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

Percentage Accurate: 76.8% → 99.7%

Time: 12.7s

Alternatives: 8

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: 76.8% 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 82.7%

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

   1. add-cube-cbrt 82.6%

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

   2. log-prod 82.6%

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

   3. pow2 82.6%

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

   4. metadata-eval 82.6%

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

   5. log-pow 82.6%

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

   6. metadata-eval 82.6%

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

4. Applied egg-rr 82.6%

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

   1. distribute-lft1-in 82.6%

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

   2. metadata-eval 82.6%

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

   3. *-commutative 82.6%

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

6. Simplified 82.6%

   \[\leadsto x \cdot \color{blue}{\left(\log \left(\sqrt[3]{\frac{x}{y}}\right) \cdot 3\right)} - z \]
7. 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%

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

8. Applied egg-rr 99.7%

   \[\leadsto x \cdot \left(\log \color{blue}{\left(\sqrt[3]{x} \cdot \frac{1}{\sqrt[3]{y}}\right)} \cdot 3\right) - z \]
9. 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%

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

10. Simplified 99.7%

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

11. Final simplification 99.7%

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

Alternative 2: 87.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \log \left(\frac{x}{y}\right)\\ \mathbf{if}\;t\_0 \leq -\infty \lor \neg \left(t\_0 \leq 10^{+308}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;t\_0 - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (log (/ x y)))))
   (if (or (<= t_0 (- INFINITY)) (not (<= t_0 1e+308))) (- 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 <= 1e+308)) {
		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 <= 1e+308)) {
		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 <= 1e+308):
		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 <= 1e+308))
		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 <= 1e+308)))
		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, 1e+308]], $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 1e308 < (*.f64 x (log.f64 (/.f64 x y)))

   1. Initial program 8.7%

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

      1. remove-double-neg 8.7%

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

      2. sub-neg 8.7%

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

      3. distribute-neg-in 8.7%

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

      4. distribute-rgt-neg-in 8.7%

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

      5. remove-double-neg 8.7%

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

      6. fma-udef 8.7%

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

      7. log-div 43.7%

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

      8. sub-neg 43.7%

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

      9. distribute-neg-in 43.7%

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

      10. remove-double-neg 43.7%

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

      11. +-commutative 43.7%

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

      12. sub-neg 43.7%

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

      13. log-div 17.7%

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

   3. Simplified 17.7%

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

   5. Taylor expanded in x around 0 47.7%

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

   if -inf.0 < (*.f64 x (log.f64 (/.f64 x y))) < 1e308

   1. Initial program 99.7%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \log \left(\frac{x}{y}\right) \leq -\infty \lor \neg \left(x \cdot \log \left(\frac{x}{y}\right) \leq 10^{+308}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log \left(\frac{x}{y}\right) - z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 88.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \log \left(\frac{x}{y}\right)\\ \mathbf{if}\;t\_0 \leq -\infty \lor \neg \left(t\_0 \leq 10^{+308}\right):\\ \;\;\;\;x \cdot \log \left(x \cdot y\right) - z\\ \mathbf{else}:\\ \;\;\;\;t\_0 - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (log (/ x y)))))
   (if (or (<= t_0 (- INFINITY)) (not (<= t_0 1e+308)))
     (- (* 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 <= 1e+308)) {
		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 <= 1e+308)) {
		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 <= 1e+308):
		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 <= 1e+308))
		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 <= 1e+308)))
		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, 1e+308]], $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 1e308 < (*.f64 x (log.f64 (/.f64 x y)))

   1. Initial program 8.7%

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

      1. log-div 43.7%

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

   4. Applied egg-rr 43.7%

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

      1. sub-neg 43.7%

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

      2. distribute-rgt-in 41.6%

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

   6. Applied egg-rr 41.6%

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

      1. distribute-rgt-out 43.7%

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

      2. pow1 43.7%

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

      3. pow1 43.7%

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

      4. rem-cube-cbrt 43.7%

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

      5. exp-to-pow 43.7%

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

      6. sub-neg 43.7%

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

      7. *-commutative 43.7%

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

   8. 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))) < 1e308

   1. Initial program 99.7%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \log \left(\frac{x}{y}\right) \leq -\infty \lor \neg \left(x \cdot \log \left(\frac{x}{y}\right) \leq 10^{+308}\right):\\ \;\;\;\;x \cdot \log \left(x \cdot y\right) - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log \left(\frac{x}{y}\right) - z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.5% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2e-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 <= -2e-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 <= (-2d-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 <= -2e-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 <= -2e-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 <= -2e-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 <= -2e-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, -2e-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 < -1.999999999999994e-310

   1. Initial program 81.4%

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

      1. frac-2neg 81.4%

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

      2. log-div 99.4%

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

   4. Applied egg-rr 99.4%

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

   if -1.999999999999994e-310 < y

   1. Initial program 84.1%

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

      1. log-div 99.5%

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

   4. Applied egg-rr 99.5%

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

4. Final simplification 99.5%

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

Alternative 5: 88.1% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2e-310)
   (- (- z) (* x (log (/ y x))))
   (- (* x (- (log x) (log y))) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2e-310) {
		tmp = -z - (x * log((y / x)));
	} 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 <= (-2d-310)) then
        tmp = -z - (x * log((y / x)))
    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 <= -2e-310) {
		tmp = -z - (x * Math.log((y / x)));
	} else {
		tmp = (x * (Math.log(x) - Math.log(y))) - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -2e-310:
		tmp = -z - (x * math.log((y / x)))
	else:
		tmp = (x * (math.log(x) - math.log(y))) - z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2e-310)
		tmp = Float64(Float64(-z) - Float64(x * log(Float64(y / x))));
	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 <= -2e-310)
		tmp = -z - (x * log((y / x)));
	else
		tmp = (x * (log(x) - log(y))) - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2e-310], N[((-z) - N[(x * N[Log[N[(y / x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $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 < -1.999999999999994e-310

   1. Initial program 81.4%

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

      1. clear-num 80.9%

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

      2. log-rec 84.0%

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

   4. Applied egg-rr 84.0%

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

   if -1.999999999999994e-310 < y

   1. Initial program 84.1%

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

      1. log-div 99.5%

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

   4. Applied egg-rr 99.5%

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

4. Final simplification 91.3%

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

Alternative 6: 67.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{-43} \lor \neg \left(z \leq 8.6 \cdot 10^{-44}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-\log \left(\frac{y}{x}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.3e-43) (not (<= z 8.6e-44))) (- z) (* x (- (log (/ y x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.3e-43) || !(z <= 8.6e-44)) {
		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 <= (-2.3d-43)) .or. (.not. (z <= 8.6d-44))) 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 <= -2.3e-43) || !(z <= 8.6e-44)) {
		tmp = -z;
	} else {
		tmp = x * -Math.log((y / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.3e-43) or not (z <= 8.6e-44):
		tmp = -z
	else:
		tmp = x * -math.log((y / x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.3e-43) || !(z <= 8.6e-44))
		tmp = Float64(-z);
	else
		tmp = Float64(x * Float64(-log(Float64(y / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -2.3e-43) || ~((z <= 8.6e-44)))
		tmp = -z;
	else
		tmp = x * -log((y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.3e-43], N[Not[LessEqual[z, 8.6e-44]], $MachinePrecision]], (-z), N[(x * (-N[Log[N[(y / x), $MachinePrecision]], $MachinePrecision])), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.2999999999999999e-43 or 8.60000000000000027e-44 < z

   1. Initial program 79.8%

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

      1. remove-double-neg 79.8%

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

      2. sub-neg 79.8%

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

      3. distribute-neg-in 79.8%

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

      4. distribute-rgt-neg-in 79.8%

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

      5. remove-double-neg 79.8%

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

      6. fma-udef 79.8%

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

      7. log-div 50.8%

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

      8. sub-neg 50.8%

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

      9. distribute-neg-in 50.8%

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

      10. remove-double-neg 50.8%

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

      11. +-commutative 50.8%

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

      12. sub-neg 50.8%

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

      13. log-div 81.6%

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

   3. Simplified 81.6%

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

   5. Taylor expanded in x around 0 77.6%

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

   if -2.2999999999999999e-43 < z < 8.60000000000000027e-44

   1. Initial program 86.8%

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

      1. remove-double-neg 86.8%

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

      2. sub-neg 86.8%

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

      3. distribute-neg-in 86.8%

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

      4. distribute-rgt-neg-in 86.8%

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

      5. remove-double-neg 86.8%

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

      6. fma-udef 86.8%

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

      7. log-div 40.7%

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

      8. sub-neg 40.7%

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

      9. distribute-neg-in 40.7%

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

      10. remove-double-neg 40.7%

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

      11. +-commutative 40.7%

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

      12. sub-neg 40.7%

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

      13. log-div 87.6%

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

   3. Simplified 87.6%

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

   5. Taylor expanded in x around inf 31.8%

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

      1. log-rec 31.8%

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

      2. sub-neg 31.8%

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

      3. log-div 72.4%

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

   7. Simplified 72.4%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{-43} \lor \neg \left(z \leq 8.6 \cdot 10^{-44}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-\log \left(\frac{y}{x}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 50.3% accurate, 53.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 82.7%

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

   1. remove-double-neg 82.7%

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

   2. sub-neg 82.7%

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

   3. distribute-neg-in 82.7%

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

   4. distribute-rgt-neg-in 82.7%

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

   5. remove-double-neg 82.7%

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

   6. fma-udef 82.7%

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

   7. log-div 46.7%

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

   8. sub-neg 46.7%

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

   9. distribute-neg-in 46.7%

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

   10. remove-double-neg 46.7%

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

   11. +-commutative 46.7%

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

   12. sub-neg 46.7%

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

   13. log-div 84.0%

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

3. Simplified 84.0%

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

5. Taylor expanded in x around 0 52.9%

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

6. Final simplification 52.9%

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

Alternative 8: 2.3% 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 82.7%

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

   1. remove-double-neg 82.7%

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

   2. sub-neg 82.7%

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

   3. distribute-neg-in 82.7%

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

   4. distribute-rgt-neg-in 82.7%

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

   5. remove-double-neg 82.7%

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

   6. fma-udef 82.7%

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

   7. log-div 46.7%

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

   8. sub-neg 46.7%

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

   9. distribute-neg-in 46.7%

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

   10. remove-double-neg 46.7%

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

   11. +-commutative 46.7%

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

   12. sub-neg 46.7%

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

   13. log-div 84.0%

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

3. Simplified 84.0%

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

5. Taylor expanded in x around 0 52.9%

   \[\leadsto -\color{blue}{z} \]
6. Step-by-step derivation

   1. add-sqr-sqrt 27.0%

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

   2. sqrt-unprod 13.9%

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

   3. sqr-neg 13.9%

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

   4. sqrt-unprod 1.0%

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

   5. add-sqr-sqrt 1.9%

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

   6. neg-sub0 1.9%

      \[\leadsto -\color{blue}{\left(0 - z\right)} \]

7. Applied egg-rr 1.9%

   \[\leadsto -\color{blue}{\left(0 - z\right)} \]

8. Taylor expanded in z around 0 1.9%

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

9. Final simplification 1.9%

   \[\leadsto z \]
10. 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 2024096 
(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))