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

Percentage Accurate: 77.7% → 99.5%

Time: 11.5s

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: 77.7% 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, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-311}:\\ \;\;\;\;x \cdot \left(\left(\log \left(-x\right) - \log \left(-\sqrt[3]{y}\right)\right) - \log \left({\left(\sqrt[3]{y}\right)}^{2}\right)\right) - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x - \log y\right) - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -5e-311)
   (- (* x (- (- (log (- x)) (log (- (cbrt y)))) (log (pow (cbrt y) 2.0)))) z)
   (- (* x (- (log x) (log y))) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -5e-311) {
		tmp = (x * ((log(-x) - log(-cbrt(y))) - log(pow(cbrt(y), 2.0)))) - z;
	} else {
		tmp = (x * (log(x) - log(y))) - z;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -5e-311) {
		tmp = (x * ((Math.log(-x) - Math.log(-Math.cbrt(y))) - Math.log(Math.pow(Math.cbrt(y), 2.0)))) - z;
	} else {
		tmp = (x * (Math.log(x) - Math.log(y))) - z;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -5e-311)
		tmp = Float64(Float64(x * Float64(Float64(log(Float64(-x)) - log(Float64(-cbrt(y)))) - log((cbrt(y) ^ 2.0)))) - z);
	else
		tmp = Float64(Float64(x * Float64(log(x) - log(y))) - z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -5e-311], N[(N[(x * N[(N[(N[Log[(-x)], $MachinePrecision] - N[Log[(-N[Power[y, 1/3], $MachinePrecision])], $MachinePrecision]), $MachinePrecision] - N[Log[N[Power[N[Power[y, 1/3], $MachinePrecision], 2.0], $MachinePrecision]], $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 < -5.00000000000023e-311

   1. Initial program 73.6%

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

      1. *-un-lft-identity 73.6%

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

      2. add-cube-cbrt 73.6%

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

      3. times-frac 73.6%

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

      4. log-prod 94.4%

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

      5. pow2 94.4%

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

   4. Applied egg-rr 94.4%

      \[\leadsto x \cdot \color{blue}{\left(\log \left(\frac{1}{{\left(\sqrt[3]{y}\right)}^{2}}\right) + \log \left(\frac{x}{\sqrt[3]{y}}\right)\right)} - z \]
   5. Step-by-step derivation

      1. +-commutative 94.4%

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

      2. log-rec 94.4%

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

      3. unsub-neg 94.4%

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

   6. Simplified 94.4%

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

      1. frac-2neg 94.4%

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

      2. log-div 99.6%

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

   8. Applied egg-rr 99.6%

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

   if -5.00000000000023e-311 < y

   1. Initial program 76.5%

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

   3. Taylor expanded in x around 0 99.5%

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

      1. log-rec 99.5%

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

      2. sub-neg 99.5%

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

   5. Simplified 99.5%

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

Alternative 2: 89.5% accurate, 0.3× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * log((x / y));
	t_1 = log((y * x));
	tmp = 0.0;
	if (t_0 <= -Inf)
		tmp = (x * abs(t_1)) - z;
	elseif (t_0 <= 5e+307)
		tmp = t_0 - z;
	else
		tmp = abs((x * t_1)) - 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]}, Block[{t$95$1 = N[Log[N[(y * x), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[t$95$0, (-Infinity)], N[(N[(x * N[Abs[t$95$1], $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision], If[LessEqual[t$95$0, 5e+307], N[(t$95$0 - z), $MachinePrecision], N[(N[Abs[N[(x * t$95$1), $MachinePrecision]], $MachinePrecision] - z), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 4.2%

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

      1. add-cbrt-cube 4.2%

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

      2. pow3 4.2%

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

   4. Applied egg-rr 4.2%

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

      1. rem-cbrt-cube 4.2%

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

      2. add-sqr-sqrt 3.3%

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

      3. sqrt-unprod 4.5%

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

      4. pow2 4.5%

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

      5. log-div 42.1%

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

      6. sub-neg 42.1%

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

      7. add-log-exp 42.1%

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

      8. sum-log 1.2%

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

      9. add-sqr-sqrt 0.0%

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

      10. sqrt-unprod 42.2%

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

      11. sqr-neg 42.2%

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

      12. sqrt-unprod 42.2%

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

      13. add-sqr-sqrt 42.2%

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

      14. add-exp-log 58.1%

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

   6. Applied egg-rr 58.1%

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

      1. unpow2 58.1%

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

      2. rem-sqrt-square 58.1%

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

   8. Simplified 58.1%

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

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

   1. Initial program 99.8%

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

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

   1. Initial program 3.8%

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

      1. add-cbrt-cube 3.8%

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

      2. pow3 3.8%

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

   4. Applied egg-rr 3.8%

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

      1. rem-square-sqrt 3.8%

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

      2. sqrt-unprod 3.8%

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

      3. pow2 3.8%

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

      4. rem-cbrt-cube 3.8%

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

      5. log-div 14.7%

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

      6. sub-neg 14.7%

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

      7. add-log-exp 14.7%

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

      8. sum-log 2.6%

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

      9. add-sqr-sqrt 2.6%

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

      10. sqrt-unprod 2.6%

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

      11. sqr-neg 2.6%

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

      12. sqrt-unprod 0.0%

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

      13. add-sqr-sqrt 7.3%

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

      14. add-exp-log 49.8%

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

   6. Applied egg-rr 49.8%

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

      1. unpow2 49.8%

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

      2. rem-sqrt-square 56.1%

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

   8. Simplified 56.1%

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

4. Final simplification 88.8%

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

Alternative 3: 89.1% accurate, 0.3× speedup

Math

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

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) (- (fabs t_1) z)))))

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 = fabs(t_1) - z;
	}
	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 = Math.abs(t_1) - z;
	}
	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 = math.fabs(t_1) - z
	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(abs(t_1) - z);
	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 = abs(t_1) - 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]}, 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[(N[Abs[t$95$1], $MachinePrecision] - z), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 4.2%

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

      1. *-un-lft-identity 4.2%

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

      2. add-cube-cbrt 4.2%

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

      3. times-frac 4.2%

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

      4. log-prod 80.4%

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

      5. pow2 80.4%

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

   4. Applied egg-rr 80.4%

      \[\leadsto x \cdot \color{blue}{\left(\log \left(\frac{1}{{\left(\sqrt[3]{y}\right)}^{2}}\right) + \log \left(\frac{x}{\sqrt[3]{y}}\right)\right)} - z \]
   5. Step-by-step derivation

      1. +-commutative 80.4%

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

      2. log-rec 80.4%

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

      3. unsub-neg 80.4%

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

   6. Simplified 80.4%

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

      1. diff-log 4.2%

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

      2. associate-/l/ 4.2%

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

      3. unpow2 4.2%

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

      4. add-cube-cbrt 4.2%

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

      5. diff-log 50.0%

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

      6. sub-neg 50.0%

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

      7. distribute-rgt-in 50.0%

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

   8. Applied egg-rr 50.0%

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

      1. distribute-rgt-out 50.0%

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

      2. sub-neg 50.0%

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

      3. log-div 4.2%

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

      4. *-commutative 4.2%

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

      5. log-div 50.0%

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

      6. sub-neg 50.0%

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

      7. add-log-exp 50.0%

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

      8. sum-log 0.9%

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

      9. add-sqr-sqrt 0.0%

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

      10. sqrt-unprod 42.2%

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

      11. sqr-neg 42.2%

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

      12. sqrt-unprod 42.2%

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

      13. add-sqr-sqrt 42.2%

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

      14. add-exp-log 56.2%

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

   10. Applied egg-rr 56.2%

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

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

   1. Initial program 99.8%

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

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

   1. Initial program 3.8%

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

      1. add-cbrt-cube 3.8%

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

      2. pow3 3.8%

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

   4. Applied egg-rr 3.8%

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

      1. rem-square-sqrt 3.8%

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

      2. sqrt-unprod 3.8%

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

      3. pow2 3.8%

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

      4. rem-cbrt-cube 3.8%

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

      5. log-div 14.7%

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

      6. sub-neg 14.7%

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

      7. add-log-exp 14.7%

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

      8. sum-log 2.6%

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

      9. add-sqr-sqrt 2.6%

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

      10. sqrt-unprod 2.6%

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

      11. sqr-neg 2.6%

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

      12. sqrt-unprod 0.0%

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

      13. add-sqr-sqrt 7.3%

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

      14. add-exp-log 49.8%

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

   6. Applied egg-rr 49.8%

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

      1. unpow2 49.8%

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

      2. rem-sqrt-square 56.1%

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

   8. Simplified 56.1%

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

4. Final simplification 88.5%

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

Alternative 4: 88.6% accurate, 0.3× speedup

Math

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

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 4.0%

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

      1. *-un-lft-identity 4.0%

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

      2. add-cube-cbrt 4.0%

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

      3. times-frac 4.0%

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

      4. log-prod 78.4%

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

      5. pow2 78.4%

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

   4. Applied egg-rr 78.4%

      \[\leadsto x \cdot \color{blue}{\left(\log \left(\frac{1}{{\left(\sqrt[3]{y}\right)}^{2}}\right) + \log \left(\frac{x}{\sqrt[3]{y}}\right)\right)} - z \]
   5. Step-by-step derivation

      1. +-commutative 78.4%

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

      2. log-rec 78.4%

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

      3. unsub-neg 78.4%

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

   6. Simplified 78.4%

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

      1. diff-log 4.0%

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

      2. associate-/l/ 4.0%

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

      3. unpow2 4.0%

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

      4. add-cube-cbrt 4.0%

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

      5. diff-log 48.4%

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

      6. sub-neg 48.4%

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

      7. distribute-rgt-in 48.5%

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

   8. Applied egg-rr 48.5%

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

      1. distribute-rgt-out 48.4%

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

      2. sub-neg 48.4%

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

      3. log-div 4.0%

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

      4. *-commutative 4.0%

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

      5. log-div 48.4%

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

      6. sub-neg 48.4%

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

      7. add-log-exp 48.4%

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

      8. sum-log 1.7%

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

      9. add-sqr-sqrt 1.2%

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

      10. sqrt-unprod 23.0%

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

      11. sqr-neg 23.0%

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

      12. sqrt-unprod 21.7%

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

      13. add-sqr-sqrt 25.9%

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

      14. add-exp-log 53.1%

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

   10. Applied egg-rr 53.1%

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

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

   1. Initial program 99.8%

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

4. Final simplification 87.7%

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

Alternative 5: 87.6% accurate, 0.3× speedup

Math

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

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 4.0%

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

   3. Taylor expanded in x around 0 50.3%

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

      1. neg-mul-1 50.3%

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

   5. Simplified 50.3%

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

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

   1. Initial program 99.8%

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

4. Final simplification 87.0%

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

Alternative 6: 93.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{+137}:\\ \;\;\;\;x \cdot \left(\log \left(-x\right) - \log \left(-y\right)\right)\\ \mathbf{elif}\;x \leq -1.12 \cdot 10^{-154}:\\ \;\;\;\;x \cdot \log \left(\frac{x}{y}\right) - z\\ \mathbf{elif}\;x \leq -1 \cdot 10^{-308}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x - \log y\right) - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -3.4e+137)
   (* x (- (log (- x)) (log (- y))))
   (if (<= x -1.12e-154)
     (- (* 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 <= -3.4e+137) {
		tmp = x * (log(-x) - log(-y));
	} else if (x <= -1.12e-154) {
		tmp = (x * log((x / y))) - z;
	} else if (x <= -1e-308) {
		tmp = -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 (x <= (-3.4d+137)) then
        tmp = x * (log(-x) - log(-y))
    else if (x <= (-1.12d-154)) then
        tmp = (x * log((x / y))) - z
    else if (x <= (-1d-308)) then
        tmp = -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 (x <= -3.4e+137) {
		tmp = x * (Math.log(-x) - Math.log(-y));
	} else if (x <= -1.12e-154) {
		tmp = (x * Math.log((x / y))) - z;
	} else if (x <= -1e-308) {
		tmp = -z;
	} else {
		tmp = (x * (Math.log(x) - Math.log(y))) - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -3.4e+137:
		tmp = x * (math.log(-x) - math.log(-y))
	elif x <= -1.12e-154:
		tmp = (x * math.log((x / y))) - z
	elif x <= -1e-308:
		tmp = -z
	else:
		tmp = (x * (math.log(x) - math.log(y))) - z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -3.4e+137)
		tmp = Float64(x * Float64(log(Float64(-x)) - log(Float64(-y))));
	elseif (x <= -1.12e-154)
		tmp = Float64(Float64(x * log(Float64(x / y))) - z);
	elseif (x <= -1e-308)
		tmp = Float64(-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 (x <= -3.4e+137)
		tmp = x * (log(-x) - log(-y));
	elseif (x <= -1.12e-154)
		tmp = (x * log((x / y))) - z;
	elseif (x <= -1e-308)
		tmp = -z;
	else
		tmp = (x * (log(x) - log(y))) - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -3.4e+137], N[(x * N[(N[Log[(-x)], $MachinePrecision] - N[Log[(-y)], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.12e-154], N[(N[(x * N[Log[N[(x / y), $MachinePrecision]], $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 4 regimes

2. if x < -3.39999999999999986e137

   1. Initial program 61.0%

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

   3. Taylor expanded in z around 0 52.7%

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

   4. Taylor expanded in y around -inf 88.2%

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

      1. metadata-eval 99.3%

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

      2. distribute-neg-frac 99.3%

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

      3. distribute-frac-neg2 99.3%

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

      4. neg-mul-1 99.3%

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

      5. log-rec 99.3%

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

      6. sub-neg 99.3%

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

   6. Simplified 88.2%

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

   if -3.39999999999999986e137 < x < -1.12e-154

   1. Initial program 89.6%

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

   if -1.12e-154 < x < -9.9999999999999991e-309

   1. Initial program 57.6%

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

   3. Taylor expanded in x around 0 93.7%

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

      1. neg-mul-1 93.7%

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

   5. Simplified 93.7%

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

   if -9.9999999999999991e-309 < x

   1. Initial program 76.5%

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

   3. Taylor expanded in x around 0 99.5%

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

      1. log-rec 99.5%

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

      2. sub-neg 99.5%

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

   5. Simplified 99.5%

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

Alternative 7: 99.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-311}:\\ \;\;\;\;x \cdot \left(\log \left(-x\right) - \log \left(-y\right)\right) - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x - \log y\right) - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -5e-311)
   (- (* x (- (log (- x)) (log (- y)))) z)
   (- (* x (- (log x) (log y))) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -5e-311) {
		tmp = (x * (log(-x) - log(-y))) - z;
	} else {
		tmp = (x * (log(x) - log(y))) - z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-5d-311)) then
        tmp = (x * (log(-x) - log(-y))) - z
    else
        tmp = (x * (log(x) - log(y))) - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -5e-311) {
		tmp = (x * (Math.log(-x) - Math.log(-y))) - z;
	} else {
		tmp = (x * (Math.log(x) - Math.log(y))) - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -5e-311:
		tmp = (x * (math.log(-x) - math.log(-y))) - z
	else:
		tmp = (x * (math.log(x) - math.log(y))) - z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -5e-311)
		tmp = Float64(Float64(x * Float64(log(Float64(-x)) - log(Float64(-y)))) - z);
	else
		tmp = Float64(Float64(x * Float64(log(x) - log(y))) - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -5e-311)
		tmp = (x * (log(-x) - log(-y))) - z;
	else
		tmp = (x * (log(x) - log(y))) - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -5e-311], 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 < -5.00000000000023e-311

   1. Initial program 73.6%

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

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

      5. log-rec 99.6%

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

      6. sub-neg 99.6%

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

   5. Simplified 99.6%

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

   if -5.00000000000023e-311 < y

   1. Initial program 76.5%

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

   3. Taylor expanded in x around 0 99.5%

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

      1. log-rec 99.5%

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

      2. sub-neg 99.5%

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

   5. Simplified 99.5%

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

Alternative 8: 65.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{+33} \lor \neg \left(x \leq 7.5\right):\\ \;\;\;\;x \cdot \left(-\log \left(\frac{y}{x}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.4e+33) (not (<= x 7.5))) (* x (- (log (/ y x)))) (- z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.4e+33) || !(x <= 7.5)) {
		tmp = x * -log((y / x));
	} else {
		tmp = -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-2.4d+33)) .or. (.not. (x <= 7.5d0))) then
        tmp = x * -log((y / x))
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.4e+33) || !(x <= 7.5)) {
		tmp = x * -Math.log((y / x));
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.4e+33) or not (x <= 7.5):
		tmp = x * -math.log((y / x))
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.4e+33) || !(x <= 7.5))
		tmp = Float64(x * Float64(-log(Float64(y / x))));
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -2.4e+33) || ~((x <= 7.5)))
		tmp = x * -log((y / x));
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.4e+33], N[Not[LessEqual[x, 7.5]], $MachinePrecision]], N[(x * (-N[Log[N[(y / x), $MachinePrecision]], $MachinePrecision])), $MachinePrecision], (-z)]

Derivation

1. Split input into 2 regimes

2. if x < -2.4e33 or 7.5 < x

   1. Initial program 76.1%

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

      1. clear-num 76.1%

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

      2. neg-log 77.2%

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

   4. Applied egg-rr 77.2%

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

   5. Taylor expanded in z around 0 60.5%

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

      1. associate-*r* 60.5%

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

      2. neg-mul-1 60.5%

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

   7. Simplified 60.5%

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

   if -2.4e33 < x < 7.5

   1. Initial program 74.0%

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

   3. Taylor expanded in x around 0 75.3%

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

      1. neg-mul-1 75.3%

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

   5. Simplified 75.3%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{+33} \lor \neg \left(x \leq 7.5\right):\\ \;\;\;\;x \cdot \left(-\log \left(\frac{y}{x}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 64.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{+27} \lor \neg \left(x \leq 370000\right):\\ \;\;\;\;x \cdot \log \left(\frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.8e+27) (not (<= x 370000.0))) (* x (log (/ x y))) (- z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.8e+27) || !(x <= 370000.0)) {
		tmp = x * log((x / y));
	} else {
		tmp = -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-2.8d+27)) .or. (.not. (x <= 370000.0d0))) then
        tmp = x * log((x / y))
    else
        tmp = -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.8e+27) || !(x <= 370000.0)) {
		tmp = x * Math.log((x / y));
	} else {
		tmp = -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.8e+27) or not (x <= 370000.0):
		tmp = x * math.log((x / y))
	else:
		tmp = -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.8e+27) || !(x <= 370000.0))
		tmp = Float64(x * log(Float64(x / y)));
	else
		tmp = Float64(-z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -2.8e+27) || ~((x <= 370000.0)))
		tmp = x * log((x / y));
	else
		tmp = -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.8e+27], N[Not[LessEqual[x, 370000.0]], $MachinePrecision]], N[(x * N[Log[N[(x / y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], (-z)]

Derivation

1. Split input into 2 regimes

2. if x < -2.7999999999999999e27 or 3.7e5 < x

   1. Initial program 76.1%

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

   3. Taylor expanded in z around 0 59.5%

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

   if -2.7999999999999999e27 < x < 3.7e5

   1. Initial program 74.0%

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

   3. Taylor expanded in x around 0 75.3%

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

      1. neg-mul-1 75.3%

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

   5. Simplified 75.3%

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

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{+27} \lor \neg \left(x \leq 370000\right):\\ \;\;\;\;x \cdot \log \left(\frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;-z\\ \end{array} \]
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 75.1%

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

3. Taylor expanded in x around 0 49.0%

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

   1. neg-mul-1 49.0%

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

5. Simplified 49.0%

   \[\leadsto \color{blue}{-z} \]
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 75.1%

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

3. Taylor expanded in x around 0 49.0%

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

   1. neg-mul-1 49.0%

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

5. Simplified 49.0%

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

   1. neg-sub0 49.0%

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

   2. sub-neg 49.0%

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

   3. add-sqr-sqrt 27.6%

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

   4. sqrt-unprod 17.3%

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

   5. sqr-neg 17.3%

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

   6. sqrt-unprod 1.0%

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

   7. add-sqr-sqrt 2.2%

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

7. Applied egg-rr 2.2%

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

   1. +-lft-identity 2.2%

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

9. Simplified 2.2%

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

Developer Target 1: 89.0% 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 2024180 
(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))