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

Percentage Accurate: 99.9% → 99.9%

Time: 9.2s

Alternatives: 7

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. Add Preprocessing

Alternative 2: 85.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.45 \cdot 10^{+47} \lor \neg \left(y \leq 82000\right):\\ \;\;\;\;y \cdot \left(\left(1 + \log z\right) - z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 0.5 - y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.45e+47) (not (<= y 82000.0)))
   (* y (- (+ 1.0 (log z)) z))
   (- (* x 0.5) (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.45e+47) || !(y <= 82000.0)) {
		tmp = y * ((1.0 + log(z)) - 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 <= (-2.45d+47)) .or. (.not. (y <= 82000.0d0))) then
        tmp = y * ((1.0d0 + log(z)) - 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 <= -2.45e+47) || !(y <= 82000.0)) {
		tmp = y * ((1.0 + Math.log(z)) - z);
	} else {
		tmp = (x * 0.5) - (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.45e+47) or not (y <= 82000.0):
		tmp = y * ((1.0 + math.log(z)) - z)
	else:
		tmp = (x * 0.5) - (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.45e+47) || !(y <= 82000.0))
		tmp = Float64(y * Float64(Float64(1.0 + log(z)) - 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 <= -2.45e+47) || ~((y <= 82000.0)))
		tmp = y * ((1.0 + log(z)) - z);
	else
		tmp = (x * 0.5) - (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.45e+47], N[Not[LessEqual[y, 82000.0]], $MachinePrecision]], N[(y * N[(N[(1.0 + N[Log[z], $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision], N[(N[(x * 0.5), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.4500000000000001e47 or 82000 < y

   1. Initial program 99.9%

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

      1. add-cube-cbrt 98.9%

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

      2. pow3 98.9%

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

      3. *-commutative 98.9%

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

   4. Applied egg-rr 98.9%

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

   5. Taylor expanded in x around inf 85.4%

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

   6. Taylor expanded in x around 0 89.3%

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

   if -2.4500000000000001e47 < y < 82000

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 88.4%

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

      1. associate-*r* 88.4%

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

      2. mul-1-neg 88.4%

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

   5. Simplified 88.4%

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

      1. distribute-lft-neg-out 88.4%

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

      2. unsub-neg 88.4%

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

      3. add-sqr-sqrt 42.3%

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

      4. sqrt-unprod 67.3%

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

      5. sqr-neg 67.3%

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

      6. sqrt-unprod 29.5%

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

      7. add-sqr-sqrt 57.8%

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

      8. *-commutative 57.8%

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

      9. add-sqr-sqrt 29.5%

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

      10. sqrt-unprod 67.3%

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

      11. sqr-neg 67.3%

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

      12. sqrt-unprod 42.3%

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

      13. add-sqr-sqrt 88.4%

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

   7. Applied egg-rr 88.4%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.45 \cdot 10^{+47} \lor \neg \left(y \leq 82000\right):\\ \;\;\;\;y \cdot \left(\left(1 + \log z\right) - z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 0.5 - y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 0.27:\\ \;\;\;\;x \cdot 0.5 + y \cdot \left(1 + \log z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 0.5 - y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z 0.27) (+ (* 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 <= 0.27) {
		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 <= 0.27d0) 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 <= 0.27) {
		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 <= 0.27:
		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 <= 0.27)
		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 <= 0.27)
		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, 0.27], 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 < 0.27000000000000002

   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 98.8%

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

      1. *-commutative 98.8%

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

   5. Simplified 98.8%

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

   if 0.27000000000000002 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 98.7%

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

      1. associate-*r* 98.7%

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

      2. mul-1-neg 98.7%

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

   5. Simplified 98.7%

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

      1. distribute-lft-neg-out 98.7%

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

      2. unsub-neg 98.7%

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

      3. add-sqr-sqrt 53.5%

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

      4. sqrt-unprod 60.4%

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

      5. sqr-neg 60.4%

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

      6. sqrt-unprod 14.3%

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

      7. add-sqr-sqrt 30.5%

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

      8. *-commutative 30.5%

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

      9. add-sqr-sqrt 14.3%

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

      10. sqrt-unprod 60.4%

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

      11. sqr-neg 60.4%

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

      12. sqrt-unprod 53.5%

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

      13. add-sqr-sqrt 98.7%

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

   7. Applied egg-rr 98.7%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 0.27:\\ \;\;\;\;x \cdot 0.5 + y \cdot \left(1 + \log z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 0.5 - y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 75.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 7 \cdot 10^{-41}:\\ \;\;\;\;y \cdot \left(1 + \log z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 0.5 - y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z 7e-41) (* y (+ 1.0 (log z))) (- (* x 0.5) (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 7e-41) {
		tmp = 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 <= 7d-41) then
        tmp = 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 <= 7e-41) {
		tmp = 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 <= 7e-41:
		tmp = 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 <= 7e-41)
		tmp = 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 <= 7e-41)
		tmp = 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, 7e-41], N[(y * N[(1.0 + 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 z < 6.9999999999999999e-41

   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 98.6%

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

      2. pow3 98.7%

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

      3. *-commutative 98.7%

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

   4. Applied egg-rr 98.7%

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

   5. Taylor expanded in x around inf 89.5%

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

   6. Taylor expanded in z around 0 89.5%

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

      1. associate-/l* 88.6%

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

   8. Simplified 88.6%

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

   9. Taylor expanded in x around 0 63.1%

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

   if 6.9999999999999999e-41 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 95.9%

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

      1. associate-*r* 95.9%

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

      2. mul-1-neg 95.9%

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

   5. Simplified 95.9%

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

      1. distribute-lft-neg-out 95.9%

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

      2. unsub-neg 95.9%

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

      3. add-sqr-sqrt 52.6%

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

      4. sqrt-unprod 59.6%

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

      5. sqr-neg 59.6%

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

      6. sqrt-unprod 14.1%

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

      7. add-sqr-sqrt 31.3%

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

      8. *-commutative 31.3%

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

      9. add-sqr-sqrt 14.1%

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

      10. sqrt-unprod 59.6%

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

      11. sqr-neg 59.6%

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

      12. sqrt-unprod 52.6%

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

      13. add-sqr-sqrt 95.9%

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

   7. Applied egg-rr 95.9%

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

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 7 \cdot 10^{-41}:\\ \;\;\;\;y \cdot \left(1 + \log z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 0.5 - y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 58.8% accurate, 12.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 4.4 \cdot 10^{+65}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= z 4.4e+65) (* x 0.5) (* y (- z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 4.4e+65) {
		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 <= 4.4d+65) 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 <= 4.4e+65) {
		tmp = x * 0.5;
	} else {
		tmp = y * -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 4.4e+65:
		tmp = x * 0.5
	else:
		tmp = y * -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 4.4e+65)
		tmp = Float64(x * 0.5);
	else
		tmp = Float64(y * Float64(-z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 4.4e+65)
		tmp = x * 0.5;
	else
		tmp = y * -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 4.4e+65], N[(x * 0.5), $MachinePrecision], N[(y * (-z)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 4.3999999999999997e65

   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 inf 52.1%

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

      1. associate-*r* 52.1%

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

      2. mul-1-neg 52.1%

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

   5. Simplified 52.1%

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

   6. Taylor expanded in x around inf 42.8%

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

   if 4.3999999999999997e65 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around inf 100.0%

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

      1. associate-*r* 100.0%

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

      2. mul-1-neg 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around inf 94.2%

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

      1. neg-mul-1 94.2%

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

      2. +-commutative 94.2%

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

      3. unsub-neg 94.2%

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

   8. Simplified 94.2%

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

   9. Taylor expanded in y around inf 76.4%

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

       1. mul-1-neg 76.4%

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

       2. *-commutative 76.4%

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

       3. distribute-rgt-neg-in 76.4%

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

   11. Simplified 76.4%

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

4. Final simplification 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 4.4 \cdot 10^{+65}:\\ \;\;\;\;x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.4% 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 73.6%

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

   1. associate-*r* 73.6%

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

   2. mul-1-neg 73.6%

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

5. Simplified 73.6%

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

   1. distribute-lft-neg-out 73.6%

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

   2. unsub-neg 73.6%

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

   3. add-sqr-sqrt 38.2%

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

   4. sqrt-unprod 49.5%

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

   5. sqr-neg 49.5%

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

   6. sqrt-unprod 17.3%

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

   7. add-sqr-sqrt 33.8%

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

   8. *-commutative 33.8%

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

   9. add-sqr-sqrt 17.3%

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

   10. sqrt-unprod 49.5%

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

   11. sqr-neg 49.5%

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

   12. sqrt-unprod 38.2%

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

   13. add-sqr-sqrt 73.6%

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

7. Applied egg-rr 73.6%

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

8. Final simplification 73.6%

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

Alternative 7: 39.6% 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 z around inf 73.6%

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

   1. associate-*r* 73.6%

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

   2. mul-1-neg 73.6%

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

5. Simplified 73.6%

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

6. Taylor expanded in x around inf 34.8%

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

7. Final simplification 34.8%

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

Developer Target 1: 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 2024180 
(FPCore (x y z)
  :name "System.Random.MWC.Distributions:gamma from mwc-random-0.13.3.2"
  :precision binary64

  :alt
  (! :herbie-platform default (- (+ y (* 1/2 x)) (* y (- z (log z)))))

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