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

Percentage Accurate: 100.0% → 100.0%

Time: 6.4s

Alternatives: 7

Speedup: 1.0×

• 20.8% 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: 61.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{-x}{z}\\ \mathbf{if}\;z \leq -7 \cdot 10^{+16}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-56}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{-143}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -2.55 \cdot 10^{-294}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+106}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+137}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (- x) z)))
   (if (<= z -7e+16)
     x
     (if (<= z -3.5e-56)
       (/ y z)
       (if (<= z -1.85e-143)
         t_0
         (if (<= z -2.55e-294)
           (/ y z)
           (if (<= z 1.0)
             t_0
             (if (<= z 1.45e+106) x (if (<= z 6.2e+137) (/ y z) x)))))))))

C

double code(double x, double y, double z) {
	double t_0 = -x / z;
	double tmp;
	if (z <= -7e+16) {
		tmp = x;
	} else if (z <= -3.5e-56) {
		tmp = y / z;
	} else if (z <= -1.85e-143) {
		tmp = t_0;
	} else if (z <= -2.55e-294) {
		tmp = y / z;
	} else if (z <= 1.0) {
		tmp = t_0;
	} else if (z <= 1.45e+106) {
		tmp = x;
	} else if (z <= 6.2e+137) {
		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 <= (-7d+16)) then
        tmp = x
    else if (z <= (-3.5d-56)) then
        tmp = y / z
    else if (z <= (-1.85d-143)) then
        tmp = t_0
    else if (z <= (-2.55d-294)) then
        tmp = y / z
    else if (z <= 1.0d0) then
        tmp = t_0
    else if (z <= 1.45d+106) then
        tmp = x
    else if (z <= 6.2d+137) 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 <= -7e+16) {
		tmp = x;
	} else if (z <= -3.5e-56) {
		tmp = y / z;
	} else if (z <= -1.85e-143) {
		tmp = t_0;
	} else if (z <= -2.55e-294) {
		tmp = y / z;
	} else if (z <= 1.0) {
		tmp = t_0;
	} else if (z <= 1.45e+106) {
		tmp = x;
	} else if (z <= 6.2e+137) {
		tmp = y / z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -x / z
	tmp = 0
	if z <= -7e+16:
		tmp = x
	elif z <= -3.5e-56:
		tmp = y / z
	elif z <= -1.85e-143:
		tmp = t_0
	elif z <= -2.55e-294:
		tmp = y / z
	elif z <= 1.0:
		tmp = t_0
	elif z <= 1.45e+106:
		tmp = x
	elif z <= 6.2e+137:
		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 <= -7e+16)
		tmp = x;
	elseif (z <= -3.5e-56)
		tmp = Float64(y / z);
	elseif (z <= -1.85e-143)
		tmp = t_0;
	elseif (z <= -2.55e-294)
		tmp = Float64(y / z);
	elseif (z <= 1.0)
		tmp = t_0;
	elseif (z <= 1.45e+106)
		tmp = x;
	elseif (z <= 6.2e+137)
		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 <= -7e+16)
		tmp = x;
	elseif (z <= -3.5e-56)
		tmp = y / z;
	elseif (z <= -1.85e-143)
		tmp = t_0;
	elseif (z <= -2.55e-294)
		tmp = y / z;
	elseif (z <= 1.0)
		tmp = t_0;
	elseif (z <= 1.45e+106)
		tmp = x;
	elseif (z <= 6.2e+137)
		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, -7e+16], x, If[LessEqual[z, -3.5e-56], N[(y / z), $MachinePrecision], If[LessEqual[z, -1.85e-143], t$95$0, If[LessEqual[z, -2.55e-294], N[(y / z), $MachinePrecision], If[LessEqual[z, 1.0], t$95$0, If[LessEqual[z, 1.45e+106], x, If[LessEqual[z, 6.2e+137], N[(y / z), $MachinePrecision], x]]]]]]]]

Derivation

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

Alternative 3: 76.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{-77} \lor \neg \left(z \leq -1.05 \cdot 10^{-134}\right) \land \left(z \leq -6.5 \cdot 10^{-298} \lor \neg \left(z \leq 0.58\right)\right):\\ \;\;\;\;x + \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{-x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -3.4e-77)
         (and (not (<= z -1.05e-134)) (or (<= z -6.5e-298) (not (<= z 0.58)))))
   (+ x (/ y z))
   (/ (- x) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -3.4e-77) || (!(z <= -1.05e-134) && ((z <= -6.5e-298) || !(z <= 0.58)))) {
		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 ((z <= (-3.4d-77)) .or. (.not. (z <= (-1.05d-134))) .and. (z <= (-6.5d-298)) .or. (.not. (z <= 0.58d0))) 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 ((z <= -3.4e-77) || (!(z <= -1.05e-134) && ((z <= -6.5e-298) || !(z <= 0.58)))) {
		tmp = x + (y / z);
	} else {
		tmp = -x / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -3.4e-77) or (not (z <= -1.05e-134) and ((z <= -6.5e-298) or not (z <= 0.58))):
		tmp = x + (y / z)
	else:
		tmp = -x / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -3.4e-77) || (!(z <= -1.05e-134) && ((z <= -6.5e-298) || !(z <= 0.58))))
		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 ((z <= -3.4e-77) || (~((z <= -1.05e-134)) && ((z <= -6.5e-298) || ~((z <= 0.58)))))
		tmp = x + (y / z);
	else
		tmp = -x / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -3.4e-77], And[N[Not[LessEqual[z, -1.05e-134]], $MachinePrecision], Or[LessEqual[z, -6.5e-298], N[Not[LessEqual[z, 0.58]], $MachinePrecision]]]], N[(x + N[(y / z), $MachinePrecision]), $MachinePrecision], N[((-x) / z), $MachinePrecision]]

Derivation

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

Alternative 4: 62.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.45 \cdot 10^{+18}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 950000000 \lor \neg \left(z \leq 1.45 \cdot 10^{+106}\right) \land z \leq 9.2 \cdot 10^{+138}:\\ \;\;\;\;\frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2.45e+18)
   x
   (if (or (<= z 950000000.0) (and (not (<= z 1.45e+106)) (<= z 9.2e+138)))
     (/ y z)
     x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.45e+18) {
		tmp = x;
	} else if ((z <= 950000000.0) || (!(z <= 1.45e+106) && (z <= 9.2e+138))) {
		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 <= (-2.45d+18)) then
        tmp = x
    else if ((z <= 950000000.0d0) .or. (.not. (z <= 1.45d+106)) .and. (z <= 9.2d+138)) 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 <= -2.45e+18) {
		tmp = x;
	} else if ((z <= 950000000.0) || (!(z <= 1.45e+106) && (z <= 9.2e+138))) {
		tmp = y / z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -2.45e+18:
		tmp = x
	elif (z <= 950000000.0) or (not (z <= 1.45e+106) and (z <= 9.2e+138)):
		tmp = y / z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -2.45e+18)
		tmp = x;
	elseif ((z <= 950000000.0) || (!(z <= 1.45e+106) && (z <= 9.2e+138)))
		tmp = Float64(y / z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -2.45e+18)
		tmp = x;
	elseif ((z <= 950000000.0) || (~((z <= 1.45e+106)) && (z <= 9.2e+138)))
		tmp = y / z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -2.45e+18], x, If[Or[LessEqual[z, 950000000.0], And[N[Not[LessEqual[z, 1.45e+106]], $MachinePrecision], LessEqual[z, 9.2e+138]]], N[(y / z), $MachinePrecision], x]]

Derivation

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

Alternative 5: 87.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{+61} \lor \neg \left(x \leq 4.8 \cdot 10^{+81}\right):\\ \;\;\;\;x - \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.8e+61) (not (<= x 4.8e+81))) (- x (/ x z)) (+ x (/ y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.8e+61) || !(x <= 4.8e+81)) {
		tmp = x - (x / z);
	} else {
		tmp = x + (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 <= (-2.8d+61)) .or. (.not. (x <= 4.8d+81))) then
        tmp = x - (x / z)
    else
        tmp = x + (y / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.8e+61) || !(x <= 4.8e+81)) {
		tmp = x - (x / z);
	} else {
		tmp = x + (y / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.8e+61) or not (x <= 4.8e+81):
		tmp = x - (x / z)
	else:
		tmp = x + (y / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.8e+61) || !(x <= 4.8e+81))
		tmp = Float64(x - Float64(x / z));
	else
		tmp = Float64(x + Float64(y / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -2.8e+61) || ~((x <= 4.8e+81)))
		tmp = x - (x / z);
	else
		tmp = x + (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.8e+61], N[Not[LessEqual[x, 4.8e+81]], $MachinePrecision]], N[(x - N[(x / z), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / z), $MachinePrecision]), $MachinePrecision]]

Derivation

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

Alternative 6: 98.9% 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 7: 37.6% 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 2023364 
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))