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

Percentage Accurate: 77.2% → 99.5%

Time: 13.3s

Alternatives: 11

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: 77.2% 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, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-309}:\\ \;\;\;\;x \cdot \left(\log \left(-x\right) - \log \left(-y\right)\right) - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(2 \cdot \log \left(\sqrt{x}\right) - \log y\right) - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1e-309)
   (- (* x (- (log (- x)) (log (- y)))) z)
   (- (* x (- (* 2.0 (log (sqrt x))) (log y))) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1e-309) {
		tmp = (x * (log(-x) - log(-y))) - z;
	} else {
		tmp = (x * ((2.0 * log(sqrt(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 <= (-1d-309)) then
        tmp = (x * (log(-x) - log(-y))) - z
    else
        tmp = (x * ((2.0d0 * log(sqrt(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 <= -1e-309) {
		tmp = (x * (Math.log(-x) - Math.log(-y))) - z;
	} else {
		tmp = (x * ((2.0 * Math.log(Math.sqrt(x))) - Math.log(y))) - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1e-309:
		tmp = (x * (math.log(-x) - math.log(-y))) - z
	else:
		tmp = (x * ((2.0 * math.log(math.sqrt(x))) - math.log(y))) - z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1e-309)
		tmp = Float64(Float64(x * Float64(log(Float64(-x)) - log(Float64(-y)))) - z);
	else
		tmp = Float64(Float64(x * Float64(Float64(2.0 * log(sqrt(x))) - log(y))) - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1e-309)
		tmp = (x * (log(-x) - log(-y))) - z;
	else
		tmp = (x * ((2.0 * log(sqrt(x))) - log(y))) - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1e-309], N[(N[(x * N[(N[Log[(-x)], $MachinePrecision] - N[Log[(-y)], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision], N[(N[(x * N[(N[(2.0 * N[Log[N[Sqrt[x], $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.000000000000002e-309

   1. Initial program 80.3%

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

   3. Taylor expanded in y around -inf 99.6%

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

      1. metadata-eval 99.6%

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

      2. distribute-neg-frac 99.6%

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

      3. distribute-frac-neg2 99.6%

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

      4. log-rec 99.6%

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

      5. sub-neg 99.6%

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

      6. neg-mul-1 99.6%

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

   5. Simplified 99.6%

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

   if -1.000000000000002e-309 < y

   1. Initial program 72.1%

      \[x \cdot \log \left(\frac{x}{y}\right) - z \]
   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. neg-mul-1 99.6%

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

      3. neg-mul-1 99.6%

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

      4. sub-neg 99.6%

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

   5. Simplified 99.6%

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

      1. add-sqr-sqrt 99.6%

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

      2. log-prod 99.6%

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

   7. Applied egg-rr 99.6%

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

      1. count-2 99.6%

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

   9. Simplified 99.6%

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

Alternative 2: 87.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \log \left(\frac{x}{y}\right)\\ t_1 := x \cdot t\_0\\ t_2 := x \cdot \log \left(y \cdot x\right)\\ \mathbf{if}\;t\_1 \leq -\infty:\\ \;\;\;\;t\_2 - z\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+307}:\\ \;\;\;\;\mathsf{fma}\left(x, t\_0, -z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - t\_2\\ \end{array} \end{array} \]

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+307) (fma x t_0 (- z)) (- (- z) t_2)))))

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+307) {
		tmp = fma(x, t_0, -z);
	} else {
		tmp = -z - t_2;
	}
	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+307)
		tmp = fma(x, t_0, Float64(-z));
	else
		tmp = Float64(Float64(-z) - t_2);
	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+307], N[(x * t$95$0 + (-z)), $MachinePrecision], N[((-z) - t$95$2), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 9.0%

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

      1. add-cube-cbrt 9.0%

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

      2. associate-/l* 9.0%

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

      3. log-prod 80.4%

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

      4. pow2 80.4%

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

   4. Applied egg-rr 80.4%

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

      1. log-div 67.5%

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

      2. associate-+r- 67.6%

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

      3. log-prod 67.6%

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

      4. unpow2 67.6%

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

      5. add-cube-cbrt 67.6%

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

      6. sub-neg 67.6%

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

      7. distribute-rgt-in 67.6%

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

   6. Applied egg-rr 67.6%

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

      1. distribute-rgt-out 67.6%

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

      2. sub-neg 67.6%

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

      3. *-commutative 67.6%

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

      4. expm1-log1p-u 0.0%

         \[\leadsto \left(\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\log x\right)\right)} - \log y\right) \cdot x - z \]

      5. expm1-log1p-u 67.6%

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

      6. sub-neg 67.6%

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

      7. add-sqr-sqrt 0.0%

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

      8. sqrt-unprod 50.6%

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

      9. sqr-neg 50.6%

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

      10. sqrt-unprod 50.6%

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

      11. add-sqr-sqrt 50.6%

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

      12. sum-log 64.1%

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

   8. Applied egg-rr 64.1%

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

   if -inf.0 < (*.f64 x (log.f64 (/.f64 x y))) < 5e307

   1. Initial program 99.6%

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

      1. fma-neg 99.6%

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

   3. Simplified 99.6%

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

   if 5e307 < (*.f64 x (log.f64 (/.f64 x y)))

   1. Initial program 6.9%

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

      1. clear-num 6.9%

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

      2. neg-log 13.2%

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

   4. Applied egg-rr 13.2%

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

      1. distribute-rgt-neg-out 13.2%

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

      2. neg-sub0 13.2%

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

      3. add-sqr-sqrt 0.9%

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

      4. sqrt-unprod 1.4%

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

      5. sqr-neg 1.4%

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

      6. sqrt-unprod 0.5%

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

      7. add-sqr-sqrt 1.6%

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

      8. neg-log 1.6%

         \[\leadsto \left(0 - x \cdot \color{blue}{\log \left(\frac{1}{\frac{y}{x}}\right)}\right) - z \]

      9. clear-num 1.6%

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

      10. diff-log 3.3%

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

      11. add-sqr-sqrt 3.3%

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

      12. add-sqr-sqrt 3.3%

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

      13. sub-neg 3.3%

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

      14. add-sqr-sqrt 3.3%

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

      15. sqrt-unprod 3.3%

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

      16. sqr-neg 3.3%

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

      17. sqrt-unprod 0.0%

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

      18. add-sqr-sqrt 7.2%

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

      19. sum-log 51.5%

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

   6. Applied egg-rr 51.5%

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

      1. neg-sub0 51.5%

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

      2. distribute-lft-neg-in 51.5%

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

   8. Simplified 51.5%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \log \left(\frac{x}{y}\right) \leq -\infty:\\ \;\;\;\;x \cdot \log \left(y \cdot x\right) - z\\ \mathbf{elif}\;x \cdot \log \left(\frac{x}{y}\right) \leq 5 \cdot 10^{+307}:\\ \;\;\;\;\mathsf{fma}\left(x, \log \left(\frac{x}{y}\right), -z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - x \cdot \log \left(y \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 87.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \log \left(\frac{x}{y}\right)\\ t_1 := x \cdot \log \left(y \cdot x\right)\\ \mathbf{if}\;t\_0 \leq -\infty:\\ \;\;\;\;t\_1 - z\\ \mathbf{elif}\;t\_0 \leq 5 \cdot 10^{+307}:\\ \;\;\;\;t\_0 - z\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (log (/ x y)))) (t_1 (* x (log (* y x)))))
   (if (<= t_0 (- INFINITY))
     (- t_1 z)
     (if (<= t_0 5e+307) (- t_0 z) (- (- z) t_1)))))

C

double code(double x, double y, double z) {
	double t_0 = x * log((x / y));
	double t_1 = x * log((y * x));
	double tmp;
	if (t_0 <= -((double) INFINITY)) {
		tmp = t_1 - z;
	} else if (t_0 <= 5e+307) {
		tmp = t_0 - z;
	} else {
		tmp = -z - t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z) {
	double t_0 = x * Math.log((x / y));
	double t_1 = x * Math.log((y * x));
	double tmp;
	if (t_0 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1 - z;
	} else if (t_0 <= 5e+307) {
		tmp = t_0 - z;
	} else {
		tmp = -z - t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * math.log((x / y))
	t_1 = x * math.log((y * x))
	tmp = 0
	if t_0 <= -math.inf:
		tmp = t_1 - z
	elif t_0 <= 5e+307:
		tmp = t_0 - z
	else:
		tmp = -z - t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * log(Float64(x / y)))
	t_1 = Float64(x * log(Float64(y * x)))
	tmp = 0.0
	if (t_0 <= Float64(-Inf))
		tmp = Float64(t_1 - z);
	elseif (t_0 <= 5e+307)
		tmp = Float64(t_0 - z);
	else
		tmp = Float64(Float64(-z) - t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * log((x / y));
	t_1 = x * log((y * x));
	tmp = 0.0;
	if (t_0 <= -Inf)
		tmp = t_1 - z;
	elseif (t_0 <= 5e+307)
		tmp = t_0 - z;
	else
		tmp = -z - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[Log[N[(x / y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x * N[Log[N[(y * x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, (-Infinity)], N[(t$95$1 - z), $MachinePrecision], If[LessEqual[t$95$0, 5e+307], N[(t$95$0 - z), $MachinePrecision], N[((-z) - t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 9.0%

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

      1. add-cube-cbrt 9.0%

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

      2. associate-/l* 9.0%

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

      3. log-prod 80.4%

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

      4. pow2 80.4%

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

   4. Applied egg-rr 80.4%

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

      1. log-div 67.5%

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

      2. associate-+r- 67.6%

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

      3. log-prod 67.6%

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

      4. unpow2 67.6%

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

      5. add-cube-cbrt 67.6%

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

      6. sub-neg 67.6%

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

      7. distribute-rgt-in 67.6%

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

   6. Applied egg-rr 67.6%

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

      1. distribute-rgt-out 67.6%

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

      2. sub-neg 67.6%

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

      3. *-commutative 67.6%

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

      4. expm1-log1p-u 0.0%

         \[\leadsto \left(\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\log x\right)\right)} - \log y\right) \cdot x - z \]

      5. expm1-log1p-u 67.6%

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

      6. sub-neg 67.6%

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

      7. add-sqr-sqrt 0.0%

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

      8. sqrt-unprod 50.6%

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

      9. sqr-neg 50.6%

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

      10. sqrt-unprod 50.6%

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

      11. add-sqr-sqrt 50.6%

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

      12. sum-log 64.1%

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

   8. Applied egg-rr 64.1%

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

   if -inf.0 < (*.f64 x (log.f64 (/.f64 x y))) < 5e307

   1. Initial program 99.6%

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

   if 5e307 < (*.f64 x (log.f64 (/.f64 x y)))

   1. Initial program 6.9%

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

      1. clear-num 6.9%

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

      2. neg-log 13.2%

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

   4. Applied egg-rr 13.2%

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

      1. distribute-rgt-neg-out 13.2%

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

      2. neg-sub0 13.2%

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

      3. add-sqr-sqrt 0.9%

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

      4. sqrt-unprod 1.4%

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

      5. sqr-neg 1.4%

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

      6. sqrt-unprod 0.5%

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

      7. add-sqr-sqrt 1.6%

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

      8. neg-log 1.6%

         \[\leadsto \left(0 - x \cdot \color{blue}{\log \left(\frac{1}{\frac{y}{x}}\right)}\right) - z \]

      9. clear-num 1.6%

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

      10. diff-log 3.3%

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

      11. add-sqr-sqrt 3.3%

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

      12. add-sqr-sqrt 3.3%

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

      13. sub-neg 3.3%

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

      14. add-sqr-sqrt 3.3%

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

      15. sqrt-unprod 3.3%

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

      16. sqr-neg 3.3%

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

      17. sqrt-unprod 0.0%

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

      18. add-sqr-sqrt 7.2%

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

      19. sum-log 51.5%

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

   6. Applied egg-rr 51.5%

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

      1. neg-sub0 51.5%

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

      2. distribute-lft-neg-in 51.5%

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

   8. Simplified 51.5%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \log \left(\frac{x}{y}\right) \leq -\infty:\\ \;\;\;\;x \cdot \log \left(y \cdot x\right) - z\\ \mathbf{elif}\;x \cdot \log \left(\frac{x}{y}\right) \leq 5 \cdot 10^{+307}:\\ \;\;\;\;x \cdot \log \left(\frac{x}{y}\right) - z\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - x \cdot \log \left(y \cdot x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 87.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \log \left(\frac{x}{y}\right)\\ \mathbf{if}\;t\_0 \leq -\infty \lor \neg \left(t\_0 \leq 5 \cdot 10^{+307}\right):\\ \;\;\;\;x \cdot \log \left(y \cdot x\right) - z\\ \mathbf{else}:\\ \;\;\;\;t\_0 - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (log (/ x y)))))
   (if (or (<= t_0 (- INFINITY)) (not (<= t_0 5e+307)))
     (- (* 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+307)) {
		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+307)) {
		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+307):
		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+307))
		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+307)))
		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+307]], $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 5e307 < (*.f64 x (log.f64 (/.f64 x y)))

   1. Initial program 8.0%

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

      1. add-cube-cbrt 8.0%

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

      2. associate-/l* 8.0%

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

      3. log-prod 78.3%

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

      4. pow2 78.3%

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

   4. Applied egg-rr 78.3%

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

      1. log-div 60.4%

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

      2. associate-+r- 60.5%

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

      3. log-prod 60.5%

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

      4. unpow2 60.5%

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

      5. add-cube-cbrt 60.5%

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

      6. sub-neg 60.5%

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

      7. distribute-rgt-in 60.5%

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

   6. Applied egg-rr 60.5%

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

      1. distribute-rgt-out 60.5%

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

      2. sub-neg 60.5%

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

      3. *-commutative 60.5%

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

      4. expm1-log1p-u 25.6%

         \[\leadsto \left(\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\log x\right)\right)} - \log y\right) \cdot x - z \]

      5. expm1-log1p-u 60.5%

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

      6. sub-neg 60.5%

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

      7. add-sqr-sqrt 25.6%

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

      8. sqrt-unprod 51.7%

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

      9. sqr-neg 51.7%

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

      10. sqrt-unprod 26.1%

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

      11. add-sqr-sqrt 29.7%

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

      12. sum-log 57.9%

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

   8. Applied egg-rr 57.9%

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

   if -inf.0 < (*.f64 x (log.f64 (/.f64 x y))) < 5e307

   1. Initial program 99.6%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \log \left(\frac{x}{y}\right) \leq -\infty \lor \neg \left(x \cdot \log \left(\frac{x}{y}\right) \leq 5 \cdot 10^{+307}\right):\\ \;\;\;\;x \cdot \log \left(y \cdot x\right) - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log \left(\frac{x}{y}\right) - z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 86.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \log \left(\frac{x}{y}\right)\\ \mathbf{if}\;t\_0 \leq -\infty \lor \neg \left(t\_0 \leq 5 \cdot 10^{+307}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;t\_0 - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (log (/ x y)))))
   (if (or (<= t_0 (- INFINITY)) (not (<= t_0 5e+307))) (- 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+307)) {
		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+307)) {
		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+307):
		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+307))
		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+307)))
		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+307]], $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 5e307 < (*.f64 x (log.f64 (/.f64 x y)))

   1. Initial program 8.0%

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

   3. Taylor expanded in x around 0 53.1%

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

      1. mul-1-neg 53.1%

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

   5. Simplified 53.1%

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

   if -inf.0 < (*.f64 x (log.f64 (/.f64 x y))) < 5e307

   1. Initial program 99.6%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \log \left(\frac{x}{y}\right) \leq -\infty \lor \neg \left(x \cdot \log \left(\frac{x}{y}\right) \leq 5 \cdot 10^{+307}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log \left(\frac{x}{y}\right) - z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 90.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{-95}:\\ \;\;\;\;\mathsf{fma}\left(x, \log \left(\frac{x}{y}\right), -z\right)\\ \mathbf{elif}\;x \leq -1 \cdot 10^{-308}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x - \log y\right) - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.7e-95)
   (fma x (log (/ x y)) (- z))
   (if (<= x -1e-308) (- z) (- (* x (- (log x) (log y))) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.7e-95) {
		tmp = fma(x, log((x / y)), -z);
	} else if (x <= -1e-308) {
		tmp = -z;
	} else {
		tmp = (x * (log(x) - log(y))) - z;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.7e-95)
		tmp = fma(x, log(Float64(x / y)), Float64(-z));
	elseif (x <= -1e-308)
		tmp = Float64(-z);
	else
		tmp = Float64(Float64(x * Float64(log(x) - log(y))) - z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.7e-95], N[(x * N[Log[N[(x / y), $MachinePrecision]], $MachinePrecision] + (-z)), $MachinePrecision], If[LessEqual[x, -1e-308], (-z), N[(N[(x * N[(N[Log[x], $MachinePrecision] - N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.69999999999999997e-95

   1. Initial program 88.9%

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

      1. fma-neg 88.9%

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

   3. Simplified 88.9%

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

   if -1.69999999999999997e-95 < x < -9.9999999999999991e-309

   1. Initial program 62.2%

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

   3. Taylor expanded in x around 0 95.1%

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

      1. mul-1-neg 95.1%

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

   5. Simplified 95.1%

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

   if -9.9999999999999991e-309 < x

   1. Initial program 72.1%

      \[x \cdot \log \left(\frac{x}{y}\right) - z \]
   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. neg-mul-1 99.6%

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

      3. neg-mul-1 99.6%

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

      4. 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 3 regimes into one program.
4. Add Preprocessing

Alternative 7: 99.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-309}:\\ \;\;\;\;x \cdot \left(\log \left(-x\right) - \log \left(-y\right)\right) - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x - \log y\right) - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1e-309)
   (- (* 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 <= -1e-309) {
		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 <= (-1d-309)) 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 <= -1e-309) {
		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 <= -1e-309:
		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 <= -1e-309)
		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 <= -1e-309)
		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, -1e-309], 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 < -1.000000000000002e-309

   1. Initial program 80.3%

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

   3. Taylor expanded in y around -inf 99.6%

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

      1. metadata-eval 99.6%

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

      2. distribute-neg-frac 99.6%

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

      3. distribute-frac-neg2 99.6%

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

      4. log-rec 99.6%

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

      5. sub-neg 99.6%

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

      6. neg-mul-1 99.6%

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

   5. Simplified 99.6%

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

   if -1.000000000000002e-309 < y

   1. Initial program 72.1%

      \[x \cdot \log \left(\frac{x}{y}\right) - z \]
   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. neg-mul-1 99.6%

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

      3. neg-mul-1 99.6%

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

      4. 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 8: 66.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.65 \cdot 10^{-105} \lor \neg \left(z \leq 5 \cdot 10^{-47}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;\left(-x\right) \cdot \log \left(\frac{y}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.65e-105) (not (<= z 5e-47))) (- z) (* (- x) (log (/ y x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.65e-105) || !(z <= 5e-47)) {
		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 <= (-2.65d-105)) .or. (.not. (z <= 5d-47))) 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 <= -2.65e-105) || !(z <= 5e-47)) {
		tmp = -z;
	} else {
		tmp = -x * Math.log((y / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.65e-105) or not (z <= 5e-47):
		tmp = -z
	else:
		tmp = -x * math.log((y / x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.65e-105) || !(z <= 5e-47))
		tmp = Float64(-z);
	else
		tmp = Float64(Float64(-x) * log(Float64(y / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -2.65e-105) || ~((z <= 5e-47)))
		tmp = -z;
	else
		tmp = -x * log((y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.65e-105], N[Not[LessEqual[z, 5e-47]], $MachinePrecision]], (-z), N[((-x) * N[Log[N[(y / x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.6500000000000001e-105 or 5.00000000000000011e-47 < z

   1. Initial program 76.5%

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

   3. Taylor expanded in x around 0 73.2%

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

      1. mul-1-neg 73.2%

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

   5. Simplified 73.2%

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

   if -2.6500000000000001e-105 < z < 5.00000000000000011e-47

   1. Initial program 75.1%

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

      1. clear-num 74.6%

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

      2. neg-log 76.6%

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

   4. Applied egg-rr 76.6%

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

   5. Taylor expanded in z around 0 67.9%

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

      1. associate-*r* 67.9%

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

      2. neg-mul-1 67.9%

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

   7. Simplified 67.9%

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

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.65 \cdot 10^{-105} \lor \neg \left(z \leq 5 \cdot 10^{-47}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;\left(-x\right) \cdot \log \left(\frac{y}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 66.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.3 \cdot 10^{-104} \lor \neg \left(z \leq 1.28 \cdot 10^{-46}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log \left(\frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -5.3e-104) (not (<= z 1.28e-46))) (- z) (* x (log (/ x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.3e-104) || !(z <= 1.28e-46)) {
		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 <= (-5.3d-104)) .or. (.not. (z <= 1.28d-46))) 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 <= -5.3e-104) || !(z <= 1.28e-46)) {
		tmp = -z;
	} else {
		tmp = x * Math.log((x / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -5.3e-104) or not (z <= 1.28e-46):
		tmp = -z
	else:
		tmp = x * math.log((x / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -5.3e-104) || !(z <= 1.28e-46))
		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 <= -5.3e-104) || ~((z <= 1.28e-46)))
		tmp = -z;
	else
		tmp = x * log((x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -5.3e-104], N[Not[LessEqual[z, 1.28e-46]], $MachinePrecision]], (-z), N[(x * N[Log[N[(x / y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.30000000000000018e-104 or 1.28e-46 < z

   1. Initial program 76.5%

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

   3. Taylor expanded in x around 0 73.2%

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

      1. mul-1-neg 73.2%

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

   5. Simplified 73.2%

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

   if -5.30000000000000018e-104 < z < 1.28e-46

   1. Initial program 75.1%

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

   3. Taylor expanded in z around 0 66.5%

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

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.3 \cdot 10^{-104} \lor \neg \left(z \leq 1.28 \cdot 10^{-46}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log \left(\frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 50.2% 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 76.0%

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

3. Taylor expanded in x around 0 50.9%

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

   1. mul-1-neg 50.9%

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

5. Simplified 50.9%

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

Alternative 11: 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 76.0%

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

3. Taylor expanded in x around 0 50.9%

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

   1. mul-1-neg 50.9%

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

5. Simplified 50.9%

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

   1. neg-sub0 50.9%

      \[\leadsto \color{blue}{0 - z} \]

   2. sub-neg 50.9%

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

   3. add-sqr-sqrt 21.1%

      \[\leadsto 0 + \color{blue}{\sqrt{-z} \cdot \sqrt{-z}} \]

   4. sqrt-unprod 13.6%

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

   5. sqr-neg 13.6%

      \[\leadsto 0 + \sqrt{\color{blue}{z \cdot z}} \]

   6. sqrt-unprod 1.3%

      \[\leadsto 0 + \color{blue}{\sqrt{z} \cdot \sqrt{z}} \]

   7. add-sqr-sqrt 2.3%

      \[\leadsto 0 + \color{blue}{z} \]

7. Applied egg-rr 2.3%

   \[\leadsto \color{blue}{0 + z} \]
8. Step-by-step derivation

   1. +-lft-identity 2.3%

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

9. Simplified 2.3%

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

Developer Target 1: 87.9% 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 2024137 
(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))