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

Percentage Accurate: 99.9% → 99.9%

Time: 9.0s

Alternatives: 8

Speedup: 1.0×

• 44.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (((x * x) + (y * y)) + (y * y)) + (y * y)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (((x * x) + (y * y)) + (y * y)) + (y * y)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(y, y, \mathsf{fma}\left(x, x, 2 \cdot \left(y \cdot y\right)\right)\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (fma y y (fma x x (* 2.0 (* y y)))))

C

double code(double x, double y) {
	return fma(y, y, fma(x, x, (2.0 * (y * y))));
}

Julia

function code(x, y)
	return fma(y, y, fma(x, x, Float64(2.0 * Float64(y * y))))
end

Wolfram

code[x_, y_] := N[(y * y + N[(x * x + N[(2.0 * N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

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

   1. +-commutative 99.9%

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

   2. sqr-neg 99.9%

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

   3. +-commutative 99.9%

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

   4. sqr-neg 99.9%

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

   5. +-commutative 99.9%

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

   6. fma-define 100.0%

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

   7. sqr-neg 100.0%

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

   8. sqr-neg 100.0%

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

   9. associate-+l+ 100.0%

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

   10. fma-define 100.0%

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

   11. count-2 100.0%

       \[\leadsto \mathsf{fma}\left(y, y, \mathsf{fma}\left(x, x, \color{blue}{2 \cdot \left(y \cdot y\right)}\right)\right) \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y, y, \mathsf{fma}\left(x, x, 2 \cdot \left(y \cdot y\right)\right)\right)} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 2: 99.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(x, x, y \cdot \left(y \cdot 3\right)\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (fma x x (* y (* y 3.0))))

C

double code(double x, double y) {
	return fma(x, x, (y * (y * 3.0)));
}

Julia

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. associate-+l+ 99.9%

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

   2. associate-+l+ 99.9%

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

   3. fma-define 99.9%

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

   4. count-2 99.9%

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

   5. distribute-rgt1-in 99.9%

      \[\leadsto \mathsf{fma}\left(x, x, \color{blue}{\left(2 + 1\right) \cdot \left(y \cdot y\right)}\right) \]

   6. metadata-eval 99.9%

      \[\leadsto \mathsf{fma}\left(x, x, \left(2 + \color{blue}{-1 \cdot -1}\right) \cdot \left(y \cdot y\right)\right) \]

   7. *-commutative 99.9%

      \[\leadsto \mathsf{fma}\left(x, x, \color{blue}{\left(y \cdot y\right) \cdot \left(2 + -1 \cdot -1\right)}\right) \]

   8. associate-*l* 99.9%

      \[\leadsto \mathsf{fma}\left(x, x, \color{blue}{y \cdot \left(y \cdot \left(2 + -1 \cdot -1\right)\right)}\right) \]

   9. metadata-eval 99.9%

      \[\leadsto \mathsf{fma}\left(x, x, y \cdot \left(y \cdot \left(2 + \color{blue}{1}\right)\right)\right) \]

   10. metadata-eval 99.9%

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

3. Simplified 99.9%

   \[\leadsto \color{blue}{\mathsf{fma}\left(x, x, y \cdot \left(y \cdot 3\right)\right)} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 3: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (y * y) + ((y * y) + ((y * y) + (x * x)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Final simplification 99.9%

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

Alternative 4: 58.1% accurate, 3.0× speedup

Math

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

FPCore

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

C

double code(double x, double y) {
	return y * (y * 3.0);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = y * (y * 3.0d0)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. add-cube-cbrt 99.2%

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

   2. pow3 99.2%

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

   3. add-sqr-sqrt 99.2%

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

   4. pow2 99.2%

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

   5. hypot-define 99.2%

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

4. Applied egg-rr 99.2%

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

5. Taylor expanded in x around 0 52.8%

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

   1. pow2 52.8%

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

   2. rem-cube-cbrt 52.9%

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

   3. flip-+ 0.0%

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

   4. distribute-lft-out-- 0.0%

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

   5. +-inverses 0.0%

      \[\leadsto \frac{\left(y \cdot y\right) \cdot \color{blue}{0}}{y \cdot y - y \cdot y} + y \cdot y \]

   6. metadata-eval 0.0%

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

   7. distribute-rgt-out-- 0.0%

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

   8. distribute-lft-out-- 0.0%

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

   9. +-inverses 0.0%

      \[\leadsto \frac{1 \cdot \color{blue}{0}}{y \cdot y - y \cdot y} + y \cdot y \]

   10. +-inverses 0.0%

       \[\leadsto \frac{1 \cdot \color{blue}{\left({\left(\sqrt[3]{{y}^{2}}\right)}^{3} \cdot {\left(\sqrt[3]{{y}^{2}}\right)}^{3} - {\left(\sqrt[3]{{y}^{2}}\right)}^{3} \cdot {\left(\sqrt[3]{{y}^{2}}\right)}^{3}\right)}}{y \cdot y - y \cdot y} + y \cdot y \]

   11. *-un-lft-identity 0.0%

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

   12. fmm-def 3.5%

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

   13. div-sub 3.5%

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

7. Applied egg-rr 0.0%

   \[\leadsto \color{blue}{\left(\frac{{y}^{4}}{0} - \frac{{y}^{4}}{0}\right)} + y \cdot y \]

9. Simplified 34.4%

   \[\leadsto \color{blue}{0} + y \cdot y \]

11. Applied egg-rr 52.9%

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

12. Final simplification 52.9%

    \[\leadsto y \cdot \left(y \cdot 3\right) \]
13. Add Preprocessing

Alternative 5: 37.7% accurate, 5.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = y * y
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. add-cube-cbrt 99.2%

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

   2. pow3 99.2%

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

   3. add-sqr-sqrt 99.2%

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

   4. pow2 99.2%

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

   5. hypot-define 99.2%

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

4. Applied egg-rr 99.2%

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

5. Taylor expanded in x around 0 52.8%

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

   1. pow2 52.8%

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

   2. rem-cube-cbrt 52.9%

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

   3. flip-+ 0.0%

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

   4. distribute-lft-out-- 0.0%

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

   5. +-inverses 0.0%

      \[\leadsto \frac{\left(y \cdot y\right) \cdot \color{blue}{0}}{y \cdot y - y \cdot y} + y \cdot y \]

   6. metadata-eval 0.0%

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

   7. distribute-rgt-out-- 0.0%

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

   8. distribute-lft-out-- 0.0%

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

   9. +-inverses 0.0%

      \[\leadsto \frac{1 \cdot \color{blue}{0}}{y \cdot y - y \cdot y} + y \cdot y \]

   10. +-inverses 0.0%

       \[\leadsto \frac{1 \cdot \color{blue}{\left({\left(\sqrt[3]{{y}^{2}}\right)}^{3} \cdot {\left(\sqrt[3]{{y}^{2}}\right)}^{3} - {\left(\sqrt[3]{{y}^{2}}\right)}^{3} \cdot {\left(\sqrt[3]{{y}^{2}}\right)}^{3}\right)}}{y \cdot y - y \cdot y} + y \cdot y \]

   11. *-un-lft-identity 0.0%

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

   12. fmm-def 3.5%

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

   13. div-sub 3.5%

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

7. Applied egg-rr 0.0%

   \[\leadsto \color{blue}{\left(\frac{{y}^{4}}{0} - \frac{{y}^{4}}{0}\right)} + y \cdot y \]

9. Simplified 34.4%

   \[\leadsto \color{blue}{0} + y \cdot y \]
10. Step-by-step derivation

    1. +-lft-identity 34.4%

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

11. Applied egg-rr 34.4%

    \[\leadsto \color{blue}{y \cdot y} \]
12. Add Preprocessing

Alternative 6: 3.7% accurate, 5.0× speedup

Math

\[\begin{array}{l} \\ y \cdot 3 \end{array} \]

FPCore

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

C

double code(double x, double y) {
	return y * 3.0;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = y * 3.0d0
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. add-cube-cbrt 99.2%

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

   2. pow3 99.2%

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

   3. add-sqr-sqrt 99.2%

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

   4. pow2 99.2%

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

   5. hypot-define 99.2%

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

4. Applied egg-rr 99.2%

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

5. Taylor expanded in x around 0 52.8%

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

   1. pow2 52.8%

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

   2. rem-cube-cbrt 52.9%

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

   3. flip-+ 0.0%

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

   4. distribute-lft-out-- 0.0%

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

   5. +-inverses 0.0%

      \[\leadsto \frac{\left(y \cdot y\right) \cdot \color{blue}{0}}{y \cdot y - y \cdot y} + y \cdot y \]

   6. metadata-eval 0.0%

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

   7. distribute-rgt-out-- 0.0%

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

   8. distribute-lft-out-- 0.0%

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

   9. +-inverses 0.0%

      \[\leadsto \frac{1 \cdot \color{blue}{0}}{y \cdot y - y \cdot y} + y \cdot y \]

   10. +-inverses 0.0%

       \[\leadsto \frac{1 \cdot \color{blue}{\left({\left(\sqrt[3]{{y}^{2}}\right)}^{3} \cdot {\left(\sqrt[3]{{y}^{2}}\right)}^{3} - {\left(\sqrt[3]{{y}^{2}}\right)}^{3} \cdot {\left(\sqrt[3]{{y}^{2}}\right)}^{3}\right)}}{y \cdot y - y \cdot y} + y \cdot y \]

   11. *-un-lft-identity 0.0%

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

   12. fmm-def 3.5%

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

   13. div-sub 3.5%

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

7. Applied egg-rr 0.0%

   \[\leadsto \color{blue}{\left(\frac{{y}^{4}}{0} - \frac{{y}^{4}}{0}\right)} + y \cdot y \]

9. Simplified 34.4%

   \[\leadsto \color{blue}{0} + y \cdot y \]
10. Step-by-step derivation

    1. +-inverses 11.3%

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

    2. +-commutative 11.3%

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

    3. associate-+r- 11.3%

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

    4. distribute-lft-in 11.3%

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

    5. add-sqr-sqrt 11.3%

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

    6. difference-of-squares 34.4%

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

11. Applied egg-rr 0.0%

    \[\leadsto \color{blue}{\left(y \cdot 3\right) \cdot \left(\frac{0}{0} - y\right)} \]

13. Simplified 3.8%

    \[\leadsto \color{blue}{y \cdot 3} \]
14. Add Preprocessing

Alternative 7: 4.3% accurate, 15.0× speedup

Math

\[\begin{array}{l} \\ 3 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 3.0)

C

double code(double x, double y) {
	return 3.0;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 3.0d0
end function

Java

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

Python

def code(x, y):
	return 3.0

Julia

function code(x, y)
	return 3.0
end

MATLAB

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

Wolfram

code[x_, y_] := 3.0

Derivation

1. Initial program 99.9%

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

   1. add-cube-cbrt 99.2%

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

   2. pow3 99.2%

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

   3. add-sqr-sqrt 99.2%

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

   4. pow2 99.2%

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

   5. hypot-define 99.2%

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

4. Applied egg-rr 99.2%

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

5. Taylor expanded in x around 0 52.8%

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

   1. sqr-pow 52.8%

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

   2. rem-cube-cbrt 52.6%

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

   3. pow2 52.6%

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

   4. sqr-pow 52.6%

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

   5. distribute-lft-out 52.6%

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

   6. pow2 52.6%

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

   7. sqrt-pow1 52.6%

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

   8. rem-cube-cbrt 52.8%

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

   9. pow2 52.8%

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

   10. sqrt-pow1 34.0%

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

   11. metadata-eval 34.0%

       \[\leadsto {y}^{\color{blue}{1}} \cdot \left({\left(\sqrt[3]{{y}^{2}}\right)}^{\left(\frac{3}{2}\right)} + {\left(\sqrt[3]{{y}^{2}}\right)}^{\left(\frac{3}{2}\right)}\right) + y \cdot y \]

   12. pow1 34.0%

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

7. Applied egg-rr 52.9%

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

8. Taylor expanded in y around 0 52.9%

   \[\leadsto \color{blue}{3 \cdot {y}^{2}} \]

10. Simplified 4.2%

    \[\leadsto \color{blue}{3} \]
11. Add Preprocessing

Alternative 8: 1.2% accurate, 15.0× speedup

Math

\[\begin{array}{l} \\ -1 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 -1.0)

C

double code(double x, double y) {
	return -1.0;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = -1.0d0
end function

Java

public static double code(double x, double y) {
	return -1.0;
}

Python

def code(x, y):
	return -1.0

Julia

function code(x, y)
	return -1.0
end

MATLAB

function tmp = code(x, y)
	tmp = -1.0;
end

Wolfram

code[x_, y_] := -1.0

Derivation

1. Initial program 99.9%

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

   1. add-cube-cbrt 99.2%

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

   2. pow3 99.2%

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

   3. add-sqr-sqrt 99.2%

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

   4. pow2 99.2%

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

   5. hypot-define 99.2%

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

4. Applied egg-rr 99.2%

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

5. Taylor expanded in x around 0 52.8%

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

   1. pow2 52.8%

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

   2. rem-cube-cbrt 52.9%

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

   3. flip-+ 0.0%

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

   4. distribute-lft-out-- 0.0%

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

   5. +-inverses 0.0%

      \[\leadsto \frac{\left(y \cdot y\right) \cdot \color{blue}{0}}{y \cdot y - y \cdot y} + y \cdot y \]

   6. metadata-eval 0.0%

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

   7. distribute-rgt-out-- 0.0%

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

   8. distribute-lft-out-- 0.0%

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

   9. +-inverses 0.0%

      \[\leadsto \frac{1 \cdot \color{blue}{0}}{y \cdot y - y \cdot y} + y \cdot y \]

   10. +-inverses 0.0%

       \[\leadsto \frac{1 \cdot \color{blue}{\left({\left(\sqrt[3]{{y}^{2}}\right)}^{3} \cdot {\left(\sqrt[3]{{y}^{2}}\right)}^{3} - {\left(\sqrt[3]{{y}^{2}}\right)}^{3} \cdot {\left(\sqrt[3]{{y}^{2}}\right)}^{3}\right)}}{y \cdot y - y \cdot y} + y \cdot y \]

   11. *-un-lft-identity 0.0%

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

   12. fmm-def 3.5%

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

   13. div-sub 3.5%

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

7. Applied egg-rr 0.0%

   \[\leadsto \color{blue}{\left(\frac{{y}^{4}}{0} - \frac{{y}^{4}}{0}\right)} + y \cdot y \]

9. Simplified 34.4%

   \[\leadsto \color{blue}{0} + y \cdot y \]

10. Taylor expanded in y around 0 34.4%

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

12. Simplified 1.2%

    \[\leadsto \color{blue}{-1} \]
13. Add Preprocessing

Developer Target 1: 99.9% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x * x) + (y * (y + (y + y)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024185 
(FPCore (x y)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, E"
  :precision binary64

  :alt
  (! :herbie-platform default (+ (* x x) (* y (+ y (+ y y)))))

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