System.Random.MWC.Distributions:gamma from mwc-random-0.13.3.2

Percentage Accurate: 99.9% → 99.6%

Time: 8.7s

Alternatives: 9

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ (* x 0.5) (* y (+ (- 1.0 z) (log z)))))

C

double code(double x, double y, double z) {
	return (x * 0.5) + (y * ((1.0 - z) + log(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 * 0.5d0) + (y * ((1.0d0 - z) + log(z)))
end function

Java

public static double code(double x, double y, double z) {
	return (x * 0.5) + (y * ((1.0 - z) + Math.log(z)));
}

Python

def code(x, y, z):
	return (x * 0.5) + (y * ((1.0 - z) + math.log(z)))

Julia

function code(x, y, z)
	return Float64(Float64(x * 0.5) + Float64(y * Float64(Float64(1.0 - z) + log(z))))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x * 0.5) + (y * ((1.0 - z) + log(z)));
end

Wolfram

code[x_, y_, z_] := N[(N[(x * 0.5), $MachinePrecision] + N[(y * N[(N[(1.0 - z), $MachinePrecision] + N[Log[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ (* x 0.5) (* y (+ (- 1.0 z) (log z)))))

C

double code(double x, double y, double z) {
	return (x * 0.5) + (y * ((1.0 - z) + log(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 * 0.5d0) + (y * ((1.0d0 - z) + log(z)))
end function

Java

public static double code(double x, double y, double z) {
	return (x * 0.5) + (y * ((1.0 - z) + Math.log(z)));
}

Python

def code(x, y, z):
	return (x * 0.5) + (y * ((1.0 - z) + math.log(z)))

Julia

function code(x, y, z)
	return Float64(Float64(x * 0.5) + Float64(y * Float64(Float64(1.0 - z) + log(z))))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x * 0.5) + (y * ((1.0 - z) + log(z)));
end

Wolfram

code[x_, y_, z_] := N[(N[(x * 0.5), $MachinePrecision] + N[(y * N[(N[(1.0 - z), $MachinePrecision] + N[Log[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ x \cdot 0.5 + \left(\left(y \cdot 2 - y \cdot z\right) + y \cdot \left(-1 - \log \left(\frac{1}{z}\right)\right)\right) \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ (* x 0.5) (+ (- (* y 2.0) (* y z)) (* y (- -1.0 (log (/ 1.0 z)))))))

C

double code(double x, double y, double z) {
	return (x * 0.5) + (((y * 2.0) - (y * z)) + (y * (-1.0 - log((1.0 / 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 * 0.5d0) + (((y * 2.0d0) - (y * z)) + (y * ((-1.0d0) - log((1.0d0 / z)))))
end function

Java

public static double code(double x, double y, double z) {
	return (x * 0.5) + (((y * 2.0) - (y * z)) + (y * (-1.0 - Math.log((1.0 / z)))));
}

Python

def code(x, y, z):
	return (x * 0.5) + (((y * 2.0) - (y * z)) + (y * (-1.0 - math.log((1.0 / z)))))

Julia

function code(x, y, z)
	return Float64(Float64(x * 0.5) + Float64(Float64(Float64(y * 2.0) - Float64(y * z)) + Float64(y * Float64(-1.0 - log(Float64(1.0 / z))))))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x * 0.5) + (((y * 2.0) - (y * z)) + (y * (-1.0 - log((1.0 / z)))));
end

Wolfram

code[x_, y_, z_] := N[(N[(x * 0.5), $MachinePrecision] + N[(N[(N[(y * 2.0), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision] + N[(y * N[(-1.0 - N[Log[N[(1.0 / z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right) \]
2. Step-by-step derivation

   1. *-commutative 99.9%

      \[\leadsto x \cdot 0.5 + \color{blue}{\left(\left(1 - z\right) + \log z\right) \cdot y} \]

   2. flip-+ 83.7%

      \[\leadsto x \cdot 0.5 + \color{blue}{\frac{\left(1 - z\right) \cdot \left(1 - z\right) - \log z \cdot \log z}{\left(1 - z\right) - \log z}} \cdot y \]

   3. associate-*l/ 81.6%

      \[\leadsto x \cdot 0.5 + \color{blue}{\frac{\left(\left(1 - z\right) \cdot \left(1 - z\right) - \log z \cdot \log z\right) \cdot y}{\left(1 - z\right) - \log z}} \]

   4. pow2 81.6%

      \[\leadsto x \cdot 0.5 + \frac{\left(\color{blue}{{\left(1 - z\right)}^{2}} - \log z \cdot \log z\right) \cdot y}{\left(1 - z\right) - \log z} \]

   5. pow2 81.6%

      \[\leadsto x \cdot 0.5 + \frac{\left({\left(1 - z\right)}^{2} - \color{blue}{{\log z}^{2}}\right) \cdot y}{\left(1 - z\right) - \log z} \]

   6. associate--l- 81.6%

      \[\leadsto x \cdot 0.5 + \frac{\left({\left(1 - z\right)}^{2} - {\log z}^{2}\right) \cdot y}{\color{blue}{1 - \left(z + \log z\right)}} \]

3. Applied egg-rr 81.6%

   \[\leadsto x \cdot 0.5 + \color{blue}{\frac{\left({\left(1 - z\right)}^{2} - {\log z}^{2}\right) \cdot y}{1 - \left(z + \log z\right)}} \]

4. Taylor expanded in z around inf 99.9%

   \[\leadsto x \cdot 0.5 + \color{blue}{\left(\left(-1 \cdot \left(y \cdot z\right) + 2 \cdot y\right) - y \cdot \left(1 - -1 \cdot \log \left(\frac{1}{z}\right)\right)\right)} \]

5. Final simplification 99.9%

   \[\leadsto x \cdot 0.5 + \left(\left(y \cdot 2 - y \cdot z\right) + y \cdot \left(-1 - \log \left(\frac{1}{z}\right)\right)\right) \]

Alternative 2: 73.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot 0.5 \leq -1 \cdot 10^{-289} \lor \neg \left(x \cdot 0.5 \leq 3.5 \cdot 10^{-258}\right):\\ \;\;\;\;x \cdot 0.5 - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 + \log z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= (* x 0.5) -1e-289) (not (<= (* x 0.5) 3.5e-258)))
   (- (* x 0.5) (* y z))
   (* y (+ 1.0 (log z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (((x * 0.5) <= -1e-289) || !((x * 0.5) <= 3.5e-258)) {
		tmp = (x * 0.5) - (y * z);
	} else {
		tmp = y * (1.0 + log(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 * 0.5d0) <= (-1d-289)) .or. (.not. ((x * 0.5d0) <= 3.5d-258))) then
        tmp = (x * 0.5d0) - (y * z)
    else
        tmp = y * (1.0d0 + log(z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (((x * 0.5) <= -1e-289) || !((x * 0.5) <= 3.5e-258)) {
		tmp = (x * 0.5) - (y * z);
	} else {
		tmp = y * (1.0 + Math.log(z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if ((x * 0.5) <= -1e-289) or not ((x * 0.5) <= 3.5e-258):
		tmp = (x * 0.5) - (y * z)
	else:
		tmp = y * (1.0 + math.log(z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((Float64(x * 0.5) <= -1e-289) || !(Float64(x * 0.5) <= 3.5e-258))
		tmp = Float64(Float64(x * 0.5) - Float64(y * z));
	else
		tmp = Float64(y * Float64(1.0 + log(z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (((x * 0.5) <= -1e-289) || ~(((x * 0.5) <= 3.5e-258)))
		tmp = (x * 0.5) - (y * z);
	else
		tmp = y * (1.0 + log(z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[N[(x * 0.5), $MachinePrecision], -1e-289], N[Not[LessEqual[N[(x * 0.5), $MachinePrecision], 3.5e-258]], $MachinePrecision]], N[(N[(x * 0.5), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision], N[(y * N[(1.0 + N[Log[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x 1/2) < -1e-289 or 3.50000000000000001e-258 < (*.f64 x 1/2)

   1. Initial program 99.9%

      \[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right) \]

   2. Taylor expanded in z around inf 81.2%

      \[\leadsto x \cdot 0.5 + \color{blue}{-1 \cdot \left(y \cdot z\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 81.2%

         \[\leadsto x \cdot 0.5 + \color{blue}{\left(-y \cdot z\right)} \]

      2. *-commutative 81.2%

         \[\leadsto x \cdot 0.5 + \left(-\color{blue}{z \cdot y}\right) \]

      3. distribute-rgt-neg-in 81.2%

         \[\leadsto x \cdot 0.5 + \color{blue}{z \cdot \left(-y\right)} \]

   4. Simplified 81.2%

      \[\leadsto x \cdot 0.5 + \color{blue}{z \cdot \left(-y\right)} \]
   5. Step-by-step derivation

      1. fma-def 81.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, 0.5, z \cdot \left(-y\right)\right)} \]

      2. distribute-rgt-neg-out 81.2%

         \[\leadsto \mathsf{fma}\left(x, 0.5, \color{blue}{-z \cdot y}\right) \]

      3. add-sqr-sqrt 44.9%

         \[\leadsto \mathsf{fma}\left(x, 0.5, -z \cdot \color{blue}{\left(\sqrt{y} \cdot \sqrt{y}\right)}\right) \]

      4. sqrt-unprod 59.8%

         \[\leadsto \mathsf{fma}\left(x, 0.5, -z \cdot \color{blue}{\sqrt{y \cdot y}}\right) \]

      5. sqr-neg 59.8%

         \[\leadsto \mathsf{fma}\left(x, 0.5, -z \cdot \sqrt{\color{blue}{\left(-y\right) \cdot \left(-y\right)}}\right) \]

      6. sqrt-unprod 18.1%

         \[\leadsto \mathsf{fma}\left(x, 0.5, -z \cdot \color{blue}{\left(\sqrt{-y} \cdot \sqrt{-y}\right)}\right) \]

      7. add-sqr-sqrt 44.0%

         \[\leadsto \mathsf{fma}\left(x, 0.5, -z \cdot \color{blue}{\left(-y\right)}\right) \]

      8. fma-neg 44.0%

         \[\leadsto \color{blue}{x \cdot 0.5 - z \cdot \left(-y\right)} \]

      9. add-sqr-sqrt 18.1%

         \[\leadsto x \cdot 0.5 - z \cdot \color{blue}{\left(\sqrt{-y} \cdot \sqrt{-y}\right)} \]

      10. sqrt-unprod 59.8%

          \[\leadsto x \cdot 0.5 - z \cdot \color{blue}{\sqrt{\left(-y\right) \cdot \left(-y\right)}} \]

      11. sqr-neg 59.8%

          \[\leadsto x \cdot 0.5 - z \cdot \sqrt{\color{blue}{y \cdot y}} \]

      12. sqrt-unprod 44.9%

          \[\leadsto x \cdot 0.5 - z \cdot \color{blue}{\left(\sqrt{y} \cdot \sqrt{y}\right)} \]

      13. add-sqr-sqrt 81.2%

          \[\leadsto x \cdot 0.5 - z \cdot \color{blue}{y} \]

      14. *-commutative 81.2%

          \[\leadsto x \cdot 0.5 - \color{blue}{y \cdot z} \]

   6. Applied egg-rr 81.2%

      \[\leadsto \color{blue}{x \cdot 0.5 - y \cdot z} \]

   if -1e-289 < (*.f64 x 1/2) < 3.50000000000000001e-258

   1. Initial program 99.4%

      \[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right) \]

   2. Taylor expanded in z around inf 99.4%

      \[\leadsto x \cdot 0.5 + y \cdot \color{blue}{\left(1 + \left(-1 \cdot z + -1 \cdot \log \left(\frac{1}{z}\right)\right)\right)} \]

   3. Taylor expanded in x around 0 99.4%

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

   4. Taylor expanded in z around 0 78.3%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot 0.5 \leq -1 \cdot 10^{-289} \lor \neg \left(x \cdot 0.5 \leq 3.5 \cdot 10^{-258}\right):\\ \;\;\;\;x \cdot 0.5 - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 + \log z\right)\\ \end{array} \]

Alternative 3: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot 0.5 + y \cdot \left(1 - \left(z + \log \left(\frac{1}{z}\right)\right)\right) \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ (* x 0.5) (* y (- 1.0 (+ z (log (/ 1.0 z)))))))

C

double code(double x, double y, double z) {
	return (x * 0.5) + (y * (1.0 - (z + log((1.0 / 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 * 0.5d0) + (y * (1.0d0 - (z + log((1.0d0 / z)))))
end function

Java

public static double code(double x, double y, double z) {
	return (x * 0.5) + (y * (1.0 - (z + Math.log((1.0 / z)))));
}

Python

def code(x, y, z):
	return (x * 0.5) + (y * (1.0 - (z + math.log((1.0 / z)))))

Julia

function code(x, y, z)
	return Float64(Float64(x * 0.5) + Float64(y * Float64(1.0 - Float64(z + log(Float64(1.0 / z))))))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x * 0.5) + (y * (1.0 - (z + log((1.0 / z)))));
end

Wolfram

code[x_, y_, z_] := N[(N[(x * 0.5), $MachinePrecision] + N[(y * N[(1.0 - N[(z + N[Log[N[(1.0 / z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right) \]

2. Taylor expanded in z around inf 99.9%

   \[\leadsto x \cdot 0.5 + y \cdot \color{blue}{\left(1 + \left(-1 \cdot z + -1 \cdot \log \left(\frac{1}{z}\right)\right)\right)} \]

3. Final simplification 99.9%

   \[\leadsto x \cdot 0.5 + y \cdot \left(1 - \left(z + \log \left(\frac{1}{z}\right)\right)\right) \]

Alternative 4: 85.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+68} \lor \neg \left(y \leq 1.35 \cdot 10^{+84}\right):\\ \;\;\;\;y \cdot \left(\left(1 - z\right) + \log z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 0.5 - y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -6e+68) (not (<= y 1.35e+84)))
   (* y (+ (- 1.0 z) (log z)))
   (- (* x 0.5) (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6e+68) || !(y <= 1.35e+84)) {
		tmp = y * ((1.0 - z) + log(z));
	} else {
		tmp = (x * 0.5) - (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 <= (-6d+68)) .or. (.not. (y <= 1.35d+84))) then
        tmp = y * ((1.0d0 - z) + log(z))
    else
        tmp = (x * 0.5d0) - (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6e+68) || !(y <= 1.35e+84)) {
		tmp = y * ((1.0 - z) + Math.log(z));
	} else {
		tmp = (x * 0.5) - (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -6e+68) or not (y <= 1.35e+84):
		tmp = y * ((1.0 - z) + math.log(z))
	else:
		tmp = (x * 0.5) - (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -6e+68) || !(y <= 1.35e+84))
		tmp = Float64(y * Float64(Float64(1.0 - z) + log(z)));
	else
		tmp = Float64(Float64(x * 0.5) - Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -6e+68) || ~((y <= 1.35e+84)))
		tmp = y * ((1.0 - z) + log(z));
	else
		tmp = (x * 0.5) - (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -6e+68], N[Not[LessEqual[y, 1.35e+84]], $MachinePrecision]], N[(y * N[(N[(1.0 - z), $MachinePrecision] + N[Log[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 0.5), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.0000000000000004e68 or 1.35e84 < y

   1. Initial program 99.8%

      \[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right) \]

   2. Taylor expanded in z around inf 99.8%

      \[\leadsto x \cdot 0.5 + y \cdot \color{blue}{\left(1 + \left(-1 \cdot z + -1 \cdot \log \left(\frac{1}{z}\right)\right)\right)} \]

   3. Taylor expanded in x around 0 93.5%

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

   4. Taylor expanded in z around 0 93.5%

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

      1. +-commutative 93.5%

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

      2. distribute-lft-in 93.4%

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

      3. *-rgt-identity 93.4%

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

      4. associate-+l+ 93.4%

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

      5. mul-1-neg 93.4%

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

      6. distribute-rgt-neg-in 93.4%

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

      7. mul-1-neg 93.4%

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

      8. distribute-lft-in 93.4%

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

      9. +-commutative 93.4%

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

      10. remove-double-neg 93.4%

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

      11. log-rec 93.4%

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

      12. mul-1-neg 93.4%

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

      13. *-rgt-identity 93.4%

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

      14. distribute-lft-in 93.5%

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

      15. +-commutative 93.5%

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

      16. +-commutative 93.5%

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

      17. associate-+r+ 93.5%

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

   6. Simplified 93.5%

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

   if -6.0000000000000004e68 < y < 1.35e84

   1. Initial program 99.9%

      \[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right) \]

   2. Taylor expanded in z around inf 88.0%

      \[\leadsto x \cdot 0.5 + \color{blue}{-1 \cdot \left(y \cdot z\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 88.0%

         \[\leadsto x \cdot 0.5 + \color{blue}{\left(-y \cdot z\right)} \]

      2. *-commutative 88.0%

         \[\leadsto x \cdot 0.5 + \left(-\color{blue}{z \cdot y}\right) \]

      3. distribute-rgt-neg-in 88.0%

         \[\leadsto x \cdot 0.5 + \color{blue}{z \cdot \left(-y\right)} \]

   4. Simplified 88.0%

      \[\leadsto x \cdot 0.5 + \color{blue}{z \cdot \left(-y\right)} \]
   5. Step-by-step derivation

      1. fma-def 88.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, 0.5, z \cdot \left(-y\right)\right)} \]

      2. distribute-rgt-neg-out 88.0%

         \[\leadsto \mathsf{fma}\left(x, 0.5, \color{blue}{-z \cdot y}\right) \]

      3. add-sqr-sqrt 50.9%

         \[\leadsto \mathsf{fma}\left(x, 0.5, -z \cdot \color{blue}{\left(\sqrt{y} \cdot \sqrt{y}\right)}\right) \]

      4. sqrt-unprod 72.8%

         \[\leadsto \mathsf{fma}\left(x, 0.5, -z \cdot \color{blue}{\sqrt{y \cdot y}}\right) \]

      5. sqr-neg 72.8%

         \[\leadsto \mathsf{fma}\left(x, 0.5, -z \cdot \sqrt{\color{blue}{\left(-y\right) \cdot \left(-y\right)}}\right) \]

      6. sqrt-unprod 25.4%

         \[\leadsto \mathsf{fma}\left(x, 0.5, -z \cdot \color{blue}{\left(\sqrt{-y} \cdot \sqrt{-y}\right)}\right) \]

      7. add-sqr-sqrt 60.5%

         \[\leadsto \mathsf{fma}\left(x, 0.5, -z \cdot \color{blue}{\left(-y\right)}\right) \]

      8. fma-neg 60.5%

         \[\leadsto \color{blue}{x \cdot 0.5 - z \cdot \left(-y\right)} \]

      9. add-sqr-sqrt 25.4%

         \[\leadsto x \cdot 0.5 - z \cdot \color{blue}{\left(\sqrt{-y} \cdot \sqrt{-y}\right)} \]

      10. sqrt-unprod 72.8%

          \[\leadsto x \cdot 0.5 - z \cdot \color{blue}{\sqrt{\left(-y\right) \cdot \left(-y\right)}} \]

      11. sqr-neg 72.8%

          \[\leadsto x \cdot 0.5 - z \cdot \sqrt{\color{blue}{y \cdot y}} \]

      12. sqrt-unprod 50.9%

          \[\leadsto x \cdot 0.5 - z \cdot \color{blue}{\left(\sqrt{y} \cdot \sqrt{y}\right)} \]

      13. add-sqr-sqrt 88.0%

          \[\leadsto x \cdot 0.5 - z \cdot \color{blue}{y} \]

      14. *-commutative 88.0%

          \[\leadsto x \cdot 0.5 - \color{blue}{y \cdot z} \]

   6. Applied egg-rr 88.0%

      \[\leadsto \color{blue}{x \cdot 0.5 - y \cdot z} \]
3. Recombined 2 regimes into one program.

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+68} \lor \neg \left(y \leq 1.35 \cdot 10^{+84}\right):\\ \;\;\;\;y \cdot \left(\left(1 - z\right) + \log z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 0.5 - y \cdot z\\ \end{array} \]

Alternative 5: 98.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 0.0002:\\ \;\;\;\;x \cdot 0.5 + y \cdot \left(1 + \log z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 0.5 - y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z 0.0002) (+ (* x 0.5) (* y (+ 1.0 (log z)))) (- (* x 0.5) (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 0.0002) {
		tmp = (x * 0.5) + (y * (1.0 + log(z)));
	} else {
		tmp = (x * 0.5) - (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 (z <= 0.0002d0) then
        tmp = (x * 0.5d0) + (y * (1.0d0 + log(z)))
    else
        tmp = (x * 0.5d0) - (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= 0.0002) {
		tmp = (x * 0.5) + (y * (1.0 + Math.log(z)));
	} else {
		tmp = (x * 0.5) - (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 0.0002:
		tmp = (x * 0.5) + (y * (1.0 + math.log(z)))
	else:
		tmp = (x * 0.5) - (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 0.0002)
		tmp = Float64(Float64(x * 0.5) + Float64(y * Float64(1.0 + log(z))));
	else
		tmp = Float64(Float64(x * 0.5) - Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 0.0002)
		tmp = (x * 0.5) + (y * (1.0 + log(z)));
	else
		tmp = (x * 0.5) - (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 0.0002], N[(N[(x * 0.5), $MachinePrecision] + N[(y * N[(1.0 + N[Log[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 0.5), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 2.0000000000000001e-4

   1. Initial program 99.8%

      \[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right) \]

   2. Taylor expanded in z around 0 99.2%

      \[\leadsto x \cdot 0.5 + \color{blue}{y \cdot \left(1 + \log z\right)} \]

   if 2.0000000000000001e-4 < z

   1. Initial program 100.0%

      \[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right) \]

   2. Taylor expanded in z around inf 98.8%

      \[\leadsto x \cdot 0.5 + \color{blue}{-1 \cdot \left(y \cdot z\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 98.8%

         \[\leadsto x \cdot 0.5 + \color{blue}{\left(-y \cdot z\right)} \]

      2. *-commutative 98.8%

         \[\leadsto x \cdot 0.5 + \left(-\color{blue}{z \cdot y}\right) \]

      3. distribute-rgt-neg-in 98.8%

         \[\leadsto x \cdot 0.5 + \color{blue}{z \cdot \left(-y\right)} \]

   4. Simplified 98.8%

      \[\leadsto x \cdot 0.5 + \color{blue}{z \cdot \left(-y\right)} \]
   5. Step-by-step derivation

      1. fma-def 98.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, 0.5, z \cdot \left(-y\right)\right)} \]

      2. distribute-rgt-neg-out 98.8%

         \[\leadsto \mathsf{fma}\left(x, 0.5, \color{blue}{-z \cdot y}\right) \]

      3. add-sqr-sqrt 51.7%

         \[\leadsto \mathsf{fma}\left(x, 0.5, -z \cdot \color{blue}{\left(\sqrt{y} \cdot \sqrt{y}\right)}\right) \]

      4. sqrt-unprod 60.9%

         \[\leadsto \mathsf{fma}\left(x, 0.5, -z \cdot \color{blue}{\sqrt{y \cdot y}}\right) \]

      5. sqr-neg 60.9%

         \[\leadsto \mathsf{fma}\left(x, 0.5, -z \cdot \sqrt{\color{blue}{\left(-y\right) \cdot \left(-y\right)}}\right) \]

      6. sqrt-unprod 13.7%

         \[\leadsto \mathsf{fma}\left(x, 0.5, -z \cdot \color{blue}{\left(\sqrt{-y} \cdot \sqrt{-y}\right)}\right) \]

      7. add-sqr-sqrt 30.3%

         \[\leadsto \mathsf{fma}\left(x, 0.5, -z \cdot \color{blue}{\left(-y\right)}\right) \]

      8. fma-neg 30.3%

         \[\leadsto \color{blue}{x \cdot 0.5 - z \cdot \left(-y\right)} \]

      9. add-sqr-sqrt 13.7%

         \[\leadsto x \cdot 0.5 - z \cdot \color{blue}{\left(\sqrt{-y} \cdot \sqrt{-y}\right)} \]

      10. sqrt-unprod 60.9%

          \[\leadsto x \cdot 0.5 - z \cdot \color{blue}{\sqrt{\left(-y\right) \cdot \left(-y\right)}} \]

      11. sqr-neg 60.9%

          \[\leadsto x \cdot 0.5 - z \cdot \sqrt{\color{blue}{y \cdot y}} \]

      12. sqrt-unprod 51.7%

          \[\leadsto x \cdot 0.5 - z \cdot \color{blue}{\left(\sqrt{y} \cdot \sqrt{y}\right)} \]

      13. add-sqr-sqrt 98.8%

          \[\leadsto x \cdot 0.5 - z \cdot \color{blue}{y} \]

      14. *-commutative 98.8%

          \[\leadsto x \cdot 0.5 - \color{blue}{y \cdot z} \]

   6. Applied egg-rr 98.8%

      \[\leadsto \color{blue}{x \cdot 0.5 - y \cdot z} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 0.0002:\\ \;\;\;\;x \cdot 0.5 + y \cdot \left(1 + \log z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 0.5 - y \cdot z\\ \end{array} \]

Alternative 6: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ (* x 0.5) (* y (+ (- 1.0 z) (log z)))))

C

double code(double x, double y, double z) {
	return (x * 0.5) + (y * ((1.0 - z) + log(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 * 0.5d0) + (y * ((1.0d0 - z) + log(z)))
end function

Java

public static double code(double x, double y, double z) {
	return (x * 0.5) + (y * ((1.0 - z) + Math.log(z)));
}

Python

def code(x, y, z):
	return (x * 0.5) + (y * ((1.0 - z) + math.log(z)))

Julia

function code(x, y, z)
	return Float64(Float64(x * 0.5) + Float64(y * Float64(Float64(1.0 - z) + log(z))))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x * 0.5) + (y * ((1.0 - z) + log(z)));
end

Wolfram

code[x_, y_, z_] := N[(N[(x * 0.5), $MachinePrecision] + N[(y * N[(N[(1.0 - z), $MachinePrecision] + N[Log[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right) \]

2. Final simplification 99.9%

   \[\leadsto x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right) \]

Alternative 7: 74.0% accurate, 15.9× speedup

Math

\[\begin{array}{l} \\ x \cdot 0.5 - y \cdot z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- (* x 0.5) (* y z)))

C

double code(double x, double y, double z) {
	return (x * 0.5) - (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 * 0.5d0) - (y * z)
end function

Java

public static double code(double x, double y, double z) {
	return (x * 0.5) - (y * z);
}

Python

def code(x, y, z):
	return (x * 0.5) - (y * z)

Julia

function code(x, y, z)
	return Float64(Float64(x * 0.5) - Float64(y * z))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x * 0.5) - (y * z);
end

Wolfram

code[x_, y_, z_] := N[(N[(x * 0.5), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right) \]

2. Taylor expanded in z around inf 78.7%

   \[\leadsto x \cdot 0.5 + \color{blue}{-1 \cdot \left(y \cdot z\right)} \]
3. Step-by-step derivation

   1. mul-1-neg 78.7%

      \[\leadsto x \cdot 0.5 + \color{blue}{\left(-y \cdot z\right)} \]

   2. *-commutative 78.7%

      \[\leadsto x \cdot 0.5 + \left(-\color{blue}{z \cdot y}\right) \]

   3. distribute-rgt-neg-in 78.7%

      \[\leadsto x \cdot 0.5 + \color{blue}{z \cdot \left(-y\right)} \]

4. Simplified 78.7%

   \[\leadsto x \cdot 0.5 + \color{blue}{z \cdot \left(-y\right)} \]
5. Step-by-step derivation

   1. fma-def 78.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, 0.5, z \cdot \left(-y\right)\right)} \]

   2. distribute-rgt-neg-out 78.7%

      \[\leadsto \mathsf{fma}\left(x, 0.5, \color{blue}{-z \cdot y}\right) \]

   3. add-sqr-sqrt 43.5%

      \[\leadsto \mathsf{fma}\left(x, 0.5, -z \cdot \color{blue}{\left(\sqrt{y} \cdot \sqrt{y}\right)}\right) \]

   4. sqrt-unprod 57.8%

      \[\leadsto \mathsf{fma}\left(x, 0.5, -z \cdot \color{blue}{\sqrt{y \cdot y}}\right) \]

   5. sqr-neg 57.8%

      \[\leadsto \mathsf{fma}\left(x, 0.5, -z \cdot \sqrt{\color{blue}{\left(-y\right) \cdot \left(-y\right)}}\right) \]

   6. sqrt-unprod 17.4%

      \[\leadsto \mathsf{fma}\left(x, 0.5, -z \cdot \color{blue}{\left(\sqrt{-y} \cdot \sqrt{-y}\right)}\right) \]

   7. add-sqr-sqrt 42.2%

      \[\leadsto \mathsf{fma}\left(x, 0.5, -z \cdot \color{blue}{\left(-y\right)}\right) \]

   8. fma-neg 42.2%

      \[\leadsto \color{blue}{x \cdot 0.5 - z \cdot \left(-y\right)} \]

   9. add-sqr-sqrt 17.4%

      \[\leadsto x \cdot 0.5 - z \cdot \color{blue}{\left(\sqrt{-y} \cdot \sqrt{-y}\right)} \]

   10. sqrt-unprod 57.8%

       \[\leadsto x \cdot 0.5 - z \cdot \color{blue}{\sqrt{\left(-y\right) \cdot \left(-y\right)}} \]

   11. sqr-neg 57.8%

       \[\leadsto x \cdot 0.5 - z \cdot \sqrt{\color{blue}{y \cdot y}} \]

   12. sqrt-unprod 43.5%

       \[\leadsto x \cdot 0.5 - z \cdot \color{blue}{\left(\sqrt{y} \cdot \sqrt{y}\right)} \]

   13. add-sqr-sqrt 78.7%

       \[\leadsto x \cdot 0.5 - z \cdot \color{blue}{y} \]

   14. *-commutative 78.7%

       \[\leadsto x \cdot 0.5 - \color{blue}{y \cdot z} \]

6. Applied egg-rr 78.7%

   \[\leadsto \color{blue}{x \cdot 0.5 - y \cdot z} \]

7. Final simplification 78.7%

   \[\leadsto x \cdot 0.5 - y \cdot z \]

Alternative 8: 58.4% accurate, 18.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 1.18 \cdot 10^{+67}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;-y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= z 1.18e+67) (* x 0.5) (- (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 1.18e+67) {
		tmp = x * 0.5;
	} else {
		tmp = -(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 (z <= 1.18d+67) then
        tmp = x * 0.5d0
    else
        tmp = -(y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= 1.18e+67) {
		tmp = x * 0.5;
	} else {
		tmp = -(y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 1.18e+67:
		tmp = x * 0.5
	else:
		tmp = -(y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 1.18e+67)
		tmp = Float64(x * 0.5);
	else
		tmp = Float64(-Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 1.18e+67)
		tmp = x * 0.5;
	else
		tmp = -(y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 1.18e+67], N[(x * 0.5), $MachinePrecision], (-N[(y * z), $MachinePrecision])]

Derivation

1. Split input into 2 regimes

2. if z < 1.17999999999999998e67

   1. Initial program 99.8%

      \[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right) \]

   2. Taylor expanded in x around inf 57.6%

      \[\leadsto \color{blue}{0.5 \cdot x} \]

   if 1.17999999999999998e67 < z

   1. Initial program 100.0%

      \[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right) \]

   2. Taylor expanded in z around inf 100.0%

      \[\leadsto x \cdot 0.5 + y \cdot \color{blue}{\left(1 + \left(-1 \cdot z + -1 \cdot \log \left(\frac{1}{z}\right)\right)\right)} \]

   3. Taylor expanded in x around 0 80.0%

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

   4. Taylor expanded in z around inf 80.0%

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

      1. mul-1-neg 80.0%

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

      2. distribute-rgt-neg-in 80.0%

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

   6. Simplified 80.0%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 1.18 \cdot 10^{+67}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;-y \cdot z\\ \end{array} \]

Alternative 9: 40.4% accurate, 37.0× speedup

Math

\[\begin{array}{l} \\ x \cdot 0.5 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* x 0.5))

C

double code(double x, double y, double z) {
	return x * 0.5;
}

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 * 0.5d0
end function

Java

public static double code(double x, double y, double z) {
	return x * 0.5;
}

Python

def code(x, y, z):
	return x * 0.5

Julia

function code(x, y, z)
	return Float64(x * 0.5)
end

MATLAB

function tmp = code(x, y, z)
	tmp = x * 0.5;
end

Wolfram

code[x_, y_, z_] := N[(x * 0.5), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right) \]

2. Taylor expanded in x around inf 43.2%

   \[\leadsto \color{blue}{0.5 \cdot x} \]

3. Final simplification 43.2%

   \[\leadsto x \cdot 0.5 \]

Developer target: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(y + 0.5 \cdot x\right) - y \cdot \left(z - \log z\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- (+ y (* 0.5 x)) (* y (- z (log z)))))

C

double code(double x, double y, double z) {
	return (y + (0.5 * x)) - (y * (z - log(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 = (y + (0.5d0 * x)) - (y * (z - log(z)))
end function

Java

public static double code(double x, double y, double z) {
	return (y + (0.5 * x)) - (y * (z - Math.log(z)));
}

Python

def code(x, y, z):
	return (y + (0.5 * x)) - (y * (z - math.log(z)))

Julia

function code(x, y, z)
	return Float64(Float64(y + Float64(0.5 * x)) - Float64(y * Float64(z - log(z))))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (y + (0.5 * x)) - (y * (z - log(z)));
end

Wolfram

code[x_, y_, z_] := N[(N[(y + N[(0.5 * x), $MachinePrecision]), $MachinePrecision] - N[(y * N[(z - N[Log[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2023311 
(FPCore (x y z)
  :name "System.Random.MWC.Distributions:gamma from mwc-random-0.13.3.2"
  :precision binary64

  :herbie-target
  (- (+ y (* 0.5 x)) (* y (- z (log z))))

  (+ (* x 0.5) (* y (+ (- 1.0 z) (log z)))))