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

Percentage Accurate: 77.3% → 99.4%

Time: 12.0s

Alternatives: 13

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: 77.3% 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: 99.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \log \left(-y\right)\\ t_1 := \log \left(-x\right)\\ \mathbf{if}\;y \leq -4 \cdot 10^{-310}:\\ \;\;\;\;\frac{{t\_1}^{3} - {t\_0}^{3}}{\left(t\_0 \cdot t\_1 + {t\_0}^{2}\right) + {t\_1}^{2}} \cdot x - z\\ \mathbf{else}:\\ \;\;\;\;\left(\log x - \log y\right) \cdot x - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (log (- y))) (t_1 (log (- x))))
   (if (<= y -4e-310)
     (-
      (*
       (/
        (- (pow t_1 3.0) (pow t_0 3.0))
        (+ (+ (* t_0 t_1) (pow t_0 2.0)) (pow t_1 2.0)))
       x)
      z)
     (- (* (- (log x) (log y)) x) z))))

C

double code(double x, double y, double z) {
	double t_0 = log(-y);
	double t_1 = log(-x);
	double tmp;
	if (y <= -4e-310) {
		tmp = (((pow(t_1, 3.0) - pow(t_0, 3.0)) / (((t_0 * t_1) + pow(t_0, 2.0)) + pow(t_1, 2.0))) * x) - z;
	} else {
		tmp = ((log(x) - log(y)) * x) - 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) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = log(-y)
    t_1 = log(-x)
    if (y <= (-4d-310)) then
        tmp = ((((t_1 ** 3.0d0) - (t_0 ** 3.0d0)) / (((t_0 * t_1) + (t_0 ** 2.0d0)) + (t_1 ** 2.0d0))) * x) - z
    else
        tmp = ((log(x) - log(y)) * x) - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.log(-y);
	double t_1 = Math.log(-x);
	double tmp;
	if (y <= -4e-310) {
		tmp = (((Math.pow(t_1, 3.0) - Math.pow(t_0, 3.0)) / (((t_0 * t_1) + Math.pow(t_0, 2.0)) + Math.pow(t_1, 2.0))) * x) - z;
	} else {
		tmp = ((Math.log(x) - Math.log(y)) * x) - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.log(-y)
	t_1 = math.log(-x)
	tmp = 0
	if y <= -4e-310:
		tmp = (((math.pow(t_1, 3.0) - math.pow(t_0, 3.0)) / (((t_0 * t_1) + math.pow(t_0, 2.0)) + math.pow(t_1, 2.0))) * x) - z
	else:
		tmp = ((math.log(x) - math.log(y)) * x) - z
	return tmp

Julia

function code(x, y, z)
	t_0 = log(Float64(-y))
	t_1 = log(Float64(-x))
	tmp = 0.0
	if (y <= -4e-310)
		tmp = Float64(Float64(Float64(Float64((t_1 ^ 3.0) - (t_0 ^ 3.0)) / Float64(Float64(Float64(t_0 * t_1) + (t_0 ^ 2.0)) + (t_1 ^ 2.0))) * x) - z);
	else
		tmp = Float64(Float64(Float64(log(x) - log(y)) * x) - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = log(-y);
	t_1 = log(-x);
	tmp = 0.0;
	if (y <= -4e-310)
		tmp = ((((t_1 ^ 3.0) - (t_0 ^ 3.0)) / (((t_0 * t_1) + (t_0 ^ 2.0)) + (t_1 ^ 2.0))) * x) - z;
	else
		tmp = ((log(x) - log(y)) * x) - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Log[(-y)], $MachinePrecision]}, Block[{t$95$1 = N[Log[(-x)], $MachinePrecision]}, If[LessEqual[y, -4e-310], N[(N[(N[(N[(N[Power[t$95$1, 3.0], $MachinePrecision] - N[Power[t$95$0, 3.0], $MachinePrecision]), $MachinePrecision] / N[(N[(N[(t$95$0 * t$95$1), $MachinePrecision] + N[Power[t$95$0, 2.0], $MachinePrecision]), $MachinePrecision] + N[Power[t$95$1, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision] - z), $MachinePrecision], N[(N[(N[(N[Log[x], $MachinePrecision] - N[Log[y], $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision] - z), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.999999999999988e-310

   1. Initial program 76.9%

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

      1. lift-log.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. frac-2neg N/A

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

      4. log-div N/A

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

      5. flip3-- N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 N/A

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

      8. lower-pow.f64 N/A

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

      9. lower-log.f64 N/A

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

      10. lower-neg.f64 N/A

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

      11. lower-pow.f64 N/A

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

      12. lower-log.f64 N/A

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

      13. lower-neg.f64 N/A

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

      14. lower-+.f64 N/A

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

   4. Applied rewrites 99.3%

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

   if -3.999999999999988e-310 < y

   1. Initial program 73.3%

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

      1. lift-log.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. log-div N/A

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

      4. lower--.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower-log.f64 99.6

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

   4. Applied rewrites 99.6%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-310}:\\ \;\;\;\;\frac{{\log \left(-x\right)}^{3} - {\log \left(-y\right)}^{3}}{\left(\log \left(-y\right) \cdot \log \left(-x\right) + {\log \left(-y\right)}^{2}\right) + {\log \left(-x\right)}^{2}} \cdot x - z\\ \mathbf{else}:\\ \;\;\;\;\left(\log x - \log y\right) \cdot x - z\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 95.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \log \left(-x\right)\\ t_1 := \log \left(\frac{-1}{y}\right) + t\_0\\ \mathbf{if}\;x \leq -4.8 \cdot 10^{+153}:\\ \;\;\;\;\frac{1}{\frac{\frac{z}{{t\_1}^{2} \cdot x} - \frac{-1}{t\_1}}{x}}\\ \mathbf{elif}\;x \leq -5 \cdot 10^{-310}:\\ \;\;\;\;\frac{{t\_0}^{2} - {\log \left(-y\right)}^{2}}{\log \left(x \cdot y\right)} \cdot x - z\\ \mathbf{else}:\\ \;\;\;\;\left(\log x - \log y\right) \cdot x - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (log (- x))) (t_1 (+ (log (/ -1.0 y)) t_0)))
   (if (<= x -4.8e+153)
     (/ 1.0 (/ (- (/ z (* (pow t_1 2.0) x)) (/ -1.0 t_1)) x))
     (if (<= x -5e-310)
       (- (* (/ (- (pow t_0 2.0) (pow (log (- y)) 2.0)) (log (* x y))) x) z)
       (- (* (- (log x) (log y)) x) z)))))

C

double code(double x, double y, double z) {
	double t_0 = log(-x);
	double t_1 = log((-1.0 / y)) + t_0;
	double tmp;
	if (x <= -4.8e+153) {
		tmp = 1.0 / (((z / (pow(t_1, 2.0) * x)) - (-1.0 / t_1)) / x);
	} else if (x <= -5e-310) {
		tmp = (((pow(t_0, 2.0) - pow(log(-y), 2.0)) / log((x * y))) * x) - z;
	} else {
		tmp = ((log(x) - log(y)) * x) - 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) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = log(-x)
    t_1 = log(((-1.0d0) / y)) + t_0
    if (x <= (-4.8d+153)) then
        tmp = 1.0d0 / (((z / ((t_1 ** 2.0d0) * x)) - ((-1.0d0) / t_1)) / x)
    else if (x <= (-5d-310)) then
        tmp = ((((t_0 ** 2.0d0) - (log(-y) ** 2.0d0)) / log((x * y))) * x) - z
    else
        tmp = ((log(x) - log(y)) * x) - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.log(-x);
	double t_1 = Math.log((-1.0 / y)) + t_0;
	double tmp;
	if (x <= -4.8e+153) {
		tmp = 1.0 / (((z / (Math.pow(t_1, 2.0) * x)) - (-1.0 / t_1)) / x);
	} else if (x <= -5e-310) {
		tmp = (((Math.pow(t_0, 2.0) - Math.pow(Math.log(-y), 2.0)) / Math.log((x * y))) * x) - z;
	} else {
		tmp = ((Math.log(x) - Math.log(y)) * x) - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.log(-x)
	t_1 = math.log((-1.0 / y)) + t_0
	tmp = 0
	if x <= -4.8e+153:
		tmp = 1.0 / (((z / (math.pow(t_1, 2.0) * x)) - (-1.0 / t_1)) / x)
	elif x <= -5e-310:
		tmp = (((math.pow(t_0, 2.0) - math.pow(math.log(-y), 2.0)) / math.log((x * y))) * x) - z
	else:
		tmp = ((math.log(x) - math.log(y)) * x) - z
	return tmp

Julia

function code(x, y, z)
	t_0 = log(Float64(-x))
	t_1 = Float64(log(Float64(-1.0 / y)) + t_0)
	tmp = 0.0
	if (x <= -4.8e+153)
		tmp = Float64(1.0 / Float64(Float64(Float64(z / Float64((t_1 ^ 2.0) * x)) - Float64(-1.0 / t_1)) / x));
	elseif (x <= -5e-310)
		tmp = Float64(Float64(Float64(Float64((t_0 ^ 2.0) - (log(Float64(-y)) ^ 2.0)) / log(Float64(x * y))) * x) - z);
	else
		tmp = Float64(Float64(Float64(log(x) - log(y)) * x) - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = log(-x);
	t_1 = log((-1.0 / y)) + t_0;
	tmp = 0.0;
	if (x <= -4.8e+153)
		tmp = 1.0 / (((z / ((t_1 ^ 2.0) * x)) - (-1.0 / t_1)) / x);
	elseif (x <= -5e-310)
		tmp = ((((t_0 ^ 2.0) - (log(-y) ^ 2.0)) / log((x * y))) * x) - z;
	else
		tmp = ((log(x) - log(y)) * x) - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Log[(-x)], $MachinePrecision]}, Block[{t$95$1 = N[(N[Log[N[(-1.0 / y), $MachinePrecision]], $MachinePrecision] + t$95$0), $MachinePrecision]}, If[LessEqual[x, -4.8e+153], N[(1.0 / N[(N[(N[(z / N[(N[Power[t$95$1, 2.0], $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] - N[(-1.0 / t$95$1), $MachinePrecision]), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -5e-310], N[(N[(N[(N[(N[Power[t$95$0, 2.0], $MachinePrecision] - N[Power[N[Log[(-y)], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] / N[Log[N[(x * y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision] - z), $MachinePrecision], N[(N[(N[(N[Log[x], $MachinePrecision] - N[Log[y], $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision] - z), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.79999999999999985e153

   1. Initial program 71.4%

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

      1. lift--.f64 N/A

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

      2. flip-- N/A

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

      3. clear-num N/A

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

      4. lower-/.f64 N/A

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

      5. clear-num N/A

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

      6. flip-- N/A

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

      7. lift--.f64 N/A

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

      8. lower-/.f64 71.3

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

      9. lift--.f64 N/A

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

      10. sub-neg N/A

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

      11. lift-*.f64 N/A

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

      12. *-commutative N/A

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

      13. lower-fma.f64 N/A

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

      14. lower-neg.f64 71.3

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

   4. Applied rewrites 71.3%

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

   5. Taylor expanded in x around -inf

      \[\leadsto \frac{1}{\color{blue}{-1 \cdot \frac{-1 \cdot \frac{z}{x \cdot {\left(\log \left(\frac{-1}{y}\right) + -1 \cdot \log \left(\frac{-1}{x}\right)\right)}^{2}} - \frac{1}{\log \left(\frac{-1}{y}\right) + -1 \cdot \log \left(\frac{-1}{x}\right)}}{x}}} \]
   6. Step-by-step derivation

      1. associate-*r/ N/A

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

   7. Applied rewrites 98.9%

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

   if -4.79999999999999985e153 < x < -4.999999999999985e-310

   1. Initial program 79.1%

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

      1. lift-log.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. frac-2neg N/A

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

      4. log-div N/A

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

      5. flip-- N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 N/A

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

      8. pow2 N/A

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

      9. lower-pow.f64 N/A

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

      10. lower-log.f64 N/A

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

      11. lower-neg.f64 N/A

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

      12. pow2 N/A

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

      13. lower-pow.f64 N/A

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

      14. lower-log.f64 N/A

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

      15. lower-neg.f64 N/A

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

      16. sum-log N/A

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

      17. lower-log.f64 N/A

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

      18. lower-*.f64 N/A

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

      19. lower-neg.f64 N/A

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

      20. lower-neg.f64 96.5

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

   4. Applied rewrites 96.5%

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

   if -4.999999999999985e-310 < x

   1. Initial program 73.3%

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

      1. lift-log.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. log-div N/A

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

      4. lower--.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower-log.f64 99.6

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

   4. Applied rewrites 99.6%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+153}:\\ \;\;\;\;\frac{1}{\frac{\frac{z}{{\left(\log \left(\frac{-1}{y}\right) + \log \left(-x\right)\right)}^{2} \cdot x} - \frac{-1}{\log \left(\frac{-1}{y}\right) + \log \left(-x\right)}}{x}}\\ \mathbf{elif}\;x \leq -5 \cdot 10^{-310}:\\ \;\;\;\;\frac{{\log \left(-x\right)}^{2} - {\log \left(-y\right)}^{2}}{\log \left(x \cdot y\right)} \cdot x - z\\ \mathbf{else}:\\ \;\;\;\;\left(\log x - \log y\right) \cdot x - z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 95.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \log \left(-x\right)\\ t_1 := \log \left(-y\right)\\ \mathbf{if}\;x \leq -3.1 \cdot 10^{+153}:\\ \;\;\;\;\left(t\_0 - t\_1\right) \cdot x\\ \mathbf{elif}\;x \leq -5 \cdot 10^{-310}:\\ \;\;\;\;\frac{{t\_0}^{2} - {t\_1}^{2}}{\log \left(x \cdot y\right)} \cdot x - z\\ \mathbf{else}:\\ \;\;\;\;\left(\log x - \log y\right) \cdot x - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (log (- x))) (t_1 (log (- y))))
   (if (<= x -3.1e+153)
     (* (- t_0 t_1) x)
     (if (<= x -5e-310)
       (- (* (/ (- (pow t_0 2.0) (pow t_1 2.0)) (log (* x y))) x) z)
       (- (* (- (log x) (log y)) x) z)))))

C

double code(double x, double y, double z) {
	double t_0 = log(-x);
	double t_1 = log(-y);
	double tmp;
	if (x <= -3.1e+153) {
		tmp = (t_0 - t_1) * x;
	} else if (x <= -5e-310) {
		tmp = (((pow(t_0, 2.0) - pow(t_1, 2.0)) / log((x * y))) * x) - z;
	} else {
		tmp = ((log(x) - log(y)) * x) - 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) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = log(-x)
    t_1 = log(-y)
    if (x <= (-3.1d+153)) then
        tmp = (t_0 - t_1) * x
    else if (x <= (-5d-310)) then
        tmp = ((((t_0 ** 2.0d0) - (t_1 ** 2.0d0)) / log((x * y))) * x) - z
    else
        tmp = ((log(x) - log(y)) * x) - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.log(-x);
	double t_1 = Math.log(-y);
	double tmp;
	if (x <= -3.1e+153) {
		tmp = (t_0 - t_1) * x;
	} else if (x <= -5e-310) {
		tmp = (((Math.pow(t_0, 2.0) - Math.pow(t_1, 2.0)) / Math.log((x * y))) * x) - z;
	} else {
		tmp = ((Math.log(x) - Math.log(y)) * x) - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.log(-x)
	t_1 = math.log(-y)
	tmp = 0
	if x <= -3.1e+153:
		tmp = (t_0 - t_1) * x
	elif x <= -5e-310:
		tmp = (((math.pow(t_0, 2.0) - math.pow(t_1, 2.0)) / math.log((x * y))) * x) - z
	else:
		tmp = ((math.log(x) - math.log(y)) * x) - z
	return tmp

Julia

function code(x, y, z)
	t_0 = log(Float64(-x))
	t_1 = log(Float64(-y))
	tmp = 0.0
	if (x <= -3.1e+153)
		tmp = Float64(Float64(t_0 - t_1) * x);
	elseif (x <= -5e-310)
		tmp = Float64(Float64(Float64(Float64((t_0 ^ 2.0) - (t_1 ^ 2.0)) / log(Float64(x * y))) * x) - z);
	else
		tmp = Float64(Float64(Float64(log(x) - log(y)) * x) - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = log(-x);
	t_1 = log(-y);
	tmp = 0.0;
	if (x <= -3.1e+153)
		tmp = (t_0 - t_1) * x;
	elseif (x <= -5e-310)
		tmp = ((((t_0 ^ 2.0) - (t_1 ^ 2.0)) / log((x * y))) * x) - z;
	else
		tmp = ((log(x) - log(y)) * x) - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[Log[(-x)], $MachinePrecision]}, Block[{t$95$1 = N[Log[(-y)], $MachinePrecision]}, If[LessEqual[x, -3.1e+153], N[(N[(t$95$0 - t$95$1), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[x, -5e-310], N[(N[(N[(N[(N[Power[t$95$0, 2.0], $MachinePrecision] - N[Power[t$95$1, 2.0], $MachinePrecision]), $MachinePrecision] / N[Log[N[(x * y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision] - z), $MachinePrecision], N[(N[(N[(N[Log[x], $MachinePrecision] - N[Log[y], $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision] - z), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.1e153

   1. Initial program 71.4%

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

   3. Taylor expanded in x around inf

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

      1. distribute-rgt-in N/A

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

      2. mul-1-neg N/A

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

      3. log-rec N/A

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

      4. remove-double-neg N/A

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

      5. distribute-rgt-in N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. log-rec N/A

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

      10. unsub-neg N/A

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

      11. lower--.f64 N/A

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

      12. lower-log.f64 N/A

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

      13. lower-log.f64 0.0

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

   5. Applied rewrites 0.0%

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

   7. Applied rewrites 98.8%

      \[\leadsto \left(\log \left(-x\right) - \log \left(-y\right)\right) \cdot x \]

   if -3.1e153 < x < -4.999999999999985e-310

   1. Initial program 79.1%

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

      1. lift-log.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. frac-2neg N/A

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

      4. log-div N/A

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

      5. flip-- N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 N/A

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

      8. pow2 N/A

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

      9. lower-pow.f64 N/A

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

      10. lower-log.f64 N/A

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

      11. lower-neg.f64 N/A

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

      12. pow2 N/A

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

      13. lower-pow.f64 N/A

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

      14. lower-log.f64 N/A

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

      15. lower-neg.f64 N/A

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

      16. sum-log N/A

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

      17. lower-log.f64 N/A

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

      18. lower-*.f64 N/A

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

      19. lower-neg.f64 N/A

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

      20. lower-neg.f64 96.5

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

   4. Applied rewrites 96.5%

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

   if -4.999999999999985e-310 < x

   1. Initial program 73.3%

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

      1. lift-log.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. log-div N/A

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

      4. lower--.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower-log.f64 99.6

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

   4. Applied rewrites 99.6%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.1 \cdot 10^{+153}:\\ \;\;\;\;\left(\log \left(-x\right) - \log \left(-y\right)\right) \cdot x\\ \mathbf{elif}\;x \leq -5 \cdot 10^{-310}:\\ \;\;\;\;\frac{{\log \left(-x\right)}^{2} - {\log \left(-y\right)}^{2}}{\log \left(x \cdot y\right)} \cdot x - z\\ \mathbf{else}:\\ \;\;\;\;\left(\log x - \log y\right) \cdot x - z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 87.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \log \left(\frac{x}{y}\right) \cdot x\\ \mathbf{if}\;t\_0 \leq -\infty:\\ \;\;\;\;-z\\ \mathbf{elif}\;t\_0 \leq 10^{+306}:\\ \;\;\;\;\log \left(\frac{\frac{-1}{y}}{\frac{-1}{x}}\right) \cdot x - z\\ \mathbf{else}:\\ \;\;\;\;\left(\log x - \log y\right) \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (log (/ x y)) x)))
   (if (<= t_0 (- INFINITY))
     (- z)
     (if (<= t_0 1e+306)
       (- (* (log (/ (/ -1.0 y) (/ -1.0 x))) x) z)
       (* (- (log x) (log y)) x)))))

C

double code(double x, double y, double z) {
	double t_0 = log((x / y)) * x;
	double tmp;
	if (t_0 <= -((double) INFINITY)) {
		tmp = -z;
	} else if (t_0 <= 1e+306) {
		tmp = (log(((-1.0 / y) / (-1.0 / x))) * x) - z;
	} else {
		tmp = (log(x) - log(y)) * x;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.log((x / y)) * x;
	double tmp;
	if (t_0 <= -Double.POSITIVE_INFINITY) {
		tmp = -z;
	} else if (t_0 <= 1e+306) {
		tmp = (Math.log(((-1.0 / y) / (-1.0 / x))) * x) - z;
	} else {
		tmp = (Math.log(x) - Math.log(y)) * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.log((x / y)) * x
	tmp = 0
	if t_0 <= -math.inf:
		tmp = -z
	elif t_0 <= 1e+306:
		tmp = (math.log(((-1.0 / y) / (-1.0 / x))) * x) - z
	else:
		tmp = (math.log(x) - math.log(y)) * x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(log(Float64(x / y)) * x)
	tmp = 0.0
	if (t_0 <= Float64(-Inf))
		tmp = Float64(-z);
	elseif (t_0 <= 1e+306)
		tmp = Float64(Float64(log(Float64(Float64(-1.0 / y) / Float64(-1.0 / x))) * x) - z);
	else
		tmp = Float64(Float64(log(x) - log(y)) * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = log((x / y)) * x;
	tmp = 0.0;
	if (t_0 <= -Inf)
		tmp = -z;
	elseif (t_0 <= 1e+306)
		tmp = (log(((-1.0 / y) / (-1.0 / x))) * x) - z;
	else
		tmp = (log(x) - log(y)) * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Log[N[(x / y), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[t$95$0, (-Infinity)], (-z), If[LessEqual[t$95$0, 1e+306], N[(N[(N[Log[N[(N[(-1.0 / y), $MachinePrecision] / N[(-1.0 / x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision] - z), $MachinePrecision], N[(N[(N[Log[x], $MachinePrecision] - N[Log[y], $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 11.2%

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

   3. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 41.9

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

   5. Applied rewrites 41.9%

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

   if -inf.0 < (*.f64 x (log.f64 (/.f64 x y))) < 1.00000000000000002e306

   1. Initial program 99.5%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. div-inv N/A

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

      4. associate-/r* N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 99.6

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

   4. Applied rewrites 99.6%

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

   if 1.00000000000000002e306 < (*.f64 x (log.f64 (/.f64 x y)))

   1. Initial program 4.5%

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

   3. Taylor expanded in x around inf

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

      1. distribute-rgt-in N/A

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

      2. mul-1-neg N/A

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

      3. log-rec N/A

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

      4. remove-double-neg N/A

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

      5. distribute-rgt-in N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. log-rec N/A

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

      10. unsub-neg N/A

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

      11. lower--.f64 N/A

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

      12. lower-log.f64 N/A

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

      13. lower-log.f64 52.6

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

   5. Applied rewrites 52.6%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\log \left(\frac{x}{y}\right) \cdot x \leq -\infty:\\ \;\;\;\;-z\\ \mathbf{elif}\;\log \left(\frac{x}{y}\right) \cdot x \leq 10^{+306}:\\ \;\;\;\;\log \left(\frac{\frac{-1}{y}}{\frac{-1}{x}}\right) \cdot x - z\\ \mathbf{else}:\\ \;\;\;\;\left(\log x - \log y\right) \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 87.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \log \left(\frac{x}{y}\right) \cdot x\\ \mathbf{if}\;t\_0 \leq -\infty:\\ \;\;\;\;-z\\ \mathbf{elif}\;t\_0 \leq 10^{+306}:\\ \;\;\;\;\log \left(\frac{\frac{-1}{y}}{\frac{-1}{x}}\right) \cdot x - z\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (log (/ x y)) x)))
   (if (<= t_0 (- INFINITY))
     (- z)
     (if (<= t_0 1e+306) (- (* (log (/ (/ -1.0 y) (/ -1.0 x))) x) z) (- z)))))

C

double code(double x, double y, double z) {
	double t_0 = log((x / y)) * x;
	double tmp;
	if (t_0 <= -((double) INFINITY)) {
		tmp = -z;
	} else if (t_0 <= 1e+306) {
		tmp = (log(((-1.0 / y) / (-1.0 / x))) * x) - z;
	} else {
		tmp = -z;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.log((x / y)) * x;
	double tmp;
	if (t_0 <= -Double.POSITIVE_INFINITY) {
		tmp = -z;
	} else if (t_0 <= 1e+306) {
		tmp = (Math.log(((-1.0 / y) / (-1.0 / x))) * x) - z;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.log((x / y)) * x
	tmp = 0
	if t_0 <= -math.inf:
		tmp = -z
	elif t_0 <= 1e+306:
		tmp = (math.log(((-1.0 / y) / (-1.0 / x))) * x) - z
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(log(Float64(x / y)) * x)
	tmp = 0.0
	if (t_0 <= Float64(-Inf))
		tmp = Float64(-z);
	elseif (t_0 <= 1e+306)
		tmp = Float64(Float64(log(Float64(Float64(-1.0 / y) / Float64(-1.0 / x))) * x) - z);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = log((x / y)) * x;
	tmp = 0.0;
	if (t_0 <= -Inf)
		tmp = -z;
	elseif (t_0 <= 1e+306)
		tmp = (log(((-1.0 / y) / (-1.0 / x))) * x) - z;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Log[N[(x / y), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[t$95$0, (-Infinity)], (-z), If[LessEqual[t$95$0, 1e+306], N[(N[(N[Log[N[(N[(-1.0 / y), $MachinePrecision] / N[(-1.0 / x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision] - z), $MachinePrecision], (-z)]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x (log.f64 (/.f64 x y))) < -inf.0 or 1.00000000000000002e306 < (*.f64 x (log.f64 (/.f64 x y)))

   1. Initial program 7.5%

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

   3. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 40.4

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

   5. Applied rewrites 40.4%

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

   if -inf.0 < (*.f64 x (log.f64 (/.f64 x y))) < 1.00000000000000002e306

   1. Initial program 99.5%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. div-inv N/A

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

      4. associate-/r* N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 99.6

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

   4. Applied rewrites 99.6%

      \[\leadsto x \cdot \log \color{blue}{\left(\frac{\frac{1}{y}}{\frac{1}{x}}\right)} - z \]
3. Recombined 2 regimes into one program.

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\log \left(\frac{x}{y}\right) \cdot x \leq -\infty:\\ \;\;\;\;-z\\ \mathbf{elif}\;\log \left(\frac{x}{y}\right) \cdot x \leq 10^{+306}:\\ \;\;\;\;\log \left(\frac{\frac{-1}{y}}{\frac{-1}{x}}\right) \cdot x - z\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 87.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \log \left(\frac{x}{y}\right) \cdot x\\ \mathbf{if}\;t\_0 \leq -\infty:\\ \;\;\;\;-z\\ \mathbf{elif}\;t\_0 \leq 10^{+306}:\\ \;\;\;\;t\_0 - z\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (log (/ x y)) x)))
   (if (<= t_0 (- INFINITY)) (- z) (if (<= t_0 1e+306) (- t_0 z) (- z)))))

C

double code(double x, double y, double z) {
	double t_0 = log((x / y)) * x;
	double tmp;
	if (t_0 <= -((double) INFINITY)) {
		tmp = -z;
	} else if (t_0 <= 1e+306) {
		tmp = t_0 - z;
	} else {
		tmp = -z;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.log((x / y)) * x;
	double tmp;
	if (t_0 <= -Double.POSITIVE_INFINITY) {
		tmp = -z;
	} else if (t_0 <= 1e+306) {
		tmp = t_0 - z;
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.log((x / y)) * x
	tmp = 0
	if t_0 <= -math.inf:
		tmp = -z
	elif t_0 <= 1e+306:
		tmp = t_0 - z
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(log(Float64(x / y)) * x)
	tmp = 0.0
	if (t_0 <= Float64(-Inf))
		tmp = Float64(-z);
	elseif (t_0 <= 1e+306)
		tmp = Float64(t_0 - z);
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = log((x / y)) * x;
	tmp = 0.0;
	if (t_0 <= -Inf)
		tmp = -z;
	elseif (t_0 <= 1e+306)
		tmp = t_0 - z;
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Log[N[(x / y), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[t$95$0, (-Infinity)], (-z), If[LessEqual[t$95$0, 1e+306], N[(t$95$0 - z), $MachinePrecision], (-z)]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x (log.f64 (/.f64 x y))) < -inf.0 or 1.00000000000000002e306 < (*.f64 x (log.f64 (/.f64 x y)))

   1. Initial program 7.5%

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

   3. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 40.4

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

   5. Applied rewrites 40.4%

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

   if -inf.0 < (*.f64 x (log.f64 (/.f64 x y))) < 1.00000000000000002e306

   1. Initial program 99.5%

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

4. Final simplification 83.8%

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

Alternative 7: 96.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \log \left(-x\right) - \log \left(-y\right)\\ \mathbf{if}\;x \leq -7.2 \cdot 10^{+153}:\\ \;\;\;\;t\_0 \cdot x\\ \mathbf{elif}\;x \leq -5 \cdot 10^{-310}:\\ \;\;\;\;\mathsf{fma}\left(t\_0, \frac{x}{z}, -1\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(\log x - \log y\right) \cdot x - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (log (- x)) (log (- y)))))
   (if (<= x -7.2e+153)
     (* t_0 x)
     (if (<= x -5e-310)
       (* (fma t_0 (/ x z) -1.0) z)
       (- (* (- (log x) (log y)) x) z)))))

C

double code(double x, double y, double z) {
	double t_0 = log(-x) - log(-y);
	double tmp;
	if (x <= -7.2e+153) {
		tmp = t_0 * x;
	} else if (x <= -5e-310) {
		tmp = fma(t_0, (x / z), -1.0) * z;
	} else {
		tmp = ((log(x) - log(y)) * x) - z;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(log(Float64(-x)) - log(Float64(-y)))
	tmp = 0.0
	if (x <= -7.2e+153)
		tmp = Float64(t_0 * x);
	elseif (x <= -5e-310)
		tmp = Float64(fma(t_0, Float64(x / z), -1.0) * z);
	else
		tmp = Float64(Float64(Float64(log(x) - log(y)) * x) - z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Log[(-x)], $MachinePrecision] - N[Log[(-y)], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -7.2e+153], N[(t$95$0 * x), $MachinePrecision], If[LessEqual[x, -5e-310], N[(N[(t$95$0 * N[(x / z), $MachinePrecision] + -1.0), $MachinePrecision] * z), $MachinePrecision], N[(N[(N[(N[Log[x], $MachinePrecision] - N[Log[y], $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision] - z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.2000000000000001e153

   1. Initial program 71.4%

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

   3. Taylor expanded in x around inf

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

      1. distribute-rgt-in N/A

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

      2. mul-1-neg N/A

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

      3. log-rec N/A

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

      4. remove-double-neg N/A

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

      5. distribute-rgt-in N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. log-rec N/A

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

      10. unsub-neg N/A

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

      11. lower--.f64 N/A

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

      12. lower-log.f64 N/A

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

      13. lower-log.f64 0.0

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

   5. Applied rewrites 0.0%

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

   7. Applied rewrites 98.8%

      \[\leadsto \left(\log \left(-x\right) - \log \left(-y\right)\right) \cdot x \]

   if -7.2000000000000001e153 < x < -4.999999999999985e-310

   1. Initial program 79.1%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. div-inv N/A

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

      4. associate-/r* N/A

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

      5. lower-/.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower-/.f64 79.1

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

   4. Applied rewrites 79.1%

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

   5. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. sub-neg N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. metadata-eval N/A

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

      7. lower-fma.f64 N/A

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

      8. lower-log.f64 N/A

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

      9. lower-/.f64 N/A

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

      10. lower-/.f64 73.5

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

   7. Applied rewrites 73.5%

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

   9. Applied rewrites 94.3%

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

   if -4.999999999999985e-310 < x

   1. Initial program 73.3%

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

      1. lift-log.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. log-div N/A

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

      4. lower--.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower-log.f64 99.6

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

   4. Applied rewrites 99.6%

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

4. Final simplification 97.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{+153}:\\ \;\;\;\;\left(\log \left(-x\right) - \log \left(-y\right)\right) \cdot x\\ \mathbf{elif}\;x \leq -5 \cdot 10^{-310}:\\ \;\;\;\;\mathsf{fma}\left(\log \left(-x\right) - \log \left(-y\right), \frac{x}{z}, -1\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;\left(\log x - \log y\right) \cdot x - z\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 93.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{+157}:\\ \;\;\;\;\left(\log \left(-x\right) - \log \left(-y\right)\right) \cdot x\\ \mathbf{elif}\;x \leq -6.2 \cdot 10^{-105}:\\ \;\;\;\;\log \left(\frac{y}{x}\right) \cdot \left(-x\right) - z\\ \mathbf{elif}\;x \leq -4 \cdot 10^{-308}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;\left(\log x - \log y\right) \cdot x - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -3.6e+157)
   (* (- (log (- x)) (log (- y))) x)
   (if (<= x -6.2e-105)
     (- (* (log (/ y x)) (- x)) z)
     (if (<= x -4e-308) (- z) (- (* (- (log x) (log y)) x) z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.6e+157) {
		tmp = (log(-x) - log(-y)) * x;
	} else if (x <= -6.2e-105) {
		tmp = (log((y / x)) * -x) - z;
	} else if (x <= -4e-308) {
		tmp = -z;
	} else {
		tmp = ((log(x) - log(y)) * x) - 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 <= (-3.6d+157)) then
        tmp = (log(-x) - log(-y)) * x
    else if (x <= (-6.2d-105)) then
        tmp = (log((y / x)) * -x) - z
    else if (x <= (-4d-308)) then
        tmp = -z
    else
        tmp = ((log(x) - log(y)) * x) - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.6e+157) {
		tmp = (Math.log(-x) - Math.log(-y)) * x;
	} else if (x <= -6.2e-105) {
		tmp = (Math.log((y / x)) * -x) - z;
	} else if (x <= -4e-308) {
		tmp = -z;
	} else {
		tmp = ((Math.log(x) - Math.log(y)) * x) - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -3.6e+157:
		tmp = (math.log(-x) - math.log(-y)) * x
	elif x <= -6.2e-105:
		tmp = (math.log((y / x)) * -x) - z
	elif x <= -4e-308:
		tmp = -z
	else:
		tmp = ((math.log(x) - math.log(y)) * x) - z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -3.6e+157)
		tmp = Float64(Float64(log(Float64(-x)) - log(Float64(-y))) * x);
	elseif (x <= -6.2e-105)
		tmp = Float64(Float64(log(Float64(y / x)) * Float64(-x)) - z);
	elseif (x <= -4e-308)
		tmp = Float64(-z);
	else
		tmp = Float64(Float64(Float64(log(x) - log(y)) * x) - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -3.6e+157)
		tmp = (log(-x) - log(-y)) * x;
	elseif (x <= -6.2e-105)
		tmp = (log((y / x)) * -x) - z;
	elseif (x <= -4e-308)
		tmp = -z;
	else
		tmp = ((log(x) - log(y)) * x) - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -3.6e+157], N[(N[(N[Log[(-x)], $MachinePrecision] - N[Log[(-y)], $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision], If[LessEqual[x, -6.2e-105], N[(N[(N[Log[N[(y / x), $MachinePrecision]], $MachinePrecision] * (-x)), $MachinePrecision] - z), $MachinePrecision], If[LessEqual[x, -4e-308], (-z), N[(N[(N[(N[Log[x], $MachinePrecision] - N[Log[y], $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision] - z), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -3.60000000000000024e157

   1. Initial program 70.6%

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

   3. Taylor expanded in x around inf

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

      1. distribute-rgt-in N/A

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

      2. mul-1-neg N/A

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

      3. log-rec N/A

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

      4. remove-double-neg N/A

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

      5. distribute-rgt-in N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. log-rec N/A

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

      10. unsub-neg N/A

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

      11. lower--.f64 N/A

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

      12. lower-log.f64 N/A

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

      13. lower-log.f64 0.0

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

   5. Applied rewrites 0.0%

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

   7. Applied rewrites 98.8%

      \[\leadsto \left(\log \left(-x\right) - \log \left(-y\right)\right) \cdot x \]

   if -3.60000000000000024e157 < x < -6.20000000000000029e-105

   1. Initial program 94.1%

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

      1. lift-log.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. clear-num N/A

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

      4. log-rec N/A

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

      5. lower-neg.f64 N/A

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

      6. lower-log.f64 N/A

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

      7. lower-/.f64 95.3

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

   4. Applied rewrites 95.3%

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

   if -6.20000000000000029e-105 < x < -4.00000000000000013e-308

   1. Initial program 60.9%

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

   3. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 81.8

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

   5. Applied rewrites 81.8%

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

   if -4.00000000000000013e-308 < x

   1. Initial program 73.3%

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

      1. lift-log.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. log-div N/A

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

      4. lower--.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower-log.f64 99.6

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

   4. Applied rewrites 99.6%

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

4. Final simplification 95.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{+157}:\\ \;\;\;\;\left(\log \left(-x\right) - \log \left(-y\right)\right) \cdot x\\ \mathbf{elif}\;x \leq -6.2 \cdot 10^{-105}:\\ \;\;\;\;\log \left(\frac{y}{x}\right) \cdot \left(-x\right) - z\\ \mathbf{elif}\;x \leq -4 \cdot 10^{-308}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;\left(\log x - \log y\right) \cdot x - z\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 90.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{-105}:\\ \;\;\;\;\log \left(\frac{y}{x}\right) \cdot \left(-x\right) - z\\ \mathbf{elif}\;x \leq -4 \cdot 10^{-308}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;\left(\log x - \log y\right) \cdot x - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -6.2e-105)
   (- (* (log (/ y x)) (- x)) z)
   (if (<= x -4e-308) (- z) (- (* (- (log x) (log y)) x) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -6.2e-105) {
		tmp = (log((y / x)) * -x) - z;
	} else if (x <= -4e-308) {
		tmp = -z;
	} else {
		tmp = ((log(x) - log(y)) * x) - 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 <= (-6.2d-105)) then
        tmp = (log((y / x)) * -x) - z
    else if (x <= (-4d-308)) then
        tmp = -z
    else
        tmp = ((log(x) - log(y)) * x) - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -6.2e-105) {
		tmp = (Math.log((y / x)) * -x) - z;
	} else if (x <= -4e-308) {
		tmp = -z;
	} else {
		tmp = ((Math.log(x) - Math.log(y)) * x) - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -6.2e-105:
		tmp = (math.log((y / x)) * -x) - z
	elif x <= -4e-308:
		tmp = -z
	else:
		tmp = ((math.log(x) - math.log(y)) * x) - z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -6.2e-105)
		tmp = Float64(Float64(log(Float64(y / x)) * Float64(-x)) - z);
	elseif (x <= -4e-308)
		tmp = Float64(-z);
	else
		tmp = Float64(Float64(Float64(log(x) - log(y)) * x) - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -6.2e-105)
		tmp = (log((y / x)) * -x) - z;
	elseif (x <= -4e-308)
		tmp = -z;
	else
		tmp = ((log(x) - log(y)) * x) - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -6.2e-105], N[(N[(N[Log[N[(y / x), $MachinePrecision]], $MachinePrecision] * (-x)), $MachinePrecision] - z), $MachinePrecision], If[LessEqual[x, -4e-308], (-z), N[(N[(N[(N[Log[x], $MachinePrecision] - N[Log[y], $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision] - z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.20000000000000029e-105

   1. Initial program 84.6%

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

      1. lift-log.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. clear-num N/A

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

      4. log-rec N/A

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

      5. lower-neg.f64 N/A

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

      6. lower-log.f64 N/A

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

      7. lower-/.f64 85.3

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

   4. Applied rewrites 85.3%

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

   if -6.20000000000000029e-105 < x < -4.00000000000000013e-308

   1. Initial program 60.9%

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

   3. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 81.8

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

   5. Applied rewrites 81.8%

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

   if -4.00000000000000013e-308 < x

   1. Initial program 73.3%

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

      1. lift-log.f64 N/A

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

      2. lift-/.f64 N/A

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

      3. log-div N/A

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

      4. lower--.f64 N/A

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

      5. lower-log.f64 N/A

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

      6. lower-log.f64 99.6

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

   4. Applied rewrites 99.6%

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

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{-105}:\\ \;\;\;\;\log \left(\frac{y}{x}\right) \cdot \left(-x\right) - z\\ \mathbf{elif}\;x \leq -4 \cdot 10^{-308}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;\left(\log x - \log y\right) \cdot x - z\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 66.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \log \left(\frac{y}{x}\right) \cdot \left(-x\right)\\ \mathbf{if}\;x \leq -1.12 \cdot 10^{-27}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{+18}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (log (/ y x)) (- x))))
   (if (<= x -1.12e-27) t_0 (if (<= x 4.4e+18) (- z) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = log((y / x)) * -x;
	double tmp;
	if (x <= -1.12e-27) {
		tmp = t_0;
	} else if (x <= 4.4e+18) {
		tmp = -z;
	} else {
		tmp = t_0;
	}
	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) :: t_0
    real(8) :: tmp
    t_0 = log((y / x)) * -x
    if (x <= (-1.12d-27)) then
        tmp = t_0
    else if (x <= 4.4d+18) then
        tmp = -z
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.log((y / x)) * -x;
	double tmp;
	if (x <= -1.12e-27) {
		tmp = t_0;
	} else if (x <= 4.4e+18) {
		tmp = -z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.log((y / x)) * -x
	tmp = 0
	if x <= -1.12e-27:
		tmp = t_0
	elif x <= 4.4e+18:
		tmp = -z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(log(Float64(y / x)) * Float64(-x))
	tmp = 0.0
	if (x <= -1.12e-27)
		tmp = t_0;
	elseif (x <= 4.4e+18)
		tmp = Float64(-z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = log((y / x)) * -x;
	tmp = 0.0;
	if (x <= -1.12e-27)
		tmp = t_0;
	elseif (x <= 4.4e+18)
		tmp = -z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Log[N[(y / x), $MachinePrecision]], $MachinePrecision] * (-x)), $MachinePrecision]}, If[LessEqual[x, -1.12e-27], t$95$0, If[LessEqual[x, 4.4e+18], (-z), t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.1199999999999999e-27 or 4.4e18 < x

   1. Initial program 76.0%

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

   3. Taylor expanded in x around inf

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

      1. distribute-rgt-in N/A

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

      2. mul-1-neg N/A

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

      3. log-rec N/A

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

      4. remove-double-neg N/A

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

      5. distribute-rgt-in N/A

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

      6. +-commutative N/A

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

      7. *-commutative N/A

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

      8. lower-*.f64 N/A

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

      9. log-rec N/A

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

      10. unsub-neg N/A

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

      11. lower--.f64 N/A

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

      12. lower-log.f64 N/A

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

      13. lower-log.f64 41.9

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

   5. Applied rewrites 41.9%

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

   7. Applied rewrites 61.5%

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

   if -1.1199999999999999e-27 < x < 4.4e18

   1. Initial program 74.0%

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

   3. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 80.5

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

   5. Applied rewrites 80.5%

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

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.12 \cdot 10^{-27}:\\ \;\;\;\;\log \left(\frac{y}{x}\right) \cdot \left(-x\right)\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{+18}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;\log \left(\frac{y}{x}\right) \cdot \left(-x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 65.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \log \left(\frac{x}{y}\right) \cdot x\\ \mathbf{if}\;x \leq -1.12 \cdot 10^{-27}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{+18}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (log (/ x y)) x)))
   (if (<= x -1.12e-27) t_0 (if (<= x 4.4e+18) (- z) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = log((x / y)) * x;
	double tmp;
	if (x <= -1.12e-27) {
		tmp = t_0;
	} else if (x <= 4.4e+18) {
		tmp = -z;
	} else {
		tmp = t_0;
	}
	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) :: t_0
    real(8) :: tmp
    t_0 = log((x / y)) * x
    if (x <= (-1.12d-27)) then
        tmp = t_0
    else if (x <= 4.4d+18) then
        tmp = -z
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = Math.log((x / y)) * x;
	double tmp;
	if (x <= -1.12e-27) {
		tmp = t_0;
	} else if (x <= 4.4e+18) {
		tmp = -z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = math.log((x / y)) * x
	tmp = 0
	if x <= -1.12e-27:
		tmp = t_0
	elif x <= 4.4e+18:
		tmp = -z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(log(Float64(x / y)) * x)
	tmp = 0.0
	if (x <= -1.12e-27)
		tmp = t_0;
	elseif (x <= 4.4e+18)
		tmp = Float64(-z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = log((x / y)) * x;
	tmp = 0.0;
	if (x <= -1.12e-27)
		tmp = t_0;
	elseif (x <= 4.4e+18)
		tmp = -z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[Log[N[(x / y), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision]}, If[LessEqual[x, -1.12e-27], t$95$0, If[LessEqual[x, 4.4e+18], (-z), t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.1199999999999999e-27 or 4.4e18 < x

   1. Initial program 76.0%

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

   3. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-log.f64 N/A

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

      4. lower-/.f64 59.9

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

   5. Applied rewrites 59.9%

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

   if -1.1199999999999999e-27 < x < 4.4e18

   1. Initial program 74.0%

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

   3. Taylor expanded in z around inf

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

      1. mul-1-neg N/A

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

      2. lower-neg.f64 80.5

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

   5. Applied rewrites 80.5%

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

Alternative 12: 49.8% accurate, 40.0× 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 Float64(-z)
end

MATLAB

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

Wolfram

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

Derivation

1. Initial program 75.1%

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

3. Taylor expanded in z around inf

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

   1. mul-1-neg N/A

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

   2. lower-neg.f64 46.4

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

5. Applied rewrites 46.4%

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

Alternative 13: 2.2% accurate, 120.0× 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 75.1%

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

3. Taylor expanded in z around inf

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

   1. mul-1-neg N/A

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

   2. lower-neg.f64 46.4

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

5. Applied rewrites 46.4%

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

7. Applied rewrites 25.2%

   \[\leadsto \frac{\left(-z\right) \cdot z}{\color{blue}{0 + z}} \]
8. Step-by-step derivation

9. Applied rewrites 2.3%

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

Developer Target 1: 88.5% accurate, 0.6× 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 2024235 
(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))