Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendInside from plot-0.2.3.4

Percentage Accurate: 99.9% → 100.0%

Time: 4.1s

Alternatives: 8

Speedup: 1.2×

Specification

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(x, 3, \mathsf{fma}\left(y, 2, z\right)\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (fma x 3.0 (fma y 2.0 z)))

C

double code(double x, double y, double z) {
	return fma(x, 3.0, fma(y, 2.0, z));
}

Julia

function code(x, y, z)
	return fma(x, 3.0, fma(y, 2.0, z))
end

Wolfram

code[x_, y_, z_] := N[(x * 3.0 + N[(y * 2.0 + z), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

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

   1. +-commutative 99.9%

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

   2. +-commutative 99.9%

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

   3. associate-+l+ 99.9%

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

   4. associate-+r+ 99.9%

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

   5. count-2 99.9%

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

   6. associate-+l+ 99.9%

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

   7. associate-+r+ 99.9%

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

   8. distribute-rgt1-in 99.9%

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

   9. *-commutative 99.9%

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

   10. fma-def 100.0%

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

   11. metadata-eval 100.0%

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

   12. count-2 100.0%

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

   13. *-commutative 100.0%

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

   14. fma-def 100.0%

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

3. Simplified 100.0%

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

4. Final simplification 100.0%

   \[\leadsto \mathsf{fma}\left(x, 3, \mathsf{fma}\left(y, 2, z\right)\right) \]

Alternative 2: 55.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.6 \cdot 10^{+85}:\\ \;\;\;\;y \cdot 2\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-298}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 1.32 \cdot 10^{-164}:\\ \;\;\;\;x \cdot 3\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-88}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-62}:\\ \;\;\;\;x \cdot 3\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+18}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;y \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -7.6e+85)
   (* y 2.0)
   (if (<= y 2.8e-298)
     (+ x z)
     (if (<= y 1.32e-164)
       (* x 3.0)
       (if (<= y 6e-88)
         (+ x z)
         (if (<= y 1.65e-62)
           (* x 3.0)
           (if (<= y 1.1e+18) (+ x z) (* y 2.0))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -7.6e+85) {
		tmp = y * 2.0;
	} else if (y <= 2.8e-298) {
		tmp = x + z;
	} else if (y <= 1.32e-164) {
		tmp = x * 3.0;
	} else if (y <= 6e-88) {
		tmp = x + z;
	} else if (y <= 1.65e-62) {
		tmp = x * 3.0;
	} else if (y <= 1.1e+18) {
		tmp = x + z;
	} else {
		tmp = y * 2.0;
	}
	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 (y <= (-7.6d+85)) then
        tmp = y * 2.0d0
    else if (y <= 2.8d-298) then
        tmp = x + z
    else if (y <= 1.32d-164) then
        tmp = x * 3.0d0
    else if (y <= 6d-88) then
        tmp = x + z
    else if (y <= 1.65d-62) then
        tmp = x * 3.0d0
    else if (y <= 1.1d+18) then
        tmp = x + z
    else
        tmp = y * 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -7.6e+85) {
		tmp = y * 2.0;
	} else if (y <= 2.8e-298) {
		tmp = x + z;
	} else if (y <= 1.32e-164) {
		tmp = x * 3.0;
	} else if (y <= 6e-88) {
		tmp = x + z;
	} else if (y <= 1.65e-62) {
		tmp = x * 3.0;
	} else if (y <= 1.1e+18) {
		tmp = x + z;
	} else {
		tmp = y * 2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -7.6e+85:
		tmp = y * 2.0
	elif y <= 2.8e-298:
		tmp = x + z
	elif y <= 1.32e-164:
		tmp = x * 3.0
	elif y <= 6e-88:
		tmp = x + z
	elif y <= 1.65e-62:
		tmp = x * 3.0
	elif y <= 1.1e+18:
		tmp = x + z
	else:
		tmp = y * 2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -7.6e+85)
		tmp = Float64(y * 2.0);
	elseif (y <= 2.8e-298)
		tmp = Float64(x + z);
	elseif (y <= 1.32e-164)
		tmp = Float64(x * 3.0);
	elseif (y <= 6e-88)
		tmp = Float64(x + z);
	elseif (y <= 1.65e-62)
		tmp = Float64(x * 3.0);
	elseif (y <= 1.1e+18)
		tmp = Float64(x + z);
	else
		tmp = Float64(y * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -7.6e+85)
		tmp = y * 2.0;
	elseif (y <= 2.8e-298)
		tmp = x + z;
	elseif (y <= 1.32e-164)
		tmp = x * 3.0;
	elseif (y <= 6e-88)
		tmp = x + z;
	elseif (y <= 1.65e-62)
		tmp = x * 3.0;
	elseif (y <= 1.1e+18)
		tmp = x + z;
	else
		tmp = y * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -7.6e+85], N[(y * 2.0), $MachinePrecision], If[LessEqual[y, 2.8e-298], N[(x + z), $MachinePrecision], If[LessEqual[y, 1.32e-164], N[(x * 3.0), $MachinePrecision], If[LessEqual[y, 6e-88], N[(x + z), $MachinePrecision], If[LessEqual[y, 1.65e-62], N[(x * 3.0), $MachinePrecision], If[LessEqual[y, 1.1e+18], N[(x + z), $MachinePrecision], N[(y * 2.0), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.59999999999999984e85 or 1.1e18 < y

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. count-2 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 71.6%

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

   if -7.59999999999999984e85 < y < 2.79999999999999992e-298 or 1.3199999999999999e-164 < y < 5.9999999999999999e-88 or 1.65000000000000002e-62 < y < 1.1e18

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. count-2 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 87.4%

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

      1. flip-+ 33.0%

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

      2. div-inv 32.9%

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

      3. swap-sqr 32.9%

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

      4. metadata-eval 32.9%

         \[\leadsto \left(\color{blue}{4} \cdot \left(x \cdot x\right) - \left(z + x\right) \cdot \left(z + x\right)\right) \cdot \frac{1}{2 \cdot x - \left(z + x\right)} \]

      5. pow2 32.9%

         \[\leadsto \left(4 \cdot \left(x \cdot x\right) - \color{blue}{{\left(z + x\right)}^{2}}\right) \cdot \frac{1}{2 \cdot x - \left(z + x\right)} \]

      6. +-commutative 32.9%

         \[\leadsto \left(4 \cdot \left(x \cdot x\right) - {\color{blue}{\left(x + z\right)}}^{2}\right) \cdot \frac{1}{2 \cdot x - \left(z + x\right)} \]

      7. add-log-exp 16.9%

         \[\leadsto \left(4 \cdot \left(x \cdot x\right) - {\left(x + z\right)}^{2}\right) \cdot \frac{1}{\color{blue}{\log \left(e^{2 \cdot x}\right)} - \left(z + x\right)} \]

      8. *-commutative 16.9%

         \[\leadsto \left(4 \cdot \left(x \cdot x\right) - {\left(x + z\right)}^{2}\right) \cdot \frac{1}{\log \left(e^{\color{blue}{x \cdot 2}}\right) - \left(z + x\right)} \]

      9. exp-lft-sqr 16.9%

         \[\leadsto \left(4 \cdot \left(x \cdot x\right) - {\left(x + z\right)}^{2}\right) \cdot \frac{1}{\log \color{blue}{\left(e^{x} \cdot e^{x}\right)} - \left(z + x\right)} \]

      10. log-prod 16.9%

          \[\leadsto \left(4 \cdot \left(x \cdot x\right) - {\left(x + z\right)}^{2}\right) \cdot \frac{1}{\color{blue}{\left(\log \left(e^{x}\right) + \log \left(e^{x}\right)\right)} - \left(z + x\right)} \]

      11. add-log-exp 16.9%

          \[\leadsto \left(4 \cdot \left(x \cdot x\right) - {\left(x + z\right)}^{2}\right) \cdot \frac{1}{\left(\color{blue}{x} + \log \left(e^{x}\right)\right) - \left(z + x\right)} \]

      12. add-log-exp 32.9%

          \[\leadsto \left(4 \cdot \left(x \cdot x\right) - {\left(x + z\right)}^{2}\right) \cdot \frac{1}{\left(x + \color{blue}{x}\right) - \left(z + x\right)} \]

      13. +-commutative 32.9%

          \[\leadsto \left(4 \cdot \left(x \cdot x\right) - {\left(x + z\right)}^{2}\right) \cdot \frac{1}{\left(x + x\right) - \color{blue}{\left(x + z\right)}} \]

   6. Applied egg-rr 32.9%

      \[\leadsto \color{blue}{\left(4 \cdot \left(x \cdot x\right) - {\left(x + z\right)}^{2}\right) \cdot \frac{1}{\left(x + x\right) - \left(x + z\right)}} \]
   7. Step-by-step derivation

      1. un-div-inv 33.0%

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

      2. metadata-eval 33.0%

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

      3. swap-sqr 33.0%

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

      4. count-2 33.0%

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

      5. count-2 33.0%

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

      6. unpow2 33.0%

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

      7. flip-+ 87.4%

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

      8. flip-+ 0.0%

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

      9. +-inverses 0.0%

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

      10. +-inverses 0.0%

          \[\leadsto \frac{0}{\color{blue}{0}} + \left(x + z\right) \]

   8. Applied egg-rr 0.0%

      \[\leadsto \color{blue}{\frac{0}{0} + \left(x + z\right)} \]

   10. Simplified 62.0%

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

   if 2.79999999999999992e-298 < y < 1.3199999999999999e-164 or 5.9999999999999999e-88 < y < 1.65000000000000002e-62

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-+l+ 99.8%

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

      3. +-commutative 99.8%

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

      4. count-2 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 79.8%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.6 \cdot 10^{+85}:\\ \;\;\;\;y \cdot 2\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{-298}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 1.32 \cdot 10^{-164}:\\ \;\;\;\;x \cdot 3\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-88}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-62}:\\ \;\;\;\;x \cdot 3\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+18}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;y \cdot 2\\ \end{array} \]

Alternative 3: 84.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+28} \lor \neg \left(y \leq 1.9 \cdot 10^{-44}\right):\\ \;\;\;\;z + y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;z + x \cdot 3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -5e+28) (not (<= y 1.9e-44))) (+ z (* y 2.0)) (+ z (* x 3.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5e+28) || !(y <= 1.9e-44)) {
		tmp = z + (y * 2.0);
	} else {
		tmp = z + (x * 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 ((y <= (-5d+28)) .or. (.not. (y <= 1.9d-44))) then
        tmp = z + (y * 2.0d0)
    else
        tmp = z + (x * 3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5e+28) || !(y <= 1.9e-44)) {
		tmp = z + (y * 2.0);
	} else {
		tmp = z + (x * 3.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -5e+28) or not (y <= 1.9e-44):
		tmp = z + (y * 2.0)
	else:
		tmp = z + (x * 3.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -5e+28) || !(y <= 1.9e-44))
		tmp = Float64(z + Float64(y * 2.0));
	else
		tmp = Float64(z + Float64(x * 3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -5e+28) || ~((y <= 1.9e-44)))
		tmp = z + (y * 2.0);
	else
		tmp = z + (x * 3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -5e+28], N[Not[LessEqual[y, 1.9e-44]], $MachinePrecision]], N[(z + N[(y * 2.0), $MachinePrecision]), $MachinePrecision], N[(z + N[(x * 3.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.99999999999999957e28 or 1.9e-44 < y

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. count-2 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around 0 86.1%

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

   if -4.99999999999999957e28 < y < 1.9e-44

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. count-2 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 95.5%

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

   5. Taylor expanded in x around 0 95.5%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+28} \lor \neg \left(y \leq 1.9 \cdot 10^{-44}\right):\\ \;\;\;\;z + y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;z + x \cdot 3\\ \end{array} \]

Alternative 4: 78.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+201}:\\ \;\;\;\;x \cdot 3\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+91}:\\ \;\;\;\;z + y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot 3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -4.8e+201) (* x 3.0) (if (<= x 3.2e+91) (+ z (* y 2.0)) (* x 3.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.8e+201) {
		tmp = x * 3.0;
	} else if (x <= 3.2e+91) {
		tmp = z + (y * 2.0);
	} else {
		tmp = x * 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 (x <= (-4.8d+201)) then
        tmp = x * 3.0d0
    else if (x <= 3.2d+91) then
        tmp = z + (y * 2.0d0)
    else
        tmp = x * 3.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.8e+201) {
		tmp = x * 3.0;
	} else if (x <= 3.2e+91) {
		tmp = z + (y * 2.0);
	} else {
		tmp = x * 3.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -4.8e+201:
		tmp = x * 3.0
	elif x <= 3.2e+91:
		tmp = z + (y * 2.0)
	else:
		tmp = x * 3.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -4.8e+201)
		tmp = Float64(x * 3.0);
	elseif (x <= 3.2e+91)
		tmp = Float64(z + Float64(y * 2.0));
	else
		tmp = Float64(x * 3.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -4.8e+201)
		tmp = x * 3.0;
	elseif (x <= 3.2e+91)
		tmp = z + (y * 2.0);
	else
		tmp = x * 3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -4.8e+201], N[(x * 3.0), $MachinePrecision], If[LessEqual[x, 3.2e+91], N[(z + N[(y * 2.0), $MachinePrecision]), $MachinePrecision], N[(x * 3.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -4.79999999999999985e201 or 3.19999999999999989e91 < x

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-+l+ 99.8%

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

      3. +-commutative 99.8%

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

      4. count-2 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 77.8%

      \[\leadsto \color{blue}{3 \cdot x} \]

   if -4.79999999999999985e201 < x < 3.19999999999999989e91

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. associate-+l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. count-2 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 86.2%

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

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+201}:\\ \;\;\;\;x \cdot 3\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+91}:\\ \;\;\;\;z + y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot 3\\ \end{array} \]

Alternative 5: 99.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ x + \left(z + 2 \cdot \left(x + y\right)\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ x (+ z (* 2.0 (+ x y)))))

C

double code(double x, double y, double z) {
	return x + (z + (2.0 * (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 + (z + (2.0d0 * (x + y)))
end function

Java

public static double code(double x, double y, double z) {
	return x + (z + (2.0 * (x + y)));
}

Python

def code(x, y, z):
	return x + (z + (2.0 * (x + y)))

Julia

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

MATLAB

function tmp = code(x, y, z)
	tmp = x + (z + (2.0 * (x + y)));
end

Wolfram

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

Derivation

1. Initial program 99.9%

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

   1. +-commutative 99.9%

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

   2. associate-+l+ 99.9%

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

   3. +-commutative 99.9%

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

   4. count-2 99.9%

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

3. Simplified 99.9%

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

4. Final simplification 99.9%

   \[\leadsto x + \left(z + 2 \cdot \left(x + y\right)\right) \]

Alternative 6: 52.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+47}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+60}:\\ \;\;\;\;y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -3.3e+47) z (if (<= z 2.5e+60) (* y 2.0) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.3e+47) {
		tmp = z;
	} else if (z <= 2.5e+60) {
		tmp = y * 2.0;
	} else {
		tmp = 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 <= (-3.3d+47)) then
        tmp = z
    else if (z <= 2.5d+60) then
        tmp = y * 2.0d0
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.3e+47) {
		tmp = z;
	} else if (z <= 2.5e+60) {
		tmp = y * 2.0;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -3.3e+47:
		tmp = z
	elif z <= 2.5e+60:
		tmp = y * 2.0
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -3.3e+47)
		tmp = z;
	elseif (z <= 2.5e+60)
		tmp = Float64(y * 2.0);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -3.3e+47)
		tmp = z;
	elseif (z <= 2.5e+60)
		tmp = y * 2.0;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -3.3e+47], z, If[LessEqual[z, 2.5e+60], N[(y * 2.0), $MachinePrecision], z]]

Derivation

1. Split input into 2 regimes

2. if z < -3.2999999999999999e47 or 2.49999999999999987e60 < z

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. count-2 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 70.2%

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

   if -3.2999999999999999e47 < z < 2.49999999999999987e60

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. count-2 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 50.4%

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

4. Final simplification 58.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+47}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+60}:\\ \;\;\;\;y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 7: 3.0% accurate, 11.0× speedup

Math

\[\begin{array}{l} \\ 2 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 2.0)

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 2.0d0
end function

Java

public static double code(double x, double y, double z) {
	return 2.0;
}

Python

def code(x, y, z):
	return 2.0

Julia

function code(x, y, z)
	return 2.0
end

MATLAB

function tmp = code(x, y, z)
	tmp = 2.0;
end

Wolfram

code[x_, y_, z_] := 2.0

Derivation

1. Initial program 99.9%

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

   1. +-commutative 99.9%

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

   2. associate-+l+ 99.9%

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

   3. +-commutative 99.9%

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

   4. count-2 99.9%

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

3. Simplified 99.9%

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

4. Taylor expanded in y around 0 65.6%

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

   1. flip-+ 24.4%

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

   2. div-inv 24.4%

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

   3. swap-sqr 24.3%

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

   4. metadata-eval 24.3%

      \[\leadsto \left(\color{blue}{4} \cdot \left(x \cdot x\right) - \left(z + x\right) \cdot \left(z + x\right)\right) \cdot \frac{1}{2 \cdot x - \left(z + x\right)} \]

   5. pow2 24.3%

      \[\leadsto \left(4 \cdot \left(x \cdot x\right) - \color{blue}{{\left(z + x\right)}^{2}}\right) \cdot \frac{1}{2 \cdot x - \left(z + x\right)} \]

   6. +-commutative 24.3%

      \[\leadsto \left(4 \cdot \left(x \cdot x\right) - {\color{blue}{\left(x + z\right)}}^{2}\right) \cdot \frac{1}{2 \cdot x - \left(z + x\right)} \]

   7. add-log-exp 10.5%

      \[\leadsto \left(4 \cdot \left(x \cdot x\right) - {\left(x + z\right)}^{2}\right) \cdot \frac{1}{\color{blue}{\log \left(e^{2 \cdot x}\right)} - \left(z + x\right)} \]

   8. *-commutative 10.5%

      \[\leadsto \left(4 \cdot \left(x \cdot x\right) - {\left(x + z\right)}^{2}\right) \cdot \frac{1}{\log \left(e^{\color{blue}{x \cdot 2}}\right) - \left(z + x\right)} \]

   9. exp-lft-sqr 10.5%

      \[\leadsto \left(4 \cdot \left(x \cdot x\right) - {\left(x + z\right)}^{2}\right) \cdot \frac{1}{\log \color{blue}{\left(e^{x} \cdot e^{x}\right)} - \left(z + x\right)} \]

   10. log-prod 10.5%

       \[\leadsto \left(4 \cdot \left(x \cdot x\right) - {\left(x + z\right)}^{2}\right) \cdot \frac{1}{\color{blue}{\left(\log \left(e^{x}\right) + \log \left(e^{x}\right)\right)} - \left(z + x\right)} \]

   11. add-log-exp 10.4%

       \[\leadsto \left(4 \cdot \left(x \cdot x\right) - {\left(x + z\right)}^{2}\right) \cdot \frac{1}{\left(\color{blue}{x} + \log \left(e^{x}\right)\right) - \left(z + x\right)} \]

   12. add-log-exp 24.3%

       \[\leadsto \left(4 \cdot \left(x \cdot x\right) - {\left(x + z\right)}^{2}\right) \cdot \frac{1}{\left(x + \color{blue}{x}\right) - \left(z + x\right)} \]

   13. +-commutative 24.3%

       \[\leadsto \left(4 \cdot \left(x \cdot x\right) - {\left(x + z\right)}^{2}\right) \cdot \frac{1}{\left(x + x\right) - \color{blue}{\left(x + z\right)}} \]

6. Applied egg-rr 24.3%

   \[\leadsto \color{blue}{\left(4 \cdot \left(x \cdot x\right) - {\left(x + z\right)}^{2}\right) \cdot \frac{1}{\left(x + x\right) - \left(x + z\right)}} \]
7. Step-by-step derivation

   1. un-div-inv 24.4%

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

   2. metadata-eval 24.4%

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

   3. swap-sqr 24.4%

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

   4. count-2 24.4%

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

   5. count-2 24.4%

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

   6. unpow2 24.4%

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

   7. flip-+ 65.6%

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

   8. flip-+ 0.0%

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

   9. flip3-+ 0.0%

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

   10. frac-add 0.0%

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

8. Applied egg-rr 0.0%

   \[\leadsto \color{blue}{\frac{0 \cdot \mathsf{fma}\left(x, x, z \cdot \left(z - x\right)\right) + 0 \cdot \left({x}^{3} + {z}^{3}\right)}{0 \cdot \mathsf{fma}\left(x, x, z \cdot \left(z - x\right)\right)}} \]

10. Simplified 3.2%

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

11. Final simplification 3.2%

    \[\leadsto 2 \]

Alternative 8: 34.6% accurate, 11.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := z

Derivation

1. Initial program 99.9%

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

   1. +-commutative 99.9%

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

   2. associate-+l+ 99.9%

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

   3. +-commutative 99.9%

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

   4. count-2 99.9%

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

3. Simplified 99.9%

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

4. Taylor expanded in z around inf 36.3%

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

5. Final simplification 36.3%

   \[\leadsto z \]

Reproduce

herbie shell --seed 2023195 
(FPCore (x y z)
  :name "Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendInside from plot-0.2.3.4"
  :precision binary64
  (+ (+ (+ (+ (+ x y) y) x) z) x))