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

Percentage Accurate: 77.5% → 99.5%

Time: 11.9s

Alternatives: 9

Speedup: 0.5×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 77.5% 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 73.7%

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

   3. Taylor expanded in y around -inf 99.4%

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

      1. metadata-eval 99.4%

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

      2. distribute-neg-frac 99.4%

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

      3. distribute-frac-neg2 99.4%

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

      4. log-rec 99.4%

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

      5. sub-neg 99.4%

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

      6. neg-mul-1 99.4%

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

   5. Simplified 99.4%

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

   if -4.999999999999985e-310 < y

   1. Initial program 74.5%

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

   3. Taylor expanded in x around 0 99.6%

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

      1. log-rec 99.6%

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

      2. sub-neg 99.6%

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

   5. Simplified 99.6%

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

Alternative 2: 88.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \log \left(\frac{x}{y}\right)\\ \mathbf{if}\;t\_0 \leq -\infty \lor \neg \left(t\_0 \leq 10^{+300}\right):\\ \;\;\;\;z \cdot \left(\log \left(y \cdot x\right) \cdot \frac{x}{z} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0 - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (log (/ x y)))))
   (if (or (<= t_0 (- INFINITY)) (not (<= t_0 1e+300)))
     (* z (+ (* (log (* y x)) (/ x z)) -1.0))
     (- 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+300)) {
		tmp = z * ((log((y * x)) * (x / z)) + -1.0);
	} 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+300)) {
		tmp = z * ((Math.log((y * x)) * (x / z)) + -1.0);
	} 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+300):
		tmp = z * ((math.log((y * x)) * (x / z)) + -1.0)
	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+300))
		tmp = Float64(z * Float64(Float64(log(Float64(y * x)) * Float64(x / z)) + -1.0));
	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+300)))
		tmp = z * ((log((y * x)) * (x / z)) + -1.0);
	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+300]], $MachinePrecision]], N[(z * N[(N[(N[Log[N[(y * x), $MachinePrecision]], $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $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 1.0000000000000001e300 < (*.f64 x (log.f64 (/.f64 x y)))

   1. Initial program 7.2%

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

   3. Taylor expanded in z around inf 7.2%

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

      1. sub-neg 7.2%

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

      2. associate-/l* 7.2%

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

      3. metadata-eval 7.2%

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

   5. Simplified 7.2%

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

      1. clear-num 7.2%

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

      2. un-div-inv 7.2%

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

      3. log-div 45.7%

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

      4. sub-neg 45.7%

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

      5. add-sqr-sqrt 14.7%

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

      6. sqrt-unprod 43.2%

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

      7. sqr-neg 43.2%

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

      8. sqrt-unprod 28.4%

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

      9. add-sqr-sqrt 34.1%

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

      10. sum-log 54.5%

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

   7. Applied egg-rr 54.5%

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

      1. associate-/r/ 54.5%

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

      2. *-commutative 54.5%

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

   9. Simplified 54.5%

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

   if -inf.0 < (*.f64 x (log.f64 (/.f64 x y))) < 1.0000000000000001e300

   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 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \log \left(\frac{x}{y}\right) \leq -\infty \lor \neg \left(x \cdot \log \left(\frac{x}{y}\right) \leq 10^{+300}\right):\\ \;\;\;\;z \cdot \left(\log \left(y \cdot x\right) \cdot \frac{x}{z} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log \left(\frac{x}{y}\right) - z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 88.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \log \left(\frac{x}{y}\right)\\ \mathbf{if}\;t\_0 \leq -\infty \lor \neg \left(t\_0 \leq 10^{+300}\right):\\ \;\;\;\;x \cdot \log \left(y \cdot x\right) - z\\ \mathbf{else}:\\ \;\;\;\;t\_0 - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (log (/ x y)))))
   (if (or (<= t_0 (- INFINITY)) (not (<= t_0 1e+300)))
     (- (* 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 <= 1e+300)) {
		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 <= 1e+300)) {
		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 <= 1e+300):
		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 <= 1e+300))
		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 <= 1e+300)))
		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, 1e+300]], $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 1.0000000000000001e300 < (*.f64 x (log.f64 (/.f64 x y)))

   1. Initial program 7.2%

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

      1. add-cube-cbrt 7.2%

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

      2. associate-/l* 7.2%

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

      3. log-prod 76.9%

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

      4. pow2 76.9%

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

   4. Applied egg-rr 76.9%

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

      1. log-div 53.5%

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

      2. associate-+r- 53.5%

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

      3. log-prod 53.5%

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

      4. unpow2 53.5%

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

      5. add-cube-cbrt 53.5%

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

      6. sub-neg 53.5%

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

      7. distribute-rgt-in 53.4%

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

   6. Applied egg-rr 53.4%

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

      1. distribute-rgt-out 53.5%

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

      2. sub-neg 53.5%

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

      3. log-div 7.2%

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

      4. *-commutative 7.2%

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

      5. log-div 53.5%

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

      6. sub-neg 53.5%

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

      7. add-sqr-sqrt 22.4%

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

      8. sqrt-unprod 50.9%

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

      9. sqr-neg 50.9%

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

      10. sqrt-unprod 28.4%

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

      11. add-sqr-sqrt 33.5%

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

      12. sum-log 53.4%

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

   8. Applied egg-rr 53.4%

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

   if -inf.0 < (*.f64 x (log.f64 (/.f64 x y))) < 1.0000000000000001e300

   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 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \log \left(\frac{x}{y}\right) \leq -\infty \lor \neg \left(x \cdot \log \left(\frac{x}{y}\right) \leq 10^{+300}\right):\\ \;\;\;\;x \cdot \log \left(y \cdot x\right) - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log \left(\frac{x}{y}\right) - z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 87.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \log \left(\frac{x}{y}\right)\\ \mathbf{if}\;t\_0 \leq -\infty \lor \neg \left(t\_0 \leq 10^{+300}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;t\_0 - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (log (/ x y)))))
   (if (or (<= t_0 (- INFINITY)) (not (<= t_0 1e+300))) (- 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+300)) {
		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+300)) {
		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+300):
		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+300))
		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+300)))
		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+300]], $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 1.0000000000000001e300 < (*.f64 x (log.f64 (/.f64 x y)))

   1. Initial program 7.2%

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

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

   if -inf.0 < (*.f64 x (log.f64 (/.f64 x y))) < 1.0000000000000001e300

   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 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \log \left(\frac{x}{y}\right) \leq -\infty \lor \neg \left(x \cdot \log \left(\frac{x}{y}\right) \leq 10^{+300}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log \left(\frac{x}{y}\right) - z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 88.7% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -5e-310)
   (- (* x (- (log (/ y x)))) 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((y / x))) - 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((y / x))) - 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((y / x))) - 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((y / x))) - 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(y / x)))) - 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((y / x))) - 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[Log[N[(y / x), $MachinePrecision]], $MachinePrecision])), $MachinePrecision] - z), $MachinePrecision], N[(N[(x * N[(N[Log[x], $MachinePrecision] - N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.999999999999985e-310

   1. Initial program 73.7%

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

      1. clear-num 72.9%

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

      2. neg-log 75.1%

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

   4. Applied egg-rr 75.1%

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

   if -4.999999999999985e-310 < y

   1. Initial program 74.5%

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

   3. Taylor expanded in x around 0 99.6%

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

      1. log-rec 99.6%

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

      2. sub-neg 99.6%

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

   5. Simplified 99.6%

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

Alternative 6: 66.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{+33} \lor \neg \left(x \leq 9.8 \cdot 10^{-36}\right):\\ \;\;\;\;x \cdot \log \left(\frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -8.2e+33) (not (<= x 9.8e-36))) (* x (log (/ x y))) (- z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -8.2e+33) || !(x <= 9.8e-36)) {
		tmp = x * log((x / y));
	} else {
		tmp = -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-8.2d+33)) .or. (.not. (x <= 9.8d-36))) then
        tmp = x * log((x / y))
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -8.2e+33) || !(x <= 9.8e-36)) {
		tmp = x * Math.log((x / y));
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -8.2e+33) or not (x <= 9.8e-36):
		tmp = x * math.log((x / y))
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -8.2e+33) || !(x <= 9.8e-36))
		tmp = Float64(x * log(Float64(x / y)));
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -8.2e+33) || ~((x <= 9.8e-36)))
		tmp = x * log((x / y));
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -8.2e+33], N[Not[LessEqual[x, 9.8e-36]], $MachinePrecision]], N[(x * N[Log[N[(x / y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], (-z)]

Derivation

1. Split input into 2 regimes

2. if x < -8.1999999999999999e33 or 9.7999999999999994e-36 < x

   1. Initial program 73.8%

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

   3. Taylor expanded in z around 0 57.1%

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

   if -8.1999999999999999e33 < x < 9.7999999999999994e-36

   1. Initial program 74.4%

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

   3. Taylor expanded in x around 0 82.6%

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

      1. mul-1-neg 82.6%

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

   5. Simplified 82.6%

      \[\leadsto \color{blue}{-z} \]
3. Recombined 2 regimes into one program.

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.2 \cdot 10^{+33} \lor \neg \left(x \leq 9.8 \cdot 10^{-36}\right):\\ \;\;\;\;x \cdot \log \left(\frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 66.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{+34}:\\ \;\;\;\;x \cdot \left(-\log \left(\frac{y}{x}\right)\right)\\ \mathbf{elif}\;x \leq 2 \cdot 10^{-35}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log \left(\frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.4e+34)
   (* x (- (log (/ y x))))
   (if (<= x 2e-35) (- z) (* x (log (/ x y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.4e+34) {
		tmp = x * -log((y / x));
	} else if (x <= 2e-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 (x <= (-1.4d+34)) then
        tmp = x * -log((y / x))
    else if (x <= 2d-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 (x <= -1.4e+34) {
		tmp = x * -Math.log((y / x));
	} else if (x <= 2e-35) {
		tmp = -z;
	} else {
		tmp = x * Math.log((x / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.4e+34:
		tmp = x * -math.log((y / x))
	elif x <= 2e-35:
		tmp = -z
	else:
		tmp = x * math.log((x / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.4e+34)
		tmp = Float64(x * Float64(-log(Float64(y / x))));
	elseif (x <= 2e-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 (x <= -1.4e+34)
		tmp = x * -log((y / x));
	elseif (x <= 2e-35)
		tmp = -z;
	else
		tmp = x * log((x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.4e+34], N[(x * (-N[Log[N[(y / x), $MachinePrecision]], $MachinePrecision])), $MachinePrecision], If[LessEqual[x, 2e-35], (-z), N[(x * N[Log[N[(x / y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.40000000000000004e34

   1. Initial program 65.7%

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

      1. clear-num 65.7%

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

      2. neg-log 68.8%

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

   4. Applied egg-rr 68.8%

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

   5. Taylor expanded in z around 0 50.0%

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

      1. associate-*r* 50.0%

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

      2. neg-mul-1 50.0%

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

   7. Simplified 50.0%

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

   if -1.40000000000000004e34 < x < 2.00000000000000002e-35

   1. Initial program 74.4%

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

   3. Taylor expanded in x around 0 82.6%

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

      1. mul-1-neg 82.6%

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

   5. Simplified 82.6%

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

   if 2.00000000000000002e-35 < x

   1. Initial program 79.9%

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

   3. Taylor expanded in z around 0 64.7%

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

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{+34}:\\ \;\;\;\;x \cdot \left(-\log \left(\frac{y}{x}\right)\right)\\ \mathbf{elif}\;x \leq 2 \cdot 10^{-35}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log \left(\frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 51.1% 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 74.1%

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

3. Taylor expanded in x around 0 53.3%

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

   1. mul-1-neg 53.3%

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

5. Simplified 53.3%

   \[\leadsto \color{blue}{-z} \]
6. Add Preprocessing

Alternative 9: 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 74.1%

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

   1. add-cube-cbrt 73.5%

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

   2. associate-*l* 73.5%

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

   3. fma-neg 73.5%

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

   4. pow2 73.5%

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

   5. add-sqr-sqrt 34.9%

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

   6. sqrt-unprod 41.0%

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

   7. sqr-neg 41.0%

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

   8. sqrt-unprod 18.6%

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

   9. add-sqr-sqrt 34.0%

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

4. Applied egg-rr 34.0%

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

5. Taylor expanded in x around 0 2.4%

   \[\leadsto \color{blue}{z} \]
6. Add Preprocessing

Developer Target 1: 88.6% 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 2024145 
(FPCore (x y z)
  :name "Numeric.SpecFunctions.Extra:bd0 from math-functions-0.1.5.2"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< y 7595077799083773/100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (* x (log (/ x y))) z) (- (* x (- (log x) (log y))) z)))

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