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

Percentage Accurate: 99.9% → 99.9%

Time: 8.9s

Alternatives: 7

Speedup: 1.0×

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, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

3. Final simplification 99.9%

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

Alternative 2: 84.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{+146}:\\ \;\;\;\;\mathsf{fma}\left(3, x, y \cdot 2\right)\\ \mathbf{elif}\;x \leq 27500000:\\ \;\;\;\;\mathsf{fma}\left(2, y, z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, 3, z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.65e+146)
   (fma 3.0 x (* y 2.0))
   (if (<= x 27500000.0) (fma 2.0 y z) (fma x 3.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.65e+146) {
		tmp = fma(3.0, x, (y * 2.0));
	} else if (x <= 27500000.0) {
		tmp = fma(2.0, y, z);
	} else {
		tmp = fma(x, 3.0, z);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.65e+146)
		tmp = fma(3.0, x, Float64(y * 2.0));
	elseif (x <= 27500000.0)
		tmp = fma(2.0, y, z);
	else
		tmp = fma(x, 3.0, z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.65e+146], N[(3.0 * x + N[(y * 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 27500000.0], N[(2.0 * y + z), $MachinePrecision], N[(x * 3.0 + z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.65000000000000008e146

   1. Initial program 99.6%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. distribute-lft-out N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-+.f64 97.4

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

   5. Simplified 97.4%

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

   6. Taylor expanded in y around inf

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

      1. lower-*.f64 N/A

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

      2. +-commutative N/A

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

      3. distribute-lft1-in N/A

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

      4. metadata-eval N/A

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

      5. lower-fma.f64 N/A

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

      6. lower-/.f64 59.2

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

   8. Simplified 59.2%

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

   9. Taylor expanded in y around 0

      \[\leadsto \color{blue}{2 \cdot y + 3 \cdot x} \]
   10. Step-by-step derivation

       1. +-commutative N/A

          \[\leadsto \color{blue}{3 \cdot x + 2 \cdot y} \]

       2. lower-fma.f64 N/A

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

       3. lower-*.f64 97.8

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

   11. Simplified 97.8%

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

   if -1.65000000000000008e146 < x < 2.75e7

   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. lower-fma.f64 90.8

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

   5. Simplified 90.8%

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

   if 2.75e7 < x

   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. *-commutative N/A

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

      6. lower-fma.f64 92.9

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

   5. Simplified 92.9%

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

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{+146}:\\ \;\;\;\;\mathsf{fma}\left(3, x, y \cdot 2\right)\\ \mathbf{elif}\;x \leq 27500000:\\ \;\;\;\;\mathsf{fma}\left(2, y, z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, 3, z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{+146}:\\ \;\;\;\;\mathsf{fma}\left(2, x + y, x\right)\\ \mathbf{elif}\;x \leq 27500000:\\ \;\;\;\;\mathsf{fma}\left(2, y, z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, 3, z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.65e+146)
   (fma 2.0 (+ x y) x)
   (if (<= x 27500000.0) (fma 2.0 y z) (fma x 3.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.65e+146) {
		tmp = fma(2.0, (x + y), x);
	} else if (x <= 27500000.0) {
		tmp = fma(2.0, y, z);
	} else {
		tmp = fma(x, 3.0, z);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.65e+146)
		tmp = fma(2.0, Float64(x + y), x);
	elseif (x <= 27500000.0)
		tmp = fma(2.0, y, z);
	else
		tmp = fma(x, 3.0, z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.65e+146], N[(2.0 * N[(x + y), $MachinePrecision] + x), $MachinePrecision], If[LessEqual[x, 27500000.0], N[(2.0 * y + z), $MachinePrecision], N[(x * 3.0 + z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.65000000000000008e146

   1. Initial program 99.6%

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

   3. Taylor expanded in z around 0

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

      1. +-commutative N/A

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

      2. distribute-lft-out N/A

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

      3. lower-fma.f64 N/A

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

      4. +-commutative N/A

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

      5. lower-+.f64 97.4

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

   5. Simplified 97.4%

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

   if -1.65000000000000008e146 < x < 2.75e7

   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. lower-fma.f64 90.8

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

   5. Simplified 90.8%

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

   if 2.75e7 < x

   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. *-commutative N/A

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

      6. lower-fma.f64 92.9

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

   5. Simplified 92.9%

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

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{+146}:\\ \;\;\;\;\mathsf{fma}\left(2, x + y, x\right)\\ \mathbf{elif}\;x \leq 27500000:\\ \;\;\;\;\mathsf{fma}\left(2, y, z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, 3, z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 82.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{+201}:\\ \;\;\;\;\mathsf{fma}\left(x, 3, z\right)\\ \mathbf{elif}\;x \leq 27500000:\\ \;\;\;\;\mathsf{fma}\left(2, y, z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(x, 3, z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.9e+201)
   (fma x 3.0 z)
   (if (<= x 27500000.0) (fma 2.0 y z) (fma x 3.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.9e+201) {
		tmp = fma(x, 3.0, z);
	} else if (x <= 27500000.0) {
		tmp = fma(2.0, y, z);
	} else {
		tmp = fma(x, 3.0, z);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.9e+201)
		tmp = fma(x, 3.0, z);
	elseif (x <= 27500000.0)
		tmp = fma(2.0, y, z);
	else
		tmp = fma(x, 3.0, z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.9e+201], N[(x * 3.0 + z), $MachinePrecision], If[LessEqual[x, 27500000.0], N[(2.0 * y + z), $MachinePrecision], N[(x * 3.0 + z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.89999999999999998e201 or 2.75e7 < 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. *-commutative N/A

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

      6. lower-fma.f64 92.0

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

   5. Simplified 92.0%

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

   if -1.89999999999999998e201 < x < 2.75e7

   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. lower-fma.f64 89.6

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

   5. Simplified 89.6%

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

Alternative 5: 79.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.12 \cdot 10^{+201}:\\ \;\;\;\;x \cdot 3\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{+98}:\\ \;\;\;\;\mathsf{fma}\left(2, y, z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2.12e+201) (* x 3.0) (if (<= x 4.6e+98) (fma 2.0 y z) (* x 3.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.12e+201) {
		tmp = x * 3.0;
	} else if (x <= 4.6e+98) {
		tmp = fma(2.0, y, z);
	} else {
		tmp = x * 3.0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.12e+201)
		tmp = Float64(x * 3.0);
	elseif (x <= 4.6e+98)
		tmp = fma(2.0, y, z);
	else
		tmp = Float64(x * 3.0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.12e+201], N[(x * 3.0), $MachinePrecision], If[LessEqual[x, 4.6e+98], N[(2.0 * y + z), $MachinePrecision], N[(x * 3.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.11999999999999998e201 or 4.60000000000000026e98 < 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. *-commutative N/A

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

      2. lower-*.f64 77.2

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

   5. Simplified 77.2%

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

   if -2.11999999999999998e201 < x < 4.60000000000000026e98

   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. lower-fma.f64 87.2

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

   5. Simplified 87.2%

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

Alternative 6: 50.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{+201}:\\ \;\;\;\;x \cdot 3\\ \mathbf{elif}\;x \leq 27500000:\\ \;\;\;\;y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot 3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.9e+201) (* x 3.0) (if (<= x 27500000.0) (* y 2.0) (* x 3.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.9e+201) {
		tmp = x * 3.0;
	} else if (x <= 27500000.0) {
		tmp = 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 <= (-1.9d+201)) then
        tmp = x * 3.0d0
    else if (x <= 27500000.0d0) then
        tmp = 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 <= -1.9e+201) {
		tmp = x * 3.0;
	} else if (x <= 27500000.0) {
		tmp = y * 2.0;
	} else {
		tmp = x * 3.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.9e+201:
		tmp = x * 3.0
	elif x <= 27500000.0:
		tmp = y * 2.0
	else:
		tmp = x * 3.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.9e+201)
		tmp = Float64(x * 3.0);
	elseif (x <= 27500000.0)
		tmp = 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 <= -1.9e+201)
		tmp = x * 3.0;
	elseif (x <= 27500000.0)
		tmp = y * 2.0;
	else
		tmp = x * 3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.9e+201], N[(x * 3.0), $MachinePrecision], If[LessEqual[x, 27500000.0], N[(y * 2.0), $MachinePrecision], N[(x * 3.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.89999999999999998e201 or 2.75e7 < 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. *-commutative N/A

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

      2. lower-*.f64 72.1

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

   5. Simplified 72.1%

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

   if -1.89999999999999998e201 < x < 2.75e7

   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. lower-*.f64 44.5

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

   5. Simplified 44.5%

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

4. Final simplification 54.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{+201}:\\ \;\;\;\;x \cdot 3\\ \mathbf{elif}\;x \leq 27500000:\\ \;\;\;\;y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot 3\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 35.0% accurate, 2.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(y * 2.0), $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. lower-*.f64 32.1

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

5. Simplified 32.1%

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

6. Final simplification 32.1%

   \[\leadsto y \cdot 2 \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024207 
(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))