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

Percentage Accurate: 99.9% → 100.0%

Time: 4.0s

Alternatives: 10

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: 52.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{+99}:\\ \;\;\;\;y \cdot 2\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-237}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-133}:\\ \;\;\;\;x \cdot 3\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+78}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -5.6e+99)
   (* y 2.0)
   (if (<= y 6.5e-237)
     z
     (if (<= y 3.2e-133) (* x 3.0) (if (<= y 9e+78) z (* y 2.0))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -5.6e+99) {
		tmp = y * 2.0;
	} else if (y <= 6.5e-237) {
		tmp = z;
	} else if (y <= 3.2e-133) {
		tmp = x * 3.0;
	} else if (y <= 9e+78) {
		tmp = 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 <= (-5.6d+99)) then
        tmp = y * 2.0d0
    else if (y <= 6.5d-237) then
        tmp = z
    else if (y <= 3.2d-133) then
        tmp = x * 3.0d0
    else if (y <= 9d+78) then
        tmp = 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 <= -5.6e+99) {
		tmp = y * 2.0;
	} else if (y <= 6.5e-237) {
		tmp = z;
	} else if (y <= 3.2e-133) {
		tmp = x * 3.0;
	} else if (y <= 9e+78) {
		tmp = z;
	} else {
		tmp = y * 2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -5.6e+99:
		tmp = y * 2.0
	elif y <= 6.5e-237:
		tmp = z
	elif y <= 3.2e-133:
		tmp = x * 3.0
	elif y <= 9e+78:
		tmp = z
	else:
		tmp = y * 2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -5.6e+99)
		tmp = Float64(y * 2.0);
	elseif (y <= 6.5e-237)
		tmp = z;
	elseif (y <= 3.2e-133)
		tmp = Float64(x * 3.0);
	elseif (y <= 9e+78)
		tmp = z;
	else
		tmp = Float64(y * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -5.6e+99)
		tmp = y * 2.0;
	elseif (y <= 6.5e-237)
		tmp = z;
	elseif (y <= 3.2e-133)
		tmp = x * 3.0;
	elseif (y <= 9e+78)
		tmp = z;
	else
		tmp = y * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -5.6e+99], N[(y * 2.0), $MachinePrecision], If[LessEqual[y, 6.5e-237], z, If[LessEqual[y, 3.2e-133], N[(x * 3.0), $MachinePrecision], If[LessEqual[y, 9e+78], z, N[(y * 2.0), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.6e99 or 8.9999999999999999e78 < 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 71.4%

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

   if -5.6e99 < y < 6.5000000000000001e-237 or 3.20000000000000013e-133 < y < 8.9999999999999999e78

   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 53.5%

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

   if 6.5000000000000001e-237 < y < 3.20000000000000013e-133

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. associate-+l+ 99.7%

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

      3. +-commutative 99.7%

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

      4. count-2 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 72.9%

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

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{+99}:\\ \;\;\;\;y \cdot 2\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-237}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-133}:\\ \;\;\;\;x \cdot 3\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+78}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot 2\\ \end{array} \]

Alternative 3: 84.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{+17}:\\ \;\;\;\;z + y \cdot 2\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{+71}:\\ \;\;\;\;z + x \cdot 3\\ \mathbf{else}:\\ \;\;\;\;x + 2 \cdot \left(x + y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.95e+17)
   (+ z (* y 2.0))
   (if (<= y 5.4e+71) (+ z (* x 3.0)) (+ x (* 2.0 (+ x y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.95e+17) {
		tmp = z + (y * 2.0);
	} else if (y <= 5.4e+71) {
		tmp = z + (x * 3.0);
	} else {
		tmp = x + (2.0 * (x + 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 <= (-1.95d+17)) then
        tmp = z + (y * 2.0d0)
    else if (y <= 5.4d+71) then
        tmp = z + (x * 3.0d0)
    else
        tmp = x + (2.0d0 * (x + y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.95e+17) {
		tmp = z + (y * 2.0);
	} else if (y <= 5.4e+71) {
		tmp = z + (x * 3.0);
	} else {
		tmp = x + (2.0 * (x + y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.95e+17:
		tmp = z + (y * 2.0)
	elif y <= 5.4e+71:
		tmp = z + (x * 3.0)
	else:
		tmp = x + (2.0 * (x + y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.95e+17)
		tmp = Float64(z + Float64(y * 2.0));
	elseif (y <= 5.4e+71)
		tmp = Float64(z + Float64(x * 3.0));
	else
		tmp = Float64(x + Float64(2.0 * Float64(x + y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.95e+17)
		tmp = z + (y * 2.0);
	elseif (y <= 5.4e+71)
		tmp = z + (x * 3.0);
	else
		tmp = x + (2.0 * (x + y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.95e+17], N[(z + N[(y * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.4e+71], N[(z + N[(x * 3.0), $MachinePrecision]), $MachinePrecision], N[(x + N[(2.0 * N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.95e17

   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 84.5%

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

   if -1.95e17 < y < 5.39999999999999993e71

   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 89.1%

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

   5. Taylor expanded in x around 0 89.1%

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

   if 5.39999999999999993e71 < 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 z around 0 90.7%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.95 \cdot 10^{+17}:\\ \;\;\;\;z + y \cdot 2\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{+71}:\\ \;\;\;\;z + x \cdot 3\\ \mathbf{else}:\\ \;\;\;\;x + 2 \cdot \left(x + y\right)\\ \end{array} \]

Alternative 4: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(N[(x * 2.0), $MachinePrecision] + N[(N[(y * 2.0), $MachinePrecision] + N[(x + z), $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. Taylor expanded in y around inf 99.9%

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

5. Final simplification 99.9%

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

Alternative 5: 84.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.7 \cdot 10^{+20} \lor \neg \left(y \leq 3.5 \cdot 10^{+86}\right):\\ \;\;\;\;z + y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;z + x \cdot 3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4.7e+20) (not (<= y 3.5e+86)))
   (+ z (* y 2.0))
   (+ z (* x 3.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.7e+20) || !(y <= 3.5e+86)) {
		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 <= (-4.7d+20)) .or. (.not. (y <= 3.5d+86))) 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 <= -4.7e+20) || !(y <= 3.5e+86)) {
		tmp = z + (y * 2.0);
	} else {
		tmp = z + (x * 3.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -4.7e+20) or not (y <= 3.5e+86):
		tmp = z + (y * 2.0)
	else:
		tmp = z + (x * 3.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -4.7e+20) || !(y <= 3.5e+86))
		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 <= -4.7e+20) || ~((y <= 3.5e+86)))
		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, -4.7e+20], N[Not[LessEqual[y, 3.5e+86]], $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 < -4.7e20 or 3.50000000000000019e86 < 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+ 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 83.9%

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

   if -4.7e20 < y < 3.50000000000000019e86

   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 89.2%

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

   5. Taylor expanded in x around 0 89.2%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.7 \cdot 10^{+20} \lor \neg \left(y \leq 3.5 \cdot 10^{+86}\right):\\ \;\;\;\;z + y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;z + x \cdot 3\\ \end{array} \]

Alternative 6: 80.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{+161}:\\ \;\;\;\;x \cdot 3\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{+154}:\\ \;\;\;\;z + y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot 3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.05e+161)
   (* x 3.0)
   (if (<= x 2.05e+154) (+ z (* y 2.0)) (* x 3.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.05e+161) {
		tmp = x * 3.0;
	} else if (x <= 2.05e+154) {
		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 <= (-1.05d+161)) then
        tmp = x * 3.0d0
    else if (x <= 2.05d+154) 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 <= -1.05e+161) {
		tmp = x * 3.0;
	} else if (x <= 2.05e+154) {
		tmp = z + (y * 2.0);
	} else {
		tmp = x * 3.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.05e+161:
		tmp = x * 3.0
	elif x <= 2.05e+154:
		tmp = z + (y * 2.0)
	else:
		tmp = x * 3.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.05e+161)
		tmp = Float64(x * 3.0);
	elseif (x <= 2.05e+154)
		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 <= -1.05e+161)
		tmp = x * 3.0;
	elseif (x <= 2.05e+154)
		tmp = z + (y * 2.0);
	else
		tmp = x * 3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.05e+161], N[(x * 3.0), $MachinePrecision], If[LessEqual[x, 2.05e+154], N[(z + N[(y * 2.0), $MachinePrecision]), $MachinePrecision], N[(x * 3.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.05e161 or 2.05e154 < x

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. associate-+l+ 99.7%

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

      3. +-commutative 99.7%

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

      4. count-2 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 81.7%

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

   if -1.05e161 < x < 2.05e154

   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 83.5%

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

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{+161}:\\ \;\;\;\;x \cdot 3\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{+154}:\\ \;\;\;\;z + y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot 3\\ \end{array} \]

Alternative 7: 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 8: 52.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.38 \cdot 10^{+101}:\\ \;\;\;\;y \cdot 2\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+79}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.38e+101) (* y 2.0) (if (<= y 4.5e+79) z (* y 2.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.38e+101) {
		tmp = y * 2.0;
	} else if (y <= 4.5e+79) {
		tmp = 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 <= (-1.38d+101)) then
        tmp = y * 2.0d0
    else if (y <= 4.5d+79) then
        tmp = 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 <= -1.38e+101) {
		tmp = y * 2.0;
	} else if (y <= 4.5e+79) {
		tmp = z;
	} else {
		tmp = y * 2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.38e+101:
		tmp = y * 2.0
	elif y <= 4.5e+79:
		tmp = z
	else:
		tmp = y * 2.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.38e+101)
		tmp = Float64(y * 2.0);
	elseif (y <= 4.5e+79)
		tmp = z;
	else
		tmp = Float64(y * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.38e+101)
		tmp = y * 2.0;
	elseif (y <= 4.5e+79)
		tmp = z;
	else
		tmp = y * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.38e+101], N[(y * 2.0), $MachinePrecision], If[LessEqual[y, 4.5e+79], z, N[(y * 2.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.38e101 or 4.49999999999999994e79 < 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 71.4%

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

   if -1.38e101 < y < 4.49999999999999994e79

   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 49.6%

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

4. Final simplification 56.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.38 \cdot 10^{+101}:\\ \;\;\;\;y \cdot 2\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+79}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot 2\\ \end{array} \]

Alternative 9: 3.1% accurate, 11.0× speedup

Math

\[\begin{array}{l} \\ -28 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 -28.0)

C

double code(double x, double y, double z) {
	return -28.0;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = -28.0d0
end function

Java

public static double code(double x, double y, double z) {
	return -28.0;
}

Python

def code(x, y, z):
	return -28.0

Julia

function code(x, y, z)
	return -28.0
end

MATLAB

function tmp = code(x, y, z)
	tmp = -28.0;
end

Wolfram

code[x_, y_, z_] := -28.0

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 66.8%

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

5. Taylor expanded in x around 0 66.8%

   \[\leadsto \color{blue}{3 \cdot x + z} \]
6. Step-by-step derivation

   1. flip3-+ 20.4%

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

   2. div-inv 20.3%

      \[\leadsto \color{blue}{\left({\left(3 \cdot x\right)}^{3} + {z}^{3}\right) \cdot \frac{1}{\left(3 \cdot x\right) \cdot \left(3 \cdot x\right) + \left(z \cdot z - \left(3 \cdot x\right) \cdot z\right)}} \]

   3. unpow-prod-down 20.3%

      \[\leadsto \left(\color{blue}{{3}^{3} \cdot {x}^{3}} + {z}^{3}\right) \cdot \frac{1}{\left(3 \cdot x\right) \cdot \left(3 \cdot x\right) + \left(z \cdot z - \left(3 \cdot x\right) \cdot z\right)} \]

   4. metadata-eval 20.3%

      \[\leadsto \left(\color{blue}{27} \cdot {x}^{3} + {z}^{3}\right) \cdot \frac{1}{\left(3 \cdot x\right) \cdot \left(3 \cdot x\right) + \left(z \cdot z - \left(3 \cdot x\right) \cdot z\right)} \]

   5. *-commutative 20.3%

      \[\leadsto \left(27 \cdot {x}^{3} + {z}^{3}\right) \cdot \frac{1}{\color{blue}{\left(x \cdot 3\right)} \cdot \left(3 \cdot x\right) + \left(z \cdot z - \left(3 \cdot x\right) \cdot z\right)} \]

   6. *-commutative 20.3%

      \[\leadsto \left(27 \cdot {x}^{3} + {z}^{3}\right) \cdot \frac{1}{\left(x \cdot 3\right) \cdot \color{blue}{\left(x \cdot 3\right)} + \left(z \cdot z - \left(3 \cdot x\right) \cdot z\right)} \]

   7. swap-sqr 20.3%

      \[\leadsto \left(27 \cdot {x}^{3} + {z}^{3}\right) \cdot \frac{1}{\color{blue}{\left(x \cdot x\right) \cdot \left(3 \cdot 3\right)} + \left(z \cdot z - \left(3 \cdot x\right) \cdot z\right)} \]

   8. metadata-eval 20.3%

      \[\leadsto \left(27 \cdot {x}^{3} + {z}^{3}\right) \cdot \frac{1}{\left(x \cdot x\right) \cdot \color{blue}{9} + \left(z \cdot z - \left(3 \cdot x\right) \cdot z\right)} \]

   9. distribute-rgt-out-- 20.3%

      \[\leadsto \left(27 \cdot {x}^{3} + {z}^{3}\right) \cdot \frac{1}{\left(x \cdot x\right) \cdot 9 + \color{blue}{z \cdot \left(z - 3 \cdot x\right)}} \]

   10. *-commutative 20.3%

       \[\leadsto \left(27 \cdot {x}^{3} + {z}^{3}\right) \cdot \frac{1}{\left(x \cdot x\right) \cdot 9 + z \cdot \left(z - \color{blue}{x \cdot 3}\right)} \]

7. Applied egg-rr 20.3%

   \[\leadsto \color{blue}{\left(27 \cdot {x}^{3} + {z}^{3}\right) \cdot \frac{1}{\left(x \cdot x\right) \cdot 9 + z \cdot \left(z - x \cdot 3\right)}} \]

9. Simplified 3.2%

   \[\leadsto \color{blue}{-28} \]

10. Final simplification 3.2%

    \[\leadsto -28 \]

Alternative 10: 34.2% 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 36.8%

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

5. Final simplification 36.8%

   \[\leadsto z \]

Reproduce

herbie shell --seed 2023181 
(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))