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

Percentage Accurate: 100.0% → 100.0%

Time: 4.4s

Alternatives: 7

Speedup: 1.0×

• 20.7% 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, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{-x}{z}\\ \mathbf{if}\;z \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -4.1 \cdot 10^{-164}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-190}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-235}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-262}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-192}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{+33}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (- x) z)))
   (if (<= z -1.0)
     x
     (if (<= z -4.1e-164)
       t_0
       (if (<= z -1.7e-190)
         (/ y z)
         (if (<= z -1.95e-235)
           t_0
           (if (<= z 1.45e-262)
             (/ y z)
             (if (<= z 6.5e-192) t_0 (if (<= z 2.45e+33) (/ y z) x)))))))))

C

double code(double x, double y, double z) {
	double t_0 = -x / z;
	double tmp;
	if (z <= -1.0) {
		tmp = x;
	} else if (z <= -4.1e-164) {
		tmp = t_0;
	} else if (z <= -1.7e-190) {
		tmp = y / z;
	} else if (z <= -1.95e-235) {
		tmp = t_0;
	} else if (z <= 1.45e-262) {
		tmp = y / z;
	} else if (z <= 6.5e-192) {
		tmp = t_0;
	} else if (z <= 2.45e+33) {
		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 <= (-1.0d0)) then
        tmp = x
    else if (z <= (-4.1d-164)) then
        tmp = t_0
    else if (z <= (-1.7d-190)) then
        tmp = y / z
    else if (z <= (-1.95d-235)) then
        tmp = t_0
    else if (z <= 1.45d-262) then
        tmp = y / z
    else if (z <= 6.5d-192) then
        tmp = t_0
    else if (z <= 2.45d+33) 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 <= -1.0) {
		tmp = x;
	} else if (z <= -4.1e-164) {
		tmp = t_0;
	} else if (z <= -1.7e-190) {
		tmp = y / z;
	} else if (z <= -1.95e-235) {
		tmp = t_0;
	} else if (z <= 1.45e-262) {
		tmp = y / z;
	} else if (z <= 6.5e-192) {
		tmp = t_0;
	} else if (z <= 2.45e+33) {
		tmp = y / z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -x / z
	tmp = 0
	if z <= -1.0:
		tmp = x
	elif z <= -4.1e-164:
		tmp = t_0
	elif z <= -1.7e-190:
		tmp = y / z
	elif z <= -1.95e-235:
		tmp = t_0
	elif z <= 1.45e-262:
		tmp = y / z
	elif z <= 6.5e-192:
		tmp = t_0
	elif z <= 2.45e+33:
		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 <= -1.0)
		tmp = x;
	elseif (z <= -4.1e-164)
		tmp = t_0;
	elseif (z <= -1.7e-190)
		tmp = Float64(y / z);
	elseif (z <= -1.95e-235)
		tmp = t_0;
	elseif (z <= 1.45e-262)
		tmp = Float64(y / z);
	elseif (z <= 6.5e-192)
		tmp = t_0;
	elseif (z <= 2.45e+33)
		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 <= -1.0)
		tmp = x;
	elseif (z <= -4.1e-164)
		tmp = t_0;
	elseif (z <= -1.7e-190)
		tmp = y / z;
	elseif (z <= -1.95e-235)
		tmp = t_0;
	elseif (z <= 1.45e-262)
		tmp = y / z;
	elseif (z <= 6.5e-192)
		tmp = t_0;
	elseif (z <= 2.45e+33)
		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, -1.0], x, If[LessEqual[z, -4.1e-164], t$95$0, If[LessEqual[z, -1.7e-190], N[(y / z), $MachinePrecision], If[LessEqual[z, -1.95e-235], t$95$0, If[LessEqual[z, 1.45e-262], N[(y / z), $MachinePrecision], If[LessEqual[z, 6.5e-192], t$95$0, If[LessEqual[z, 2.45e+33], N[(y / z), $MachinePrecision], x]]]]]]]]

Derivation

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

Alternative 3: 74.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{-25} \lor \neg \left(x \leq 1.95 \cdot 10^{-33}\right):\\ \;\;\;\;x - \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.8e-25) (not (<= x 1.95e-33))) (- x (/ x z)) (/ y z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.8e-25) || !(x <= 1.95e-33)) {
		tmp = x - (x / z);
	} 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 <= (-1.8d-25)) .or. (.not. (x <= 1.95d-33))) then
        tmp = x - (x / z)
    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 <= -1.8e-25) || !(x <= 1.95e-33)) {
		tmp = x - (x / z);
	} else {
		tmp = y / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.8e-25) or not (x <= 1.95e-33):
		tmp = x - (x / z)
	else:
		tmp = y / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.8e-25) || !(x <= 1.95e-33))
		tmp = Float64(x - Float64(x / z));
	else
		tmp = Float64(y / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.8e-25) || ~((x <= 1.95e-33)))
		tmp = x - (x / z);
	else
		tmp = y / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.8e-25], N[Not[LessEqual[x, 1.95e-33]], $MachinePrecision]], N[(x - N[(x / z), $MachinePrecision]), $MachinePrecision], N[(y / z), $MachinePrecision]]

Derivation

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

Alternative 4: 98.8% accurate, 0.8× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.0) || !(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 <= (-1.0d0)) .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 <= -1.0) || !(z <= 1.0)) {
		tmp = x + (y / z);
	} else {
		tmp = (y - x) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.0) 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 <= -1.0) || !(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 <= -1.0) || ~((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, -1.0], 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 5: 85.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.16 \cdot 10^{+37}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 27:\\ \;\;\;\;\frac{y - x}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.16e+37) x (if (<= z 27.0) (/ (- y x) z) (- x (/ x z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.16e+37) {
		tmp = x;
	} else if (z <= 27.0) {
		tmp = (y - x) / 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 (z <= (-1.16d+37)) then
        tmp = x
    else if (z <= 27.0d0) then
        tmp = (y - x) / 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 (z <= -1.16e+37) {
		tmp = x;
	} else if (z <= 27.0) {
		tmp = (y - x) / z;
	} else {
		tmp = x - (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.16e+37:
		tmp = x
	elif z <= 27.0:
		tmp = (y - x) / z
	else:
		tmp = x - (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.16e+37)
		tmp = x;
	elseif (z <= 27.0)
		tmp = Float64(Float64(y - x) / z);
	else
		tmp = Float64(x - Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.16e+37)
		tmp = x;
	elseif (z <= 27.0)
		tmp = (y - x) / z;
	else
		tmp = x - (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.16e+37], x, If[LessEqual[z, 27.0], N[(N[(y - x), $MachinePrecision] / z), $MachinePrecision], N[(x - N[(x / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

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

Alternative 6: 61.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+32}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+33}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -3e+32) x (if (<= z 2.6e+33) (/ y z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -3e+32) {
		tmp = x;
	} else if (z <= 2.6e+33) {
		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 <= (-3d+32)) then
        tmp = x
    else if (z <= 2.6d+33) 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 <= -3e+32) {
		tmp = x;
	} else if (z <= 2.6e+33) {
		tmp = y / z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -3e+32:
		tmp = x
	elif z <= 2.6e+33:
		tmp = y / z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -3e+32)
		tmp = x;
	elseif (z <= 2.6e+33)
		tmp = Float64(y / z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -3e+32)
		tmp = x;
	elseif (z <= 2.6e+33)
		tmp = y / z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -3e+32], x, If[LessEqual[z, 2.6e+33], N[(y / z), $MachinePrecision], x]]

Derivation

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

Alternative 7: 37.1% 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 2024008 
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))