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

Percentage Accurate: 99.9% → 99.9%

Time: 5.9s

Alternatives: 7

Speedup: 1.2×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_] := N[(2.0 * N[(x + y), $MachinePrecision] + N[(z + x), $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. Step-by-step derivation

   1. lift-+.f64 N/A

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

   2. lift-+.f64 N/A

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

   3. associate-+l+ N/A

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

   4. lift-+.f64 N/A

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

   5. lift-+.f64 N/A

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

   6. associate-+l+ N/A

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

   7. +-commutative N/A

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

   8. lift-+.f64 N/A

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

   9. count-2 N/A

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

   10. +-commutative N/A

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

   11. lower-fma.f64 N/A

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

   12. lift-+.f64 N/A

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

   13. +-commutative N/A

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

   14. lower-+.f64 N/A

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

   15. +-commutative N/A

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

   16. lower-+.f64 99.9

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

4. Applied rewrites 99.9%

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

5. Final simplification 99.9%

   \[\leadsto \mathsf{fma}\left(2, x + y, z + x\right) \]
6. Add Preprocessing

Alternative 2: 84.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.7 \cdot 10^{+129}:\\ \;\;\;\;\mathsf{fma}\left(y, 2, z\right)\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-59}:\\ \;\;\;\;\mathsf{fma}\left(3, x, z\right)\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{+67}:\\ \;\;\;\;\mathsf{fma}\left(3, x, y + y\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(3, x, z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -4.7e+129)
   (fma y 2.0 z)
   (if (<= z -9.5e-59)
     (fma 3.0 x z)
     (if (<= z 5.6e+67) (fma 3.0 x (+ y y)) (fma 3.0 x z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -4.7e+129) {
		tmp = fma(y, 2.0, z);
	} else if (z <= -9.5e-59) {
		tmp = fma(3.0, x, z);
	} else if (z <= 5.6e+67) {
		tmp = fma(3.0, x, (y + y));
	} else {
		tmp = fma(3.0, x, z);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -4.7e+129)
		tmp = fma(y, 2.0, z);
	elseif (z <= -9.5e-59)
		tmp = fma(3.0, x, z);
	elseif (z <= 5.6e+67)
		tmp = fma(3.0, x, Float64(y + y));
	else
		tmp = fma(3.0, x, z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -4.7e+129], N[(y * 2.0 + z), $MachinePrecision], If[LessEqual[z, -9.5e-59], N[(3.0 * x + z), $MachinePrecision], If[LessEqual[z, 5.6e+67], N[(3.0 * x + N[(y + y), $MachinePrecision]), $MachinePrecision], N[(3.0 * x + z), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.70000000000000008e129

   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 92.6

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

   5. Applied rewrites 92.6%

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

   if -4.70000000000000008e129 < z < -9.4999999999999994e-59 or 5.5999999999999995e67 < 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 85.7

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

   5. Applied rewrites 85.7%

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

   if -9.4999999999999994e-59 < z < 5.5999999999999995e67

   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

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

      1. associate-+r+ N/A

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

      2. distribute-rgt1-in N/A

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

      3. metadata-eval N/A

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

      4. lower-fma.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 93.6

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

   5. Applied rewrites 93.6%

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

   7. Applied rewrites 93.6%

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

Alternative 3: 86.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.55 \cdot 10^{+110}:\\ \;\;\;\;\mathsf{fma}\left(3, x, z\right)\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+42}:\\ \;\;\;\;\mathsf{fma}\left(y, 2, z\right) + x\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(3, x, y + y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2.55e+110)
   (fma 3.0 x z)
   (if (<= x 9.5e+42) (+ (fma y 2.0 z) x) (fma 3.0 x (+ y y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.55e+110) {
		tmp = fma(3.0, x, z);
	} else if (x <= 9.5e+42) {
		tmp = fma(y, 2.0, z) + x;
	} else {
		tmp = fma(3.0, x, (y + y));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.55e+110)
		tmp = fma(3.0, x, z);
	elseif (x <= 9.5e+42)
		tmp = Float64(fma(y, 2.0, z) + x);
	else
		tmp = fma(3.0, x, Float64(y + y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.55e+110], N[(3.0 * x + z), $MachinePrecision], If[LessEqual[x, 9.5e+42], N[(N[(y * 2.0 + z), $MachinePrecision] + x), $MachinePrecision], N[(3.0 * x + N[(y + y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.5500000000000001e110

   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 90.9

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

   5. Applied rewrites 90.9%

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

   if -2.5500000000000001e110 < x < 9.50000000000000019e42

   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

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 88.3

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

   5. Applied rewrites 88.3%

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

   if 9.50000000000000019e42 < 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 z around 0

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

      1. associate-+r+ N/A

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

      2. distribute-rgt1-in N/A

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

      3. metadata-eval N/A

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

      4. lower-fma.f64 N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 92.2

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

   5. Applied rewrites 92.2%

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

   7. Applied rewrites 92.2%

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

Alternative 4: 84.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{-10}:\\ \;\;\;\;\mathsf{fma}\left(y, 2, z\right)\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+78}:\\ \;\;\;\;\mathsf{fma}\left(3, x, z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, 2, z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.02e-10)
   (fma y 2.0 z)
   (if (<= y 1.4e+78) (fma 3.0 x z) (fma y 2.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.02e-10) {
		tmp = fma(y, 2.0, z);
	} else if (y <= 1.4e+78) {
		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 <= -1.02e-10)
		tmp = fma(y, 2.0, z);
	elseif (y <= 1.4e+78)
		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, -1.02e-10], N[(y * 2.0 + z), $MachinePrecision], If[LessEqual[y, 1.4e+78], N[(3.0 * x + z), $MachinePrecision], N[(y * 2.0 + z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.01999999999999997e-10 or 1.4000000000000001e78 < 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 82.7

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

   5. Applied rewrites 82.7%

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

   if -1.01999999999999997e-10 < y < 1.4000000000000001e78

   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 91.6

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

   5. Applied rewrites 91.6%

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

Alternative 5: 80.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{+91}:\\ \;\;\;\;y + y\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+151}:\\ \;\;\;\;\mathsf{fma}\left(3, x, z\right)\\ \mathbf{else}:\\ \;\;\;\;y + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -2.15e+91) (+ y y) (if (<= y 2.4e+151) (fma 3.0 x z) (+ y y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -2.15e+91) {
		tmp = y + y;
	} else if (y <= 2.4e+151) {
		tmp = fma(3.0, x, z);
	} else {
		tmp = y + y;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -2.15e+91)
		tmp = Float64(y + y);
	elseif (y <= 2.4e+151)
		tmp = fma(3.0, x, z);
	else
		tmp = Float64(y + y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -2.15e+91], N[(y + y), $MachinePrecision], If[LessEqual[y, 2.4e+151], N[(3.0 * x + z), $MachinePrecision], N[(y + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.15e91 or 2.4000000000000001e151 < 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 77.3

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

   5. Applied rewrites 77.3%

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

   7. Applied rewrites 77.3%

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

   if -2.15e91 < y < 2.4000000000000001e151

   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 86.5

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

   5. Applied rewrites 86.5%

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

Alternative 6: 52.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{-16}:\\ \;\;\;\;y + y\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+78}:\\ \;\;\;\;3 \cdot x\\ \mathbf{else}:\\ \;\;\;\;y + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.3e-16) (+ y y) (if (<= y 1.35e+78) (* 3.0 x) (+ y y))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.3e-16) {
		tmp = y + y;
	} else if (y <= 1.35e+78) {
		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 <= (-3.3d-16)) then
        tmp = y + y
    else if (y <= 1.35d+78) 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 <= -3.3e-16) {
		tmp = y + y;
	} else if (y <= 1.35e+78) {
		tmp = 3.0 * x;
	} else {
		tmp = y + y;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.3e-16:
		tmp = y + y
	elif y <= 1.35e+78:
		tmp = 3.0 * x
	else:
		tmp = y + y
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.3e-16)
		tmp = Float64(y + y);
	elseif (y <= 1.35e+78)
		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 <= -3.3e-16)
		tmp = y + y;
	elseif (y <= 1.35e+78)
		tmp = 3.0 * x;
	else
		tmp = y + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.3e-16], N[(y + y), $MachinePrecision], If[LessEqual[y, 1.35e+78], N[(3.0 * x), $MachinePrecision], N[(y + y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.29999999999999988e-16 or 1.35000000000000002e78 < 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 65.0

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

   5. Applied rewrites 65.0%

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

   7. Applied rewrites 65.0%

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

   if -3.29999999999999988e-16 < y < 1.35000000000000002e78

   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 54.2

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

   5. Applied rewrites 54.2%

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

Alternative 7: 35.2% 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 34.0

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

5. Applied rewrites 34.0%

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

7. Applied rewrites 34.0%

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

Reproduce

herbie shell --seed 2024249 
(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))