Graphics.Rasterific.CubicBezier:isSufficientlyFlat from Rasterific-0.6.1

Percentage Accurate: 100.0% → 100.0%
Time: 2.9s
Alternatives: 3
Speedup: 1.0×

Specification

?
\[\begin{array}{l} \\ \left(x \cdot 16\right) \cdot x \end{array} \]
(FPCore (x) :precision binary64 (* (* x 16.0) x))
double code(double x) {
	return (x * 16.0) * x;
}

real(8) function code(x)
    real(8), intent (in) :: x
    code = (x * 16.0d0) * x
end function

public static double code(double x) {
	return (x * 16.0) * x;
}

def code(x):
	return (x * 16.0) * x

function code(x)
	return Float64(Float64(x * 16.0) * x)
end

function tmp = code(x)
	tmp = (x * 16.0) * x;
end

code[x_] := N[(N[(x * 16.0), $MachinePrecision] * x), $MachinePrecision]

\begin{array}{l}

\\
\left(x \cdot 16\right) \cdot x
\end{array}

Sampling outcomes in binary64 precision:

Local Percentage Accuracy vs ?

The average percentage accuracy by input value. Horizontal axis shows value of an input variable; the variable is choosen in the title. Vertical axis is accuracy; higher is better. Red represent the original program, while blue represents Herbie's suggestion. These can be toggled with buttons below the plot. The line is an average while dots represent individual samples.

Accuracy vs Speed?

Herbie found 3 alternatives:

AlternativeAccuracySpeedup
The accuracy (vertical axis) and speed (horizontal axis) of each alternatives. Up and to the right is better. The red square shows the initial program, and each blue circle shows an alternative.The line shows the best available speed-accuracy tradeoffs.

Initial Program: 100.0% accurate, 1.0× speedup?

\[\begin{array}{l} \\ \left(x \cdot 16\right) \cdot x \end{array} \]
(FPCore (x) :precision binary64 (* (* x 16.0) x))
double code(double x) {
	return (x * 16.0) * x;
}

real(8) function code(x)
    real(8), intent (in) :: x
    code = (x * 16.0d0) * x
end function

public static double code(double x) {
	return (x * 16.0) * x;
}

def code(x):
	return (x * 16.0) * x

function code(x)
	return Float64(Float64(x * 16.0) * x)
end

function tmp = code(x)
	tmp = (x * 16.0) * x;
end

code[x_] := N[(N[(x * 16.0), $MachinePrecision] * x), $MachinePrecision]

\begin{array}{l}

\\
\left(x \cdot 16\right) \cdot x
\end{array}

Alternative 1: 100.0% accurate, 1.0× speedup?

\[\begin{array}{l} \\ \left(16 \cdot x\right) \cdot x \end{array} \]
(FPCore (x) :precision binary64 (* (* 16.0 x) x))
double code(double x) {
	return (16.0 * x) * x;
}

real(8) function code(x)
    real(8), intent (in) :: x
    code = (16.0d0 * x) * x
end function

public static double code(double x) {
	return (16.0 * x) * x;
}

def code(x):
	return (16.0 * x) * x

function code(x)
	return Float64(Float64(16.0 * x) * x)
end

function tmp = code(x)
	tmp = (16.0 * x) * x;
end

code[x_] := N[(N[(16.0 * x), $MachinePrecision] * x), $MachinePrecision]

\begin{array}{l}

\\
\left(16 \cdot x\right) \cdot x
\end{array}
Derivation

  1. Initial program 100.0%

    \[\left(x \cdot 16\right) \cdot x \]
  2. Add Preprocessing

  3. Final simplification100.0%

    \[\leadsto \left(16 \cdot x\right) \cdot x \]
  4. Add Preprocessing

Alternative 2: 4.8% accurate, 1.8× speedup?

\[\begin{array}{l} \\ 16 \cdot x \end{array} \]
(FPCore (x) :precision binary64 (* 16.0 x))
double code(double x) {
	return 16.0 * x;
}

real(8) function code(x)
    real(8), intent (in) :: x
    code = 16.0d0 * x
end function

public static double code(double x) {
	return 16.0 * x;
}

def code(x):
	return 16.0 * x

function code(x)
	return Float64(16.0 * x)
end

function tmp = code(x)
	tmp = 16.0 * x;
end

code[x_] := N[(16.0 * x), $MachinePrecision]

\begin{array}{l}

\\
16 \cdot x
\end{array}
Derivation

  1. Initial program 100.0%

    \[\left(x \cdot 16\right) \cdot x \]
  2. Add Preprocessing

  4. Applied rewrites4.8%

    \[\leadsto \color{blue}{16} \cdot x \]
  5. Add Preprocessing

Alternative 3: 4.2% accurate, 11.0× speedup?

\[\begin{array}{l} \\ 16 \end{array} \]
(FPCore (x) :precision binary64 16.0)
double code(double x) {
	return 16.0;
}

real(8) function code(x)
    real(8), intent (in) :: x
    code = 16.0d0
end function

public static double code(double x) {
	return 16.0;
}

def code(x):
	return 16.0

function code(x)
	return 16.0
end

function tmp = code(x)
	tmp = 16.0;
end

code[x_] := 16.0

\begin{array}{l}

\\
16
\end{array}
Derivation

  1. Initial program 100.0%

    \[\left(x \cdot 16\right) \cdot x \]
  2. Add Preprocessing

  4. Applied rewrites4.5%

    \[\leadsto \color{blue}{16} \]
  5. Add Preprocessing

Reproduce

?
herbie shell --seed 2024240 
(FPCore (x)
  :name "Graphics.Rasterific.CubicBezier:isSufficientlyFlat from Rasterific-0.6.1"
  :precision binary64
  (* (* x 16.0) x))