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

Percentage Accurate: 99.9% → 99.9%

Time: 11.5s

Alternatives: 6

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, 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. Add Preprocessing

3. Final simplification 99.9%

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

Alternative 2: 85.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+138} \lor \neg \left(y \leq -2.2 \cdot 10^{+92} \lor \neg \left(y \leq -1.05 \cdot 10^{+23}\right) \land y \leq 3.3 \cdot 10^{+79}\right):\\ \;\;\;\;y \cdot \left(\left(1 - z\right) + \log z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 0.5 - y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.9e+138)
         (not
          (or (<= y -2.2e+92) (and (not (<= y -1.05e+23)) (<= y 3.3e+79)))))
   (* y (+ (- 1.0 z) (log z)))
   (- (* x 0.5) (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.9e+138) || !((y <= -2.2e+92) || (!(y <= -1.05e+23) && (y <= 3.3e+79)))) {
		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 <= (-2.9d+138)) .or. (.not. (y <= (-2.2d+92)) .or. (.not. (y <= (-1.05d+23))) .and. (y <= 3.3d+79))) 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 <= -2.9e+138) || !((y <= -2.2e+92) || (!(y <= -1.05e+23) && (y <= 3.3e+79)))) {
		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 <= -2.9e+138) or not ((y <= -2.2e+92) or (not (y <= -1.05e+23) and (y <= 3.3e+79))):
		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 <= -2.9e+138) || !((y <= -2.2e+92) || (!(y <= -1.05e+23) && (y <= 3.3e+79))))
		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 <= -2.9e+138) || ~(((y <= -2.2e+92) || (~((y <= -1.05e+23)) && (y <= 3.3e+79)))))
		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, -2.9e+138], N[Not[Or[LessEqual[y, -2.2e+92], And[N[Not[LessEqual[y, -1.05e+23]], $MachinePrecision], LessEqual[y, 3.3e+79]]]], $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 < -2.9000000000000001e138 or -2.19999999999999992e92 < y < -1.0500000000000001e23 or 3.3000000000000002e79 < y

   1. Initial program 99.8%

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

      1. add-cube-cbrt 98.8%

         \[\leadsto x \cdot 0.5 + \color{blue}{\left(\sqrt[3]{y \cdot \left(\left(1 - z\right) + \log z\right)} \cdot \sqrt[3]{y \cdot \left(\left(1 - z\right) + \log z\right)}\right) \cdot \sqrt[3]{y \cdot \left(\left(1 - z\right) + \log z\right)}} \]

      2. pow3 98.9%

         \[\leadsto x \cdot 0.5 + \color{blue}{{\left(\sqrt[3]{y \cdot \left(\left(1 - z\right) + \log z\right)}\right)}^{3}} \]

   4. Applied egg-rr 98.9%

      \[\leadsto x \cdot 0.5 + \color{blue}{{\left(\sqrt[3]{y \cdot \left(\left(1 - z\right) + \log z\right)}\right)}^{3}} \]

   5. Taylor expanded in x around 0 95.4%

      \[\leadsto \color{blue}{{1}^{0.3333333333333333} \cdot \left(y \cdot \left(\left(1 + \log z\right) - z\right)\right)} \]
   6. Step-by-step derivation

      1. pow-base-1 95.4%

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

      2. associate-*r* 95.4%

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

      3. *-lft-identity 95.4%

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

      4. +-commutative 95.4%

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

      5. associate-+r- 95.4%

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

   7. Simplified 95.4%

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

   if -2.9000000000000001e138 < y < -2.19999999999999992e92 or -1.0500000000000001e23 < y < 3.3000000000000002e79

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 86.7%

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

      1. mul-1-neg 86.7%

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

      2. *-commutative 86.7%

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

      3. distribute-rgt-neg-in 86.7%

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

   5. Simplified 86.7%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+138} \lor \neg \left(y \leq -2.2 \cdot 10^{+92} \lor \neg \left(y \leq -1.05 \cdot 10^{+23}\right) \land y \leq 3.3 \cdot 10^{+79}\right):\\ \;\;\;\;y \cdot \left(\left(1 - z\right) + \log z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 0.5 - y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 4 \cdot 10^{-185} \lor \neg \left(z \leq 1.45 \cdot 10^{-117}\right):\\ \;\;\;\;x \cdot 0.5 - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 + \log z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z 4e-185) (not (<= z 1.45e-117)))
   (- (* x 0.5) (* y z))
   (* y (+ 1.0 (log z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= 4e-185) || !(z <= 1.45e-117)) {
		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 ((z <= 4d-185) .or. (.not. (z <= 1.45d-117))) 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 ((z <= 4e-185) || !(z <= 1.45e-117)) {
		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 (z <= 4e-185) or not (z <= 1.45e-117):
		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 ((z <= 4e-185) || !(z <= 1.45e-117))
		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 ((z <= 4e-185) || ~((z <= 1.45e-117)))
		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[z, 4e-185], N[Not[LessEqual[z, 1.45e-117]], $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 z < 4e-185 or 1.45e-117 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in z around inf 81.5%

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

      1. mul-1-neg 81.5%

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

      2. *-commutative 81.5%

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

      3. distribute-rgt-neg-in 81.5%

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

   5. Simplified 81.5%

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

   if 4e-185 < z < 1.45e-117

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. fma-define 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in z around 0 99.6%

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

   6. Taylor expanded in y around inf 79.1%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 4 \cdot 10^{-185} \lor \neg \left(z \leq 1.45 \cdot 10^{-117}\right):\\ \;\;\;\;x \cdot 0.5 - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 + \log z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 7 \cdot 10^{-6}:\\ \;\;\;\;x \cdot 0.5 + y \cdot \left(1 + \log z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 0.5 + y \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z 7e-6)
   (+ (* x 0.5) (* y (+ 1.0 (log z))))
   (+ (* x 0.5) (* y (- 1.0 z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 7e-6) {
		tmp = (x * 0.5) + (y * (1.0 + log(z)));
	} else {
		tmp = (x * 0.5) + (y * (1.0 - 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 <= 7d-6) then
        tmp = (x * 0.5d0) + (y * (1.0d0 + log(z)))
    else
        tmp = (x * 0.5d0) + (y * (1.0d0 - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= 7e-6) {
		tmp = (x * 0.5) + (y * (1.0 + Math.log(z)));
	} else {
		tmp = (x * 0.5) + (y * (1.0 - z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 7e-6:
		tmp = (x * 0.5) + (y * (1.0 + math.log(z)))
	else:
		tmp = (x * 0.5) + (y * (1.0 - z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 7e-6)
		tmp = Float64(Float64(x * 0.5) + Float64(y * Float64(1.0 + log(z))));
	else
		tmp = Float64(Float64(x * 0.5) + Float64(y * Float64(1.0 - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 7e-6)
		tmp = (x * 0.5) + (y * (1.0 + log(z)));
	else
		tmp = (x * 0.5) + (y * (1.0 - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 7e-6], 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 * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 6.99999999999999989e-6

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 99.3%

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

   if 6.99999999999999989e-6 < z

   1. Initial program 100.0%

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

      1. distribute-lft-in 99.2%

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

   4. Applied egg-rr 99.2%

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

      1. add-sqr-sqrt 45.8%

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

      2. pow2 45.8%

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

   6. Applied egg-rr 45.8%

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

   7. Taylor expanded in y around 0 97.6%

      \[\leadsto x \cdot 0.5 + \color{blue}{y \cdot \left(1 - z\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 7 \cdot 10^{-6}:\\ \;\;\;\;x \cdot 0.5 + y \cdot \left(1 + \log z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 0.5 + y \cdot \left(1 - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.8% 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. Add Preprocessing

3. Taylor expanded in z around inf 75.3%

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

   1. mul-1-neg 75.3%

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

   2. *-commutative 75.3%

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

   3. distribute-rgt-neg-in 75.3%

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

5. Simplified 75.3%

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

6. Final simplification 75.3%

   \[\leadsto x \cdot 0.5 - y \cdot z \]
7. Add Preprocessing

Alternative 6: 39.2% 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. Add Preprocessing

3. Taylor expanded in x around inf 40.7%

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

4. Final simplification 40.7%

   \[\leadsto x \cdot 0.5 \]
5. Add Preprocessing

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 2024045 
(FPCore (x y z)
  :name "System.Random.MWC.Distributions:gamma from mwc-random-0.13.3.2"
  :precision binary64

  :alt
  (- (+ y (* 0.5 x)) (* y (- z (log z))))

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