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

Percentage Accurate: 99.9% → 100.0%

Time: 6.3s

Alternatives: 6

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, 1.2× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_] := N[(x * 3.0 + N[(N[(y + y), $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. Add Preprocessing

3. Taylor expanded in z around 0

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

   1. associate-+r+ N/A

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

   2. associate-+r+ N/A

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

   3. +-commutative N/A

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

   4. *-commutative N/A

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

   5. lower-fma.f64 N/A

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

   6. +-commutative N/A

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

   7. associate-+r+ N/A

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

   8. distribute-rgt1-in N/A

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

   9. metadata-eval N/A

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

   10. lower-fma.f64 99.9

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

5. Applied rewrites 99.9%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y, 2, \mathsf{fma}\left(3, x, z\right)\right)} \]
6. Step-by-step derivation

7. Applied rewrites 100.0%

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

8. Final simplification 100.0%

   \[\leadsto \mathsf{fma}\left(x, 3, \left(y + y\right) + z\right) \]
9. Add Preprocessing

Alternative 2: 85.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+89}:\\ \;\;\;\;\mathsf{fma}\left(y, 2, z\right)\\ \mathbf{elif}\;z \leq 1.62 \cdot 10^{+40}:\\ \;\;\;\;\mathsf{fma}\left(x, 3, y + y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(3, x, z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.95e+89)
   (fma y 2.0 z)
   (if (<= z 1.62e+40) (fma x 3.0 (+ y y)) (fma 3.0 x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.95e+89) {
		tmp = fma(y, 2.0, z);
	} else if (z <= 1.62e+40) {
		tmp = fma(x, 3.0, (y + y));
	} else {
		tmp = fma(3.0, x, z);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.95e+89)
		tmp = fma(y, 2.0, z);
	elseif (z <= 1.62e+40)
		tmp = fma(x, 3.0, Float64(y + y));
	else
		tmp = fma(3.0, x, z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.95e+89], N[(y * 2.0 + z), $MachinePrecision], If[LessEqual[z, 1.62e+40], N[(x * 3.0 + N[(y + y), $MachinePrecision]), $MachinePrecision], N[(3.0 * x + z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.95000000000000005e89

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 93.4

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

   5. Applied rewrites 93.4%

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

   if -1.95000000000000005e89 < z < 1.62e40

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0

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

      1. associate-+r+ N/A

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

      2. associate-+r+ N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. +-commutative N/A

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

      7. associate-+r+ N/A

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

      8. distribute-rgt1-in N/A

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

      9. metadata-eval N/A

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

      10. lower-fma.f64 99.9

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

   5. Applied rewrites 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, 2, \mathsf{fma}\left(3, x, z\right)\right)} \]
   6. Step-by-step derivation

   7. Applied rewrites 100.0%

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

   8. Taylor expanded in z around 0

      \[\leadsto \mathsf{fma}\left(x, 3, 2 \cdot y\right) \]
   9. Step-by-step derivation

   10. Applied rewrites 90.5%

       \[\leadsto \mathsf{fma}\left(x, 3, y \cdot 2\right) \]
   11. Step-by-step derivation

   12. Applied rewrites 90.5%

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

   if 1.62e40 < z

   1. Initial program 99.9%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate-+r+ N/A

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

      3. distribute-rgt1-in N/A

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

      4. metadata-eval N/A

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

      5. lower-fma.f64 86.8

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

   5. Applied rewrites 86.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(3, x, z\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 3: 85.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+24}:\\ \;\;\;\;\mathsf{fma}\left(y, 2, z\right)\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+84}:\\ \;\;\;\;\mathsf{fma}\left(3, x, z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, 2, z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -7e+24)
   (fma y 2.0 z)
   (if (<= y 1.4e+84) (fma 3.0 x z) (fma y 2.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -7e+24) {
		tmp = fma(y, 2.0, z);
	} else if (y <= 1.4e+84) {
		tmp = fma(3.0, x, z);
	} else {
		tmp = fma(y, 2.0, z);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -7e+24)
		tmp = fma(y, 2.0, z);
	elseif (y <= 1.4e+84)
		tmp = fma(3.0, x, z);
	else
		tmp = fma(y, 2.0, z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -7e+24], N[(y * 2.0 + z), $MachinePrecision], If[LessEqual[y, 1.4e+84], N[(3.0 * x + z), $MachinePrecision], N[(y * 2.0 + z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -7.0000000000000004e24 or 1.39999999999999991e84 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 86.9

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

   5. Applied rewrites 86.9%

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

   if -7.0000000000000004e24 < y < 1.39999999999999991e84

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate-+r+ N/A

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

      3. distribute-rgt1-in N/A

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

      4. metadata-eval N/A

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

      5. lower-fma.f64 89.7

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

   5. Applied rewrites 89.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(3, x, z\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 79.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+127}:\\ \;\;\;\;y + y\\ \mathbf{elif}\;y \leq 5.3 \cdot 10^{+113}:\\ \;\;\;\;\mathsf{fma}\left(3, x, z\right)\\ \mathbf{else}:\\ \;\;\;\;y + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -8.2e+127) (+ y y) (if (<= y 5.3e+113) (fma 3.0 x z) (+ y y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -8.2e+127) {
		tmp = y + y;
	} else if (y <= 5.3e+113) {
		tmp = fma(3.0, x, z);
	} else {
		tmp = y + y;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -8.2e+127)
		tmp = Float64(y + y);
	elseif (y <= 5.3e+113)
		tmp = fma(3.0, x, z);
	else
		tmp = Float64(y + y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -8.2e+127], N[(y + y), $MachinePrecision], If[LessEqual[y, 5.3e+113], N[(3.0 * x + z), $MachinePrecision], N[(y + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -8.19999999999999965e127 or 5.29999999999999967e113 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 75.1

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

   5. Applied rewrites 75.1%

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

   7. Applied rewrites 75.1%

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

   if -8.19999999999999965e127 < y < 5.29999999999999967e113

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. associate-+r+ N/A

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

      3. distribute-rgt1-in N/A

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

      4. metadata-eval N/A

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

      5. lower-fma.f64 87.2

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

   5. Applied rewrites 87.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(3, x, z\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 52.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.45 \cdot 10^{+56}:\\ \;\;\;\;y + y\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+109}:\\ \;\;\;\;3 \cdot x\\ \mathbf{else}:\\ \;\;\;\;y + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.45e+56) (+ y y) (if (<= y 4.2e+109) (* 3.0 x) (+ y y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.45e+56) {
		tmp = y + y;
	} else if (y <= 4.2e+109) {
		tmp = 3.0 * x;
	} else {
		tmp = y + 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 <= (-3.45d+56)) then
        tmp = y + y
    else if (y <= 4.2d+109) then
        tmp = 3.0d0 * x
    else
        tmp = y + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.45e+56) {
		tmp = y + y;
	} else if (y <= 4.2e+109) {
		tmp = 3.0 * x;
	} else {
		tmp = y + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.45e+56:
		tmp = y + y
	elif y <= 4.2e+109:
		tmp = 3.0 * x
	else:
		tmp = y + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.45e+56)
		tmp = Float64(y + y);
	elseif (y <= 4.2e+109)
		tmp = Float64(3.0 * x);
	else
		tmp = Float64(y + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3.45e+56)
		tmp = y + y;
	elseif (y <= 4.2e+109)
		tmp = 3.0 * x;
	else
		tmp = y + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.45e+56], N[(y + y), $MachinePrecision], If[LessEqual[y, 4.2e+109], N[(3.0 * x), $MachinePrecision], N[(y + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.45e56 or 4.2000000000000003e109 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 68.9

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

   5. Applied rewrites 68.9%

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

   7. Applied rewrites 68.9%

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

   if -3.45e56 < y < 4.2000000000000003e109

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 49.8

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

   5. Applied rewrites 49.8%

      \[\leadsto \color{blue}{3 \cdot x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 33.1% accurate, 4.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Taylor expanded in y around inf

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

   1. *-commutative N/A

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

   2. lower-*.f64 31.5

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

5. Applied rewrites 31.5%

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

7. Applied rewrites 31.5%

   \[\leadsto y + \color{blue}{y} \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2024240 
(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))