Statistics.Sample:robustSumVarWeighted from math-functions-0.1.5.2

Percentage Accurate: 99.9% → 99.9%

Time: 6.7s

Alternatives: 3

Speedup: 1.0×

• 25.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

   \[x + \left(y \cdot z\right) \cdot z \]
2. Add Preprocessing

3. Final simplification 99.9%

   \[\leadsto x + z \cdot \left(y \cdot z\right) \]
4. Add Preprocessing

Alternative 2: 93.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

   \[x + \left(y \cdot z\right) \cdot z \]
2. Add Preprocessing
3. Step-by-step derivation

   1. add-sqr-sqrt 63.1%

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

   2. pow2 63.1%

      \[\leadsto x + \color{blue}{{\left(\sqrt{\left(y \cdot z\right) \cdot z}\right)}^{2}} \]

   3. associate-*l* 62.7%

      \[\leadsto x + {\left(\sqrt{\color{blue}{y \cdot \left(z \cdot z\right)}}\right)}^{2} \]

   4. sqrt-prod 47.8%

      \[\leadsto x + {\color{blue}{\left(\sqrt{y} \cdot \sqrt{z \cdot z}\right)}}^{2} \]

   5. sqrt-prod 26.1%

      \[\leadsto x + {\left(\sqrt{y} \cdot \color{blue}{\left(\sqrt{z} \cdot \sqrt{z}\right)}\right)}^{2} \]

   6. add-sqr-sqrt 51.8%

      \[\leadsto x + {\left(\sqrt{y} \cdot \color{blue}{z}\right)}^{2} \]

4. Applied egg-rr 51.8%

   \[\leadsto x + \color{blue}{{\left(\sqrt{y} \cdot z\right)}^{2}} \]
5. Step-by-step derivation

   1. unpow2 51.8%

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

   2. swap-sqr 47.8%

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

   3. add-sqr-sqrt 92.8%

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

   4. associate-*r* 99.9%

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

   5. add-sqr-sqrt 50.2%

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

   6. associate-*l* 50.2%

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

   7. *-commutative 50.2%

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

   8. associate-*l* 48.5%

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

   9. pow1 48.5%

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

   10. pow1/2 48.5%

       \[\leadsto x + \sqrt{z} \cdot \left(y \cdot \left({z}^{1} \cdot \color{blue}{{z}^{0.5}}\right)\right) \]

   11. pow-prod-up 48.5%

       \[\leadsto x + \sqrt{z} \cdot \left(y \cdot \color{blue}{{z}^{\left(1 + 0.5\right)}}\right) \]

   12. metadata-eval 48.5%

       \[\leadsto x + \sqrt{z} \cdot \left(y \cdot {z}^{\color{blue}{1.5}}\right) \]

6. Applied egg-rr 48.5%

   \[\leadsto x + \color{blue}{\sqrt{z} \cdot \left(y \cdot {z}^{1.5}\right)} \]
7. Step-by-step derivation

   1. *-commutative 48.5%

      \[\leadsto x + \color{blue}{\left(y \cdot {z}^{1.5}\right) \cdot \sqrt{z}} \]

   2. associate-*l* 45.1%

      \[\leadsto x + \color{blue}{y \cdot \left({z}^{1.5} \cdot \sqrt{z}\right)} \]

   3. metadata-eval 45.1%

      \[\leadsto x + y \cdot \left({z}^{\color{blue}{\left(0.5 + 1\right)}} \cdot \sqrt{z}\right) \]

   4. pow-plus 45.1%

      \[\leadsto x + y \cdot \left(\color{blue}{\left({z}^{0.5} \cdot z\right)} \cdot \sqrt{z}\right) \]

   5. unpow1/2 45.1%

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

   6. rem-square-sqrt 45.0%

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

   7. cube-mult 45.0%

      \[\leadsto x + y \cdot \left(\color{blue}{{\left(\sqrt{z}\right)}^{3}} \cdot \sqrt{z}\right) \]

   8. pow-plus 45.0%

      \[\leadsto x + y \cdot \color{blue}{{\left(\sqrt{z}\right)}^{\left(3 + 1\right)}} \]

   9. metadata-eval 45.0%

      \[\leadsto x + y \cdot {\left(\sqrt{z}\right)}^{\color{blue}{4}} \]

8. Simplified 45.0%

   \[\leadsto x + \color{blue}{y \cdot {\left(\sqrt{z}\right)}^{4}} \]
9. Step-by-step derivation

   1. sqrt-pow2 92.8%

      \[\leadsto x + y \cdot \color{blue}{{z}^{\left(\frac{4}{2}\right)}} \]

   2. metadata-eval 92.8%

      \[\leadsto x + y \cdot {z}^{\color{blue}{2}} \]

   3. unpow2 92.8%

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

10. Applied egg-rr 92.8%

    \[\leadsto x + y \cdot \color{blue}{\left(z \cdot z\right)} \]
11. Add Preprocessing

Alternative 3: 51.4% 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

1. Initial program 99.9%

   \[x + \left(y \cdot z\right) \cdot z \]
2. Add Preprocessing

3. Taylor expanded in x around inf 49.6%

   \[\leadsto \color{blue}{x} \]
4. Add Preprocessing

Reproduce

herbie shell --seed 2024119 
(FPCore (x y z)
  :name "Statistics.Sample:robustSumVarWeighted from math-functions-0.1.5.2"
  :precision binary64
  (+ x (* (* y z) z)))