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

Percentage Accurate: 77.1% → 99.7%

Time: 11.0s

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: 77.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \log \left(\frac{\sqrt[3]{x}}{\sqrt[3]{y}}\right) \cdot \left(x \cdot 3\right) - z \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (- (* (log (/ (cbrt x) (cbrt y))) (* x 3.0)) z))

C

double code(double x, double y, double z) {
	return (log((cbrt(x) / cbrt(y))) * (x * 3.0)) - z;
}

Java

public static double code(double x, double y, double z) {
	return (Math.log((Math.cbrt(x) / Math.cbrt(y))) * (x * 3.0)) - z;
}

Julia

function code(x, y, z)
	return Float64(Float64(log(Float64(cbrt(x) / cbrt(y))) * Float64(x * 3.0)) - z)
end

Wolfram

code[x_, y_, z_] := N[(N[(N[Log[N[(N[Power[x, 1/3], $MachinePrecision] / N[Power[y, 1/3], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(x * 3.0), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]

Derivation

1. Initial program 71.6%

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

   1. add-cube-cbrt 71.6%

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

   2. log-prod 71.5%

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

   3. pow2 71.5%

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

4. Applied egg-rr 71.5%

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

   1. log-pow 71.5%

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

   2. distribute-lft1-in 71.5%

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

   3. metadata-eval 71.5%

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

6. Simplified 71.5%

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

   1. add0 71.5%

      \[\leadsto \color{blue}{\left(x \cdot \left(3 \cdot \log \left(\sqrt[3]{\frac{x}{y}}\right)\right) + 0\right)} - z \]

   2. associate-*r* 71.5%

      \[\leadsto \left(\color{blue}{\left(x \cdot 3\right) \cdot \log \left(\sqrt[3]{\frac{x}{y}}\right)} + 0\right) - z \]

   3. fma-define 71.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x \cdot 3, \log \left(\sqrt[3]{\frac{x}{y}}\right), 0\right)} - z \]

8. Applied egg-rr 71.5%

   \[\leadsto \color{blue}{\mathsf{fma}\left(x \cdot 3, \log \left(\sqrt[3]{\frac{x}{y}}\right), 0\right)} - z \]
9. Step-by-step derivation

   1. fma-undefine 71.5%

      \[\leadsto \color{blue}{\left(\left(x \cdot 3\right) \cdot \log \left(\sqrt[3]{\frac{x}{y}}\right) + 0\right)} - z \]

   2. add0 71.5%

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

   3. *-commutative 71.5%

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

10. Simplified 71.5%

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

    1. cbrt-div 99.7%

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

    2. div-inv 99.7%

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

12. Applied egg-rr 99.7%

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

    1. associate-*r/ 99.7%

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

    2. *-rgt-identity 99.7%

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

14. Simplified 99.7%

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

15. Final simplification 99.7%

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

Alternative 2: 87.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \log \left(\frac{x}{y}\right)\\ t_1 := x \cdot \log \left(x \cdot y\right)\\ \mathbf{if}\;t\_0 \leq -\infty:\\ \;\;\;\;t\_1 - z\\ \mathbf{elif}\;t\_0 \leq 2 \cdot 10^{+292}:\\ \;\;\;\;t\_0 - z\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (log (/ x y)))) (t_1 (* x (log (* x y)))))
   (if (<= t_0 (- INFINITY))
     (- t_1 z)
     (if (<= t_0 2e+292) (- t_0 z) (- (- z) t_1)))))

C

double code(double x, double y, double z) {
	double t_0 = x * log((x / y));
	double t_1 = x * log((x * y));
	double tmp;
	if (t_0 <= -((double) INFINITY)) {
		tmp = t_1 - z;
	} else if (t_0 <= 2e+292) {
		tmp = t_0 - z;
	} else {
		tmp = -z - t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z) {
	double t_0 = x * Math.log((x / y));
	double t_1 = x * Math.log((x * y));
	double tmp;
	if (t_0 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1 - z;
	} else if (t_0 <= 2e+292) {
		tmp = t_0 - z;
	} else {
		tmp = -z - t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * math.log((x / y))
	t_1 = x * math.log((x * y))
	tmp = 0
	if t_0 <= -math.inf:
		tmp = t_1 - z
	elif t_0 <= 2e+292:
		tmp = t_0 - z
	else:
		tmp = -z - t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * log(Float64(x / y)))
	t_1 = Float64(x * log(Float64(x * y)))
	tmp = 0.0
	if (t_0 <= Float64(-Inf))
		tmp = Float64(t_1 - z);
	elseif (t_0 <= 2e+292)
		tmp = Float64(t_0 - z);
	else
		tmp = Float64(Float64(-z) - t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * log((x / y));
	t_1 = x * log((x * y));
	tmp = 0.0;
	if (t_0 <= -Inf)
		tmp = t_1 - z;
	elseif (t_0 <= 2e+292)
		tmp = t_0 - z;
	else
		tmp = -z - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[Log[N[(x / y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x * N[Log[N[(x * y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, (-Infinity)], N[(t$95$1 - z), $MachinePrecision], If[LessEqual[t$95$0, 2e+292], N[(t$95$0 - z), $MachinePrecision], N[((-z) - t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

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

   1. Initial program 7.1%

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

      1. add-cube-cbrt 7.1%

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

      2. log-prod 7.1%

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

      3. pow2 7.1%

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

   4. Applied egg-rr 7.1%

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

      1. log-pow 7.1%

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

      2. distribute-lft1-in 7.1%

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

      3. metadata-eval 7.1%

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

   6. Simplified 7.1%

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

      1. add-log-exp 7.1%

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

      2. *-commutative 7.1%

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

      3. exp-prod 7.1%

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

      4. *-commutative 7.1%

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

      5. exp-to-pow 7.1%

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

      6. pow3 7.1%

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

      7. add-cube-cbrt 7.1%

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

      8. exp-to-pow 7.1%

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

      9. diff-log 33.0%

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

      10. *-commutative 33.0%

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

      11. add-log-exp 37.5%

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

      12. sub-neg 37.5%

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

      13. distribute-rgt-in 37.5%

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

   8. Applied egg-rr 37.5%

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

      1. distribute-rgt-out 37.5%

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

      2. unsub-neg 37.5%

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

      3. log-div 7.1%

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

      4. clear-num 7.1%

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

      5. neg-log 9.6%

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

      6. *-commutative 9.6%

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

      7. neg-log 7.1%

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

      8. clear-num 7.1%

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

      9. log-div 37.5%

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

      10. unsub-neg 37.5%

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

      11. add-log-exp 37.5%

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

      12. sum-log 0.9%

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

      13. add-sqr-sqrt 0.0%

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

      14. sqrt-unprod 33.4%

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

      15. sqr-neg 33.4%

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

      16. sqrt-unprod 33.4%

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

      17. add-sqr-sqrt 33.4%

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

      18. add-exp-log 51.4%

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

   10. Applied egg-rr 51.4%

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

   if -inf.0 < (*.f64 x (log.f64 (/.f64 x y))) < 2e292

   1. Initial program 99.8%

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

   if 2e292 < (*.f64 x (log.f64 (/.f64 x y)))

   1. Initial program 4.7%

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

      1. add-cube-cbrt 4.7%

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

      2. log-prod 4.7%

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

      3. pow2 4.7%

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

   4. Applied egg-rr 4.7%

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

      1. log-pow 4.7%

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

      2. distribute-lft1-in 4.7%

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

      3. metadata-eval 4.7%

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

   6. Simplified 4.7%

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

      1. add-log-exp 4.7%

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

      2. *-commutative 4.7%

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

      3. exp-prod 4.7%

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

      4. *-commutative 4.7%

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

      5. exp-to-pow 4.7%

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

      6. pow3 4.7%

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

      7. add-cube-cbrt 4.7%

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

      8. exp-to-pow 4.7%

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

      9. diff-log 3.1%

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

      10. *-commutative 3.1%

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

      11. add-log-exp 43.1%

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

      12. sub-neg 43.1%

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

      13. distribute-rgt-in 43.0%

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

   8. Applied egg-rr 43.0%

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

      1. distribute-rgt-out 43.1%

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

      2. unsub-neg 43.1%

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

      3. log-div 4.7%

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

      4. clear-num 4.7%

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

      5. neg-log 11.7%

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

      6. distribute-rgt-neg-out 11.7%

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

      7. distribute-lft-neg-in 11.7%

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

      8. add-sqr-sqrt 1.6%

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

      9. sqrt-unprod 4.4%

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

      10. sqr-neg 4.4%

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

      11. sqrt-unprod 2.8%

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

      12. add-sqr-sqrt 4.0%

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

      13. neg-log 1.3%

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

      14. clear-num 1.3%

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

      15. log-div 5.5%

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

      16. unsub-neg 5.5%

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

      17. add-log-exp 5.5%

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

      18. sum-log 0.1%

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

      19. add-sqr-sqrt 0.1%

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

      20. sqrt-unprod 0.1%

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

      21. sqr-neg 0.1%

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

      22. sqrt-unprod 0.0%

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

   10. Applied egg-rr 53.6%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \log \left(\frac{x}{y}\right) \leq -\infty:\\ \;\;\;\;x \cdot \log \left(x \cdot y\right) - z\\ \mathbf{elif}\;x \cdot \log \left(\frac{x}{y}\right) \leq 2 \cdot 10^{+292}:\\ \;\;\;\;x \cdot \log \left(\frac{x}{y}\right) - z\\ \mathbf{else}:\\ \;\;\;\;\left(-z\right) - x \cdot \log \left(x \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 86.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \log \left(\frac{x}{y}\right)\\ \mathbf{if}\;t\_0 \leq -\infty \lor \neg \left(t\_0 \leq 2 \cdot 10^{+292}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;t\_0 - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (log (/ x y)))))
   (if (or (<= t_0 (- INFINITY)) (not (<= t_0 2e+292))) (- 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 <= 2e+292)) {
		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 <= 2e+292)) {
		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 <= 2e+292):
		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 <= 2e+292))
		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 <= 2e+292)))
		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, 2e+292]], $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 2e292 < (*.f64 x (log.f64 (/.f64 x y)))

   1. Initial program 5.9%

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

      1. remove-double-neg 5.9%

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

      2. sub-neg 5.9%

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

      3. distribute-neg-in 5.9%

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

      4. sub-neg 5.9%

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

      5. distribute-lft-neg-in 5.9%

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

      6. distribute-lft-neg-in 5.9%

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

      7. distribute-rgt-neg-in 5.9%

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

      8. log-div 40.2%

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

      9. sub-neg 40.2%

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

      10. distribute-neg-in 40.2%

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

      11. remove-double-neg 40.2%

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

      12. +-commutative 40.2%

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

      13. sub-neg 40.2%

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

      14. log-div 10.6%

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

      15. fma-neg 10.6%

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

      16. remove-double-neg 10.6%

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

   3. Simplified 10.6%

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

   5. Taylor expanded in x around 0 48.1%

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

   if -inf.0 < (*.f64 x (log.f64 (/.f64 x y))) < 2e292

   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 84.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \log \left(\frac{x}{y}\right) \leq -\infty \lor \neg \left(x \cdot \log \left(\frac{x}{y}\right) \leq 2 \cdot 10^{+292}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log \left(\frac{x}{y}\right) - z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 87.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \log \left(\frac{x}{y}\right)\\ \mathbf{if}\;t\_0 \leq -\infty \lor \neg \left(t\_0 \leq 2 \cdot 10^{+292}\right):\\ \;\;\;\;x \cdot \log \left(x \cdot y\right) - z\\ \mathbf{else}:\\ \;\;\;\;t\_0 - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (log (/ x y)))))
   (if (or (<= t_0 (- INFINITY)) (not (<= t_0 2e+292)))
     (- (* x (log (* x y))) z)
     (- t_0 z))))

C

double code(double x, double y, double z) {
	double t_0 = x * log((x / y));
	double tmp;
	if ((t_0 <= -((double) INFINITY)) || !(t_0 <= 2e+292)) {
		tmp = (x * log((x * y))) - z;
	} else {
		tmp = t_0 - z;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z) {
	double t_0 = x * Math.log((x / y));
	double tmp;
	if ((t_0 <= -Double.POSITIVE_INFINITY) || !(t_0 <= 2e+292)) {
		tmp = (x * Math.log((x * y))) - z;
	} else {
		tmp = t_0 - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * math.log((x / y))
	tmp = 0
	if (t_0 <= -math.inf) or not (t_0 <= 2e+292):
		tmp = (x * math.log((x * y))) - z
	else:
		tmp = t_0 - z
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * log(Float64(x / y)))
	tmp = 0.0
	if ((t_0 <= Float64(-Inf)) || !(t_0 <= 2e+292))
		tmp = Float64(Float64(x * log(Float64(x * y))) - z);
	else
		tmp = Float64(t_0 - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * log((x / y));
	tmp = 0.0;
	if ((t_0 <= -Inf) || ~((t_0 <= 2e+292)))
		tmp = (x * log((x * y))) - z;
	else
		tmp = t_0 - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[Log[N[(x / y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, (-Infinity)], N[Not[LessEqual[t$95$0, 2e+292]], $MachinePrecision]], N[(N[(x * N[Log[N[(x * y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision], N[(t$95$0 - z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x (log.f64 (/.f64 x y))) < -inf.0 or 2e292 < (*.f64 x (log.f64 (/.f64 x y)))

   1. Initial program 5.9%

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

      1. add-cube-cbrt 5.9%

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

      2. log-prod 5.9%

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

      3. pow2 5.9%

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

   4. Applied egg-rr 5.9%

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

      1. log-pow 5.9%

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

      2. distribute-lft1-in 5.9%

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

      3. metadata-eval 5.9%

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

   6. Simplified 5.9%

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

      1. add-log-exp 5.9%

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

      2. *-commutative 5.9%

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

      3. exp-prod 5.9%

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

      4. *-commutative 5.9%

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

      5. exp-to-pow 5.9%

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

      6. pow3 5.9%

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

      7. add-cube-cbrt 5.9%

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

      8. exp-to-pow 5.9%

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

      9. diff-log 18.6%

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

      10. *-commutative 18.6%

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

      11. add-log-exp 40.2%

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

      12. sub-neg 40.2%

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

      13. distribute-rgt-in 40.1%

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

   8. Applied egg-rr 40.1%

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

      1. distribute-rgt-out 40.2%

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

      2. unsub-neg 40.2%

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

      3. log-div 5.9%

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

      4. clear-num 5.9%

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

      5. neg-log 10.6%

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

      6. *-commutative 10.6%

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

      7. neg-log 5.9%

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

      8. clear-num 5.9%

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

      9. log-div 40.2%

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

      10. unsub-neg 40.2%

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

      11. add-log-exp 40.2%

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

      12. sum-log 2.0%

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

      13. add-sqr-sqrt 1.5%

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

      14. sqrt-unprod 18.8%

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

      15. sqr-neg 18.8%

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

      16. sqrt-unprod 17.3%

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

      17. add-sqr-sqrt 21.9%

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

      18. add-exp-log 52.4%

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

   10. Applied egg-rr 52.4%

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

   if -inf.0 < (*.f64 x (log.f64 (/.f64 x y))) < 2e292

   1. Initial program 99.8%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \log \left(\frac{x}{y}\right) \leq -\infty \lor \neg \left(x \cdot \log \left(\frac{x}{y}\right) \leq 2 \cdot 10^{+292}\right):\\ \;\;\;\;x \cdot \log \left(x \cdot y\right) - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log \left(\frac{x}{y}\right) - z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 99.4% accurate, 0.3× speedup

Math

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

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -5e-310)
   (- (fma x (- (log (- y)) (log (- x))) z))
   (- (- (* x (log x)) (* x (log y))) z)))

C

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

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -5e-310)
		tmp = Float64(-fma(x, Float64(log(Float64(-y)) - log(Float64(-x))), z));
	else
		tmp = Float64(Float64(Float64(x * log(x)) - Float64(x * log(y))) - z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -5e-310], (-N[(x * N[(N[Log[(-y)], $MachinePrecision] - N[Log[(-x)], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision]), N[(N[(N[(x * N[Log[x], $MachinePrecision]), $MachinePrecision] - N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.999999999999985e-310

   1. Initial program 69.9%

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

      1. remove-double-neg 69.9%

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

      2. sub-neg 69.9%

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

      3. distribute-neg-in 69.9%

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

      4. sub-neg 69.9%

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

      5. distribute-lft-neg-in 69.9%

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

      6. distribute-lft-neg-in 69.9%

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

      7. distribute-rgt-neg-in 69.9%

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

      8. log-div 0.0%

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

      9. sub-neg 0.0%

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

      10. distribute-neg-in 0.0%

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

      11. remove-double-neg 0.0%

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

      12. +-commutative 0.0%

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

      13. sub-neg 0.0%

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

      14. log-div 68.5%

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

      15. fma-neg 68.5%

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

      16. remove-double-neg 68.5%

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

   3. Simplified 68.5%

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

      1. frac-2neg 68.5%

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

      2. log-div 99.6%

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

   6. Applied egg-rr 99.6%

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

   if -4.999999999999985e-310 < y

   1. Initial program 73.8%

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

      1. clear-num 72.9%

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

      2. log-rec 75.2%

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

   4. Applied egg-rr 75.2%

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

      1. neg-log 72.9%

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

      2. clear-num 73.8%

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

      3. log-div 99.5%

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

      4. unsub-neg 99.5%

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

      5. distribute-rgt-out 99.5%

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

      6. distribute-lft-neg-out 99.5%

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

      7. unsub-neg 99.5%

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

      8. *-commutative 99.5%

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

      9. *-commutative 99.5%

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

   6. Applied egg-rr 99.5%

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

4. Final simplification 99.6%

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

Alternative 6: 99.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(\log \left(\frac{\sqrt[3]{x}}{\sqrt[3]{y}}\right) \cdot 3\right) - z \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (- (* x (* (log (/ (cbrt x) (cbrt y))) 3.0)) z))

C

double code(double x, double y, double z) {
	return (x * (log((cbrt(x) / cbrt(y))) * 3.0)) - z;
}

Java

public static double code(double x, double y, double z) {
	return (x * (Math.log((Math.cbrt(x) / Math.cbrt(y))) * 3.0)) - z;
}

Julia

function code(x, y, z)
	return Float64(Float64(x * Float64(log(Float64(cbrt(x) / cbrt(y))) * 3.0)) - z)
end

Wolfram

code[x_, y_, z_] := N[(N[(x * N[(N[Log[N[(N[Power[x, 1/3], $MachinePrecision] / N[Power[y, 1/3], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * 3.0), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]

Derivation

1. Initial program 71.6%

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

   1. add-cube-cbrt 71.6%

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

   2. log-prod 71.5%

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

   3. pow2 71.5%

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

4. Applied egg-rr 71.5%

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

   1. log-pow 71.5%

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

   2. distribute-lft1-in 71.5%

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

   3. metadata-eval 71.5%

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

6. Simplified 71.5%

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

   1. cbrt-div 99.7%

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

   2. div-inv 99.7%

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

8. Applied egg-rr 99.7%

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

   1. associate-*r/ 99.7%

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

   2. *-rgt-identity 99.7%

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

10. Simplified 99.7%

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

11. Final simplification 99.7%

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

Alternative 7: 91.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.52 \cdot 10^{-158}:\\ \;\;\;\;x \cdot \log \left(\frac{x}{y}\right) - z\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-308}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x - \log y\right) - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.52e-158)
   (- (* x (log (/ x y))) z)
   (if (<= x -2e-308) (- z) (- (* x (- (log x) (log y))) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.52e-158) {
		tmp = (x * log((x / y))) - z;
	} else if (x <= -2e-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 <= (-1.52d-158)) then
        tmp = (x * log((x / y))) - z
    else if (x <= (-2d-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 <= -1.52e-158) {
		tmp = (x * Math.log((x / y))) - z;
	} else if (x <= -2e-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 <= -1.52e-158:
		tmp = (x * math.log((x / y))) - z
	elif x <= -2e-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 <= -1.52e-158)
		tmp = Float64(Float64(x * log(Float64(x / y))) - z);
	elseif (x <= -2e-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 <= -1.52e-158)
		tmp = (x * log((x / y))) - z;
	elseif (x <= -2e-308)
		tmp = -z;
	else
		tmp = (x * (log(x) - log(y))) - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.52e-158], N[(N[(x * N[Log[N[(x / y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision], If[LessEqual[x, -2e-308], (-z), N[(N[(x * N[(N[Log[x], $MachinePrecision] - N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.52e-158

   1. Initial program 74.1%

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

   if -1.52e-158 < x < -1.9999999999999998e-308

   1. Initial program 55.8%

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

      1. remove-double-neg 55.8%

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

      2. sub-neg 55.8%

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

      3. distribute-neg-in 55.8%

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

      4. sub-neg 55.8%

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

      5. distribute-lft-neg-in 55.8%

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

      6. distribute-lft-neg-in 55.8%

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

      7. distribute-rgt-neg-in 55.8%

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

      8. log-div 0.0%

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

      9. sub-neg 0.0%

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

      10. distribute-neg-in 0.0%

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

      11. remove-double-neg 0.0%

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

      12. +-commutative 0.0%

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

      13. sub-neg 0.0%

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

      14. log-div 52.8%

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

      15. fma-neg 52.8%

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

      16. remove-double-neg 52.8%

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

   3. Simplified 52.8%

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

   5. Taylor expanded in x around 0 88.9%

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

   if -1.9999999999999998e-308 < x

   1. Initial program 73.8%

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

      1. log-div 99.5%

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

   4. Applied egg-rr 99.5%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.52 \cdot 10^{-158}:\\ \;\;\;\;x \cdot \log \left(\frac{x}{y}\right) - z\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-308}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x - \log y\right) - z\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 99.5% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -5e-310)
   (- (* x (- (log (- x)) (log (- y)))) z)
   (- (* x (- (log x) (log y))) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -5e-310) {
		tmp = (x * (log(-x) - log(-y))) - z;
	} else {
		tmp = (x * (log(x) - log(y))) - z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-5d-310)) then
        tmp = (x * (log(-x) - log(-y))) - z
    else
        tmp = (x * (log(x) - log(y))) - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -5e-310) {
		tmp = (x * (Math.log(-x) - Math.log(-y))) - z;
	} else {
		tmp = (x * (Math.log(x) - Math.log(y))) - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -5e-310:
		tmp = (x * (math.log(-x) - math.log(-y))) - z
	else:
		tmp = (x * (math.log(x) - math.log(y))) - z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -5e-310)
		tmp = Float64(Float64(x * Float64(log(Float64(-x)) - log(Float64(-y)))) - z);
	else
		tmp = Float64(Float64(x * Float64(log(x) - log(y))) - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -5e-310)
		tmp = (x * (log(-x) - log(-y))) - z;
	else
		tmp = (x * (log(x) - log(y))) - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -5e-310], N[(N[(x * N[(N[Log[(-x)], $MachinePrecision] - N[Log[(-y)], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision], N[(N[(x * N[(N[Log[x], $MachinePrecision] - N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.999999999999985e-310

   1. Initial program 69.9%

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

      1. frac-2neg 69.9%

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

      2. log-div 99.6%

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

   4. Applied egg-rr 99.6%

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

   if -4.999999999999985e-310 < y

   1. Initial program 73.8%

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

      1. log-div 99.5%

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

   4. Applied egg-rr 99.5%

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

4. Final simplification 99.6%

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

Alternative 9: 99.4% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -5e-310)
   (- (* x (- (log (- x)) (log (- y)))) z)
   (- (- (* x (log x)) (* x (log y))) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -5e-310) {
		tmp = (x * (log(-x) - log(-y))) - z;
	} else {
		tmp = ((x * log(x)) - (x * log(y))) - z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-5d-310)) then
        tmp = (x * (log(-x) - log(-y))) - z
    else
        tmp = ((x * log(x)) - (x * log(y))) - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -5e-310) {
		tmp = (x * (Math.log(-x) - Math.log(-y))) - z;
	} else {
		tmp = ((x * Math.log(x)) - (x * Math.log(y))) - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -5e-310:
		tmp = (x * (math.log(-x) - math.log(-y))) - z
	else:
		tmp = ((x * math.log(x)) - (x * math.log(y))) - z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -5e-310)
		tmp = Float64(Float64(x * Float64(log(Float64(-x)) - log(Float64(-y)))) - z);
	else
		tmp = Float64(Float64(Float64(x * log(x)) - Float64(x * log(y))) - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -5e-310)
		tmp = (x * (log(-x) - log(-y))) - z;
	else
		tmp = ((x * log(x)) - (x * log(y))) - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -5e-310], N[(N[(x * N[(N[Log[(-x)], $MachinePrecision] - N[Log[(-y)], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision], N[(N[(N[(x * N[Log[x], $MachinePrecision]), $MachinePrecision] - N[(x * N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.999999999999985e-310

   1. Initial program 69.9%

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

      1. frac-2neg 69.9%

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

      2. log-div 99.6%

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

   4. Applied egg-rr 99.6%

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

   if -4.999999999999985e-310 < y

   1. Initial program 73.8%

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

      1. clear-num 72.9%

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

      2. log-rec 75.2%

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

   4. Applied egg-rr 75.2%

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

      1. neg-log 72.9%

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

      2. clear-num 73.8%

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

      3. log-div 99.5%

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

      4. unsub-neg 99.5%

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

      5. distribute-rgt-out 99.5%

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

      6. distribute-lft-neg-out 99.5%

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

      7. unsub-neg 99.5%

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

      8. *-commutative 99.5%

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

      9. *-commutative 99.5%

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

   6. Applied egg-rr 99.5%

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

4. Final simplification 99.6%

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

Alternative 10: 66.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{-120} \lor \neg \left(z \leq 5.8 \cdot 10^{-69}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;\left(-x\right) \cdot \log \left(\frac{y}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.35e-120) (not (<= z 5.8e-69)))
   (- z)
   (* (- x) (log (/ y x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.35e-120) || !(z <= 5.8e-69)) {
		tmp = -z;
	} else {
		tmp = -x * log((y / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-1.35d-120)) .or. (.not. (z <= 5.8d-69))) then
        tmp = -z
    else
        tmp = -x * log((y / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.35e-120) || !(z <= 5.8e-69)) {
		tmp = -z;
	} else {
		tmp = -x * Math.log((y / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.35e-120) or not (z <= 5.8e-69):
		tmp = -z
	else:
		tmp = -x * math.log((y / x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.35e-120) || !(z <= 5.8e-69))
		tmp = Float64(-z);
	else
		tmp = Float64(Float64(-x) * log(Float64(y / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.35e-120) || ~((z <= 5.8e-69)))
		tmp = -z;
	else
		tmp = -x * log((y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.35e-120], N[Not[LessEqual[z, 5.8e-69]], $MachinePrecision]], (-z), N[((-x) * N[Log[N[(y / x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.3499999999999999e-120 or 5.7999999999999997e-69 < z

   1. Initial program 73.7%

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

      1. remove-double-neg 73.7%

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

      2. sub-neg 73.7%

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

      3. distribute-neg-in 73.7%

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

      4. sub-neg 73.7%

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

      5. distribute-lft-neg-in 73.7%

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

      6. distribute-lft-neg-in 73.7%

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

      7. distribute-rgt-neg-in 73.7%

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

      8. log-div 43.1%

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

      9. sub-neg 43.1%

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

      10. distribute-neg-in 43.1%

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

      11. remove-double-neg 43.1%

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

      12. +-commutative 43.1%

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

      13. sub-neg 43.1%

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

      14. log-div 72.6%

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

      15. fma-neg 72.6%

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

      16. remove-double-neg 72.6%

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

   3. Simplified 72.6%

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

   5. Taylor expanded in x around 0 73.0%

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

   if -1.3499999999999999e-120 < z < 5.7999999999999997e-69

   1. Initial program 67.3%

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

      1. remove-double-neg 67.3%

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

      2. sub-neg 67.3%

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

      3. distribute-neg-in 67.3%

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

      4. sub-neg 67.3%

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

      5. distribute-lft-neg-in 67.3%

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

      6. distribute-lft-neg-in 67.3%

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

      7. distribute-rgt-neg-in 67.3%

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

      8. log-div 45.6%

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

      9. sub-neg 45.6%

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

      10. distribute-neg-in 45.6%

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

      11. remove-double-neg 45.6%

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

      12. +-commutative 45.6%

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

      13. sub-neg 45.6%

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

      14. log-div 69.2%

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

      15. fma-neg 69.2%

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

      16. remove-double-neg 69.2%

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

   3. Simplified 69.2%

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

   5. Taylor expanded in x around inf 37.7%

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

      1. log-rec 37.7%

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

      2. sub-neg 37.7%

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

      3. log-div 62.8%

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

      4. add0 62.8%

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

      5. distribute-lft-in 62.8%

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

      6. mul0-rgt 62.8%

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

      7. add0 62.8%

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

   7. Simplified 62.8%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{-120} \lor \neg \left(z \leq 5.8 \cdot 10^{-69}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;\left(-x\right) \cdot \log \left(\frac{y}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 50.4% 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 71.6%

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

   1. remove-double-neg 71.6%

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

   2. sub-neg 71.6%

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

   3. distribute-neg-in 71.6%

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

   4. sub-neg 71.6%

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

   5. distribute-lft-neg-in 71.6%

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

   6. distribute-lft-neg-in 71.6%

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

   7. distribute-rgt-neg-in 71.6%

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

   8. log-div 43.9%

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

   9. sub-neg 43.9%

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

   10. distribute-neg-in 43.9%

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

   11. remove-double-neg 43.9%

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

   12. +-commutative 43.9%

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

   13. sub-neg 43.9%

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

   14. log-div 71.4%

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

   15. fma-neg 71.4%

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

   16. remove-double-neg 71.4%

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

3. Simplified 71.4%

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

5. Taylor expanded in x around 0 53.3%

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

6. Final simplification 53.3%

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

Developer target: 88.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y < 7.595077799083773 \cdot 10^{-308}:\\ \;\;\;\;x \cdot \log \left(\frac{x}{y}\right) - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x - \log y\right) - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (< y 7.595077799083773e-308)
   (- (* x (log (/ x y))) z)
   (- (* x (- (log x) (log y))) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y < 7.595077799083773e-308) {
		tmp = (x * log((x / y))) - z;
	} else {
		tmp = (x * (log(x) - log(y))) - z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y < 7.595077799083773d-308) then
        tmp = (x * log((x / y))) - z
    else
        tmp = (x * (log(x) - log(y))) - z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y < 7.595077799083773e-308) {
		tmp = (x * Math.log((x / y))) - z;
	} else {
		tmp = (x * (Math.log(x) - Math.log(y))) - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y < 7.595077799083773e-308:
		tmp = (x * math.log((x / y))) - z
	else:
		tmp = (x * (math.log(x) - math.log(y))) - z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y < 7.595077799083773e-308)
		tmp = Float64(Float64(x * log(Float64(x / y))) - z);
	else
		tmp = Float64(Float64(x * Float64(log(x) - log(y))) - z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y < 7.595077799083773e-308)
		tmp = (x * log((x / y))) - z;
	else
		tmp = (x * (log(x) - log(y))) - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Less[y, 7.595077799083773e-308], N[(N[(x * N[Log[N[(x / y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision], N[(N[(x * N[(N[Log[x], $MachinePrecision] - N[Log[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]]

Reproduce

herbie shell --seed 2024046 
(FPCore (x y z)
  :name "Numeric.SpecFunctions.Extra:bd0 from math-functions-0.1.5.2"
  :precision binary64

  :alt
  (if (< y 7.595077799083773e-308) (- (* x (log (/ x y))) z) (- (* x (- (log x) (log y))) z))

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