Statistics.Sample:robustSumVarWeighted from math-functions-0.1.5.2

Percentage Accurate: 99.9% → 99.9%

Time: 5.2s

Alternatives: 5

Speedup: 1.0×

• 25.4% 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 99.8%

   \[x + \left(y \cdot z\right) \cdot z \]

2. Final simplification 99.8%

   \[\leadsto x + z \cdot \left(y \cdot z\right) \]

Alternative 2: 85.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(y \cdot z\right)\\ \mathbf{if}\;t_0 \leq -1 \cdot 10^{+137} \lor \neg \left(t_0 \leq -1 \cdot 10^{+35} \lor \neg \left(t_0 \leq -2 \cdot 10^{-143}\right) \land t_0 \leq 5 \cdot 10^{-24}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (* y z))))
   (if (or (<= t_0 -1e+137)
           (not
            (or (<= t_0 -1e+35) (and (not (<= t_0 -2e-143)) (<= t_0 5e-24)))))
     t_0
     x)))

C

double code(double x, double y, double z) {
	double t_0 = z * (y * z);
	double tmp;
	if ((t_0 <= -1e+137) || !((t_0 <= -1e+35) || (!(t_0 <= -2e-143) && (t_0 <= 5e-24)))) {
		tmp = t_0;
	} 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 = z * (y * z)
    if ((t_0 <= (-1d+137)) .or. (.not. (t_0 <= (-1d+35)) .or. (.not. (t_0 <= (-2d-143))) .and. (t_0 <= 5d-24))) then
        tmp = t_0
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * (y * z);
	double tmp;
	if ((t_0 <= -1e+137) || !((t_0 <= -1e+35) || (!(t_0 <= -2e-143) && (t_0 <= 5e-24)))) {
		tmp = t_0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (y * z)
	tmp = 0
	if (t_0 <= -1e+137) or not ((t_0 <= -1e+35) or (not (t_0 <= -2e-143) and (t_0 <= 5e-24))):
		tmp = t_0
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(y * z))
	tmp = 0.0
	if ((t_0 <= -1e+137) || !((t_0 <= -1e+35) || (!(t_0 <= -2e-143) && (t_0 <= 5e-24))))
		tmp = t_0;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (y * z);
	tmp = 0.0;
	if ((t_0 <= -1e+137) || ~(((t_0 <= -1e+35) || (~((t_0 <= -2e-143)) && (t_0 <= 5e-24)))))
		tmp = t_0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, -1e+137], N[Not[Or[LessEqual[t$95$0, -1e+35], And[N[Not[LessEqual[t$95$0, -2e-143]], $MachinePrecision], LessEqual[t$95$0, 5e-24]]]], $MachinePrecision]], t$95$0, x]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 y z) z) < -1e137 or -9.9999999999999997e34 < (*.f64 (*.f64 y z) z) < -1.9999999999999999e-143 or 4.9999999999999998e-24 < (*.f64 (*.f64 y z) z)

   1. Initial program 99.8%

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

      1. associate-*l* 92.2%

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

   3. Simplified 92.2%

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

      1. +-commutative 92.2%

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

      2. associate-*r* 99.8%

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

      3. add-sqr-sqrt 45.0%

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

      4. associate-*r* 45.0%

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

      5. fma-def 45.0%

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

   5. Applied egg-rr 45.0%

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

   6. Taylor expanded in y around inf 82.7%

      \[\leadsto \color{blue}{y \cdot {z}^{2}} \]
   7. Step-by-step derivation

      1. unpow2 82.7%

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

   8. Simplified 82.7%

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

      1. *-commutative 82.7%

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

      2. pow2 82.7%

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

      3. add-sqr-sqrt 44.9%

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

      4. pow2 44.9%

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

      5. pow-prod-down 47.3%

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

   10. Applied egg-rr 47.3%

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

       1. unpow2 47.3%

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

       2. swap-sqr 44.9%

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

       3. add-sqr-sqrt 82.7%

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

       4. *-commutative 82.7%

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

       5. associate-*l* 90.2%

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

   12. Applied egg-rr 90.2%

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

   if -1e137 < (*.f64 (*.f64 y z) z) < -9.9999999999999997e34 or -1.9999999999999999e-143 < (*.f64 (*.f64 y z) z) < 4.9999999999999998e-24

   1. Initial program 99.9%

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

      1. associate-*l* 98.5%

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

   3. Simplified 98.5%

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

   4. Taylor expanded in x around inf 87.6%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot \left(y \cdot z\right) \leq -1 \cdot 10^{+137} \lor \neg \left(z \cdot \left(y \cdot z\right) \leq -1 \cdot 10^{+35} \lor \neg \left(z \cdot \left(y \cdot z\right) \leq -2 \cdot 10^{-143}\right) \land z \cdot \left(y \cdot z\right) \leq 5 \cdot 10^{-24}\right):\\ \;\;\;\;z \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 64.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 1.85 \cdot 10^{-66}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-47} \lor \neg \left(z \leq 2.9 \cdot 10^{-17}\right):\\ \;\;\;\;y \cdot \left(z \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z 1.85e-66)
   x
   (if (or (<= z 3.8e-47) (not (<= z 2.9e-17))) (* y (* z z)) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 1.85e-66) {
		tmp = x;
	} else if ((z <= 3.8e-47) || !(z <= 2.9e-17)) {
		tmp = y * (z * 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 <= 1.85d-66) then
        tmp = x
    else if ((z <= 3.8d-47) .or. (.not. (z <= 2.9d-17))) then
        tmp = y * (z * 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 <= 1.85e-66) {
		tmp = x;
	} else if ((z <= 3.8e-47) || !(z <= 2.9e-17)) {
		tmp = y * (z * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 1.85e-66:
		tmp = x
	elif (z <= 3.8e-47) or not (z <= 2.9e-17):
		tmp = y * (z * z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 1.85e-66)
		tmp = x;
	elseif ((z <= 3.8e-47) || !(z <= 2.9e-17))
		tmp = Float64(y * Float64(z * z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 1.85e-66)
		tmp = x;
	elseif ((z <= 3.8e-47) || ~((z <= 2.9e-17)))
		tmp = y * (z * z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 1.85e-66], x, If[Or[LessEqual[z, 3.8e-47], N[Not[LessEqual[z, 2.9e-17]], $MachinePrecision]], N[(y * N[(z * z), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < 1.8500000000000001e-66 or 3.80000000000000015e-47 < z < 2.9000000000000003e-17

   1. Initial program 99.9%

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

      1. associate-*l* 96.2%

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

   3. Simplified 96.2%

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

   4. Taylor expanded in x around inf 54.1%

      \[\leadsto \color{blue}{x} \]

   if 1.8500000000000001e-66 < z < 3.80000000000000015e-47 or 2.9000000000000003e-17 < z

   1. Initial program 99.7%

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

      1. associate-*l* 91.1%

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

   3. Simplified 91.1%

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

      1. +-commutative 91.1%

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

      2. associate-*r* 99.7%

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

      3. add-sqr-sqrt 99.6%

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

      4. associate-*r* 99.5%

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

      5. fma-def 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in y around inf 79.7%

      \[\leadsto \color{blue}{y \cdot {z}^{2}} \]
   7. Step-by-step derivation

      1. unpow2 79.7%

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

   8. Simplified 79.7%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot z\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 60.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 1.85 \cdot 10^{-66}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.8 \cdot 10^{-47} \lor \neg \left(z \leq 2.9 \cdot 10^{-17}\right):\\ \;\;\;\;y \cdot \left(z \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 95.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 2.45 \cdot 10^{+148}:\\ \;\;\;\;x + y \cdot \left(z \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z 2.45e+148) (+ x (* y (* z z))) (* z (* y z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 2.45e+148) {
		tmp = x + (y * (z * z));
	} else {
		tmp = z * (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 (z <= 2.45d+148) then
        tmp = x + (y * (z * z))
    else
        tmp = z * (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= 2.45e+148) {
		tmp = x + (y * (z * z));
	} else {
		tmp = z * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 2.45e+148:
		tmp = x + (y * (z * z))
	else:
		tmp = z * (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 2.45e+148)
		tmp = Float64(x + Float64(y * Float64(z * z)));
	else
		tmp = Float64(z * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 2.45e+148)
		tmp = x + (y * (z * z));
	else
		tmp = z * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 2.45e+148], N[(x + N[(y * N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 2.45e148

   1. Initial program 99.8%

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

      1. associate-*l* 96.8%

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

   3. Simplified 96.8%

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

   if 2.45e148 < z

   1. Initial program 99.9%

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

      1. associate-*l* 76.8%

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

   3. Simplified 76.8%

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

      1. +-commutative 76.8%

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

      2. associate-*r* 99.9%

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

      3. add-sqr-sqrt 99.9%

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

      4. associate-*r* 99.9%

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

      5. fma-def 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in y around inf 76.8%

      \[\leadsto \color{blue}{y \cdot {z}^{2}} \]
   7. Step-by-step derivation

      1. unpow2 76.8%

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

   8. Simplified 76.8%

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

      1. *-commutative 76.8%

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

      2. pow2 76.8%

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

      3. add-sqr-sqrt 42.0%

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

      4. pow2 42.0%

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

      5. pow-prod-down 45.8%

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

   10. Applied egg-rr 45.8%

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

       1. unpow2 45.8%

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

       2. swap-sqr 42.0%

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

       3. add-sqr-sqrt 76.8%

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

       4. *-commutative 76.8%

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

       5. associate-*l* 99.9%

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

   12. Applied egg-rr 99.9%

       \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot z} \]
3. Recombined 2 regimes into one program.

4. Final simplification 97.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 2.45 \cdot 10^{+148}:\\ \;\;\;\;x + y \cdot \left(z \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot z\right)\\ \end{array} \]

Alternative 5: 50.8% 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 99.8%

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

   1. associate-*l* 94.9%

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

3. Simplified 94.9%

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

4. Taylor expanded in x around inf 43.6%

   \[\leadsto \color{blue}{x} \]

5. Final simplification 43.6%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023229 
(FPCore (x y z)
  :name "Statistics.Sample:robustSumVarWeighted from math-functions-0.1.5.2"
  :precision binary64
  (+ x (* (* y z) z)))