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

Percentage Accurate: 77.4% → 99.5%

Time: 12.4s

Alternatives: 10

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: 99.5% 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 76.3%

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

   3. Taylor expanded in y around -inf 99.5%

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

      1. metadata-eval 99.5%

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

      2. distribute-neg-frac 99.5%

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

      3. distribute-frac-neg2 99.5%

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

      4. neg-mul-1 99.5%

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

      5. log-rec 99.5%

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

      6. 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 -4.999999999999985e-310 < y

   1. Initial program 81.5%

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

   3. Taylor expanded in x around 0 99.4%

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

      1. log-rec 99.4%

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

      2. sub-neg 99.4%

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

   5. Simplified 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%

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

Alternative 2: 89.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \log \left(\frac{x}{y}\right)\\ t_1 := x \cdot t\_0\\ t_2 := x \cdot \log \left(y \cdot x\right)\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;t\_2 - z\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+305}:\\ \;\;\;\;\mathsf{fma}\left(x, t\_0, -z\right)\\ \mathbf{else}:\\ \;\;\;\;\left|t\_2\right| - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (log (/ x y))) (t_1 (* x t_0)) (t_2 (* x (log (* y x)))))
   (if (<= t_1 (- INFINITY))
     (- t_2 z)
     (if (<= t_1 5e+305) (fma x t_0 (- z)) (- (fabs t_2) z)))))

C

double code(double x, double y, double z) {
	double t_0 = log((x / y));
	double t_1 = x * t_0;
	double t_2 = x * log((y * x));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = t_2 - z;
	} else if (t_1 <= 5e+305) {
		tmp = fma(x, t_0, -z);
	} else {
		tmp = fabs(t_2) - z;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = log(Float64(x / y))
	t_1 = Float64(x * t_0)
	t_2 = Float64(x * log(Float64(y * x)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(t_2 - z);
	elseif (t_1 <= 5e+305)
		tmp = fma(x, t_0, Float64(-z));
	else
		tmp = Float64(abs(t_2) - z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Log[N[(x / y), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[(x * t$95$0), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[Log[N[(y * x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(t$95$2 - z), $MachinePrecision], If[LessEqual[t$95$1, 5e+305], N[(x * t$95$0 + (-z)), $MachinePrecision], N[(N[Abs[t$95$2], $MachinePrecision] - z), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 7.7%

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

      1. add-cube-cbrt 7.7%

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

      2. pow3 7.7%

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

   4. Applied egg-rr 7.7%

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

      1. rem-cube-cbrt 7.7%

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

      2. diff-log 40.6%

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

      3. sub-neg 40.6%

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

      4. distribute-rgt-in 40.6%

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

   6. Applied egg-rr 40.6%

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

      1. distribute-rgt-out 40.6%

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

      2. sub-neg 40.6%

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

      3. log-div 7.7%

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

      4. *-commutative 7.7%

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

      5. log-div 40.6%

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

      6. sub-neg 40.6%

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

      7. add-log-exp 40.6%

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

      8. sum-log 1.0%

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

      9. add-sqr-sqrt 0.0%

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

      10. sqrt-unprod 36.9%

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

      11. sqr-neg 36.9%

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

      12. sqrt-unprod 36.9%

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

      13. add-sqr-sqrt 36.9%

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

      14. add-exp-log 48.9%

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

   8. Applied egg-rr 48.9%

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

   if -inf.0 < (*.f64 x (log.f64 (/.f64 x y))) < 5.00000000000000009e305

   1. Initial program 99.8%

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

      1. fma-neg 99.8%

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

   3. Simplified 99.8%

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

   if 5.00000000000000009e305 < (*.f64 x (log.f64 (/.f64 x y)))

   1. Initial program 8.2%

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

      1. add-cube-cbrt 8.2%

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

      2. pow3 8.2%

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

   4. Applied egg-rr 8.2%

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

      1. rem-cube-cbrt 8.2%

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

      2. diff-log 49.8%

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

      3. sub-neg 49.8%

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

      4. distribute-rgt-in 49.9%

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

   6. Applied egg-rr 49.9%

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

      1. add-sqr-sqrt 49.7%

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

      2. sqrt-unprod 17.5%

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

      3. pow2 17.5%

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

      4. distribute-rgt-out 17.5%

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

      5. add-log-exp 17.5%

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

      6. sum-log 6.5%

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

      7. add-sqr-sqrt 2.7%

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

      8. sqrt-unprod 6.5%

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

      9. sqr-neg 6.5%

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

      10. sqrt-unprod 3.8%

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

      11. add-sqr-sqrt 14.4%

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

      12. add-exp-log 58.0%

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

   8. Applied egg-rr 58.0%

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

      1. unpow2 58.0%

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

      2. rem-sqrt-square 71.3%

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

   10. Simplified 71.3%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \log \left(\frac{x}{y}\right) \leq -\infty:\\ \;\;\;\;x \cdot \log \left(y \cdot x\right) - z\\ \mathbf{elif}\;x \cdot \log \left(\frac{x}{y}\right) \leq 5 \cdot 10^{+305}:\\ \;\;\;\;\mathsf{fma}\left(x, \log \left(\frac{x}{y}\right), -z\right)\\ \mathbf{else}:\\ \;\;\;\;\left|x \cdot \log \left(y \cdot x\right)\right| - z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 89.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \log \left(\frac{x}{y}\right)\\ t_1 := x \cdot t\_0\\ t_2 := \log \left(y \cdot x\right)\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;x \cdot \left|t\_2\right| - z\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+305}:\\ \;\;\;\;\mathsf{fma}\left(x, t\_0, -z\right)\\ \mathbf{else}:\\ \;\;\;\;\left|x \cdot t\_2\right| - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (log (/ x y))) (t_1 (* x t_0)) (t_2 (log (* y x))))
   (if (<= t_1 (- INFINITY))
     (- (* x (fabs t_2)) z)
     (if (<= t_1 5e+305) (fma x t_0 (- z)) (- (fabs (* x t_2)) z)))))

C

double code(double x, double y, double z) {
	double t_0 = log((x / y));
	double t_1 = x * t_0;
	double t_2 = log((y * x));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = (x * fabs(t_2)) - z;
	} else if (t_1 <= 5e+305) {
		tmp = fma(x, t_0, -z);
	} else {
		tmp = fabs((x * t_2)) - z;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = log(Float64(x / y))
	t_1 = Float64(x * t_0)
	t_2 = log(Float64(y * x))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(Float64(x * abs(t_2)) - z);
	elseif (t_1 <= 5e+305)
		tmp = fma(x, t_0, Float64(-z));
	else
		tmp = Float64(abs(Float64(x * t_2)) - z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Log[N[(x / y), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[(x * t$95$0), $MachinePrecision]}, Block[{t$95$2 = N[Log[N[(y * x), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(N[(x * N[Abs[t$95$2], $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision], If[LessEqual[t$95$1, 5e+305], N[(x * t$95$0 + (-z)), $MachinePrecision], N[(N[Abs[N[(x * t$95$2), $MachinePrecision]], $MachinePrecision] - z), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 7.7%

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

      1. add-cube-cbrt 7.7%

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

      2. pow3 7.7%

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

   4. Applied egg-rr 7.7%

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

      1. rem-cube-cbrt 7.7%

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

      2. add-sqr-sqrt 6.6%

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

      3. sqrt-unprod 7.3%

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

      4. pow2 7.3%

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

      5. log-div 36.8%

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

      6. sub-neg 36.8%

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

      7. add-log-exp 36.8%

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

      8. sum-log 0.6%

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

      9. add-sqr-sqrt 0.0%

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

      10. sqrt-unprod 36.8%

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

      11. sqr-neg 36.8%

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

      12. sqrt-unprod 36.8%

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

      13. add-sqr-sqrt 36.8%

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

      14. add-exp-log 52.0%

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

   6. Applied egg-rr 52.0%

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

      1. unpow2 52.0%

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

      2. rem-sqrt-square 52.0%

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

   8. Simplified 52.0%

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

   if -inf.0 < (*.f64 x (log.f64 (/.f64 x y))) < 5.00000000000000009e305

   1. Initial program 99.8%

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

      1. fma-neg 99.8%

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

   3. Simplified 99.8%

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

   if 5.00000000000000009e305 < (*.f64 x (log.f64 (/.f64 x y)))

   1. Initial program 8.2%

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

      1. add-cube-cbrt 8.2%

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

      2. pow3 8.2%

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

   4. Applied egg-rr 8.2%

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

      1. rem-cube-cbrt 8.2%

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

      2. diff-log 49.8%

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

      3. sub-neg 49.8%

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

      4. distribute-rgt-in 49.9%

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

   6. Applied egg-rr 49.9%

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

      1. add-sqr-sqrt 49.7%

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

      2. sqrt-unprod 17.5%

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

      3. pow2 17.5%

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

      4. distribute-rgt-out 17.5%

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

      5. add-log-exp 17.5%

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

      6. sum-log 6.5%

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

      7. add-sqr-sqrt 2.7%

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

      8. sqrt-unprod 6.5%

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

      9. sqr-neg 6.5%

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

      10. sqrt-unprod 3.8%

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

      11. add-sqr-sqrt 14.4%

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

      12. add-exp-log 58.0%

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

   8. Applied egg-rr 58.0%

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

      1. unpow2 58.0%

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

      2. rem-sqrt-square 71.3%

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

   10. Simplified 71.3%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \log \left(\frac{x}{y}\right) \leq -\infty:\\ \;\;\;\;x \cdot \left|\log \left(y \cdot x\right)\right| - z\\ \mathbf{elif}\;x \cdot \log \left(\frac{x}{y}\right) \leq 5 \cdot 10^{+305}:\\ \;\;\;\;\mathsf{fma}\left(x, \log \left(\frac{x}{y}\right), -z\right)\\ \mathbf{else}:\\ \;\;\;\;\left|x \cdot \log \left(y \cdot x\right)\right| - z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 88.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \log \left(\frac{x}{y}\right)\\ t_1 := x \cdot t\_0\\ \mathbf{if}\;t\_1 \leq -\infty \lor \neg \left(t\_1 \leq 5 \cdot 10^{+305}\right):\\ \;\;\;\;x \cdot \log \left(y \cdot x\right) - z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, t\_0, -z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (log (/ x y))) (t_1 (* x t_0)))
   (if (or (<= t_1 (- INFINITY)) (not (<= t_1 5e+305)))
     (- (* x (log (* y x))) z)
     (fma x t_0 (- z)))))

C

double code(double x, double y, double z) {
	double t_0 = log((x / y));
	double t_1 = x * t_0;
	double tmp;
	if ((t_1 <= -((double) INFINITY)) || !(t_1 <= 5e+305)) {
		tmp = (x * log((y * x))) - z;
	} else {
		tmp = fma(x, t_0, -z);
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = log(Float64(x / y))
	t_1 = Float64(x * t_0)
	tmp = 0.0
	if ((t_1 <= Float64(-Inf)) || !(t_1 <= 5e+305))
		tmp = Float64(Float64(x * log(Float64(y * x))) - z);
	else
		tmp = fma(x, t_0, Float64(-z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Log[N[(x / y), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[(x * t$95$0), $MachinePrecision]}, If[Or[LessEqual[t$95$1, (-Infinity)], N[Not[LessEqual[t$95$1, 5e+305]], $MachinePrecision]], N[(N[(x * N[Log[N[(y * x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision], N[(x * t$95$0 + (-z)), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x (log.f64 (/.f64 x y))) < -inf.0 or 5.00000000000000009e305 < (*.f64 x (log.f64 (/.f64 x y)))

   1. Initial program 7.9%

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

      1. add-cube-cbrt 7.9%

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

      2. pow3 7.9%

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

   4. Applied egg-rr 7.9%

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

      1. rem-cube-cbrt 7.9%

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

      2. diff-log 44.7%

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

      3. sub-neg 44.7%

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

      4. distribute-rgt-in 44.8%

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

   6. Applied egg-rr 44.8%

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

      1. distribute-rgt-out 44.7%

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

      2. sub-neg 44.7%

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

      3. log-div 7.9%

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

      4. *-commutative 7.9%

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

      5. log-div 44.7%

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

      6. sub-neg 44.7%

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

      7. add-log-exp 44.7%

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

      8. sum-log 3.5%

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

      9. add-sqr-sqrt 1.2%

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

      10. sqrt-unprod 23.3%

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

      11. sqr-neg 23.3%

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

      12. sqrt-unprod 22.1%

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

      13. add-sqr-sqrt 31.6%

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

      14. add-exp-log 57.3%

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

   8. Applied egg-rr 57.3%

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

   if -inf.0 < (*.f64 x (log.f64 (/.f64 x y))) < 5.00000000000000009e305

   1. Initial program 99.8%

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

      1. fma-neg 99.8%

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

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, \log \left(\frac{x}{y}\right), -z\right)} \]
   4. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \log \left(\frac{x}{y}\right) \leq -\infty \lor \neg \left(x \cdot \log \left(\frac{x}{y}\right) \leq 5 \cdot 10^{+305}\right):\\ \;\;\;\;x \cdot \log \left(y \cdot x\right) - z\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, \log \left(\frac{x}{y}\right), -z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 87.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \log \left(\frac{x}{y}\right)\\ \mathbf{if}\;t\_0 \leq -\infty \lor \neg \left(t\_0 \leq 5 \cdot 10^{+305}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;t\_0 - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (log (/ x y)))))
   (if (or (<= t_0 (- INFINITY)) (not (<= t_0 5e+305))) (- 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 <= 5e+305)) {
		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 <= 5e+305)) {
		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 <= 5e+305):
		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 <= 5e+305))
		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 <= 5e+305)))
		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, 5e+305]], $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 5.00000000000000009e305 < (*.f64 x (log.f64 (/.f64 x y)))

   1. Initial program 7.9%

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

   3. Taylor expanded in x around 0 51.1%

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

      1. mul-1-neg 51.1%

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

   5. Simplified 51.1%

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

   if -inf.0 < (*.f64 x (log.f64 (/.f64 x y))) < 5.00000000000000009e305

   1. Initial program 99.8%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \log \left(\frac{x}{y}\right) \leq -\infty \lor \neg \left(x \cdot \log \left(\frac{x}{y}\right) \leq 5 \cdot 10^{+305}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log \left(\frac{x}{y}\right) - z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 88.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \log \left(\frac{x}{y}\right)\\ \mathbf{if}\;t\_0 \leq -\infty \lor \neg \left(t\_0 \leq 5 \cdot 10^{+305}\right):\\ \;\;\;\;x \cdot \log \left(y \cdot x\right) - z\\ \mathbf{else}:\\ \;\;\;\;t\_0 - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (log (/ x y)))))
   (if (or (<= t_0 (- INFINITY)) (not (<= t_0 5e+305)))
     (- (* x (log (* y x))) 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 <= 5e+305)) {
		tmp = (x * log((y * x))) - 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 <= 5e+305)) {
		tmp = (x * Math.log((y * x))) - 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 <= 5e+305):
		tmp = (x * math.log((y * x))) - 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 <= 5e+305))
		tmp = Float64(Float64(x * log(Float64(y * x))) - 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 <= 5e+305)))
		tmp = (x * log((y * x))) - 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, 5e+305]], $MachinePrecision]], N[(N[(x * N[Log[N[(y * x), $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 5.00000000000000009e305 < (*.f64 x (log.f64 (/.f64 x y)))

   1. Initial program 7.9%

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

      1. add-cube-cbrt 7.9%

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

      2. pow3 7.9%

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

   4. Applied egg-rr 7.9%

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

      1. rem-cube-cbrt 7.9%

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

      2. diff-log 44.7%

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

      3. sub-neg 44.7%

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

      4. distribute-rgt-in 44.8%

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

   6. Applied egg-rr 44.8%

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

      1. distribute-rgt-out 44.7%

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

      2. sub-neg 44.7%

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

      3. log-div 7.9%

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

      4. *-commutative 7.9%

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

      5. log-div 44.7%

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

      6. sub-neg 44.7%

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

      7. add-log-exp 44.7%

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

      8. sum-log 3.5%

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

      9. add-sqr-sqrt 1.2%

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

      10. sqrt-unprod 23.3%

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

      11. sqr-neg 23.3%

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

      12. sqrt-unprod 22.1%

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

      13. add-sqr-sqrt 31.6%

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

      14. add-exp-log 57.3%

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

   8. Applied egg-rr 57.3%

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

   if -inf.0 < (*.f64 x (log.f64 (/.f64 x y))) < 5.00000000000000009e305

   1. Initial program 99.8%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \log \left(\frac{x}{y}\right) \leq -\infty \lor \neg \left(x \cdot \log \left(\frac{x}{y}\right) \leq 5 \cdot 10^{+305}\right):\\ \;\;\;\;x \cdot \log \left(y \cdot x\right) - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log \left(\frac{x}{y}\right) - z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 66.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{-114} \lor \neg \left(z \leq 2.6 \cdot 10^{-48}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;\left(-x\right) \cdot \log \left(\frac{y}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -8e-114) (not (<= z 2.6e-48))) (- z) (* (- x) (log (/ y x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -8e-114) || !(z <= 2.6e-48)) {
		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 <= (-8d-114)) .or. (.not. (z <= 2.6d-48))) 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 <= -8e-114) || !(z <= 2.6e-48)) {
		tmp = -z;
	} else {
		tmp = -x * Math.log((y / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -8e-114) or not (z <= 2.6e-48):
		tmp = -z
	else:
		tmp = -x * math.log((y / x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -8e-114) || !(z <= 2.6e-48))
		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 <= -8e-114) || ~((z <= 2.6e-48)))
		tmp = -z;
	else
		tmp = -x * log((y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -8e-114], N[Not[LessEqual[z, 2.6e-48]], $MachinePrecision]], (-z), N[((-x) * N[Log[N[(y / x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.0000000000000004e-114 or 2.59999999999999987e-48 < z

   1. Initial program 77.3%

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

   3. Taylor expanded in x around 0 68.6%

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

      1. mul-1-neg 68.6%

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

   5. Simplified 68.6%

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

   if -8.0000000000000004e-114 < z < 2.59999999999999987e-48

   1. Initial program 81.9%

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

      1. clear-num 81.9%

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

      2. log-div 83.9%

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

      3. metadata-eval 83.9%

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

   4. Applied egg-rr 83.9%

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

      1. neg-sub0 83.9%

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

   6. Simplified 83.9%

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

   7. Taylor expanded in z around 0 79.1%

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

      1. neg-mul-1 79.1%

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

      2. distribute-lft-neg-in 79.1%

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

      3. *-commutative 79.1%

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

   9. Simplified 79.1%

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

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{-114} \lor \neg \left(z \leq 2.6 \cdot 10^{-48}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;\left(-x\right) \cdot \log \left(\frac{y}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 66.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.48 \cdot 10^{-117} \lor \neg \left(z \leq 4.4 \cdot 10^{-49}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log \left(\frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.48e-117) (not (<= z 4.4e-49))) (- z) (* x (log (/ x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.48e-117) || !(z <= 4.4e-49)) {
		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 <= (-1.48d-117)) .or. (.not. (z <= 4.4d-49))) 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 <= -1.48e-117) || !(z <= 4.4e-49)) {
		tmp = -z;
	} else {
		tmp = x * Math.log((x / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.48e-117) or not (z <= 4.4e-49):
		tmp = -z
	else:
		tmp = x * math.log((x / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.48e-117) || !(z <= 4.4e-49))
		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 <= -1.48e-117) || ~((z <= 4.4e-49)))
		tmp = -z;
	else
		tmp = x * log((x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.48e-117], N[Not[LessEqual[z, 4.4e-49]], $MachinePrecision]], (-z), N[(x * N[Log[N[(x / y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.48000000000000006e-117 or 4.3999999999999998e-49 < z

   1. Initial program 77.3%

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

   3. Taylor expanded in x around 0 68.6%

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

      1. mul-1-neg 68.6%

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

   5. Simplified 68.6%

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

   if -1.48000000000000006e-117 < z < 4.3999999999999998e-49

   1. Initial program 81.9%

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

   3. Taylor expanded in z around 0 77.1%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.48 \cdot 10^{-117} \lor \neg \left(z \leq 4.4 \cdot 10^{-49}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log \left(\frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

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 79.0%

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

3. Taylor expanded in x around 0 48.8%

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

   1. mul-1-neg 48.8%

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

5. Simplified 48.8%

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

6. Final simplification 48.8%

   \[\leadsto -z \]
7. Add Preprocessing

Alternative 10: 2.2% accurate, 107.0× 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 z
end

MATLAB

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

Wolfram

code[x_, y_, z_] := z

Derivation

1. Initial program 79.0%

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

3. Taylor expanded in x around inf 47.2%

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

   1. log-rec 47.2%

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

   2. mul-1-neg 47.2%

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

   3. unsub-neg 47.2%

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

   4. mul-1-neg 47.2%

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

   5. log-rec 47.2%

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

   6. remove-double-neg 47.2%

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

   7. associate-+r- 47.2%

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

   8. +-commutative 47.2%

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

   9. sub-neg 47.2%

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

5. Simplified 47.2%

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

6. Taylor expanded in x around 0 38.6%

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

   1. mul-1-neg 38.6%

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

   2. distribute-frac-neg2 38.6%

      \[\leadsto x \cdot \color{blue}{\frac{z}{-x}} \]

8. Simplified 38.6%

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

   1. clear-num 38.5%

      \[\leadsto x \cdot \color{blue}{\frac{1}{\frac{-x}{z}}} \]

   2. un-div-inv 39.1%

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

   3. add-sqr-sqrt 17.9%

      \[\leadsto \frac{x}{\frac{\color{blue}{\sqrt{-x} \cdot \sqrt{-x}}}{z}} \]

   4. sqrt-unprod 12.3%

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

   5. sqr-neg 12.3%

      \[\leadsto \frac{x}{\frac{\sqrt{\color{blue}{x \cdot x}}}{z}} \]

   6. sqrt-unprod 1.1%

      \[\leadsto \frac{x}{\frac{\color{blue}{\sqrt{x} \cdot \sqrt{x}}}{z}} \]

   7. add-sqr-sqrt 2.2%

      \[\leadsto \frac{x}{\frac{\color{blue}{x}}{z}} \]

10. Applied egg-rr 2.2%

    \[\leadsto \color{blue}{\frac{x}{\frac{x}{z}}} \]
11. Step-by-step derivation

    1. associate-/r/ 2.2%

       \[\leadsto \color{blue}{\frac{x}{x} \cdot z} \]

    2. *-inverses 2.2%

       \[\leadsto \color{blue}{1} \cdot z \]

    3. *-lft-identity 2.2%

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

12. Simplified 2.2%

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

13. Final simplification 2.2%

    \[\leadsto z \]
14. Add Preprocessing

Developer target: 88.3% 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 2024082 
(FPCore (x y z)
  :name "Numeric.SpecFunctions.Extra:bd0 from math-functions-0.1.5.2"
  :precision binary64

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

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