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

Percentage Accurate: 99.9% → 99.9%

Time: 6.8s

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: 84.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(y, 2, z\right) + x\\ \mathbf{if}\;y \leq -4.5 \cdot 10^{+151}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{+39}:\\ \;\;\;\;\mathsf{fma}\left(3, x, z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ (fma y 2.0 z) x)))
   (if (<= y -4.5e+151) t_0 (if (<= y 1.3e+39) (fma 3.0 x z) t_0))))

C

double code(double x, double y, double z) {
	double t_0 = fma(y, 2.0, z) + x;
	double tmp;
	if (y <= -4.5e+151) {
		tmp = t_0;
	} else if (y <= 1.3e+39) {
		tmp = fma(3.0, x, z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y, z)
	t_0 = Float64(fma(y, 2.0, z) + x)
	tmp = 0.0
	if (y <= -4.5e+151)
		tmp = t_0;
	elseif (y <= 1.3e+39)
		tmp = fma(3.0, x, z);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(y * 2.0 + z), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[y, -4.5e+151], t$95$0, If[LessEqual[y, 1.3e+39], N[(3.0 * x + z), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.4999999999999999e151 or 1.3e39 < 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

      \[\leadsto \color{blue}{\left(z + 2 \cdot y\right)} + x \]
   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 86.3

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

   5. Applied rewrites 86.3%

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

   if -4.4999999999999999e151 < y < 1.3e39

   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 84.3

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

   5. Applied rewrites 84.3%

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

Reproduce

herbie shell --seed 2024230 
(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))