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

Percentage Accurate: 100.0% → 100.0%

Time: 934.0ms

Alternatives: 4

Speedup: 1.0×

• 20.0% 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. Add Preprocessing
3. Add Preprocessing

Alternative 2: 74.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + \left(x + \left(y - x\right)\right)\\ \mathbf{if}\;z \leq -2.4 \cdot 10^{+40}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 106000000:\\ \;\;\;\;\frac{y - x}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (+ x (- y x)))))
   (if (<= z -2.4e+40) t_0 (if (<= z 106000000.0) (/ (- y x) z) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = x + (x + (y - x));
	double tmp;
	if (z <= -2.4e+40) {
		tmp = t_0;
	} else if (z <= 106000000.0) {
		tmp = (y - x) / z;
	} else {
		tmp = t_0;
	}
	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 + (x + (y - x))
    if (z <= (-2.4d+40)) then
        tmp = t_0
    else if (z <= 106000000.0d0) then
        tmp = (y - x) / z
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x + (x + (y - x));
	double tmp;
	if (z <= -2.4e+40) {
		tmp = t_0;
	} else if (z <= 106000000.0) {
		tmp = (y - x) / z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x + (x + (y - x))
	tmp = 0
	if z <= -2.4e+40:
		tmp = t_0
	elif z <= 106000000.0:
		tmp = (y - x) / z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x + Float64(x + Float64(y - x)))
	tmp = 0.0
	if (z <= -2.4e+40)
		tmp = t_0;
	elseif (z <= 106000000.0)
		tmp = Float64(Float64(y - x) / z);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x + (x + (y - x));
	tmp = 0.0;
	if (z <= -2.4e+40)
		tmp = t_0;
	elseif (z <= 106000000.0)
		tmp = (y - x) / z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x + N[(x + N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.4e+40], t$95$0, If[LessEqual[z, 106000000.0], N[(N[(y - x), $MachinePrecision] / z), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.4e40 or 1.06e8 < z

   1. Initial program 100.0%

      \[x + \frac{y - x}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 3.6%

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

   6. Taylor expanded in x around 0

      \[\leadsto x + y \]

   8. Applied rewrites 51.9%

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

   if -2.4e40 < z < 1.06e8

   1. Initial program 100.0%

      \[x + \frac{y - x}{z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 98.0%

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

Alternative 3: 26.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ x + \left(x + \left(y - x\right)\right) \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[x + \frac{y - x}{z} \]
2. Add Preprocessing

3. Taylor expanded in x around 0

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

5. Applied rewrites 3.3%

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

6. Taylor expanded in x around 0

   \[\leadsto x + y \]

8. Applied rewrites 30.2%

   \[\leadsto x + \left(x + \color{blue}{\left(y - x\right)}\right) \]
9. Add Preprocessing

Alternative 4: 3.1% accurate, 4.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[x + \frac{y - x}{z} \]
2. Add Preprocessing

3. Taylor expanded in x around 0

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

5. Applied rewrites 58.9%

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

6. Taylor expanded in x around 0

   \[\leadsto -1 \cdot \frac{x}{z} + \color{blue}{\frac{y}{z}} \]

8. Applied rewrites 3.5%

   \[\leadsto y - \color{blue}{x} \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024313 
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))