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

Percentage Accurate: 99.9% → 99.9%

Time: 10.1s

Alternatives: 8

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

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_] := N[(y * N[(N[(1.0 - z), $MachinePrecision] + N[Log[z], $MachinePrecision]), $MachinePrecision] + 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. fma-define 99.9%

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

3. Simplified 99.9%

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

Alternative 2: 84.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot 0.5 \leq -5 \cdot 10^{+77} \lor \neg \left(x \cdot 0.5 \leq 100000000\right):\\ \;\;\;\;x \cdot 0.5 - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\left(1 + \log z\right) - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= (* x 0.5) -5e+77) (not (<= (* x 0.5) 100000000.0)))
   (- (* x 0.5) (* y z))
   (* y (- (+ 1.0 (log z)) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (((x * 0.5) <= -5e+77) || !((x * 0.5) <= 100000000.0)) {
		tmp = (x * 0.5) - (y * z);
	} else {
		tmp = y * ((1.0 + log(z)) - 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) <= (-5d+77)) .or. (.not. ((x * 0.5d0) <= 100000000.0d0))) then
        tmp = (x * 0.5d0) - (y * z)
    else
        tmp = y * ((1.0d0 + log(z)) - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (((x * 0.5) <= -5e+77) || !((x * 0.5) <= 100000000.0)) {
		tmp = (x * 0.5) - (y * z);
	} else {
		tmp = y * ((1.0 + Math.log(z)) - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if ((x * 0.5) <= -5e+77) or not ((x * 0.5) <= 100000000.0):
		tmp = (x * 0.5) - (y * z)
	else:
		tmp = y * ((1.0 + math.log(z)) - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((Float64(x * 0.5) <= -5e+77) || !(Float64(x * 0.5) <= 100000000.0))
		tmp = Float64(Float64(x * 0.5) - Float64(y * z));
	else
		tmp = Float64(y * Float64(Float64(1.0 + log(z)) - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (((x * 0.5) <= -5e+77) || ~(((x * 0.5) <= 100000000.0)))
		tmp = (x * 0.5) - (y * z);
	else
		tmp = y * ((1.0 + log(z)) - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[N[(x * 0.5), $MachinePrecision], -5e+77], N[Not[LessEqual[N[(x * 0.5), $MachinePrecision], 100000000.0]], $MachinePrecision]], N[(N[(x * 0.5), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(1.0 + N[Log[z], $MachinePrecision]), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x #s(literal 1/2 binary64)) < -5.00000000000000004e77 or 1e8 < (*.f64 x #s(literal 1/2 binary64))

   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 89.2%

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

      1. associate-*r* 89.2%

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

      2. neg-mul-1 89.2%

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

   5. Simplified 89.2%

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

   6. Taylor expanded in x around 0 89.2%

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

      1. +-commutative 89.2%

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

      2. *-commutative 89.2%

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

      3. neg-mul-1 89.2%

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

      4. unsub-neg 89.2%

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

      5. *-commutative 89.2%

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

   8. Simplified 89.2%

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

   if -5.00000000000000004e77 < (*.f64 x #s(literal 1/2 binary64)) < 1e8

   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 y around inf 99.0%

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

   4. Taylor expanded in y around inf 82.4%

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

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot 0.5 \leq -5 \cdot 10^{+77} \lor \neg \left(x \cdot 0.5 \leq 100000000\right):\\ \;\;\;\;x \cdot 0.5 - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\left(1 + \log z\right) - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 0.035:\\ \;\;\;\;x \cdot 0.5 + y \cdot \left(1 + \log z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 0.5 - y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z 0.035) (+ (* 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 <= 0.035) {
		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 <= 0.035d0) 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 <= 0.035) {
		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 <= 0.035:
		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 <= 0.035)
		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 <= 0.035)
		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, 0.035], 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 < 0.035000000000000003

   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 99.4%

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

      1. *-commutative 99.4%

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

   5. Simplified 99.4%

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

   if 0.035000000000000003 < 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. neg-mul-1 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. Taylor expanded in x around 0 98.7%

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

      1. +-commutative 98.7%

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

      2. *-commutative 98.7%

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

      3. neg-mul-1 98.7%

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

      4. unsub-neg 98.7%

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

      5. *-commutative 98.7%

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

   8. Simplified 98.7%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 0.035:\\ \;\;\;\;x \cdot 0.5 + y \cdot \left(1 + \log z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 0.5 - y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 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 5: 74.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+187}:\\ \;\;\;\;y \cdot \left(1 + \log z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 0.5 - y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.2e+187) (* y (+ 1.0 (log z))) (- (* x 0.5) (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.2e+187) {
		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 (y <= (-2.2d+187)) 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 (y <= -2.2e+187) {
		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 y <= -2.2e+187:
		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 (y <= -2.2e+187)
		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 (y <= -2.2e+187)
		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[y, -2.2e+187], 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 y < -2.1999999999999998e187

   1. Initial program 99.6%

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

   3. Taylor expanded in z around inf 41.2%

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

      1. +-commutative 41.2%

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

      2. neg-mul-1 41.2%

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

      3. unsub-neg 41.2%

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

      4. fma-define 41.2%

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

      5. *-commutative 41.2%

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

      6. associate-/l* 41.2%

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

      7. mul-1-neg 41.2%

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

      8. log-rec 41.2%

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

      9. remove-double-neg 41.2%

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

   5. Simplified 41.2%

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

   6. Taylor expanded in x around 0 42.4%

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

      1. sub-neg 42.4%

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

      2. associate-/l* 42.4%

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

      3. neg-mul-1 42.4%

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

      4. *-commutative 42.4%

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

      5. distribute-lft-out 42.4%

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

      6. +-commutative 42.4%

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

   8. Simplified 42.4%

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

   9. Taylor expanded in z around 0 76.5%

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

   if -2.1999999999999998e187 < y

   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 75.7%

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

      1. associate-*r* 75.7%

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

      2. neg-mul-1 75.7%

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

   5. Simplified 75.7%

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

   6. Taylor expanded in x around 0 75.7%

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

      1. +-commutative 75.7%

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

      2. *-commutative 75.7%

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

      3. neg-mul-1 75.7%

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

      4. unsub-neg 75.7%

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

      5. *-commutative 75.7%

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

   8. Simplified 75.7%

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

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+187}:\\ \;\;\;\;y \cdot \left(1 + \log z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 0.5 - y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 54.4% accurate, 7.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.02 \cdot 10^{+77} \lor \neg \left(x \leq 3.3 \cdot 10^{-9}\right):\\ \;\;\;\;x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.02e+77) (not (<= x 3.3e-9))) (* x 0.5) (* y (- z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.02e+77) || !(x <= 3.3e-9)) {
		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 ((x <= (-1.02d+77)) .or. (.not. (x <= 3.3d-9))) 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 ((x <= -1.02e+77) || !(x <= 3.3e-9)) {
		tmp = x * 0.5;
	} else {
		tmp = y * -z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.02e+77) or not (x <= 3.3e-9):
		tmp = x * 0.5
	else:
		tmp = y * -z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.02e+77) || !(x <= 3.3e-9))
		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 ((x <= -1.02e+77) || ~((x <= 3.3e-9)))
		tmp = x * 0.5;
	else
		tmp = y * -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.02e+77], N[Not[LessEqual[x, 3.3e-9]], $MachinePrecision]], N[(x * 0.5), $MachinePrecision], N[(y * (-z)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.02e77 or 3.30000000000000018e-9 < x

   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 87.1%

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

      1. associate-*r* 87.1%

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

      2. neg-mul-1 87.1%

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

   5. Simplified 87.1%

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

   6. Taylor expanded in x around inf 73.1%

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

   if -1.02e77 < x < 3.30000000000000018e-9

   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 54.9%

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

      1. associate-*r* 54.9%

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

      2. neg-mul-1 54.9%

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

   5. Simplified 54.9%

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

   6. Taylor expanded in y around inf 54.1%

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

      1. +-commutative 54.1%

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

      2. mul-1-neg 54.1%

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

      3. unsub-neg 54.1%

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

      4. associate-*r/ 54.1%

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

      5. *-commutative 54.1%

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

      6. associate-/l* 54.0%

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

   8. Simplified 54.0%

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

   9. Taylor expanded in y around inf 41.4%

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

       1. associate-*r* 41.4%

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

       2. neg-mul-1 41.4%

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

       3. *-commutative 41.4%

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

   11. Simplified 41.4%

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

4. Final simplification 58.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.02 \cdot 10^{+77} \lor \neg \left(x \leq 3.3 \cdot 10^{-9}\right):\\ \;\;\;\;x \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 75.3% 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 72.4%

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

   1. associate-*r* 72.4%

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

   2. neg-mul-1 72.4%

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

5. Simplified 72.4%

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

6. Taylor expanded in x around 0 72.4%

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

   1. +-commutative 72.4%

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

   2. *-commutative 72.4%

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

   3. neg-mul-1 72.4%

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

   4. unsub-neg 72.4%

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

   5. *-commutative 72.4%

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

8. Simplified 72.4%

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

9. Final simplification 72.4%

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

Alternative 8: 39.4% 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. Add Preprocessing

3. Taylor expanded in z around inf 72.4%

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

   1. associate-*r* 72.4%

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

   2. neg-mul-1 72.4%

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

5. Simplified 72.4%

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

6. Taylor expanded in x around inf 47.5%

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

7. Final simplification 47.5%

   \[\leadsto x \cdot 0.5 \]
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 2024144 
(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)))))