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

Percentage Accurate: 99.9% → 99.5%

Time: 11.6s

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: 99.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(N[(x * 0.5), $MachinePrecision] + N[(N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision] + N[(y * 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. Step-by-step derivation

   1. distribute-lft-in 99.9%

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

4. Applied egg-rr 99.9%

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

Alternative 2: 85.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot 0.5 \leq -5 \cdot 10^{-101} \lor \neg \left(x \cdot 0.5 \leq 5 \cdot 10^{-44}\right):\\ \;\;\;\;x \cdot 0.5 - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\left(1 + \log z\right) - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= (* x 0.5) -5e-101) (not (<= (* x 0.5) 5e-44)))
   (- (* 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-101) || !((x * 0.5) <= 5e-44)) {
		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-101)) .or. (.not. ((x * 0.5d0) <= 5d-44))) 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-101) || !((x * 0.5) <= 5e-44)) {
		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-101) or not ((x * 0.5) <= 5e-44):
		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-101) || !(Float64(x * 0.5) <= 5e-44))
		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-101) || ~(((x * 0.5) <= 5e-44)))
		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-101], N[Not[LessEqual[N[(x * 0.5), $MachinePrecision], 5e-44]], $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)) < -5.0000000000000001e-101 or 5.00000000000000039e-44 < (*.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 90.8%

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

      1. associate-*r* 90.8%

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

      2. mul-1-neg 90.8%

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

   5. Simplified 90.8%

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

   6. Taylor expanded in x around inf 90.2%

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

      1. mul-1-neg 90.2%

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

      2. unsub-neg 90.2%

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

      3. associate-/l* 90.2%

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

   8. Simplified 90.2%

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

   9. Taylor expanded in x around 0 90.8%

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

       1. neg-mul-1 90.8%

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

       2. +-commutative 90.8%

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

       3. sub-neg 90.8%

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

       4. *-commutative 90.8%

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

       5. *-commutative 90.8%

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

   11. Simplified 90.8%

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

   if -5.0000000000000001e-101 < (*.f64 x #s(literal 1/2 binary64)) < 5.00000000000000039e-44

   1. Initial program 99.7%

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

      1. distribute-lft-in 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in x around 0 92.3%

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

   6. Taylor expanded in y around 0 92.3%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot 0.5 \leq -5 \cdot 10^{-101} \lor \neg \left(x \cdot 0.5 \leq 5 \cdot 10^{-44}\right):\\ \;\;\;\;x \cdot 0.5 - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\left(1 + \log z\right) - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot 0.5 \leq 2 \cdot 10^{-223} \lor \neg \left(x \cdot 0.5 \leq 4 \cdot 10^{-200}\right):\\ \;\;\;\;x \cdot 0.5 - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 + \log z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= (* x 0.5) 2e-223) (not (<= (* x 0.5) 4e-200)))
   (- (* x 0.5) (* y z))
   (* y (+ 1.0 (log z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (((x * 0.5) <= 2e-223) || !((x * 0.5) <= 4e-200)) {
		tmp = (x * 0.5) - (y * z);
	} else {
		tmp = y * (1.0 + log(z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (((x * 0.5d0) <= 2d-223) .or. (.not. ((x * 0.5d0) <= 4d-200))) then
        tmp = (x * 0.5d0) - (y * z)
    else
        tmp = y * (1.0d0 + log(z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (((x * 0.5) <= 2e-223) || !((x * 0.5) <= 4e-200)) {
		tmp = (x * 0.5) - (y * z);
	} else {
		tmp = y * (1.0 + Math.log(z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if ((x * 0.5) <= 2e-223) or not ((x * 0.5) <= 4e-200):
		tmp = (x * 0.5) - (y * z)
	else:
		tmp = y * (1.0 + math.log(z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((Float64(x * 0.5) <= 2e-223) || !(Float64(x * 0.5) <= 4e-200))
		tmp = Float64(Float64(x * 0.5) - Float64(y * z));
	else
		tmp = Float64(y * Float64(1.0 + log(z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (((x * 0.5) <= 2e-223) || ~(((x * 0.5) <= 4e-200)))
		tmp = (x * 0.5) - (y * z);
	else
		tmp = y * (1.0 + log(z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[N[(x * 0.5), $MachinePrecision], 2e-223], N[Not[LessEqual[N[(x * 0.5), $MachinePrecision], 4e-200]], $MachinePrecision]], N[(N[(x * 0.5), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision], N[(y * N[(1.0 + N[Log[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x #s(literal 1/2 binary64)) < 1.9999999999999999e-223 or 3.9999999999999999e-200 < (*.f64 x #s(literal 1/2 binary64))

   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 81.2%

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

      1. associate-*r* 81.2%

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

      2. mul-1-neg 81.2%

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

   5. Simplified 81.2%

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

   6. Taylor expanded in x around inf 77.4%

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

      1. mul-1-neg 77.4%

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

      2. unsub-neg 77.4%

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

      3. associate-/l* 72.3%

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

   8. Simplified 72.3%

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

   9. Taylor expanded in x around 0 81.2%

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

       1. neg-mul-1 81.2%

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

       2. +-commutative 81.2%

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

       3. sub-neg 81.2%

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

       4. *-commutative 81.2%

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

       5. *-commutative 81.2%

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

   11. Simplified 81.2%

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

   if 1.9999999999999999e-223 < (*.f64 x #s(literal 1/2 binary64)) < 3.9999999999999999e-200

   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 0 100.0%

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

   4. Taylor expanded in x around 0 90.7%

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

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot 0.5 \leq 2 \cdot 10^{-223} \lor \neg \left(x \cdot 0.5 \leq 4 \cdot 10^{-200}\right):\\ \;\;\;\;x \cdot 0.5 - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 + \log z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 0.28:\\ \;\;\;\;x \cdot 0.5 + y \cdot \left(1 + \log z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 0.5 - y \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z 0.28) (+ (* 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 <= 0.28) {
		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 <= 0.28d0) 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 <= 0.28) {
		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 <= 0.28:
		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 <= 0.28)
		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 <= 0.28)
		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, 0.28], 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 < 0.28000000000000003

   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%

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

   if 0.28000000000000003 < 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 99.2%

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

      1. associate-*r* 99.2%

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

      2. mul-1-neg 99.2%

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

   5. Simplified 99.2%

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

   6. Taylor expanded in x around inf 92.0%

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

      1. mul-1-neg 92.0%

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

      2. unsub-neg 92.0%

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

      3. associate-/l* 82.3%

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

   8. Simplified 82.3%

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

   9. Taylor expanded in x around 0 99.2%

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

       1. neg-mul-1 99.2%

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

       2. +-commutative 99.2%

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

       3. sub-neg 99.2%

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

       4. *-commutative 99.2%

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

       5. *-commutative 99.2%

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

   11. Simplified 99.2%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 0.28:\\ \;\;\;\;x \cdot 0.5 + y \cdot \left(1 + \log z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 0.5 - y \cdot z\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 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 6: 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 79.4%

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

   1. associate-*r* 79.4%

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

   2. mul-1-neg 79.4%

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

5. Simplified 79.4%

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

6. Taylor expanded in x around inf 75.7%

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

   1. mul-1-neg 75.7%

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

   2. unsub-neg 75.7%

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

   3. associate-/l* 70.7%

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

8. Simplified 70.7%

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

9. Taylor expanded in x around 0 79.4%

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

    1. neg-mul-1 79.4%

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

    2. +-commutative 79.4%

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

    3. sub-neg 79.4%

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

    4. *-commutative 79.4%

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

    5. *-commutative 79.4%

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

11. Simplified 79.4%

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

12. Final simplification 79.4%

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

Alternative 7: 40.5% 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 42.9%

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

4. Final simplification 42.9%

   \[\leadsto x \cdot 0.5 \]
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 2024110 
(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)))))