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

Percentage Accurate: 100.0% → 100.0%

Time: 4.5s

Alternatives: 5

Speedup: 1.0×

• 21.1% 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: 80.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{-62} \lor \neg \left(x \leq 5.8 \cdot 10^{-24}\right):\\ \;\;\;\;x - \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1e-62) (not (<= x 5.8e-24))) (- x (/ x z)) (/ (- y x) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1e-62) || !(x <= 5.8e-24)) {
		tmp = x - (x / 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 ((x <= (-1d-62)) .or. (.not. (x <= 5.8d-24))) then
        tmp = x - (x / 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 ((x <= -1e-62) || !(x <= 5.8e-24)) {
		tmp = x - (x / z);
	} else {
		tmp = (y - x) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1e-62) or not (x <= 5.8e-24):
		tmp = x - (x / z)
	else:
		tmp = (y - x) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1e-62) || !(x <= 5.8e-24))
		tmp = Float64(x - Float64(x / z));
	else
		tmp = Float64(Float64(y - x) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1e-62) || ~((x <= 5.8e-24)))
		tmp = x - (x / z);
	else
		tmp = (y - x) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1e-62], N[Not[LessEqual[x, 5.8e-24]], $MachinePrecision]], N[(x - N[(x / z), $MachinePrecision]), $MachinePrecision], N[(N[(y - x), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1e-62 or 5.7999999999999997e-24 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{1}{z}\right)} \]
   4. Step-by-step derivation

      1. distribute-rgt-out-- N/A

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

      2. *-lft-identity N/A

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

      3. associate-*l/ N/A

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

      4. *-lft-identity N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 88.9

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

   5. Applied rewrites 88.9%

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

   if -1e-62 < x < 5.7999999999999997e-24

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\frac{y - x}{z}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

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

      2. lower--.f64 80.8

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

   5. Applied rewrites 80.8%

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

4. Final simplification 85.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{-62} \lor \neg \left(x \leq 5.8 \cdot 10^{-24}\right):\\ \;\;\;\;x - \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y - x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{-82} \lor \neg \left(x \leq 7.2 \cdot 10^{-68}\right):\\ \;\;\;\;x - \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.35e-82) (not (<= x 7.2e-68))) (- x (/ x z)) (/ y z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.35e-82) || !(x <= 7.2e-68)) {
		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 <= (-1.35d-82)) .or. (.not. (x <= 7.2d-68))) 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 <= -1.35e-82) || !(x <= 7.2e-68)) {
		tmp = x - (x / z);
	} else {
		tmp = y / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.35e-82) or not (x <= 7.2e-68):
		tmp = x - (x / z)
	else:
		tmp = y / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.35e-82) || !(x <= 7.2e-68))
		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 <= -1.35e-82) || ~((x <= 7.2e-68)))
		tmp = x - (x / z);
	else
		tmp = y / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.35e-82], N[Not[LessEqual[x, 7.2e-68]], $MachinePrecision]], N[(x - N[(x / z), $MachinePrecision]), $MachinePrecision], N[(y / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.3500000000000001e-82 or 7.20000000000000015e-68 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(1 - \frac{1}{z}\right)} \]
   4. Step-by-step derivation

      1. distribute-rgt-out-- N/A

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

      2. *-lft-identity N/A

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

      3. associate-*l/ N/A

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

      4. *-lft-identity N/A

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

      5. lower--.f64 N/A

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

      6. lower-/.f64 85.2

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

   5. Applied rewrites 85.2%

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

   if -1.3500000000000001e-82 < x < 7.20000000000000015e-68

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{y}{z}} \]
   4. Step-by-step derivation

      1. lower-/.f64 73.5

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

   5. Applied rewrites 73.5%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{-82} \lor \neg \left(x \leq 7.2 \cdot 10^{-68}\right):\\ \;\;\;\;x - \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 51.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.02 \cdot 10^{+37} \lor \neg \left(x \leq 6.2 \cdot 10^{-24}\right):\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.02e+37) (not (<= x 6.2e-24))) (/ (- x) z) (/ y z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.02e+37) || !(x <= 6.2e-24)) {
		tmp = -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 <= (-2.02d+37)) .or. (.not. (x <= 6.2d-24))) then
        tmp = -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 <= -2.02e+37) || !(x <= 6.2e-24)) {
		tmp = -x / z;
	} else {
		tmp = y / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.02e+37) or not (x <= 6.2e-24):
		tmp = -x / z
	else:
		tmp = y / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.02e+37) || !(x <= 6.2e-24))
		tmp = Float64(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 <= -2.02e+37) || ~((x <= 6.2e-24)))
		tmp = -x / z;
	else
		tmp = y / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.02e+37], N[Not[LessEqual[x, 6.2e-24]], $MachinePrecision]], N[((-x) / z), $MachinePrecision], N[(y / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.0199999999999999e37 or 6.2000000000000001e-24 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0

      \[\leadsto \color{blue}{\frac{y - x}{z}} \]
   4. Step-by-step derivation

      1. lower-/.f64 N/A

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

      2. lower--.f64 48.3

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

   5. Applied rewrites 48.3%

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

   6. Taylor expanded in x around inf

      \[\leadsto \frac{-1 \cdot x}{z} \]
   7. Step-by-step derivation

   8. Applied rewrites 40.6%

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

   if -2.0199999999999999e37 < x < 6.2000000000000001e-24

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{y}{z}} \]
   4. Step-by-step derivation

      1. lower-/.f64 64.6

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

   5. Applied rewrites 64.6%

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

4. Final simplification 53.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.02 \cdot 10^{+37} \lor \neg \left(x \leq 6.2 \cdot 10^{-24}\right):\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 41.5% accurate, 1.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{\frac{y}{z}} \]
4. Step-by-step derivation

   1. lower-/.f64 41.7

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

5. Applied rewrites 41.7%

   \[\leadsto \color{blue}{\frac{y}{z}} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024298 
(FPCore (x y z)
  :name "Statistics.Sample:$swelfordMean from math-functions-0.1.5.2"
  :precision binary64
  (+ x (/ (- y x) z)))