Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendOutside from plot-0.2.3.4, C

Percentage Accurate: 99.9% → 99.9%

Time: 5.5s

Alternatives: 5

Speedup: 1.0×

• 21.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ x \cdot \left(y + z\right) + z \cdot 5 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ (* x (+ y z)) (* z 5.0)))

C

double code(double x, double y, double z) {
	return (x * (y + z)) + (z * 5.0);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x * (y + z)) + (z * 5.0d0)
end function

Java

public static double code(double x, double y, double z) {
	return (x * (y + z)) + (z * 5.0);
}

Python

def code(x, y, z):
	return (x * (y + z)) + (z * 5.0)

Julia

function code(x, y, z)
	return Float64(Float64(x * Float64(y + z)) + Float64(z * 5.0))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x * (y + z)) + (z * 5.0);
end

Wolfram

code[x_, y_, z_] := N[(N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision] + N[(z * 5.0), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(y + z\right) + z \cdot 5 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ (* x (+ y z)) (* z 5.0)))

C

double code(double x, double y, double z) {
	return (x * (y + z)) + (z * 5.0);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x * (y + z)) + (z * 5.0d0)
end function

Java

public static double code(double x, double y, double z) {
	return (x * (y + z)) + (z * 5.0);
}

Python

def code(x, y, z):
	return (x * (y + z)) + (z * 5.0)

Julia

function code(x, y, z)
	return Float64(Float64(x * Float64(y + z)) + Float64(z * 5.0))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x * (y + z)) + (z * 5.0);
end

Wolfram

code[x_, y_, z_] := N[(N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision] + N[(z * 5.0), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(y + z\right) + z \cdot 5 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ (* x (+ y z)) (* z 5.0)))

C

double code(double x, double y, double z) {
	return (x * (y + z)) + (z * 5.0);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x * (y + z)) + (z * 5.0d0)
end function

Java

public static double code(double x, double y, double z) {
	return (x * (y + z)) + (z * 5.0);
}

Python

def code(x, y, z):
	return (x * (y + z)) + (z * 5.0)

Julia

function code(x, y, z)
	return Float64(Float64(x * Float64(y + z)) + Float64(z * 5.0))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x * (y + z)) + (z * 5.0);
end

Wolfram

code[x_, y_, z_] := N[(N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision] + N[(z * 5.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[x \cdot \left(y + z\right) + z \cdot 5 \]
2. Add Preprocessing

3. Final simplification 100.0%

   \[\leadsto x \cdot \left(y + z\right) + z \cdot 5 \]
4. Add Preprocessing

Alternative 2: 76.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ z \cdot 5 + x \cdot y \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ (* z 5.0) (* x y)))

C

double code(double x, double y, double z) {
	return (z * 5.0) + (x * 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 = (z * 5.0d0) + (x * y)
end function

Java

public static double code(double x, double y, double z) {
	return (z * 5.0) + (x * y);
}

Python

def code(x, y, z):
	return (z * 5.0) + (x * y)

Julia

function code(x, y, z)
	return Float64(Float64(z * 5.0) + Float64(x * y))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (z * 5.0) + (x * y);
end

Wolfram

code[x_, y_, z_] := N[(N[(z * 5.0), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[x \cdot \left(y + z\right) + z \cdot 5 \]
2. Step-by-step derivation

   1. distribute-rgt-in 98.8%

      \[\leadsto \color{blue}{\left(y \cdot x + z \cdot x\right)} + z \cdot 5 \]

   2. associate-+l+ 98.8%

      \[\leadsto \color{blue}{y \cdot x + \left(z \cdot x + z \cdot 5\right)} \]

   3. *-commutative 98.8%

      \[\leadsto \color{blue}{x \cdot y} + \left(z \cdot x + z \cdot 5\right) \]

   4. fma-def 99.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, z \cdot x + z \cdot 5\right)} \]

   5. distribute-lft-out 99.6%

      \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{z \cdot \left(x + 5\right)}\right) \]

3. Simplified 99.6%

   \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, z \cdot \left(x + 5\right)\right)} \]
4. Add Preprocessing
5. Step-by-step derivation

   1. *-commutative 99.6%

      \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{\left(x + 5\right) \cdot z}\right) \]

   2. flip-+ 86.3%

      \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{\frac{x \cdot x - 5 \cdot 5}{x - 5}} \cdot z\right) \]

   3. associate-*l/ 84.1%

      \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{\frac{\left(x \cdot x - 5 \cdot 5\right) \cdot z}{x - 5}}\right) \]

   4. fma-neg 84.1%

      \[\leadsto \mathsf{fma}\left(x, y, \frac{\color{blue}{\mathsf{fma}\left(x, x, -5 \cdot 5\right)} \cdot z}{x - 5}\right) \]

   5. metadata-eval 84.1%

      \[\leadsto \mathsf{fma}\left(x, y, \frac{\mathsf{fma}\left(x, x, -\color{blue}{25}\right) \cdot z}{x - 5}\right) \]

   6. metadata-eval 84.1%

      \[\leadsto \mathsf{fma}\left(x, y, \frac{\mathsf{fma}\left(x, x, \color{blue}{-25}\right) \cdot z}{x - 5}\right) \]

   7. sub-neg 84.1%

      \[\leadsto \mathsf{fma}\left(x, y, \frac{\mathsf{fma}\left(x, x, -25\right) \cdot z}{\color{blue}{x + \left(-5\right)}}\right) \]

   8. metadata-eval 84.1%

      \[\leadsto \mathsf{fma}\left(x, y, \frac{\mathsf{fma}\left(x, x, -25\right) \cdot z}{x + \color{blue}{-5}}\right) \]

6. Applied egg-rr 84.1%

   \[\leadsto \mathsf{fma}\left(x, y, \color{blue}{\frac{\mathsf{fma}\left(x, x, -25\right) \cdot z}{x + -5}}\right) \]

7. Taylor expanded in x around 0 74.6%

   \[\leadsto \mathsf{fma}\left(x, y, \frac{\color{blue}{-25 \cdot z}}{x + -5}\right) \]
8. Step-by-step derivation

   1. *-commutative 74.6%

      \[\leadsto \mathsf{fma}\left(x, y, \frac{\color{blue}{z \cdot -25}}{x + -5}\right) \]

9. Simplified 74.6%

   \[\leadsto \mathsf{fma}\left(x, y, \frac{\color{blue}{z \cdot -25}}{x + -5}\right) \]
10. Step-by-step derivation

    1. fma-udef 74.6%

       \[\leadsto \color{blue}{x \cdot y + \frac{z \cdot -25}{x + -5}} \]

    2. +-commutative 74.6%

       \[\leadsto \color{blue}{\frac{z \cdot -25}{x + -5} + x \cdot y} \]

    3. *-commutative 74.6%

       \[\leadsto \frac{\color{blue}{-25 \cdot z}}{x + -5} + x \cdot y \]

    4. associate-/l* 74.6%

       \[\leadsto \color{blue}{\frac{-25}{\frac{x + -5}{z}}} + x \cdot y \]

11. Applied egg-rr 74.6%

    \[\leadsto \color{blue}{\frac{-25}{\frac{x + -5}{z}} + x \cdot y} \]

12. Taylor expanded in x around 0 74.6%

    \[\leadsto \color{blue}{5 \cdot z} + x \cdot y \]

13. Final simplification 74.6%

    \[\leadsto z \cdot 5 + x \cdot y \]
14. Add Preprocessing

Alternative 3: 64.5% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[x \cdot \left(y + z\right) + z \cdot 5 \]
2. Add Preprocessing

3. Taylor expanded in x around inf 66.1%

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

   1. +-commutative 66.1%

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

5. Simplified 66.1%

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

6. Final simplification 66.1%

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

Alternative 4: 36.9% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ z \cdot 5 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* z 5.0))

C

double code(double x, double y, double z) {
	return z * 5.0;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = z * 5.0d0
end function

Java

public static double code(double x, double y, double z) {
	return z * 5.0;
}

Python

def code(x, y, z):
	return z * 5.0

Julia

function code(x, y, z)
	return Float64(z * 5.0)
end

MATLAB

function tmp = code(x, y, z)
	tmp = z * 5.0;
end

Wolfram

code[x_, y_, z_] := N[(z * 5.0), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[x \cdot \left(y + z\right) + z \cdot 5 \]
2. Add Preprocessing

3. Taylor expanded in x around 0 35.0%

   \[\leadsto \color{blue}{5 \cdot z} \]

4. Final simplification 35.0%

   \[\leadsto z \cdot 5 \]
5. Add Preprocessing

Alternative 5: 41.4% accurate, 3.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[x \cdot \left(y + z\right) + z \cdot 5 \]
2. Add Preprocessing

3. Taylor expanded in y around inf 41.7%

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

4. Final simplification 41.7%

   \[\leadsto x \cdot y \]
5. Add Preprocessing

Developer target: 98.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x + 5\right) \cdot z + x \cdot y \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ (* (+ x 5.0) z) (* x y)))

C

double code(double x, double y, double z) {
	return ((x + 5.0) * z) + (x * 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 = ((x + 5.0d0) * z) + (x * y)
end function

Java

public static double code(double x, double y, double z) {
	return ((x + 5.0) * z) + (x * y);
}

Python

def code(x, y, z):
	return ((x + 5.0) * z) + (x * y)

Julia

function code(x, y, z)
	return Float64(Float64(Float64(x + 5.0) * z) + Float64(x * y))
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((x + 5.0) * z) + (x * y);
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(x + 5.0), $MachinePrecision] * z), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024033 
(FPCore (x y z)
  :name "Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendOutside from plot-0.2.3.4, C"
  :precision binary64

  :herbie-target
  (+ (* (+ x 5.0) z) (* x y))

  (+ (* x (+ y z)) (* z 5.0)))