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

Percentage Accurate: 99.9% → 99.9%

Time: 8.8s

Alternatives: 10

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: 99.9% accurate, 0.5× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return fma((1.0 + (log(z) - z)), y, (x * 0.5));
}

Julia

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

Wolfram

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

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

   2. *-commutative 99.9%

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

   3. fma-def 99.9%

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

   4. sub-neg 99.9%

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

   5. associate-+l+ 99.9%

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

   6. +-commutative 99.9%

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

   7. sub-neg 99.9%

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

3. Applied egg-rr 99.9%

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

4. Final simplification 99.9%

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

Alternative 2: 75.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 3.7 \cdot 10^{-294} \lor \neg \left(z \leq 2.6 \cdot 10^{-241}\right) \land z \leq 4 \cdot 10^{-158}:\\ \;\;\;\;y \cdot \left(1 + \log z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 0.5 - z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z 3.7e-294) (and (not (<= z 2.6e-241)) (<= z 4e-158)))
   (* y (+ 1.0 (log z)))
   (- (* x 0.5) (* z y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= 3.7e-294) || (!(z <= 2.6e-241) && (z <= 4e-158))) {
		tmp = y * (1.0 + log(z));
	} else {
		tmp = (x * 0.5) - (z * 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 <= 3.7d-294) .or. (.not. (z <= 2.6d-241)) .and. (z <= 4d-158)) then
        tmp = y * (1.0d0 + log(z))
    else
        tmp = (x * 0.5d0) - (z * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= 3.7e-294) || (!(z <= 2.6e-241) && (z <= 4e-158))) {
		tmp = y * (1.0 + Math.log(z));
	} else {
		tmp = (x * 0.5) - (z * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= 3.7e-294) or (not (z <= 2.6e-241) and (z <= 4e-158)):
		tmp = y * (1.0 + math.log(z))
	else:
		tmp = (x * 0.5) - (z * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= 3.7e-294) || (!(z <= 2.6e-241) && (z <= 4e-158)))
		tmp = Float64(y * Float64(1.0 + log(z)));
	else
		tmp = Float64(Float64(x * 0.5) - Float64(z * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= 3.7e-294) || (~((z <= 2.6e-241)) && (z <= 4e-158)))
		tmp = y * (1.0 + log(z));
	else
		tmp = (x * 0.5) - (z * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, 3.7e-294], And[N[Not[LessEqual[z, 2.6e-241]], $MachinePrecision], LessEqual[z, 4e-158]]], N[(y * N[(1.0 + N[Log[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 0.5), $MachinePrecision] - N[(z * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 3.69999999999999994e-294 or 2.5999999999999999e-241 < z < 4.00000000000000026e-158

   1. Initial program 99.6%

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

   2. Taylor expanded in z around 0 99.6%

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

   3. Taylor expanded in x around 0 67.6%

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

   if 3.69999999999999994e-294 < z < 2.5999999999999999e-241 or 4.00000000000000026e-158 < z

   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 88.6%

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

      1. mul-1-neg 88.6%

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

      2. distribute-rgt-neg-out 88.6%

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

   4. Simplified 88.6%

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

4. Final simplification 85.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 3.7 \cdot 10^{-294} \lor \neg \left(z \leq 2.6 \cdot 10^{-241}\right) \land z \leq 4 \cdot 10^{-158}:\\ \;\;\;\;y \cdot \left(1 + \log z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 0.5 - z \cdot y\\ \end{array} \]

Alternative 3: 75.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 4.6 \cdot 10^{-295}:\\ \;\;\;\;y \cdot \left(1 + \log z\right)\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-241} \lor \neg \left(z \leq 4.4 \cdot 10^{-158}\right):\\ \;\;\;\;x \cdot 0.5 - z \cdot y\\ \mathbf{else}:\\ \;\;\;\;y + \log z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z 4.6e-295)
   (* y (+ 1.0 (log z)))
   (if (or (<= z 2.9e-241) (not (<= z 4.4e-158)))
     (- (* x 0.5) (* z y))
     (+ y (* (log z) y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 4.6e-295) {
		tmp = y * (1.0 + log(z));
	} else if ((z <= 2.9e-241) || !(z <= 4.4e-158)) {
		tmp = (x * 0.5) - (z * y);
	} else {
		tmp = y + (log(z) * 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 <= 4.6d-295) then
        tmp = y * (1.0d0 + log(z))
    else if ((z <= 2.9d-241) .or. (.not. (z <= 4.4d-158))) then
        tmp = (x * 0.5d0) - (z * y)
    else
        tmp = y + (log(z) * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= 4.6e-295) {
		tmp = y * (1.0 + Math.log(z));
	} else if ((z <= 2.9e-241) || !(z <= 4.4e-158)) {
		tmp = (x * 0.5) - (z * y);
	} else {
		tmp = y + (Math.log(z) * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 4.6e-295:
		tmp = y * (1.0 + math.log(z))
	elif (z <= 2.9e-241) or not (z <= 4.4e-158):
		tmp = (x * 0.5) - (z * y)
	else:
		tmp = y + (math.log(z) * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 4.6e-295)
		tmp = Float64(y * Float64(1.0 + log(z)));
	elseif ((z <= 2.9e-241) || !(z <= 4.4e-158))
		tmp = Float64(Float64(x * 0.5) - Float64(z * y));
	else
		tmp = Float64(y + Float64(log(z) * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 4.6e-295)
		tmp = y * (1.0 + log(z));
	elseif ((z <= 2.9e-241) || ~((z <= 4.4e-158)))
		tmp = (x * 0.5) - (z * y);
	else
		tmp = y + (log(z) * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 4.6e-295], N[(y * N[(1.0 + N[Log[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 2.9e-241], N[Not[LessEqual[z, 4.4e-158]], $MachinePrecision]], N[(N[(x * 0.5), $MachinePrecision] - N[(z * y), $MachinePrecision]), $MachinePrecision], N[(y + N[(N[Log[z], $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < 4.6e-295

   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 99.8%

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

   3. Taylor expanded in x around 0 87.7%

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

   if 4.6e-295 < z < 2.8999999999999999e-241 or 4.4000000000000002e-158 < z

   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 88.6%

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

      1. mul-1-neg 88.6%

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

      2. distribute-rgt-neg-out 88.6%

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

   4. Simplified 88.6%

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

   if 2.8999999999999999e-241 < z < 4.4000000000000002e-158

   1. Initial program 99.5%

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

      1. sub-neg 99.5%

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

      2. associate-+l+ 99.5%

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

      3. distribute-lft-in 99.6%

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

      4. *-rgt-identity 99.6%

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

      5. associate-+r+ 99.6%

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

      6. fma-def 99.6%

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

      7. +-commutative 99.6%

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

      8. unsub-neg 99.6%

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

   3. Simplified 99.6%

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

      1. flip-- 99.4%

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

      2. associate-*r/ 99.4%

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

      3. pow2 99.4%

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

      4. +-commutative 99.4%

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

   5. Applied egg-rr 99.4%

      \[\leadsto \mathsf{fma}\left(x, 0.5, y\right) + \color{blue}{\frac{y \cdot \left({\log z}^{2} - z \cdot z\right)}{z + \log z}} \]
   6. Step-by-step derivation

      1. *-commutative 99.4%

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

      2. associate-/l* 99.5%

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

   7. Simplified 99.5%

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

   8. Taylor expanded in x around 0 63.0%

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

      1. associate-/l* 63.0%

         \[\leadsto y + \color{blue}{\frac{{\log z}^{2} - {z}^{2}}{\frac{\log z + z}{y}}} \]

      2. unpow2 63.0%

         \[\leadsto y + \frac{{\log z}^{2} - \color{blue}{z \cdot z}}{\frac{\log z + z}{y}} \]

      3. +-commutative 63.0%

         \[\leadsto y + \frac{{\log z}^{2} - z \cdot z}{\frac{\color{blue}{z + \log z}}{y}} \]

   10. Simplified 63.0%

       \[\leadsto \color{blue}{y + \frac{{\log z}^{2} - z \cdot z}{\frac{z + \log z}{y}}} \]

   11. Taylor expanded in z around 0 63.1%

       \[\leadsto \color{blue}{y \cdot \log z + y} \]
3. Recombined 3 regimes into one program.

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 4.6 \cdot 10^{-295}:\\ \;\;\;\;y \cdot \left(1 + \log z\right)\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-241} \lor \neg \left(z \leq 4.4 \cdot 10^{-158}\right):\\ \;\;\;\;x \cdot 0.5 - z \cdot y\\ \mathbf{else}:\\ \;\;\;\;y + \log z \cdot y\\ \end{array} \]

Alternative 4: 85.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+52} \lor \neg \left(y \leq 1.9 \cdot 10^{+46}\right):\\ \;\;\;\;y \cdot \left(\left(1 + \log z\right) - z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 0.5 - z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3e+52) (not (<= y 1.9e+46)))
   (* y (- (+ 1.0 (log z)) z))
   (- (* x 0.5) (* z y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3e+52) || !(y <= 1.9e+46)) {
		tmp = y * ((1.0 + log(z)) - z);
	} else {
		tmp = (x * 0.5) - (z * 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 ((y <= (-3d+52)) .or. (.not. (y <= 1.9d+46))) then
        tmp = y * ((1.0d0 + log(z)) - z)
    else
        tmp = (x * 0.5d0) - (z * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3e+52) || !(y <= 1.9e+46)) {
		tmp = y * ((1.0 + Math.log(z)) - z);
	} else {
		tmp = (x * 0.5) - (z * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3e+52) or not (y <= 1.9e+46):
		tmp = y * ((1.0 + math.log(z)) - z)
	else:
		tmp = (x * 0.5) - (z * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3e+52) || !(y <= 1.9e+46))
		tmp = Float64(y * Float64(Float64(1.0 + log(z)) - z));
	else
		tmp = Float64(Float64(x * 0.5) - Float64(z * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -3e+52) || ~((y <= 1.9e+46)))
		tmp = y * ((1.0 + log(z)) - z);
	else
		tmp = (x * 0.5) - (z * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3e+52], N[Not[LessEqual[y, 1.9e+46]], $MachinePrecision]], N[(y * N[(N[(1.0 + N[Log[z], $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision], N[(N[(x * 0.5), $MachinePrecision] - N[(z * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3e52 or 1.9e46 < y

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. *-commutative 99.8%

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

      3. fma-def 99.8%

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

      4. sub-neg 99.8%

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

      5. associate-+l+ 99.8%

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

      6. +-commutative 99.8%

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

      7. sub-neg 99.8%

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

   3. Applied egg-rr 99.8%

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

   4. Taylor expanded in y around inf 88.5%

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

   if -3e52 < y < 1.9e46

   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 91.7%

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

      1. mul-1-neg 91.7%

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

      2. distribute-rgt-neg-out 91.7%

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

   4. Simplified 91.7%

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

4. Final simplification 90.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+52} \lor \neg \left(y \leq 1.9 \cdot 10^{+46}\right):\\ \;\;\;\;y \cdot \left(\left(1 + \log z\right) - z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 0.5 - z \cdot y\\ \end{array} \]

Alternative 5: 98.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 0.041:\\ \;\;\;\;x \cdot 0.5 + y \cdot \left(1 + \log z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 0.5 - z \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z 0.041) (+ (* x 0.5) (* y (+ 1.0 (log z)))) (- (* x 0.5) (* z y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 0.041) {
		tmp = (x * 0.5) + (y * (1.0 + log(z)));
	} else {
		tmp = (x * 0.5) - (z * 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 <= 0.041d0) then
        tmp = (x * 0.5d0) + (y * (1.0d0 + log(z)))
    else
        tmp = (x * 0.5d0) - (z * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= 0.041) {
		tmp = (x * 0.5) + (y * (1.0 + Math.log(z)));
	} else {
		tmp = (x * 0.5) - (z * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 0.041:
		tmp = (x * 0.5) + (y * (1.0 + math.log(z)))
	else:
		tmp = (x * 0.5) - (z * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 0.041)
		tmp = Float64(Float64(x * 0.5) + Float64(y * Float64(1.0 + log(z))));
	else
		tmp = Float64(Float64(x * 0.5) - Float64(z * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 0.041)
		tmp = (x * 0.5) + (y * (1.0 + log(z)));
	else
		tmp = (x * 0.5) - (z * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 0.041], 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[(z * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 0.0410000000000000017

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0 98.8%

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

   if 0.0410000000000000017 < 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 99.6%

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

      1. mul-1-neg 99.6%

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

      2. distribute-rgt-neg-out 99.6%

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

   4. Simplified 99.6%

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

4. Final simplification 99.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 0.041:\\ \;\;\;\;x \cdot 0.5 + y \cdot \left(1 + \log z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 0.5 - z \cdot y\\ \end{array} \]

Alternative 6: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

Alternative 7: 74.3% accurate, 15.9× speedup

Math

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

FPCore

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

C

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

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) - (z * y)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(N[(x * 0.5), $MachinePrecision] - N[(z * y), $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 79.3%

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

   1. mul-1-neg 79.3%

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

   2. distribute-rgt-neg-out 79.3%

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

4. Simplified 79.3%

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

5. Final simplification 79.3%

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

Alternative 8: 57.8% accurate, 18.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 1.7 \cdot 10^{+94}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= z 1.7e+94) (* x 0.5) (* z (- y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 1.7e+94) {
		tmp = x * 0.5;
	} else {
		tmp = z * -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 <= 1.7d+94) then
        tmp = x * 0.5d0
    else
        tmp = z * -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= 1.7e+94) {
		tmp = x * 0.5;
	} else {
		tmp = z * -y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 1.7e+94:
		tmp = x * 0.5
	else:
		tmp = z * -y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 1.7e+94)
		tmp = Float64(x * 0.5);
	else
		tmp = Float64(z * Float64(-y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 1.7e+94)
		tmp = x * 0.5;
	else
		tmp = z * -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 1.7e+94], N[(x * 0.5), $MachinePrecision], N[(z * (-y)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 1.7000000000000001e94

   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 55.6%

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

   if 1.7000000000000001e94 < z

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. *-commutative 100.0%

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

      3. fma-def 100.0%

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

      4. sub-neg 100.0%

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

      5. associate-+l+ 100.0%

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

      6. +-commutative 100.0%

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

      7. sub-neg 100.0%

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

   3. Applied egg-rr 100.0%

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

   4. Taylor expanded in z around inf 82.4%

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

      1. mul-1-neg 82.4%

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

      2. *-commutative 82.4%

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

      3. distribute-rgt-neg-in 82.4%

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

   6. Simplified 82.4%

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

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 1.7 \cdot 10^{+94}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \end{array} \]

Alternative 9: 40.1% 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 41.7%

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

3. Final simplification 41.7%

   \[\leadsto x \cdot 0.5 \]

Alternative 10: 1.8% accurate, 111.0× speedup

Math

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

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := y

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. sub-neg 99.9%

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

   2. associate-+l+ 99.9%

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

   3. distribute-lft-in 99.8%

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

   4. *-rgt-identity 99.8%

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

   5. associate-+r+ 99.8%

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

   6. fma-def 99.8%

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

   7. +-commutative 99.8%

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

   8. unsub-neg 99.8%

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

3. Simplified 99.8%

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

   1. flip-- 82.3%

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

   2. associate-*r/ 79.1%

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

   3. pow2 79.1%

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

   4. +-commutative 79.1%

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

5. Applied egg-rr 79.1%

   \[\leadsto \mathsf{fma}\left(x, 0.5, y\right) + \color{blue}{\frac{y \cdot \left({\log z}^{2} - z \cdot z\right)}{z + \log z}} \]
6. Step-by-step derivation

   1. *-commutative 79.1%

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

   2. associate-/l* 80.8%

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

7. Simplified 80.8%

   \[\leadsto \mathsf{fma}\left(x, 0.5, y\right) + \color{blue}{\frac{{\log z}^{2} - z \cdot z}{\frac{z + \log z}{y}}} \]
8. Step-by-step derivation

   1. add-cube-cbrt 80.4%

      \[\leadsto \mathsf{fma}\left(x, 0.5, y\right) + \color{blue}{\left(\sqrt[3]{\frac{{\log z}^{2} - z \cdot z}{\frac{z + \log z}{y}}} \cdot \sqrt[3]{\frac{{\log z}^{2} - z \cdot z}{\frac{z + \log z}{y}}}\right) \cdot \sqrt[3]{\frac{{\log z}^{2} - z \cdot z}{\frac{z + \log z}{y}}}} \]

   2. pow3 80.4%

      \[\leadsto \mathsf{fma}\left(x, 0.5, y\right) + \color{blue}{{\left(\sqrt[3]{\frac{{\log z}^{2} - z \cdot z}{\frac{z + \log z}{y}}}\right)}^{3}} \]

   3. associate-/r/ 81.9%

      \[\leadsto \mathsf{fma}\left(x, 0.5, y\right) + {\left(\sqrt[3]{\color{blue}{\frac{{\log z}^{2} - z \cdot z}{z + \log z} \cdot y}}\right)}^{3} \]

   4. unpow2 81.9%

      \[\leadsto \mathsf{fma}\left(x, 0.5, y\right) + {\left(\sqrt[3]{\frac{\color{blue}{\log z \cdot \log z} - z \cdot z}{z + \log z} \cdot y}\right)}^{3} \]

   5. +-commutative 81.9%

      \[\leadsto \mathsf{fma}\left(x, 0.5, y\right) + {\left(\sqrt[3]{\frac{\log z \cdot \log z - z \cdot z}{\color{blue}{\log z + z}} \cdot y}\right)}^{3} \]

   6. flip-- 99.0%

      \[\leadsto \mathsf{fma}\left(x, 0.5, y\right) + {\left(\sqrt[3]{\color{blue}{\left(\log z - z\right)} \cdot y}\right)}^{3} \]

9. Applied egg-rr 99.0%

   \[\leadsto \mathsf{fma}\left(x, 0.5, y\right) + \color{blue}{{\left(\sqrt[3]{\left(\log z - z\right) \cdot y}\right)}^{3}} \]

10. Taylor expanded in y around inf 2.0%

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

11. Final simplification 2.0%

    \[\leadsto y \]

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 2023174 
(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)))))