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

Percentage Accurate: 99.9% → 99.9%

Time: 6.4s

Alternatives: 9

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: 99.9% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

Alternative 2: 53.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + 2 \cdot y\\ \mathbf{if}\;y \leq -10500000000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -5.4 \cdot 10^{-274}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-88}:\\ \;\;\;\;x \cdot 3\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{+92}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (* 2.0 y))))
   (if (<= y -10500000000000.0)
     t_0
     (if (<= y -5.4e-274)
       z
       (if (<= y 7.2e-88) (* x 3.0) (if (<= y 9.8e+92) z t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = x + (2.0 * y);
	double tmp;
	if (y <= -10500000000000.0) {
		tmp = t_0;
	} else if (y <= -5.4e-274) {
		tmp = z;
	} else if (y <= 7.2e-88) {
		tmp = x * 3.0;
	} else if (y <= 9.8e+92) {
		tmp = z;
	} else {
		tmp = t_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) :: t_0
    real(8) :: tmp
    t_0 = x + (2.0d0 * y)
    if (y <= (-10500000000000.0d0)) then
        tmp = t_0
    else if (y <= (-5.4d-274)) then
        tmp = z
    else if (y <= 7.2d-88) then
        tmp = x * 3.0d0
    else if (y <= 9.8d+92) then
        tmp = z
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x + (2.0 * y);
	double tmp;
	if (y <= -10500000000000.0) {
		tmp = t_0;
	} else if (y <= -5.4e-274) {
		tmp = z;
	} else if (y <= 7.2e-88) {
		tmp = x * 3.0;
	} else if (y <= 9.8e+92) {
		tmp = z;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x + (2.0 * y)
	tmp = 0
	if y <= -10500000000000.0:
		tmp = t_0
	elif y <= -5.4e-274:
		tmp = z
	elif y <= 7.2e-88:
		tmp = x * 3.0
	elif y <= 9.8e+92:
		tmp = z
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x + Float64(2.0 * y))
	tmp = 0.0
	if (y <= -10500000000000.0)
		tmp = t_0;
	elseif (y <= -5.4e-274)
		tmp = z;
	elseif (y <= 7.2e-88)
		tmp = Float64(x * 3.0);
	elseif (y <= 9.8e+92)
		tmp = z;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x + (2.0 * y);
	tmp = 0.0;
	if (y <= -10500000000000.0)
		tmp = t_0;
	elseif (y <= -5.4e-274)
		tmp = z;
	elseif (y <= 7.2e-88)
		tmp = x * 3.0;
	elseif (y <= 9.8e+92)
		tmp = z;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x + N[(2.0 * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -10500000000000.0], t$95$0, If[LessEqual[y, -5.4e-274], z, If[LessEqual[y, 7.2e-88], N[(x * 3.0), $MachinePrecision], If[LessEqual[y, 9.8e+92], z, t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.05e13 or 9.8000000000000003e92 < y

   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. Step-by-step derivation

      1. +-commutative 100.0%

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

      2. flip-+ 25.8%

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

      3. div-inv 25.8%

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

      4. fma-def 25.8%

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

      5. pow2 25.8%

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

      6. fma-neg 25.8%

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

   5. Applied egg-rr 25.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left({\left(2 \cdot \left(x + y\right)\right)}^{2} - z \cdot z, \frac{1}{\mathsf{fma}\left(2, x + y, -z\right)}, x\right)} \]
   6. Step-by-step derivation

      1. fma-udef 25.8%

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

      2. +-commutative 25.8%

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

      3. associate-*r/ 25.8%

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

      4. *-rgt-identity 25.8%

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

      5. +-commutative 25.8%

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

      6. fma-neg 25.8%

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

      7. +-commutative 25.8%

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

   7. Simplified 25.8%

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

   8. Taylor expanded in y around inf 70.1%

      \[\leadsto x + \color{blue}{2 \cdot y} \]
   9. Step-by-step derivation

      1. *-commutative 70.1%

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

   10. Simplified 70.1%

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

   if -1.05e13 < y < -5.400000000000001e-274 or 7.1999999999999999e-88 < y < 9.8000000000000003e92

   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 56.0%

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

   if -5.400000000000001e-274 < y < 7.1999999999999999e-88

   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 59.0%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -10500000000000:\\ \;\;\;\;x + 2 \cdot y\\ \mathbf{elif}\;y \leq -5.4 \cdot 10^{-274}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-88}:\\ \;\;\;\;x \cdot 3\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{+92}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x + 2 \cdot y\\ \end{array} \]

Alternative 3: 52.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -12600000000000:\\ \;\;\;\;2 \cdot y\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-273}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-88}:\\ \;\;\;\;x \cdot 3\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+93}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;2 \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -12600000000000.0)
   (* 2.0 y)
   (if (<= y -1.8e-273)
     z
     (if (<= y 3e-88) (* x 3.0) (if (<= y 3.2e+93) z (* 2.0 y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -12600000000000.0) {
		tmp = 2.0 * y;
	} else if (y <= -1.8e-273) {
		tmp = z;
	} else if (y <= 3e-88) {
		tmp = x * 3.0;
	} else if (y <= 3.2e+93) {
		tmp = z;
	} else {
		tmp = 2.0 * y;
	}
	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 <= (-12600000000000.0d0)) then
        tmp = 2.0d0 * y
    else if (y <= (-1.8d-273)) then
        tmp = z
    else if (y <= 3d-88) then
        tmp = x * 3.0d0
    else if (y <= 3.2d+93) then
        tmp = z
    else
        tmp = 2.0d0 * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -12600000000000.0) {
		tmp = 2.0 * y;
	} else if (y <= -1.8e-273) {
		tmp = z;
	} else if (y <= 3e-88) {
		tmp = x * 3.0;
	} else if (y <= 3.2e+93) {
		tmp = z;
	} else {
		tmp = 2.0 * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -12600000000000.0:
		tmp = 2.0 * y
	elif y <= -1.8e-273:
		tmp = z
	elif y <= 3e-88:
		tmp = x * 3.0
	elif y <= 3.2e+93:
		tmp = z
	else:
		tmp = 2.0 * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -12600000000000.0)
		tmp = Float64(2.0 * y);
	elseif (y <= -1.8e-273)
		tmp = z;
	elseif (y <= 3e-88)
		tmp = Float64(x * 3.0);
	elseif (y <= 3.2e+93)
		tmp = z;
	else
		tmp = Float64(2.0 * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -12600000000000.0)
		tmp = 2.0 * y;
	elseif (y <= -1.8e-273)
		tmp = z;
	elseif (y <= 3e-88)
		tmp = x * 3.0;
	elseif (y <= 3.2e+93)
		tmp = z;
	else
		tmp = 2.0 * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -12600000000000.0], N[(2.0 * y), $MachinePrecision], If[LessEqual[y, -1.8e-273], z, If[LessEqual[y, 3e-88], N[(x * 3.0), $MachinePrecision], If[LessEqual[y, 3.2e+93], z, N[(2.0 * y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.26e13 or 3.2000000000000001e93 < y

   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 y around inf 68.0%

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

   if -1.26e13 < y < -1.79999999999999996e-273 or 2.9999999999999999e-88 < y < 3.2000000000000001e93

   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 56.0%

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

   if -1.79999999999999996e-273 < y < 2.9999999999999999e-88

   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 59.0%

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

4. Final simplification 61.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -12600000000000:\\ \;\;\;\;2 \cdot y\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-273}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-88}:\\ \;\;\;\;x \cdot 3\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+93}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;2 \cdot y\\ \end{array} \]

Alternative 4: 84.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{+50} \lor \neg \left(x \leq 8 \cdot 10^{+53}\right):\\ \;\;\;\;x + 2 \cdot \left(x + y\right)\\ \mathbf{else}:\\ \;\;\;\;z + 2 \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -8e+50) (not (<= x 8e+53)))
   (+ x (* 2.0 (+ x y)))
   (+ z (* 2.0 y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -8e+50) || !(x <= 8e+53)) {
		tmp = x + (2.0 * (x + y));
	} else {
		tmp = z + (2.0 * y);
	}
	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 <= (-8d+50)) .or. (.not. (x <= 8d+53))) then
        tmp = x + (2.0d0 * (x + y))
    else
        tmp = z + (2.0d0 * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -8e+50) || !(x <= 8e+53)) {
		tmp = x + (2.0 * (x + y));
	} else {
		tmp = z + (2.0 * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -8e+50) or not (x <= 8e+53):
		tmp = x + (2.0 * (x + y))
	else:
		tmp = z + (2.0 * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -8e+50) || !(x <= 8e+53))
		tmp = Float64(x + Float64(2.0 * Float64(x + y)));
	else
		tmp = Float64(z + Float64(2.0 * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -8e+50) || ~((x <= 8e+53)))
		tmp = x + (2.0 * (x + y));
	else
		tmp = z + (2.0 * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -8e+50], N[Not[LessEqual[x, 8e+53]], $MachinePrecision]], N[(x + N[(2.0 * N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z + N[(2.0 * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -8.0000000000000006e50 or 7.9999999999999999e53 < 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+ 99.9%

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

      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 0 86.0%

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

      1. +-commutative 86.0%

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

   6. Simplified 86.0%

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

   if -8.0000000000000006e50 < x < 7.9999999999999999e53

   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 94.6%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{+50} \lor \neg \left(x \leq 8 \cdot 10^{+53}\right):\\ \;\;\;\;x + 2 \cdot \left(x + y\right)\\ \mathbf{else}:\\ \;\;\;\;z + 2 \cdot y\\ \end{array} \]

Alternative 5: 85.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+50} \lor \neg \left(x \leq 9.5 \cdot 10^{+56}\right):\\ \;\;\;\;z + x \cdot 3\\ \mathbf{else}:\\ \;\;\;\;z + 2 \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -4.8e+50) (not (<= x 9.5e+56)))
   (+ z (* x 3.0))
   (+ z (* 2.0 y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -4.8e+50) || !(x <= 9.5e+56)) {
		tmp = z + (x * 3.0);
	} else {
		tmp = z + (2.0 * y);
	}
	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+50)) .or. (.not. (x <= 9.5d+56))) then
        tmp = z + (x * 3.0d0)
    else
        tmp = z + (2.0d0 * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -4.8e+50) || !(x <= 9.5e+56)) {
		tmp = z + (x * 3.0);
	} else {
		tmp = z + (2.0 * y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -4.8e+50) or not (x <= 9.5e+56):
		tmp = z + (x * 3.0)
	else:
		tmp = z + (2.0 * y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -4.8e+50) || !(x <= 9.5e+56))
		tmp = Float64(z + Float64(x * 3.0));
	else
		tmp = Float64(z + Float64(2.0 * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -4.8e+50) || ~((x <= 9.5e+56)))
		tmp = z + (x * 3.0);
	else
		tmp = z + (2.0 * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -4.8e+50], N[Not[LessEqual[x, 9.5e+56]], $MachinePrecision]], N[(z + N[(x * 3.0), $MachinePrecision]), $MachinePrecision], N[(z + N[(2.0 * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.8000000000000004e50 or 9.4999999999999997e56 < 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+ 99.9%

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

      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 76.0%

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

      1. +-commutative 76.0%

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

      2. *-commutative 76.0%

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

      3. associate-+l+ 76.0%

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

      4. *-commutative 76.0%

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

      5. distribute-lft1-in 76.0%

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

      6. metadata-eval 76.0%

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

   6. Simplified 76.0%

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

   if -4.8000000000000004e50 < x < 9.4999999999999997e56

   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 94.1%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+50} \lor \neg \left(x \leq 9.5 \cdot 10^{+56}\right):\\ \;\;\;\;z + x \cdot 3\\ \mathbf{else}:\\ \;\;\;\;z + 2 \cdot y\\ \end{array} \]

Alternative 6: 79.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.95 \cdot 10^{+101}:\\ \;\;\;\;x \cdot 3\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{+177}:\\ \;\;\;\;z + 2 \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot 3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.95e+101)
   (* x 3.0)
   (if (<= x 1.5e+177) (+ z (* 2.0 y)) (* x 3.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.95e+101) {
		tmp = x * 3.0;
	} else if (x <= 1.5e+177) {
		tmp = z + (2.0 * y);
	} 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 <= (-1.95d+101)) then
        tmp = x * 3.0d0
    else if (x <= 1.5d+177) then
        tmp = z + (2.0d0 * y)
    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 <= -1.95e+101) {
		tmp = x * 3.0;
	} else if (x <= 1.5e+177) {
		tmp = z + (2.0 * y);
	} else {
		tmp = x * 3.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.95e+101:
		tmp = x * 3.0
	elif x <= 1.5e+177:
		tmp = z + (2.0 * y)
	else:
		tmp = x * 3.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.95e+101)
		tmp = Float64(x * 3.0);
	elseif (x <= 1.5e+177)
		tmp = Float64(z + Float64(2.0 * y));
	else
		tmp = Float64(x * 3.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.95e+101)
		tmp = x * 3.0;
	elseif (x <= 1.5e+177)
		tmp = z + (2.0 * y);
	else
		tmp = x * 3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.95e+101], N[(x * 3.0), $MachinePrecision], If[LessEqual[x, 1.5e+177], N[(z + N[(2.0 * y), $MachinePrecision]), $MachinePrecision], N[(x * 3.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.95e101 or 1.5e177 < 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 75.2%

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

   if -1.95e101 < x < 1.5e177

   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 87.0%

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

4. Final simplification 84.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.95 \cdot 10^{+101}:\\ \;\;\;\;x \cdot 3\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{+177}:\\ \;\;\;\;z + 2 \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot 3\\ \end{array} \]

Alternative 7: 52.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -18000000000000:\\ \;\;\;\;2 \cdot y\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{+92}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;2 \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -18000000000000.0) (* 2.0 y) (if (<= y 9.8e+92) z (* 2.0 y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -18000000000000.0) {
		tmp = 2.0 * y;
	} else if (y <= 9.8e+92) {
		tmp = z;
	} else {
		tmp = 2.0 * y;
	}
	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 <= (-18000000000000.0d0)) then
        tmp = 2.0d0 * y
    else if (y <= 9.8d+92) then
        tmp = z
    else
        tmp = 2.0d0 * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -18000000000000.0) {
		tmp = 2.0 * y;
	} else if (y <= 9.8e+92) {
		tmp = z;
	} else {
		tmp = 2.0 * y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -18000000000000.0:
		tmp = 2.0 * y
	elif y <= 9.8e+92:
		tmp = z
	else:
		tmp = 2.0 * y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -18000000000000.0)
		tmp = Float64(2.0 * y);
	elseif (y <= 9.8e+92)
		tmp = z;
	else
		tmp = Float64(2.0 * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -18000000000000.0)
		tmp = 2.0 * y;
	elseif (y <= 9.8e+92)
		tmp = z;
	else
		tmp = 2.0 * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -18000000000000.0], N[(2.0 * y), $MachinePrecision], If[LessEqual[y, 9.8e+92], z, N[(2.0 * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.8e13 or 9.8000000000000003e92 < y

   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 y around inf 68.0%

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

   if -1.8e13 < y < 9.8000000000000003e92

   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 49.7%

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

4. Final simplification 57.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -18000000000000:\\ \;\;\;\;2 \cdot y\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{+92}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;2 \cdot y\\ \end{array} \]

Alternative 8: 7.9% accurate, 11.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 99.9%

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

   1. +-commutative 99.9%

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

   2. associate-+l+ 99.9%

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

   3. *-commutative 99.9%

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

   4. add-cube-cbrt 98.9%

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

   5. associate-*l* 98.9%

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

   6. fma-def 98.8%

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

   7. pow2 98.8%

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

5. Applied egg-rr 98.8%

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

6. Taylor expanded in x around inf 7.1%

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

7. Final simplification 7.1%

   \[\leadsto x \]

Alternative 9: 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 35.7%

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

5. Final simplification 35.7%

   \[\leadsto z \]

Reproduce

herbie shell --seed 2023290 
(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))