%

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

      20. remove-double-neg 78.3%

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

   3. Simplified 78.3%

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

   4. Taylor expanded in x around 0 73.2%

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

   if -2.5499999999999999e-14 < z < 4.0999999999999998e-37

   1. Initial program 80.7%

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

      1. sub-neg 80.7%

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

      2. +-commutative 80.7%

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

      3. neg-sub0 80.7%

         \[\leadsto \color{blue}{\left(0 - z\right)} + x \cdot \log \left(\frac{x}{y}\right) \]

      4. associate-+l- 80.7%

         \[\leadsto \color{blue}{0 - \left(z - x \cdot \log \left(\frac{x}{y}\right)\right)} \]

      5. sub0-neg 80.7%

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

      6. cancel-sign-sub-inv 80.7%

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

      7. +-commutative 80.7%

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

      8. remove-double-neg 80.7%

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

      9. sub-neg 80.7%

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

      10. distribute-lft-neg-in 80.7%

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

      11. distribute-rgt-neg-in 80.7%

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

      12. log-div 59.7%

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

      13. sub-neg 59.7%

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

      14. distribute-neg-in 59.7%

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

      15. remove-double-neg 59.7%

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

      16. +-commutative 59.7%

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

      17. sub-neg 59.7%

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

      18. log-div 80.7%

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

      19. fma-neg 80.7%

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

      20. remove-double-neg 80.7%

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

   3. Simplified 80.7%

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

   4. Taylor expanded in x around inf 49.3%

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

      1. distribute-lft-in 49.2%

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

      2. log-rec 49.2%

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

      3. distribute-lft-in 49.3%

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

      4. sub-neg 49.3%

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

      5. log-div 72.1%

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

   6. Simplified 72.1%

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

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.55 \cdot 10^{-14} \lor \neg \left(z \leq 4.1 \cdot 10^{-37}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;\left(-x\right) \cdot \log \left(\frac{y}{x}\right)\\ \end{array} \]

Alternative 8: 66.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-12} \lor \neg \left(z \leq 1.65 \cdot 10^{-35}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log \left(\frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.8e-12) (not (<= z 1.65e-35))) (- z) (* x (log (/ x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.8e-12) || !(z <= 1.65e-35)) {
		tmp = -z;
	} else {
		tmp = x * log((x / y));
	}
	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 <= (-1.8d-12)) .or. (.not. (z <= 1.65d-35))) then
        tmp = -z
    else
        tmp = x * log((x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.8e-12) || !(z <= 1.65e-35)) {
		tmp = -z;
	} else {
		tmp = x * Math.log((x / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.8e-12) or not (z <= 1.65e-35):
		tmp = -z
	else:
		tmp = x * math.log((x / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.8e-12) || !(z <= 1.65e-35))
		tmp = Float64(-z);
	else
		tmp = Float64(x * log(Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.8e-12) || ~((z <= 1.65e-35)))
		tmp = -z;
	else
		tmp = x * log((x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.8e-12], N[Not[LessEqual[z, 1.65e-35]], $MachinePrecision]], (-z), N[(x * N[Log[N[(x / y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.8e-12 or 1.65e-35 < z

   1. Initial program 79.6%

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

      1. sub-neg 79.6%

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

      2. +-commutative 79.6%

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

      3. neg-sub0 79.6%

         \[\leadsto \color{blue}{\left(0 - z\right)} + x \cdot \log \left(\frac{x}{y}\right) \]

      4. associate-+l- 79.6%

         \[\leadsto \color{blue}{0 - \left(z - x \cdot \log \left(\frac{x}{y}\right)\right)} \]

      5. sub0-neg 79.6%

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

      6. cancel-sign-sub-inv 79.6%

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

      7. +-commutative 79.6%

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

      8. remove-double-neg 79.6%

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

      9. sub-neg 79.6%

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

      10. distribute-lft-neg-in 79.6%

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

      11. distribute-rgt-neg-in 79.6%

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

      12. log-div 50.7%

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

      13. sub-neg 50.7%

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

      14. distribute-neg-in 50.7%

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

      15. remove-double-neg 50.7%

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

      16. +-commutative 50.7%

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

      17. sub-neg 50.7%

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

      18. log-div 78.3%

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

      19. fma-neg 78.3%

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

      20. remove-double-neg 78.3%

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

   3. Simplified 78.3%

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

   4. Taylor expanded in x around 0 73.2%

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

   if -1.8e-12 < z < 1.65e-35

   1. Initial program 80.7%

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

      1. flip-- 52.7%

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

      2. clear-num 52.7%

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

      3. *-un-lft-identity 52.7%

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

      4. associate-/l* 52.6%

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

      5. flip-- 80.4%

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

      6. fma-neg 80.4%

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

   3. Applied egg-rr 80.4%

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

   4. Taylor expanded in z around 0 72.0%

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

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-12} \lor \neg \left(z \leq 1.65 \cdot 10^{-35}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log \left(\frac{x}{y}\right)\\ \end{array} \]

Alternative 9: 50.5% 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 80.1%

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

   1. sub-neg 80.1%

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

   2. +-commutative 80.1%

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

   3. neg-sub0 80.1%

      \[\leadsto \color{blue}{\left(0 - z\right)} + x \cdot \log \left(\frac{x}{y}\right) \]

   4. associate-+l- 80.1%

      \[\leadsto \color{blue}{0 - \left(z - x \cdot \log \left(\frac{x}{y}\right)\right)} \]

   5. sub0-neg 80.1%

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

   6. cancel-sign-sub-inv 80.1%

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

   7. +-commutative 80.1%

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

   8. remove-double-neg 80.1%

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

   9. sub-neg 80.1%

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

   10. distribute-lft-neg-in 80.1%

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

   11. distribute-rgt-neg-in 80.1%

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

   12. log-div 54.8%

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

   13. sub-neg 54.8%

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

   14. distribute-neg-in 54.8%

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

   15. remove-double-neg 54.8%

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

   16. +-commutative 54.8%

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

   17. sub-neg 54.8%

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

   18. log-div 79.4%

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

   19. fma-neg 79.4%

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

   20. remove-double-neg 79.4%

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

3. Simplified 79.4%

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

4. Taylor expanded in x around 0 47.9%

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

5. Final simplification 47.9%

   \[\leadsto -z \]

Developer target: 88.1% 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 2023301 
(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))