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

Percentage Accurate: 77.2% → 99.5%

Time: 12.1s

Alternatives: 8

Speedup: 0.5×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 77.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.5% accurate, 0.5× 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 67.6%

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

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

      5. sub-neg 99.6%

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

      6. neg-mul-1 99.6%

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

   5. Simplified 99.6%

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

   if -4.999999999999985e-310 < y

   1. Initial program 76.7%

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

   3. Taylor expanded in x around 0 99.6%

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

      1. log-rec 99.6%

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

      2. sub-neg 99.6%

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

   5. Simplified 99.6%

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

Alternative 2: 88.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \log \left(\frac{x}{y}\right)\\ \mathbf{if}\;t\_0 \leq -\infty \lor \neg \left(t\_0 \leq 5 \cdot 10^{+303}\right):\\ \;\;\;\;x \cdot \log \left(y \cdot x\right) - z\\ \mathbf{else}:\\ \;\;\;\;t\_0 - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (log (/ x y)))))
   (if (or (<= t_0 (- INFINITY)) (not (<= t_0 5e+303)))
     (- (* 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+303)) {
		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+303)) {
		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+303):
		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+303))
		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+303)))
		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+303]], $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 4.9999999999999997e303 < (*.f64 x (log.f64 (/.f64 x y)))

   1. Initial program 9.1%

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

      1. *-un-lft-identity 9.1%

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

      2. add-cube-cbrt 9.1%

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

      3. times-frac 9.1%

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

      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 9.1%

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

      2. associate-/l/ 9.1%

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

      3. unpow2 9.1%

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

      4. add-cube-cbrt 9.1%

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

      5. diff-log 40.9%

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

      6. sub-neg 40.9%

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

      7. distribute-rgt-in 39.7%

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

   8. Applied egg-rr 39.7%

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

      1. distribute-rgt-out 40.9%

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

      2. sub-neg 40.9%

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

      3. rem-cbrt-cube 40.9%

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

      4. *-commutative 40.9%

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

      5. rem-cbrt-cube 40.9%

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

      6. sub-neg 40.9%

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

      7. add-sqr-sqrt 22.9%

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

      8. sqrt-unprod 40.9%

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

      9. sqr-neg 40.9%

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

      10. sqrt-unprod 17.9%

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

      11. add-sqr-sqrt 25.3%

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

      12. sum-log 51.7%

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

   10. Applied egg-rr 51.7%

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

   if -inf.0 < (*.f64 x (log.f64 (/.f64 x y))) < 4.9999999999999997e303

   1. Initial program 99.6%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \log \left(\frac{x}{y}\right) \leq -\infty \lor \neg \left(x \cdot \log \left(\frac{x}{y}\right) \leq 5 \cdot 10^{+303}\right):\\ \;\;\;\;x \cdot \log \left(y \cdot x\right) - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log \left(\frac{x}{y}\right) - z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 87.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \log \left(\frac{x}{y}\right)\\ \mathbf{if}\;t\_0 \leq -\infty \lor \neg \left(t\_0 \leq 5 \cdot 10^{+303}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;t\_0 - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (log (/ x y)))))
   (if (or (<= t_0 (- INFINITY)) (not (<= t_0 5e+303))) (- 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+303)) {
		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+303)) {
		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+303):
		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+303))
		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+303)))
		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+303]], $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 4.9999999999999997e303 < (*.f64 x (log.f64 (/.f64 x y)))

   1. Initial program 9.1%

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

   3. Taylor expanded in x around 0 43.7%

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

      1. mul-1-neg 43.7%

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

   5. Simplified 43.7%

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

   if -inf.0 < (*.f64 x (log.f64 (/.f64 x y))) < 4.9999999999999997e303

   1. Initial program 99.6%

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

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \log \left(\frac{x}{y}\right) \leq -\infty \lor \neg \left(x \cdot \log \left(\frac{x}{y}\right) \leq 5 \cdot 10^{+303}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log \left(\frac{x}{y}\right) - z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 87.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \log \left(\frac{x}{y}\right)\\ \mathbf{if}\;t\_0 \leq -\infty:\\ \;\;\;\;x \cdot \left(\log \left(-x\right) - \log \left(-y\right)\right)\\ \mathbf{elif}\;t\_0 \leq 5 \cdot 10^{+303}:\\ \;\;\;\;t\_0 - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log \left(y \cdot x\right) - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (log (/ x y)))))
   (if (<= t_0 (- INFINITY))
     (* x (- (log (- x)) (log (- y))))
     (if (<= t_0 5e+303) (- t_0 z) (- (* x (log (* y x))) z)))))

C

double code(double x, double y, double z) {
	double t_0 = x * log((x / y));
	double tmp;
	if (t_0 <= -((double) INFINITY)) {
		tmp = x * (log(-x) - log(-y));
	} else if (t_0 <= 5e+303) {
		tmp = t_0 - z;
	} else {
		tmp = (x * log((y * x))) - 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) {
		tmp = x * (Math.log(-x) - Math.log(-y));
	} else if (t_0 <= 5e+303) {
		tmp = t_0 - z;
	} else {
		tmp = (x * Math.log((y * x))) - z;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * math.log((x / y))
	tmp = 0
	if t_0 <= -math.inf:
		tmp = x * (math.log(-x) - math.log(-y))
	elif t_0 <= 5e+303:
		tmp = t_0 - z
	else:
		tmp = (x * math.log((y * x))) - 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))
		tmp = Float64(x * Float64(log(Float64(-x)) - log(Float64(-y))));
	elseif (t_0 <= 5e+303)
		tmp = Float64(t_0 - z);
	else
		tmp = Float64(Float64(x * log(Float64(y * x))) - 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)
		tmp = x * (log(-x) - log(-y));
	elseif (t_0 <= 5e+303)
		tmp = t_0 - z;
	else
		tmp = (x * log((y * x))) - 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[LessEqual[t$95$0, (-Infinity)], N[(x * N[(N[Log[(-x)], $MachinePrecision] - N[Log[(-y)], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 5e+303], N[(t$95$0 - z), $MachinePrecision], N[(N[(x * N[Log[N[(y * x), $MachinePrecision]], $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 9.4%

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

      1. add-sqr-sqrt 8.7%

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

      2. pow2 8.7%

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

   4. Applied egg-rr 8.7%

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

   5. Taylor expanded in y around -inf 65.2%

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

      1. metadata-eval 65.2%

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

      2. distribute-neg-frac 65.2%

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

      3. distribute-frac-neg2 65.2%

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

      4. log-rec 65.2%

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

      5. sub-neg 65.2%

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

      6. neg-mul-1 65.2%

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

   7. Simplified 65.2%

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

   8. Taylor expanded in z around 0 61.1%

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

   if -inf.0 < (*.f64 x (log.f64 (/.f64 x y))) < 4.9999999999999997e303

   1. Initial program 99.6%

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

   if 4.9999999999999997e303 < (*.f64 x (log.f64 (/.f64 x y)))

   1. Initial program 8.9%

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

      1. *-un-lft-identity 8.9%

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

      2. add-cube-cbrt 8.9%

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

      3. times-frac 8.9%

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

      4. log-prod 75.8%

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

      5. pow2 75.8%

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

   4. Applied egg-rr 75.8%

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

      1. +-commutative 75.8%

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

      2. log-rec 75.8%

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

      3. unsub-neg 75.8%

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

   6. Simplified 75.8%

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

      1. diff-log 8.9%

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

      2. associate-/l/ 8.9%

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

      3. unpow2 8.9%

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

      4. add-cube-cbrt 8.9%

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

      5. diff-log 47.3%

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

      6. sub-neg 47.3%

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

      7. distribute-rgt-in 44.8%

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

   8. Applied egg-rr 44.8%

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

      1. distribute-rgt-out 47.3%

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

      2. sub-neg 47.3%

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

      3. rem-cbrt-cube 47.2%

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

      4. *-commutative 47.2%

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

      5. rem-cbrt-cube 47.3%

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

      6. sub-neg 47.3%

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

      7. add-sqr-sqrt 44.7%

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

      8. sqrt-unprod 47.3%

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

      9. sqr-neg 47.3%

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

      10. sqrt-unprod 2.5%

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

      11. add-sqr-sqrt 16.9%

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

      12. sum-log 57.3%

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

   10. Applied egg-rr 57.3%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \log \left(\frac{x}{y}\right) \leq -\infty:\\ \;\;\;\;x \cdot \left(\log \left(-x\right) - \log \left(-y\right)\right)\\ \mathbf{elif}\;x \cdot \log \left(\frac{x}{y}\right) \leq 5 \cdot 10^{+303}:\\ \;\;\;\;x \cdot \log \left(\frac{x}{y}\right) - z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log \left(y \cdot x\right) - z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 93.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{+144}:\\ \;\;\;\;x \cdot \left(\log \left(-x\right) - \log \left(-y\right)\right)\\ \mathbf{elif}\;x \leq -6.4 \cdot 10^{-137}:\\ \;\;\;\;x \cdot \log \left(\frac{x}{y}\right) - z\\ \mathbf{elif}\;x \leq -5 \cdot 10^{-308}:\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\log x - \log y\right) - z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.8e+144)
   (* x (- (log (- x)) (log (- y))))
   (if (<= x -6.4e-137)
     (- (* x (log (/ x y))) z)
     (if (<= x -5e-308) (- z) (- (* x (- (log x) (log y))) z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.8e+144) {
		tmp = x * (log(-x) - log(-y));
	} else if (x <= -6.4e-137) {
		tmp = (x * log((x / y))) - z;
	} else if (x <= -5e-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 <= (-1.8d+144)) then
        tmp = x * (log(-x) - log(-y))
    else if (x <= (-6.4d-137)) then
        tmp = (x * log((x / y))) - z
    else if (x <= (-5d-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 <= -1.8e+144) {
		tmp = x * (Math.log(-x) - Math.log(-y));
	} else if (x <= -6.4e-137) {
		tmp = (x * Math.log((x / y))) - z;
	} else if (x <= -5e-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 <= -1.8e+144:
		tmp = x * (math.log(-x) - math.log(-y))
	elif x <= -6.4e-137:
		tmp = (x * math.log((x / y))) - z
	elif x <= -5e-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 <= -1.8e+144)
		tmp = Float64(x * Float64(log(Float64(-x)) - log(Float64(-y))));
	elseif (x <= -6.4e-137)
		tmp = Float64(Float64(x * log(Float64(x / y))) - z);
	elseif (x <= -5e-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 <= -1.8e+144)
		tmp = x * (log(-x) - log(-y));
	elseif (x <= -6.4e-137)
		tmp = (x * log((x / y))) - z;
	elseif (x <= -5e-308)
		tmp = -z;
	else
		tmp = (x * (log(x) - log(y))) - z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.8e+144], N[(x * N[(N[Log[(-x)], $MachinePrecision] - N[Log[(-y)], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -6.4e-137], N[(N[(x * N[Log[N[(x / y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision], If[LessEqual[x, -5e-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 < -1.7999999999999999e144

   1. Initial program 56.6%

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

      1. add-sqr-sqrt 46.0%

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

      2. pow2 46.0%

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

   4. Applied egg-rr 46.0%

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

   5. Taylor expanded in y around -inf 88.9%

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

      1. metadata-eval 88.9%

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

      2. distribute-neg-frac 88.9%

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

      3. distribute-frac-neg2 88.9%

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

      4. log-rec 88.9%

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

      5. sub-neg 88.9%

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

      6. neg-mul-1 88.9%

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

   7. Simplified 88.9%

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

   8. Taylor expanded in z around 0 92.6%

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

   if -1.7999999999999999e144 < x < -6.40000000000000043e-137

   1. Initial program 84.7%

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

   if -6.40000000000000043e-137 < x < -4.99999999999999955e-308

   1. Initial program 50.9%

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

   3. Taylor expanded in x around 0 80.4%

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

      1. mul-1-neg 80.4%

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

   5. Simplified 80.4%

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

   if -4.99999999999999955e-308 < x

   1. Initial program 76.7%

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

   3. Taylor expanded in x around 0 99.6%

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

      1. log-rec 99.6%

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

      2. sub-neg 99.6%

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

   5. Simplified 99.6%

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

Alternative 6: 66.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{-20} \lor \neg \left(z \leq 5.6 \cdot 10^{+21}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log \left(\frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.15e-20) (not (<= z 5.6e+21))) (- z) (* x (log (/ x y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.15e-20) || !(z <= 5.6e+21)) {
		tmp = -z;
	} else {
		tmp = x * log((x / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-2.15d-20)) .or. (.not. (z <= 5.6d+21))) then
        tmp = -z
    else
        tmp = x * log((x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.15e-20) || !(z <= 5.6e+21)) {
		tmp = -z;
	} else {
		tmp = x * Math.log((x / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.15e-20) or not (z <= 5.6e+21):
		tmp = -z
	else:
		tmp = x * math.log((x / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.15e-20) || !(z <= 5.6e+21))
		tmp = Float64(-z);
	else
		tmp = Float64(x * log(Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -2.15e-20) || ~((z <= 5.6e+21)))
		tmp = -z;
	else
		tmp = x * log((x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.15e-20], N[Not[LessEqual[z, 5.6e+21]], $MachinePrecision]], (-z), N[(x * N[Log[N[(x / y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.15000000000000006e-20 or 5.6e21 < z

   1. Initial program 74.9%

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

   3. Taylor expanded in x around 0 72.5%

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

      1. mul-1-neg 72.5%

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

   5. Simplified 72.5%

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

   if -2.15000000000000006e-20 < z < 5.6e21

   1. Initial program 69.1%

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

   3. Taylor expanded in z around 0 58.0%

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

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.15 \cdot 10^{-20} \lor \neg \left(z \leq 5.6 \cdot 10^{+21}\right):\\ \;\;\;\;-z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \log \left(\frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 50.7% 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 72.0%

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

3. Taylor expanded in x around 0 48.8%

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

   1. mul-1-neg 48.8%

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

5. Simplified 48.8%

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

Alternative 8: 2.2% accurate, 107.0× speedup

Math

\[\begin{array}{l} \\ z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 z)

C

double code(double x, double y, double z) {
	return z;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = z
end function

Java

public static double code(double x, double y, double z) {
	return z;
}

Python

def code(x, y, z):
	return z

Julia

function code(x, y, z)
	return z
end

MATLAB

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

Wolfram

code[x_, y_, z_] := z

Derivation

1. Initial program 72.0%

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

3. Taylor expanded in x around 0 48.8%

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

   1. mul-1-neg 48.8%

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

5. Simplified 48.8%

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

   1. neg-sub0 48.8%

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

   2. sub-neg 48.8%

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

   3. add-sqr-sqrt 24.9%

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

   4. sqrt-unprod 18.1%

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

   5. sqr-neg 18.1%

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

   6. sqrt-unprod 1.1%

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

   7. add-sqr-sqrt 2.4%

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

7. Applied egg-rr 2.4%

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

   1. +-lft-identity 2.4%

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

9. Simplified 2.4%

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

Developer Target 1: 88.5% 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 2024165 
(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))