Linear.Quaternion:$c/ from linear-1.19.1.3, A

Percentage Accurate: 98.1% → 98.1%

Time: 7.5s

Alternatives: 5

Speedup: 1.0×

• 34.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Final simplification 99.9%

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

Alternative 2: 86.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot z \leq 5 \cdot 10^{+32}:\\ \;\;\;\;z \cdot z + \left(x \cdot y + z \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(z \cdot 3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (* z z) 5e+32) (+ (* z z) (+ (* x y) (* z z))) (* z (* z 3.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z * z) <= 5e+32) {
		tmp = (z * z) + ((x * y) + (z * z));
	} else {
		tmp = z * (z * 3.0);
	}
	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) :: tmp
    if ((z * z) <= 5d+32) then
        tmp = (z * z) + ((x * y) + (z * z))
    else
        tmp = z * (z * 3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z * z) <= 5e+32) {
		tmp = (z * z) + ((x * y) + (z * z));
	} else {
		tmp = z * (z * 3.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z * z) <= 5e+32:
		tmp = (z * z) + ((x * y) + (z * z))
	else:
		tmp = z * (z * 3.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(z * z) <= 5e+32)
		tmp = Float64(Float64(z * z) + Float64(Float64(x * y) + Float64(z * z)));
	else
		tmp = Float64(z * Float64(z * 3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z * z) <= 5e+32)
		tmp = (z * z) + ((x * y) + (z * z));
	else
		tmp = z * (z * 3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(z * z), $MachinePrecision], 5e+32], N[(N[(z * z), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(z * 3.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z z) < 4.9999999999999997e32

   1. Initial program 99.9%

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

      1. add-cube-cbrt 98.3%

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

      2. pow3 98.3%

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

      3. fma-def 98.3%

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

      4. pow2 98.3%

         \[\leadsto \left({\left(\sqrt[3]{\mathsf{fma}\left(x, y, \color{blue}{{z}^{2}}\right)}\right)}^{3} + z \cdot z\right) + z \cdot z \]

   4. Applied egg-rr 98.3%

      \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(x, y, {z}^{2}\right)}\right)}^{3}} + z \cdot z\right) + z \cdot z \]

   5. Taylor expanded in z around 0 87.6%

      \[\leadsto \left(\color{blue}{{1}^{0.3333333333333333} \cdot \left(x \cdot y\right)} + z \cdot z\right) + z \cdot z \]
   6. Step-by-step derivation

      1. pow-base-1 87.6%

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

      2. *-lft-identity 87.6%

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

   7. Simplified 87.6%

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

   if 4.9999999999999997e32 < (*.f64 z z)

   1. Initial program 99.9%

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

      1. add-cube-cbrt 99.6%

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

      2. pow3 99.6%

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

      3. fma-def 99.7%

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

      4. pow2 99.7%

         \[\leadsto \left({\left(\sqrt[3]{\mathsf{fma}\left(x, y, \color{blue}{{z}^{2}}\right)}\right)}^{3} + z \cdot z\right) + z \cdot z \]

   4. Applied egg-rr 99.7%

      \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(x, y, {z}^{2}\right)}\right)}^{3}} + z \cdot z\right) + z \cdot z \]

   5. Taylor expanded in x around 0 85.7%

      \[\leadsto \left({\color{blue}{\left({\left({z}^{2}\right)}^{0.3333333333333333}\right)}}^{3} + z \cdot z\right) + z \cdot z \]
   6. Step-by-step derivation

      1. unpow1/3 88.0%

         \[\leadsto \left({\color{blue}{\left(\sqrt[3]{{z}^{2}}\right)}}^{3} + z \cdot z\right) + z \cdot z \]

   7. Simplified 88.0%

      \[\leadsto \left({\color{blue}{\left(\sqrt[3]{{z}^{2}}\right)}}^{3} + z \cdot z\right) + z \cdot z \]
   8. Step-by-step derivation

      1. rem-cube-cbrt 88.1%

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

      2. add-exp-log 86.1%

         \[\leadsto \left(\color{blue}{e^{\log \left({z}^{2}\right)}} + z \cdot z\right) + z \cdot z \]

      3. log-pow 40.5%

         \[\leadsto \left(e^{\color{blue}{2 \cdot \log z}} + z \cdot z\right) + z \cdot z \]

   9. Applied egg-rr 40.5%

      \[\leadsto \left(\color{blue}{e^{2 \cdot \log z}} + z \cdot z\right) + z \cdot z \]
   10. Step-by-step derivation

       1. associate-+l+ 40.5%

          \[\leadsto \color{blue}{e^{2 \cdot \log z} + \left(z \cdot z + z \cdot z\right)} \]

       2. *-commutative 40.5%

          \[\leadsto e^{\color{blue}{\log z \cdot 2}} + \left(z \cdot z + z \cdot z\right) \]

       3. pow-to-exp 88.1%

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

       4. pow2 88.1%

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

       5. count-2 88.1%

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

       6. distribute-rgt1-in 88.1%

          \[\leadsto \color{blue}{\left(2 + 1\right) \cdot \left(z \cdot z\right)} \]

       7. metadata-eval 88.1%

          \[\leadsto \color{blue}{3} \cdot \left(z \cdot z\right) \]

       8. associate-*r* 88.1%

          \[\leadsto \color{blue}{\left(3 \cdot z\right) \cdot z} \]

   11. Applied egg-rr 88.1%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot z \leq 5 \cdot 10^{+32}:\\ \;\;\;\;z \cdot z + \left(x \cdot y + z \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(z \cdot 3\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 86.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot z \leq 5 \cdot 10^{+32}:\\ \;\;\;\;z \cdot z + \left(x \cdot y + z \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot z + \left(z \cdot z + z \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (* z z) 5e+32)
   (+ (* z z) (+ (* x y) (* z z)))
   (+ (* z z) (+ (* z z) (* z z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z * z) <= 5e+32) {
		tmp = (z * z) + ((x * y) + (z * z));
	} else {
		tmp = (z * z) + ((z * z) + (z * 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 * z) <= 5d+32) then
        tmp = (z * z) + ((x * y) + (z * z))
    else
        tmp = (z * z) + ((z * z) + (z * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z * z) <= 5e+32) {
		tmp = (z * z) + ((x * y) + (z * z));
	} else {
		tmp = (z * z) + ((z * z) + (z * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z * z) <= 5e+32:
		tmp = (z * z) + ((x * y) + (z * z))
	else:
		tmp = (z * z) + ((z * z) + (z * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(z * z) <= 5e+32)
		tmp = Float64(Float64(z * z) + Float64(Float64(x * y) + Float64(z * z)));
	else
		tmp = Float64(Float64(z * z) + Float64(Float64(z * z) + Float64(z * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z * z) <= 5e+32)
		tmp = (z * z) + ((x * y) + (z * z));
	else
		tmp = (z * z) + ((z * z) + (z * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(z * z), $MachinePrecision], 5e+32], N[(N[(z * z), $MachinePrecision] + N[(N[(x * y), $MachinePrecision] + N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(z * z), $MachinePrecision] + N[(N[(z * z), $MachinePrecision] + N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z z) < 4.9999999999999997e32

   1. Initial program 99.9%

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

      1. add-cube-cbrt 98.3%

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

      2. pow3 98.3%

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

      3. fma-def 98.3%

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

      4. pow2 98.3%

         \[\leadsto \left({\left(\sqrt[3]{\mathsf{fma}\left(x, y, \color{blue}{{z}^{2}}\right)}\right)}^{3} + z \cdot z\right) + z \cdot z \]

   4. Applied egg-rr 98.3%

      \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(x, y, {z}^{2}\right)}\right)}^{3}} + z \cdot z\right) + z \cdot z \]

   5. Taylor expanded in z around 0 87.6%

      \[\leadsto \left(\color{blue}{{1}^{0.3333333333333333} \cdot \left(x \cdot y\right)} + z \cdot z\right) + z \cdot z \]
   6. Step-by-step derivation

      1. pow-base-1 87.6%

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

      2. *-lft-identity 87.6%

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

   7. Simplified 87.6%

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

   if 4.9999999999999997e32 < (*.f64 z z)

   1. Initial program 99.9%

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

      1. add-cube-cbrt 99.6%

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

      2. pow3 99.6%

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

      3. fma-def 99.7%

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

      4. pow2 99.7%

         \[\leadsto \left({\left(\sqrt[3]{\mathsf{fma}\left(x, y, \color{blue}{{z}^{2}}\right)}\right)}^{3} + z \cdot z\right) + z \cdot z \]

   4. Applied egg-rr 99.7%

      \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(x, y, {z}^{2}\right)}\right)}^{3}} + z \cdot z\right) + z \cdot z \]

   5. Taylor expanded in x around 0 85.7%

      \[\leadsto \left({\color{blue}{\left({\left({z}^{2}\right)}^{0.3333333333333333}\right)}}^{3} + z \cdot z\right) + z \cdot z \]
   6. Step-by-step derivation

      1. unpow1/3 88.0%

         \[\leadsto \left({\color{blue}{\left(\sqrt[3]{{z}^{2}}\right)}}^{3} + z \cdot z\right) + z \cdot z \]

   7. Simplified 88.0%

      \[\leadsto \left({\color{blue}{\left(\sqrt[3]{{z}^{2}}\right)}}^{3} + z \cdot z\right) + z \cdot z \]
   8. Step-by-step derivation

      1. rem-cube-cbrt 88.1%

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

      2. pow2 88.1%

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

   9. Applied egg-rr 88.1%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot z \leq 5 \cdot 10^{+32}:\\ \;\;\;\;z \cdot z + \left(x \cdot y + z \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot z + \left(z \cdot z + z \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 69.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 1.16 \cdot 10^{+20}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(z \cdot 3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z 1.16e+20) (* x y) (* z (* z 3.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 1.16e+20) {
		tmp = x * y;
	} else {
		tmp = z * (z * 3.0);
	}
	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) :: tmp
    if (z <= 1.16d+20) then
        tmp = x * y
    else
        tmp = z * (z * 3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= 1.16e+20) {
		tmp = x * y;
	} else {
		tmp = z * (z * 3.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 1.16e+20:
		tmp = x * y
	else:
		tmp = z * (z * 3.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 1.16e+20)
		tmp = Float64(x * y);
	else
		tmp = Float64(z * Float64(z * 3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 1.16e+20)
		tmp = x * y;
	else
		tmp = z * (z * 3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 1.16e+20], N[(x * y), $MachinePrecision], N[(z * N[(z * 3.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 1.16e20

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 62.5%

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

   if 1.16e20 < z

   1. Initial program 99.9%

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

      1. add-cube-cbrt 99.6%

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

      2. pow3 99.6%

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

      3. fma-def 99.6%

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

      4. pow2 99.6%

         \[\leadsto \left({\left(\sqrt[3]{\mathsf{fma}\left(x, y, \color{blue}{{z}^{2}}\right)}\right)}^{3} + z \cdot z\right) + z \cdot z \]

   4. Applied egg-rr 99.6%

      \[\leadsto \left(\color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(x, y, {z}^{2}\right)}\right)}^{3}} + z \cdot z\right) + z \cdot z \]

   5. Taylor expanded in x around 0 86.5%

      \[\leadsto \left({\color{blue}{\left({\left({z}^{2}\right)}^{0.3333333333333333}\right)}}^{3} + z \cdot z\right) + z \cdot z \]
   6. Step-by-step derivation

      1. unpow1/3 88.1%

         \[\leadsto \left({\color{blue}{\left(\sqrt[3]{{z}^{2}}\right)}}^{3} + z \cdot z\right) + z \cdot z \]

   7. Simplified 88.1%

      \[\leadsto \left({\color{blue}{\left(\sqrt[3]{{z}^{2}}\right)}}^{3} + z \cdot z\right) + z \cdot z \]
   8. Step-by-step derivation

      1. rem-cube-cbrt 88.2%

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

      2. add-exp-log 86.9%

         \[\leadsto \left(\color{blue}{e^{\log \left({z}^{2}\right)}} + z \cdot z\right) + z \cdot z \]

      3. log-pow 86.9%

         \[\leadsto \left(e^{\color{blue}{2 \cdot \log z}} + z \cdot z\right) + z \cdot z \]

   9. Applied egg-rr 86.9%

      \[\leadsto \left(\color{blue}{e^{2 \cdot \log z}} + z \cdot z\right) + z \cdot z \]
   10. Step-by-step derivation

       1. associate-+l+ 86.9%

          \[\leadsto \color{blue}{e^{2 \cdot \log z} + \left(z \cdot z + z \cdot z\right)} \]

       2. *-commutative 86.9%

          \[\leadsto e^{\color{blue}{\log z \cdot 2}} + \left(z \cdot z + z \cdot z\right) \]

       3. pow-to-exp 88.2%

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

       4. pow2 88.2%

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

       5. count-2 88.2%

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

       6. distribute-rgt1-in 88.2%

          \[\leadsto \color{blue}{\left(2 + 1\right) \cdot \left(z \cdot z\right)} \]

       7. metadata-eval 88.2%

          \[\leadsto \color{blue}{3} \cdot \left(z \cdot z\right) \]

       8. associate-*r* 88.1%

          \[\leadsto \color{blue}{\left(3 \cdot z\right) \cdot z} \]

   11. Applied egg-rr 88.1%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 1.16 \cdot 10^{+20}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(z \cdot 3\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 52.8% accurate, 5.0× speedup

Math

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

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in x around inf 52.5%

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

4. Final simplification 52.5%

   \[\leadsto x \cdot y \]
5. Add Preprocessing

Developer target: 98.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \left(3 \cdot z\right) \cdot z + y \cdot x \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ (* (* 3.0 z) z) (* y x)))

C

double code(double x, double y, double z) {
	return ((3.0 * z) * z) + (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 = ((3.0d0 * z) * z) + (y * x)
end function

Java

public static double code(double x, double y, double z) {
	return ((3.0 * z) * z) + (y * x);
}

Python

def code(x, y, z):
	return ((3.0 * z) * z) + (y * x)

Julia

function code(x, y, z)
	return Float64(Float64(Float64(3.0 * z) * z) + Float64(y * x))
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((3.0 * z) * z) + (y * x);
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(3.0 * z), $MachinePrecision] * z), $MachinePrecision] + N[(y * x), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024031 
(FPCore (x y z)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, A"
  :precision binary64

  :herbie-target
  (+ (* (* 3.0 z) z) (* y x))

  (+ (+ (+ (* x y) (* z z)) (* z z)) (* z z)))