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

Percentage Accurate: 99.9% → 100.0%

Time: 5.4s

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

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_] := N[(x * 3.0 + N[(2.0 * y + 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 100.0

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

5. Applied rewrites 100.0%

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

7. Applied rewrites 100.0%

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

Alternative 2: 84.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+16}:\\ \;\;\;\;\mathsf{fma}\left(y, 2, z\right)\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+94}:\\ \;\;\;\;\mathsf{fma}\left(x, 3, y + y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(3, x, z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2.7e+16)
   (fma y 2.0 z)
   (if (<= z 2.15e+94) (fma x 3.0 (+ y y)) (fma 3.0 x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.7e+16) {
		tmp = fma(y, 2.0, z);
	} else if (z <= 2.15e+94) {
		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 <= -2.7e+16)
		tmp = fma(y, 2.0, z);
	elseif (z <= 2.15e+94)
		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, -2.7e+16], N[(y * 2.0 + z), $MachinePrecision], If[LessEqual[z, 2.15e+94], 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 < -2.7e16

   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 87.4

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

   5. Applied rewrites 87.4%

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

   if -2.7e16 < z < 2.15e94

   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 100.0

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

   5. Applied rewrites 100.0%

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

   7. Applied rewrites 100.0%

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

   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 93.1%

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

   12. Applied rewrites 93.1%

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

   if 2.15e94 < 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 87.9

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

   5. Applied rewrites 87.9%

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

Alternative 3: 83.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{+175}:\\ \;\;\;\;\mathsf{fma}\left(3, x, z\right)\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+52}:\\ \;\;\;\;\mathsf{fma}\left(y, 2, z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(3, x, z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -8.5e+175)
   (fma 3.0 x z)
   (if (<= x 2.8e+52) (fma y 2.0 z) (fma 3.0 x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -8.5e+175) {
		tmp = fma(3.0, x, z);
	} else if (x <= 2.8e+52) {
		tmp = fma(y, 2.0, z);
	} else {
		tmp = fma(3.0, x, z);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -8.5e+175)
		tmp = fma(3.0, x, z);
	elseif (x <= 2.8e+52)
		tmp = fma(y, 2.0, z);
	else
		tmp = fma(3.0, x, z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -8.5e+175], N[(3.0 * x + z), $MachinePrecision], If[LessEqual[x, 2.8e+52], N[(y * 2.0 + z), $MachinePrecision], N[(3.0 * x + z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -8.50000000000000034e175 or 2.8e52 < x

   1. Initial program 99.7%

      \[\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x \]
   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%

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

   if -8.50000000000000034e175 < x < 2.8e52

   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 86.5

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

   5. Applied rewrites 86.5%

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

Alternative 4: 79.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+70}:\\ \;\;\;\;y + y\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{+140}:\\ \;\;\;\;\mathsf{fma}\left(3, x, z\right)\\ \mathbf{else}:\\ \;\;\;\;y + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.1e+70) (+ y y) (if (<= y 7.6e+140) (fma 3.0 x z) (+ y y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.1e+70) {
		tmp = y + y;
	} else if (y <= 7.6e+140) {
		tmp = fma(3.0, x, z);
	} else {
		tmp = y + y;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.1e+70)
		tmp = Float64(y + y);
	elseif (y <= 7.6e+140)
		tmp = fma(3.0, x, z);
	else
		tmp = Float64(y + y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.1e+70], N[(y + y), $MachinePrecision], If[LessEqual[y, 7.6e+140], N[(3.0 * x + z), $MachinePrecision], N[(y + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.1000000000000003e70 or 7.6000000000000002e140 < 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 70.7

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

   5. Applied rewrites 70.7%

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

   7. Applied rewrites 70.7%

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

   if -3.1000000000000003e70 < y < 7.6000000000000002e140

   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 85.8

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

   5. Applied rewrites 85.8%

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

Alternative 5: 51.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.05 \cdot 10^{+140}:\\ \;\;\;\;3 \cdot x\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{+52}:\\ \;\;\;\;y + y\\ \mathbf{else}:\\ \;\;\;\;3 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.05e+140) (* 3.0 x) (if (<= x 2.7e+52) (+ y y) (* 3.0 x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.05e+140) {
		tmp = 3.0 * x;
	} else if (x <= 2.7e+52) {
		tmp = y + y;
	} else {
		tmp = 3.0 * x;
	}
	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+140)) then
        tmp = 3.0d0 * x
    else if (x <= 2.7d+52) then
        tmp = y + y
    else
        tmp = 3.0d0 * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.05e+140) {
		tmp = 3.0 * x;
	} else if (x <= 2.7e+52) {
		tmp = y + y;
	} else {
		tmp = 3.0 * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.05e+140:
		tmp = 3.0 * x
	elif x <= 2.7e+52:
		tmp = y + y
	else:
		tmp = 3.0 * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.05e+140)
		tmp = Float64(3.0 * x);
	elseif (x <= 2.7e+52)
		tmp = Float64(y + y);
	else
		tmp = Float64(3.0 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.05e+140)
		tmp = 3.0 * x;
	elseif (x <= 2.7e+52)
		tmp = y + y;
	else
		tmp = 3.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.05e+140], N[(3.0 * x), $MachinePrecision], If[LessEqual[x, 2.7e+52], N[(y + y), $MachinePrecision], N[(3.0 * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.0500000000000001e140 or 2.7e52 < x

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 71.7

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

   5. Applied rewrites 71.7%

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

   if -1.0500000000000001e140 < x < 2.7e52

   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 48.9

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

   5. Applied rewrites 48.9%

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

   7. Applied rewrites 48.9%

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

Alternative 6: 33.7% 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 35.0

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

5. Applied rewrites 35.0%

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

7. Applied rewrites 35.0%

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

Reproduce

herbie shell --seed 2024235 
(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))