Statistics.Sample:$swelfordMean from math-functions-0.1.5.2

Percentage Accurate: 100.0% → 100.0%

Time: 4.8s

Alternatives: 7

Speedup: 1.0×

• 20.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return x + ((y - 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 = x + ((y - x) / z)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return x + ((y - 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 = x + ((y - x) / z)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return x + ((y - 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 = x + ((y - x) / z)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 2: 61.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{-x}{z}\\ \mathbf{if}\;z \leq -1.08 \cdot 10^{+36}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-31}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-75}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{-107}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq -4.6 \cdot 10^{-169}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-163}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-146}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-100}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 0.08:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+47}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (- x) z)))
   (if (<= z -1.08e+36)
     x
     (if (<= z -6.8e-31)
       (/ y z)
       (if (<= z -3.5e-75)
         t_0
         (if (<= z -1.45e-107)
           (/ y z)
           (if (<= z -4.6e-169)
             t_0
             (if (<= z 6.5e-163)
               (/ y z)
               (if (<= z 7.5e-146)
                 t_0
                 (if (<= z 1.45e-100)
                   (/ y z)
                   (if (<= z 0.08) t_0 (if (<= z 4.4e+47) (/ y z) x))))))))))))

C

double code(double x, double y, double z) {
	double t_0 = -x / z;
	double tmp;
	if (z <= -1.08e+36) {
		tmp = x;
	} else if (z <= -6.8e-31) {
		tmp = y / z;
	} else if (z <= -3.5e-75) {
		tmp = t_0;
	} else if (z <= -1.45e-107) {
		tmp = y / z;
	} else if (z <= -4.6e-169) {
		tmp = t_0;
	} else if (z <= 6.5e-163) {
		tmp = y / z;
	} else if (z <= 7.5e-146) {
		tmp = t_0;
	} else if (z <= 1.45e-100) {
		tmp = y / z;
	} else if (z <= 0.08) {
		tmp = t_0;
	} else if (z <= 4.4e+47) {
		tmp = y / z;
	} else {
		tmp = x;
	}
	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) :: t_0
    real(8) :: tmp
    t_0 = -x / z
    if (z <= (-1.08d+36)) then
        tmp = x
    else if (z <= (-6.8d-31)) then
        tmp = y / z
    else if (z <= (-3.5d-75)) then
        tmp = t_0
    else if (z <= (-1.45d-107)) then
        tmp = y / z
    else if (z <= (-4.6d-169)) then
        tmp = t_0
    else if (z <= 6.5d-163) then
        tmp = y / z
    else if (z <= 7.5d-146) then
        tmp = t_0
    else if (z <= 1.45d-100) then
        tmp = y / z
    else if (z <= 0.08d0) then
        tmp = t_0
    else if (z <= 4.4d+47) then
        tmp = y / z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -x / z;
	double tmp;
	if (z <= -1.08e+36) {
		tmp = x;
	} else if (z <= -6.8e-31) {
		tmp = y / z;
	} else if (z <= -3.5e-75) {
		tmp = t_0;
	} else if (z <= -1.45e-107) {
		tmp = y / z;
	} else if (z <= -4.6e-169) {
		tmp = t_0;
	} else if (z <= 6.5e-163) {
		tmp = y / z;
	} else if (z <= 7.5e-146) {
		tmp = t_0;
	} else if (z <= 1.45e-100) {
		tmp = y / z;
	} else if (z <= 0.08) {
		tmp = t_0;
	} else if (z <= 4.4e+47) {
		tmp = y / z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -x / z
	tmp = 0
	if z <= -1.08e+36:
		tmp = x
	elif z <= -6.8e-31:
		tmp = y / z
	elif z <= -3.5e-75:
		tmp = t_0
	elif z <= -1.45e-107:
		tmp = y / z
	elif z <= -4.6e-169:
		tmp = t_0
	elif z <= 6.5e-163:
		tmp = y / z
	elif z <= 7.5e-146:
		tmp = t_0
	elif z <= 1.45e-100:
		tmp = y / z
	elif z <= 0.08:
		tmp = t_0
	elif z <= 4.4e+47:
		tmp = y / z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(-x) / z)
	tmp = 0.0
	if (z <= -1.08e+36)
		tmp = x;
	elseif (z <= -6.8e-31)
		tmp = Float64(y / z);
	elseif (z <= -3.5e-75)
		tmp = t_0;
	elseif (z <= -1.45e-107)
		tmp = Float64(y / z);
	elseif (z <= -4.6e-169)
		tmp = t_0;
	elseif (z <= 6.5e-163)
		tmp = Float64(y / z);
	elseif (z <= 7.5e-146)
		tmp = t_0;
	elseif (z <= 1.45e-100)
		tmp = Float64(y / z);
	elseif (z <= 0.08)
		tmp = t_0;
	elseif (z <= 4.4e+47)
		tmp = Float64(y / z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -x / z;
	tmp = 0.0;
	if (z <= -1.08e+36)
		tmp = x;
	elseif (z <= -6.8e-31)
		tmp = y / z;
	elseif (z <= -3.5e-75)
		tmp = t_0;
	elseif (z <= -1.45e-107)
		tmp = y / z;
	elseif (z <= -4.6e-169)
		tmp = t_0;
	elseif (z <= 6.5e-163)
		tmp = y / z;
	elseif (z <= 7.5e-146)
		tmp = t_0;
	elseif (z <= 1.45e-100)
		tmp = y / z;
	elseif (z <= 0.08)
		tmp = t_0;
	elseif (z <= 4.4e+47)
		tmp = y / z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[((-x) / z), $MachinePrecision]}, If[LessEqual[z, -1.08e+36], x, If[LessEqual[z, -6.8e-31], N[(y / z), $MachinePrecision], If[LessEqual[z, -3.5e-75], t$95$0, If[LessEqual[z, -1.45e-107], N[(y / z), $MachinePrecision], If[LessEqual[z, -4.6e-169], t$95$0, If[LessEqual[z, 6.5e-163], N[(y / z), $MachinePrecision], If[LessEqual[z, 7.5e-146], t$95$0, If[LessEqual[z, 1.45e-100], N[(y / z), $MachinePrecision], If[LessEqual[z, 0.08], t$95$0, If[LessEqual[z, 4.4e+47], N[(y / z), $MachinePrecision], x]]]]]]]]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 3: 75.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{-258} \lor \neg \left(y \leq 1.1 \cdot 10^{-185}\right):\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3.2e-258) (not (<= y 1.1e-185))) (+ x (/ y z)) (/ (- x) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.2e-258) || !(y <= 1.1e-185)) {
		tmp = x + (y / z);
	} else {
		tmp = -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 ((y <= (-3.2d-258)) .or. (.not. (y <= 1.1d-185))) then
        tmp = x + (y / z)
    else
        tmp = -x / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.2e-258) || !(y <= 1.1e-185)) {
		tmp = x + (y / z);
	} else {
		tmp = -x / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3.2e-258) or not (y <= 1.1e-185):
		tmp = x + (y / z)
	else:
		tmp = -x / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3.2e-258) || !(y <= 1.1e-185))
		tmp = Float64(x + Float64(y / z));
	else
		tmp = Float64(Float64(-x) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -3.2e-258) || ~((y <= 1.1e-185)))
		tmp = x + (y / z);
	else
		tmp = -x / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3.2e-258], N[Not[LessEqual[y, 1.1e-185]], $MachinePrecision]], N[(x + N[(y / z), $MachinePrecision]), $MachinePrecision], N[((-x) / z), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 4: 86.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{-56} \lor \neg \left(y \leq 2.7 \cdot 10^{-98}\right):\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.05e-56) (not (<= y 2.7e-98))) (+ x (/ y z)) (- x (/ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.05e-56) || !(y <= 2.7e-98)) {
		tmp = x + (y / z);
	} else {
		tmp = x - (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 ((y <= (-1.05d-56)) .or. (.not. (y <= 2.7d-98))) then
        tmp = x + (y / z)
    else
        tmp = x - (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.05e-56) || !(y <= 2.7e-98)) {
		tmp = x + (y / z);
	} else {
		tmp = x - (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.05e-56) or not (y <= 2.7e-98):
		tmp = x + (y / z)
	else:
		tmp = x - (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.05e-56) || !(y <= 2.7e-98))
		tmp = Float64(x + Float64(y / z));
	else
		tmp = Float64(x - Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.05e-56) || ~((y <= 2.7e-98)))
		tmp = x + (y / z);
	else
		tmp = x - (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.05e-56], N[Not[LessEqual[y, 2.7e-98]], $MachinePrecision]], N[(x + N[(y / z), $MachinePrecision]), $MachinePrecision], N[(x - N[(x / z), $MachinePrecision]), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 5: 98.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.16 \cdot 10^{+23} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.16e+23) (not (<= z 1.0))) (+ x (/ y z)) (/ (- y x) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.16e+23) || !(z <= 1.0)) {
		tmp = x + (y / z);
	} else {
		tmp = (y - 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 <= (-1.16d+23)) .or. (.not. (z <= 1.0d0))) then
        tmp = x + (y / z)
    else
        tmp = (y - x) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.16e+23) || !(z <= 1.0)) {
		tmp = x + (y / z);
	} else {
		tmp = (y - x) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.16e+23) or not (z <= 1.0):
		tmp = x + (y / z)
	else:
		tmp = (y - x) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.16e+23) || !(z <= 1.0))
		tmp = Float64(x + Float64(y / z));
	else
		tmp = Float64(Float64(y - x) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.16e+23) || ~((z <= 1.0)))
		tmp = x + (y / z);
	else
		tmp = (y - x) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.16e+23], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(x + N[(y / z), $MachinePrecision]), $MachinePrecision], N[(N[(y - x), $MachinePrecision] / z), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 6: 62.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+36}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{+47}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.5e+36) x (if (<= z 1.55e+47) (/ y z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.5e+36) {
		tmp = x;
	} else if (z <= 1.55e+47) {
		tmp = y / z;
	} else {
		tmp = x;
	}
	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 <= (-1.5d+36)) then
        tmp = x
    else if (z <= 1.55d+47) then
        tmp = y / z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.5e+36) {
		tmp = x;
	} else if (z <= 1.55e+47) {
		tmp = y / z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.5e+36:
		tmp = x
	elif z <= 1.55e+47:
		tmp = y / z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.5e+36)
		tmp = x;
	elseif (z <= 1.55e+47)
		tmp = Float64(y / z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.5e+36)
		tmp = x;
	elseif (z <= 1.55e+47)
		tmp = y / z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.5e+36], x, If[LessEqual[z, 1.55e+47], N[(y / z), $MachinePrecision], x]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 7: 36.9% accurate, 7.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 x)

C

double code(double x, double y, double z) {
	return x;
}

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
end function

Java

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

Python

def code(x, y, z):
	return x

Julia

function code(x, y, z)
	return x
end

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Reproduce

herbie shell --seed 2023350 
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))