Statistics.Distribution.Beta:$cvariance from math-functions-0.1.5.2

Percentage Accurate: 83.4% → 95.9%

Time: 5.4s

Alternatives: 7

Speedup: 1.0×

• 25.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

(FPCore (x y z) :precision binary64 (/ (* x y) (* (* z z) (+ z 1.0))))

C

double code(double x, double y, double z) {
	return (x * y) / ((z * z) * (z + 1.0));
}

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 * y) / ((z * z) * (z + 1.0d0))
end function

Java

public static double code(double x, double y, double z) {
	return (x * y) / ((z * z) * (z + 1.0));
}

Python

def code(x, y, z):
	return (x * y) / ((z * z) * (z + 1.0))

Julia

function code(x, y, z)
	return Float64(Float64(x * y) / Float64(Float64(z * z) * Float64(z + 1.0)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x * y) / ((z * z) * (z + 1.0));
end

Wolfram

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

Initial Program: 83.4% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z) :precision binary64 (/ (* x y) (* (* z z) (+ z 1.0))))

C

double code(double x, double y, double z) {
	return (x * y) / ((z * z) * (z + 1.0));
}

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 * y) / ((z * z) * (z + 1.0d0))
end function

Java

public static double code(double x, double y, double z) {
	return (x * y) / ((z * z) * (z + 1.0));
}

Python

def code(x, y, z):
	return (x * y) / ((z * z) * (z + 1.0))

Julia

function code(x, y, z)
	return Float64(Float64(x * y) / Float64(Float64(z * z) * Float64(z + 1.0)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x * y) / ((z * z) * (z + 1.0));
end

Wolfram

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

Alternative 1: 95.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot y \leq 5 \cdot 10^{-64}:\\ \;\;\;\;\frac{\frac{\frac{x}{z}}{z + 1} \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z + 1}}{\frac{z}{y} \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (* x y) 5e-64)
   (/ (* (/ (/ x z) (+ z 1.0)) y) z)
   (/ (/ x (+ z 1.0)) (* (/ z y) z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x * y) <= 5e-64) {
		tmp = (((x / z) / (z + 1.0)) * y) / z;
	} else {
		tmp = (x / (z + 1.0)) / ((z / 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 * y) <= 5d-64) then
        tmp = (((x / z) / (z + 1.0d0)) * y) / z
    else
        tmp = (x / (z + 1.0d0)) / ((z / y) * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x * y) <= 5e-64) {
		tmp = (((x / z) / (z + 1.0)) * y) / z;
	} else {
		tmp = (x / (z + 1.0)) / ((z / y) * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x * y) <= 5e-64:
		tmp = (((x / z) / (z + 1.0)) * y) / z
	else:
		tmp = (x / (z + 1.0)) / ((z / y) * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(x * y) <= 5e-64)
		tmp = Float64(Float64(Float64(Float64(x / z) / Float64(z + 1.0)) * y) / z);
	else
		tmp = Float64(Float64(x / Float64(z + 1.0)) / Float64(Float64(z / y) * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x * y) <= 5e-64)
		tmp = (((x / z) / (z + 1.0)) * y) / z;
	else
		tmp = (x / (z + 1.0)) / ((z / y) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(x * y), $MachinePrecision], 5e-64], N[(N[(N[(N[(x / z), $MachinePrecision] / N[(z + 1.0), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision] / z), $MachinePrecision], N[(N[(x / N[(z + 1.0), $MachinePrecision]), $MachinePrecision] / N[(N[(z / y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x y) < 5.00000000000000033e-64

   1. Initial program 81.9%

      \[\frac{x \cdot y}{\left(z \cdot z\right) \cdot \left(z + 1\right)} \]

   3. Applied egg-rr 0

      \[\leadsto expr\]

   5. Applied egg-rr 0

      \[\leadsto expr\]

   if 5.00000000000000033e-64 < (*.f64 x y)

   1. Initial program 88.2%

      \[\frac{x \cdot y}{\left(z \cdot z\right) \cdot \left(z + 1\right)} \]

   3. Applied egg-rr 0

      \[\leadsto expr\]

   5. Applied egg-rr 0

      \[\leadsto expr\]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 96.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{\frac{\frac{y}{z}}{\frac{z + 1}{x}}}{z} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (/ (/ (/ y z) (/ (+ z 1.0) x)) z))

C

double code(double x, double y, double z) {
	return ((y / z) / ((z + 1.0) / x)) / 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 / z) / ((z + 1.0d0) / x)) / z
end function

Java

public static double code(double x, double y, double z) {
	return ((y / z) / ((z + 1.0) / x)) / z;
}

Python

def code(x, y, z):
	return ((y / z) / ((z + 1.0) / x)) / z

Julia

function code(x, y, z)
	return Float64(Float64(Float64(y / z) / Float64(Float64(z + 1.0) / x)) / z)
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((y / z) / ((z + 1.0) / x)) / z;
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(y / z), $MachinePrecision] / N[(N[(z + 1.0), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]

Derivation

1. Initial program 83.9%

   \[\frac{x \cdot y}{\left(z \cdot z\right) \cdot \left(z + 1\right)} \]

3. Applied egg-rr 0

   \[\leadsto expr\]

5. Applied egg-rr 0

   \[\leadsto expr\]
6. Add Preprocessing

Alternative 3: 96.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{\frac{x \cdot \frac{y}{z}}{z + 1}}{z} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (/ (/ (* x (/ y z)) (+ z 1.0)) z))

C

double code(double x, double y, double z) {
	return ((x * (y / z)) / (z + 1.0)) / z;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = ((x * (y / z)) / (z + 1.0d0)) / z
end function

Java

public static double code(double x, double y, double z) {
	return ((x * (y / z)) / (z + 1.0)) / z;
}

Python

def code(x, y, z):
	return ((x * (y / z)) / (z + 1.0)) / z

Julia

function code(x, y, z)
	return Float64(Float64(Float64(x * Float64(y / z)) / Float64(z + 1.0)) / z)
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((x * (y / z)) / (z + 1.0)) / z;
end

Wolfram

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

Derivation

1. Initial program 83.9%

   \[\frac{x \cdot y}{\left(z \cdot z\right) \cdot \left(z + 1\right)} \]

3. Applied egg-rr 0

   \[\leadsto expr\]

5. Applied egg-rr 0

   \[\leadsto expr\]
6. Add Preprocessing

Alternative 4: 96.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{\frac{y}{z + 1} \cdot \frac{x}{z}}{z} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (/ (* (/ y (+ z 1.0)) (/ x z)) z))

C

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

Java

public static double code(double x, double y, double z) {
	return ((y / (z + 1.0)) * (x / z)) / z;
}

Python

def code(x, y, z):
	return ((y / (z + 1.0)) * (x / z)) / z

Julia

function code(x, y, z)
	return Float64(Float64(Float64(y / Float64(z + 1.0)) * Float64(x / z)) / z)
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((y / (z + 1.0)) * (x / z)) / z;
end

Wolfram

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

Derivation

1. Initial program 83.9%

   \[\frac{x \cdot y}{\left(z \cdot z\right) \cdot \left(z + 1\right)} \]

3. Applied egg-rr 0

   \[\leadsto expr\]
4. Add Preprocessing

Alternative 5: 94.2% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z) :precision binary64 (/ (* (/ y z) x) (* z (+ z 1.0))))

C

double code(double x, double y, double z) {
	return ((y / z) * x) / (z * (z + 1.0));
}

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 / z) * x) / (z * (z + 1.0d0))
end function

Java

public static double code(double x, double y, double z) {
	return ((y / z) * x) / (z * (z + 1.0));
}

Python

def code(x, y, z):
	return ((y / z) * x) / (z * (z + 1.0))

Julia

function code(x, y, z)
	return Float64(Float64(Float64(y / z) * x) / Float64(z * Float64(z + 1.0)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((y / z) * x) / (z * (z + 1.0));
end

Wolfram

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

Derivation

1. Initial program 83.9%

   \[\frac{x \cdot y}{\left(z \cdot z\right) \cdot \left(z + 1\right)} \]

3. Applied egg-rr 0

   \[\leadsto expr\]
4. Add Preprocessing

Alternative 6: 94.1% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z) :precision binary64 (/ (* x (/ y (* z (+ z 1.0)))) z))

C

double code(double x, double y, double z) {
	return (x * (y / (z * (z + 1.0)))) / z;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x * (y / (z * (z + 1.0d0)))) / z
end function

Java

public static double code(double x, double y, double z) {
	return (x * (y / (z * (z + 1.0)))) / z;
}

Python

def code(x, y, z):
	return (x * (y / (z * (z + 1.0)))) / z

Julia

function code(x, y, z)
	return Float64(Float64(x * Float64(y / Float64(z * Float64(z + 1.0)))) / z)
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x * (y / (z * (z + 1.0)))) / z;
end

Wolfram

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

Derivation

1. Initial program 83.9%

   \[\frac{x \cdot y}{\left(z \cdot z\right) \cdot \left(z + 1\right)} \]

3. Applied egg-rr 0

   \[\leadsto expr\]
4. Add Preprocessing

Alternative 7: 94.2% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z) :precision binary64 (* (/ y (* z (+ z 1.0))) (/ x z)))

C

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

Java

public static double code(double x, double y, double z) {
	return (y / (z * (z + 1.0))) * (x / z);
}

Python

def code(x, y, z):
	return (y / (z * (z + 1.0))) * (x / z)

Julia

function code(x, y, z)
	return Float64(Float64(y / Float64(z * Float64(z + 1.0))) * Float64(x / z))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (y / (z * (z + 1.0))) * (x / z);
end

Wolfram

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

Derivation

1. Initial program 83.9%

   \[\frac{x \cdot y}{\left(z \cdot z\right) \cdot \left(z + 1\right)} \]

3. Applied egg-rr 0

   \[\leadsto expr\]
4. Add Preprocessing

Developer target: 95.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z < 249.6182814532307:\\ \;\;\;\;\frac{y \cdot \frac{x}{z}}{z + z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\frac{y}{z}}{1 + z} \cdot x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (< z 249.6182814532307)
   (/ (* y (/ x z)) (+ z (* z z)))
   (/ (* (/ (/ y z) (+ 1.0 z)) x) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z < 249.6182814532307) {
		tmp = (y * (x / z)) / (z + (z * z));
	} else {
		tmp = (((y / z) / (1.0 + z)) * x) / 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 < 249.6182814532307d0) then
        tmp = (y * (x / z)) / (z + (z * z))
    else
        tmp = (((y / z) / (1.0d0 + z)) * x) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z < 249.6182814532307) {
		tmp = (y * (x / z)) / (z + (z * z));
	} else {
		tmp = (((y / z) / (1.0 + z)) * x) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z < 249.6182814532307:
		tmp = (y * (x / z)) / (z + (z * z))
	else:
		tmp = (((y / z) / (1.0 + z)) * x) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z < 249.6182814532307)
		tmp = Float64(Float64(y * Float64(x / z)) / Float64(z + Float64(z * z)));
	else
		tmp = Float64(Float64(Float64(Float64(y / z) / Float64(1.0 + z)) * x) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z < 249.6182814532307)
		tmp = (y * (x / z)) / (z + (z * z));
	else
		tmp = (((y / z) / (1.0 + z)) * x) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Less[z, 249.6182814532307], N[(N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision] / N[(z + N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(y / z), $MachinePrecision] / N[(1.0 + z), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision] / z), $MachinePrecision]]

Reproduce

herbie shell --seed 2024107 
(FPCore (x y z)
  :name "Statistics.Distribution.Beta:$cvariance from math-functions-0.1.5.2"
  :precision binary64

  :alt
  (if (< z 249.6182814532307) (/ (* y (/ x z)) (+ z (* z z))) (/ (* (/ (/ y z) (+ 1.0 z)) x) z))

  (/ (* x y) (* (* z z) (+ z 1.0))))