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

Percentage Accurate: 100.0% → 100.0%

Time: 2.9s

Alternatives: 3

Speedup: 1.0×

• 20.4% 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

1. Initial program 100.0%

   \[x + \frac{y - x}{z} \]

2. Final simplification 100.0%

   \[\leadsto x + \frac{y - x}{z} \]

Alternative 2: 85.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.7 \cdot 10^{+59} \lor \neg \left(x \leq 1.2 \cdot 10^{-73}\right) \land \left(x \leq 4.7 \cdot 10^{-7} \lor \neg \left(x \leq 1.62 \cdot 10^{+70}\right)\right):\\ \;\;\;\;x - \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -6.7e+59)
         (and (not (<= x 1.2e-73)) (or (<= x 4.7e-7) (not (<= x 1.62e+70)))))
   (- x (/ x z))
   (+ x (/ y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -6.7e+59) || (!(x <= 1.2e-73) && ((x <= 4.7e-7) || !(x <= 1.62e+70)))) {
		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 <= (-6.7d+59)) .or. (.not. (x <= 1.2d-73)) .and. (x <= 4.7d-7) .or. (.not. (x <= 1.62d+70))) 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 <= -6.7e+59) || (!(x <= 1.2e-73) && ((x <= 4.7e-7) || !(x <= 1.62e+70)))) {
		tmp = x - (x / z);
	} else {
		tmp = x + (y / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -6.7e+59) or (not (x <= 1.2e-73) and ((x <= 4.7e-7) or not (x <= 1.62e+70))):
		tmp = x - (x / z)
	else:
		tmp = x + (y / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -6.7e+59) || (!(x <= 1.2e-73) && ((x <= 4.7e-7) || !(x <= 1.62e+70))))
		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 <= -6.7e+59) || (~((x <= 1.2e-73)) && ((x <= 4.7e-7) || ~((x <= 1.62e+70)))))
		tmp = x - (x / z);
	else
		tmp = x + (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -6.7e+59], And[N[Not[LessEqual[x, 1.2e-73]], $MachinePrecision], Or[LessEqual[x, 4.7e-7], N[Not[LessEqual[x, 1.62e+70]], $MachinePrecision]]]], N[(x - N[(x / z), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.7000000000000004e59 or 1.20000000000000003e-73 < x < 4.7e-7 or 1.62000000000000004e70 < x

   1. Initial program 100.0%

      \[x + \frac{y - x}{z} \]

   2. Taylor expanded in y around 0 94.7%

      \[\leadsto x + \color{blue}{-1 \cdot \frac{x}{z}} \]
   3. Step-by-step derivation

      1. neg-mul-1 94.7%

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

      2. distribute-neg-frac 94.7%

         \[\leadsto x + \color{blue}{\frac{-x}{z}} \]

   4. Simplified 94.7%

      \[\leadsto x + \color{blue}{\frac{-x}{z}} \]

   if -6.7000000000000004e59 < x < 1.20000000000000003e-73 or 4.7e-7 < x < 1.62000000000000004e70

   1. Initial program 100.0%

      \[x + \frac{y - x}{z} \]

   2. Taylor expanded in y around inf 91.6%

      \[\leadsto x + \color{blue}{\frac{y}{z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.7 \cdot 10^{+59} \lor \neg \left(x \leq 1.2 \cdot 10^{-73}\right) \land \left(x \leq 4.7 \cdot 10^{-7} \lor \neg \left(x \leq 1.62 \cdot 10^{+70}\right)\right):\\ \;\;\;\;x - \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z}\\ \end{array} \]

Alternative 3: 76.3% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[x + \frac{y - x}{z} \]

2. Taylor expanded in y around inf 76.3%

   \[\leadsto x + \color{blue}{\frac{y}{z}} \]

3. Final simplification 76.3%

   \[\leadsto x + \frac{y}{z} \]

Reproduce

herbie shell --seed 2023228 
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))