Graphics.Rendering.Chart.Plot.Vectors:renderPlotVectors from Chart-1.5.3

Percentage Accurate: 77.4% → 100.0%
Time: 6.8s
Alternatives: 6
Speedup: 1.5×

Specification

?
\[\begin{array}{l} \\ x + \left(1 - x\right) \cdot \left(1 - y\right) \end{array} \]
(FPCore (x y) :precision binary64 (+ x (* (- 1.0 x) (- 1.0 y))))
double code(double x, double y) {
	return x + ((1.0 - x) * (1.0 - y));
}
real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x + ((1.0d0 - x) * (1.0d0 - y))
end function
public static double code(double x, double y) {
	return x + ((1.0 - x) * (1.0 - y));
}
def code(x, y):
	return x + ((1.0 - x) * (1.0 - y))
function code(x, y)
	return Float64(x + Float64(Float64(1.0 - x) * Float64(1.0 - y)))
end
function tmp = code(x, y)
	tmp = x + ((1.0 - x) * (1.0 - y));
end
code[x_, y_] := N[(x + N[(N[(1.0 - x), $MachinePrecision] * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}

\\
x + \left(1 - x\right) \cdot \left(1 - y\right)
\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 6 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: 77.4% accurate, 1.0× speedup?

\[\begin{array}{l} \\ x + \left(1 - x\right) \cdot \left(1 - y\right) \end{array} \]
(FPCore (x y) :precision binary64 (+ x (* (- 1.0 x) (- 1.0 y))))
double code(double x, double y) {
	return x + ((1.0 - x) * (1.0 - y));
}
real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x + ((1.0d0 - x) * (1.0d0 - y))
end function
public static double code(double x, double y) {
	return x + ((1.0 - x) * (1.0 - y));
}
def code(x, y):
	return x + ((1.0 - x) * (1.0 - y))
function code(x, y)
	return Float64(x + Float64(Float64(1.0 - x) * Float64(1.0 - y)))
end
function tmp = code(x, y)
	tmp = x + ((1.0 - x) * (1.0 - y));
end
code[x_, y_] := N[(x + N[(N[(1.0 - x), $MachinePrecision] * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}

\\
x + \left(1 - x\right) \cdot \left(1 - y\right)
\end{array}

Alternative 1: 100.0% accurate, 1.5× speedup?

\[\begin{array}{l} \\ \mathsf{fma}\left(x - 1, y, 1\right) \end{array} \]
(FPCore (x y) :precision binary64 (fma (- x 1.0) y 1.0))
double code(double x, double y) {
	return fma((x - 1.0), y, 1.0);
}
function code(x, y)
	return fma(Float64(x - 1.0), y, 1.0)
end
code[x_, y_] := N[(N[(x - 1.0), $MachinePrecision] * y + 1.0), $MachinePrecision]
\begin{array}{l}

\\
\mathsf{fma}\left(x - 1, y, 1\right)
\end{array}
Derivation
  1. Initial program 76.8%

    \[x + \left(1 - x\right) \cdot \left(1 - y\right) \]
  2. Add Preprocessing
  3. Taylor expanded in y around 0

    \[\leadsto \color{blue}{1 + -1 \cdot \left(y \cdot \left(1 - x\right)\right)} \]
  4. Step-by-step derivation
    1. +-commutativeN/A

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(1 - x\right)\right) + 1} \]
    2. *-commutativeN/A

      \[\leadsto -1 \cdot \color{blue}{\left(\left(1 - x\right) \cdot y\right)} + 1 \]
    3. associate-*r*N/A

      \[\leadsto \color{blue}{\left(-1 \cdot \left(1 - x\right)\right) \cdot y} + 1 \]
    4. lower-fma.f64N/A

      \[\leadsto \color{blue}{\mathsf{fma}\left(-1 \cdot \left(1 - x\right), y, 1\right)} \]
    5. mul-1-negN/A

      \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(\left(1 - x\right)\right)}, y, 1\right) \]
    6. sub-negN/A

      \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{\left(1 + \left(\mathsf{neg}\left(x\right)\right)\right)}\right), y, 1\right) \]
    7. +-commutativeN/A

      \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(\color{blue}{\left(\left(\mathsf{neg}\left(x\right)\right) + 1\right)}\right), y, 1\right) \]
    8. distribute-neg-inN/A

      \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right) + \left(\mathsf{neg}\left(1\right)\right)}, y, 1\right) \]
    9. remove-double-negN/A

      \[\leadsto \mathsf{fma}\left(\color{blue}{x} + \left(\mathsf{neg}\left(1\right)\right), y, 1\right) \]
    10. sub-negN/A

      \[\leadsto \mathsf{fma}\left(\color{blue}{x - 1}, y, 1\right) \]
    11. lower--.f64100.0

      \[\leadsto \mathsf{fma}\left(\color{blue}{x - 1}, y, 1\right) \]
  5. Applied rewrites100.0%

    \[\leadsto \color{blue}{\mathsf{fma}\left(x - 1, y, 1\right)} \]
  6. Add Preprocessing

Alternative 2: 86.2% accurate, 0.7× speedup?

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{+48}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+15}:\\ \;\;\;\;1 - y\\ \mathbf{else}:\\ \;\;\;\;\left(x - 1\right) \cdot y\\ \end{array} \end{array} \]
(FPCore (x y)
 :precision binary64
 (if (<= x -2.2e+48) (* y x) (if (<= x 9.5e+15) (- 1.0 y) (* (- x 1.0) y))))
double code(double x, double y) {
	double tmp;
	if (x <= -2.2e+48) {
		tmp = y * x;
	} else if (x <= 9.5e+15) {
		tmp = 1.0 - y;
	} else {
		tmp = (x - 1.0) * y;
	}
	return tmp;
}
real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-2.2d+48)) then
        tmp = y * x
    else if (x <= 9.5d+15) then
        tmp = 1.0d0 - y
    else
        tmp = (x - 1.0d0) * y
    end if
    code = tmp
end function
public static double code(double x, double y) {
	double tmp;
	if (x <= -2.2e+48) {
		tmp = y * x;
	} else if (x <= 9.5e+15) {
		tmp = 1.0 - y;
	} else {
		tmp = (x - 1.0) * y;
	}
	return tmp;
}
def code(x, y):
	tmp = 0
	if x <= -2.2e+48:
		tmp = y * x
	elif x <= 9.5e+15:
		tmp = 1.0 - y
	else:
		tmp = (x - 1.0) * y
	return tmp
function code(x, y)
	tmp = 0.0
	if (x <= -2.2e+48)
		tmp = Float64(y * x);
	elseif (x <= 9.5e+15)
		tmp = Float64(1.0 - y);
	else
		tmp = Float64(Float64(x - 1.0) * y);
	end
	return tmp
end
function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2.2e+48)
		tmp = y * x;
	elseif (x <= 9.5e+15)
		tmp = 1.0 - y;
	else
		tmp = (x - 1.0) * y;
	end
	tmp_2 = tmp;
end
code[x_, y_] := If[LessEqual[x, -2.2e+48], N[(y * x), $MachinePrecision], If[LessEqual[x, 9.5e+15], N[(1.0 - y), $MachinePrecision], N[(N[(x - 1.0), $MachinePrecision] * y), $MachinePrecision]]]
\begin{array}{l}

\\
\begin{array}{l}
\mathbf{if}\;x \leq -2.2 \cdot 10^{+48}:\\
\;\;\;\;y \cdot x\\

\mathbf{elif}\;x \leq 9.5 \cdot 10^{+15}:\\
\;\;\;\;1 - y\\

\mathbf{else}:\\
\;\;\;\;\left(x - 1\right) \cdot y\\


\end{array}
\end{array}
Derivation
  1. Split input into 3 regimes
  2. if x < -2.1999999999999999e48

    1. Initial program 51.4%

      \[x + \left(1 - x\right) \cdot \left(1 - y\right) \]
    2. Add Preprocessing
    3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \left(1 - y\right)\right)} \]
    4. Step-by-step derivation
      1. mul-1-negN/A

        \[\leadsto x \cdot \left(1 + \color{blue}{\left(\mathsf{neg}\left(\left(1 - y\right)\right)\right)}\right) \]
      2. unsub-negN/A

        \[\leadsto x \cdot \color{blue}{\left(1 - \left(1 - y\right)\right)} \]
      3. sub-negN/A

        \[\leadsto x \cdot \left(1 - \color{blue}{\left(1 + \left(\mathsf{neg}\left(y\right)\right)\right)}\right) \]
      4. associate--r+N/A

        \[\leadsto x \cdot \color{blue}{\left(\left(1 - 1\right) - \left(\mathsf{neg}\left(y\right)\right)\right)} \]
      5. metadata-evalN/A

        \[\leadsto x \cdot \left(\color{blue}{0} - \left(\mathsf{neg}\left(y\right)\right)\right) \]
      6. neg-sub0N/A

        \[\leadsto x \cdot \color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(y\right)\right)\right)\right)} \]
      7. remove-double-negN/A

        \[\leadsto x \cdot \color{blue}{y} \]
      8. lower-*.f6479.5

        \[\leadsto \color{blue}{x \cdot y} \]
    5. Applied rewrites79.5%

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

    if -2.1999999999999999e48 < x < 9.5e15

    1. Initial program 96.9%

      \[x + \left(1 - x\right) \cdot \left(1 - y\right) \]
    2. Add Preprocessing
    3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{1 - y} \]
    4. Step-by-step derivation
      1. lower--.f6497.4

        \[\leadsto \color{blue}{1 - y} \]
    5. Applied rewrites97.4%

      \[\leadsto \color{blue}{1 - y} \]

    if 9.5e15 < x

    1. Initial program 51.4%

      \[x + \left(1 - x\right) \cdot \left(1 - y\right) \]
    2. Add Preprocessing
    3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(1 - x\right)\right)} \]
    4. Step-by-step derivation
      1. *-commutativeN/A

        \[\leadsto -1 \cdot \color{blue}{\left(\left(1 - x\right) \cdot y\right)} \]
      2. associate-*r*N/A

        \[\leadsto \color{blue}{\left(-1 \cdot \left(1 - x\right)\right) \cdot y} \]
      3. lower-*.f64N/A

        \[\leadsto \color{blue}{\left(-1 \cdot \left(1 - x\right)\right) \cdot y} \]
      4. mul-1-negN/A

        \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\left(1 - x\right)\right)\right)} \cdot y \]
      5. sub-negN/A

        \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(1 + \left(\mathsf{neg}\left(x\right)\right)\right)}\right)\right) \cdot y \]
      6. +-commutativeN/A

        \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(\left(\mathsf{neg}\left(x\right)\right) + 1\right)}\right)\right) \cdot y \]
      7. distribute-neg-inN/A

        \[\leadsto \color{blue}{\left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right) + \left(\mathsf{neg}\left(1\right)\right)\right)} \cdot y \]
      8. remove-double-negN/A

        \[\leadsto \left(\color{blue}{x} + \left(\mathsf{neg}\left(1\right)\right)\right) \cdot y \]
      9. sub-negN/A

        \[\leadsto \color{blue}{\left(x - 1\right)} \cdot y \]
      10. lower--.f6481.1

        \[\leadsto \color{blue}{\left(x - 1\right)} \cdot y \]
    5. Applied rewrites81.1%

      \[\leadsto \color{blue}{\left(x - 1\right) \cdot y} \]
  3. Recombined 3 regimes into one program.
  4. Final simplification89.9%

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{+48}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+15}:\\ \;\;\;\;1 - y\\ \mathbf{else}:\\ \;\;\;\;\left(x - 1\right) \cdot y\\ \end{array} \]
  5. Add Preprocessing

Alternative 3: 61.5% accurate, 0.7× speedup?

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;1 - y \leq -1 \cdot 10^{+17}:\\ \;\;\;\;-y\\ \mathbf{elif}\;1 - y \leq 2:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]
(FPCore (x y)
 :precision binary64
 (if (<= (- 1.0 y) -1e+17) (- y) (if (<= (- 1.0 y) 2.0) 1.0 (- y))))
double code(double x, double y) {
	double tmp;
	if ((1.0 - y) <= -1e+17) {
		tmp = -y;
	} else if ((1.0 - y) <= 2.0) {
		tmp = 1.0;
	} else {
		tmp = -y;
	}
	return tmp;
}
real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((1.0d0 - y) <= (-1d+17)) then
        tmp = -y
    else if ((1.0d0 - y) <= 2.0d0) then
        tmp = 1.0d0
    else
        tmp = -y
    end if
    code = tmp
end function
public static double code(double x, double y) {
	double tmp;
	if ((1.0 - y) <= -1e+17) {
		tmp = -y;
	} else if ((1.0 - y) <= 2.0) {
		tmp = 1.0;
	} else {
		tmp = -y;
	}
	return tmp;
}
def code(x, y):
	tmp = 0
	if (1.0 - y) <= -1e+17:
		tmp = -y
	elif (1.0 - y) <= 2.0:
		tmp = 1.0
	else:
		tmp = -y
	return tmp
function code(x, y)
	tmp = 0.0
	if (Float64(1.0 - y) <= -1e+17)
		tmp = Float64(-y);
	elseif (Float64(1.0 - y) <= 2.0)
		tmp = 1.0;
	else
		tmp = Float64(-y);
	end
	return tmp
end
function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((1.0 - y) <= -1e+17)
		tmp = -y;
	elseif ((1.0 - y) <= 2.0)
		tmp = 1.0;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end
code[x_, y_] := If[LessEqual[N[(1.0 - y), $MachinePrecision], -1e+17], (-y), If[LessEqual[N[(1.0 - y), $MachinePrecision], 2.0], 1.0, (-y)]]
\begin{array}{l}

\\
\begin{array}{l}
\mathbf{if}\;1 - y \leq -1 \cdot 10^{+17}:\\
\;\;\;\;-y\\

\mathbf{elif}\;1 - y \leq 2:\\
\;\;\;\;1\\

\mathbf{else}:\\
\;\;\;\;-y\\


\end{array}
\end{array}
Derivation
  1. Split input into 2 regimes
  2. if (-.f64 #s(literal 1 binary64) y) < -1e17 or 2 < (-.f64 #s(literal 1 binary64) y)

    1. Initial program 99.9%

      \[x + \left(1 - x\right) \cdot \left(1 - y\right) \]
    2. Add Preprocessing
    3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{1 - y} \]
    4. Step-by-step derivation
      1. lower--.f6453.9

        \[\leadsto \color{blue}{1 - y} \]
    5. Applied rewrites53.9%

      \[\leadsto \color{blue}{1 - y} \]
    6. Taylor expanded in y around inf

      \[\leadsto -1 \cdot \color{blue}{y} \]
    7. Step-by-step derivation
      1. Applied rewrites53.9%

        \[\leadsto -y \]

      if -1e17 < (-.f64 #s(literal 1 binary64) y) < 2

      1. Initial program 56.5%

        \[x + \left(1 - x\right) \cdot \left(1 - y\right) \]
      2. Add Preprocessing
      3. Taylor expanded in y around 0

        \[\leadsto \color{blue}{1} \]
      4. Step-by-step derivation
        1. Applied rewrites72.1%

          \[\leadsto \color{blue}{1} \]
      5. Recombined 2 regimes into one program.
      6. Add Preprocessing

      Alternative 4: 86.2% accurate, 0.8× speedup?

      \[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{+48}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+15}:\\ \;\;\;\;1 - y\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]
      (FPCore (x y)
       :precision binary64
       (if (<= x -2.2e+48) (* y x) (if (<= x 9.5e+15) (- 1.0 y) (* y x))))
      double code(double x, double y) {
      	double tmp;
      	if (x <= -2.2e+48) {
      		tmp = y * x;
      	} else if (x <= 9.5e+15) {
      		tmp = 1.0 - y;
      	} else {
      		tmp = y * x;
      	}
      	return tmp;
      }
      
      real(8) function code(x, y)
          real(8), intent (in) :: x
          real(8), intent (in) :: y
          real(8) :: tmp
          if (x <= (-2.2d+48)) then
              tmp = y * x
          else if (x <= 9.5d+15) then
              tmp = 1.0d0 - y
          else
              tmp = y * x
          end if
          code = tmp
      end function
      
      public static double code(double x, double y) {
      	double tmp;
      	if (x <= -2.2e+48) {
      		tmp = y * x;
      	} else if (x <= 9.5e+15) {
      		tmp = 1.0 - y;
      	} else {
      		tmp = y * x;
      	}
      	return tmp;
      }
      
      def code(x, y):
      	tmp = 0
      	if x <= -2.2e+48:
      		tmp = y * x
      	elif x <= 9.5e+15:
      		tmp = 1.0 - y
      	else:
      		tmp = y * x
      	return tmp
      
      function code(x, y)
      	tmp = 0.0
      	if (x <= -2.2e+48)
      		tmp = Float64(y * x);
      	elseif (x <= 9.5e+15)
      		tmp = Float64(1.0 - y);
      	else
      		tmp = Float64(y * x);
      	end
      	return tmp
      end
      
      function tmp_2 = code(x, y)
      	tmp = 0.0;
      	if (x <= -2.2e+48)
      		tmp = y * x;
      	elseif (x <= 9.5e+15)
      		tmp = 1.0 - y;
      	else
      		tmp = y * x;
      	end
      	tmp_2 = tmp;
      end
      
      code[x_, y_] := If[LessEqual[x, -2.2e+48], N[(y * x), $MachinePrecision], If[LessEqual[x, 9.5e+15], N[(1.0 - y), $MachinePrecision], N[(y * x), $MachinePrecision]]]
      
      \begin{array}{l}
      
      \\
      \begin{array}{l}
      \mathbf{if}\;x \leq -2.2 \cdot 10^{+48}:\\
      \;\;\;\;y \cdot x\\
      
      \mathbf{elif}\;x \leq 9.5 \cdot 10^{+15}:\\
      \;\;\;\;1 - y\\
      
      \mathbf{else}:\\
      \;\;\;\;y \cdot x\\
      
      
      \end{array}
      \end{array}
      
      Derivation
      1. Split input into 2 regimes
      2. if x < -2.1999999999999999e48 or 9.5e15 < x

        1. Initial program 51.4%

          \[x + \left(1 - x\right) \cdot \left(1 - y\right) \]
        2. Add Preprocessing
        3. Taylor expanded in x around inf

          \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \left(1 - y\right)\right)} \]
        4. Step-by-step derivation
          1. mul-1-negN/A

            \[\leadsto x \cdot \left(1 + \color{blue}{\left(\mathsf{neg}\left(\left(1 - y\right)\right)\right)}\right) \]
          2. unsub-negN/A

            \[\leadsto x \cdot \color{blue}{\left(1 - \left(1 - y\right)\right)} \]
          3. sub-negN/A

            \[\leadsto x \cdot \left(1 - \color{blue}{\left(1 + \left(\mathsf{neg}\left(y\right)\right)\right)}\right) \]
          4. associate--r+N/A

            \[\leadsto x \cdot \color{blue}{\left(\left(1 - 1\right) - \left(\mathsf{neg}\left(y\right)\right)\right)} \]
          5. metadata-evalN/A

            \[\leadsto x \cdot \left(\color{blue}{0} - \left(\mathsf{neg}\left(y\right)\right)\right) \]
          6. neg-sub0N/A

            \[\leadsto x \cdot \color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(y\right)\right)\right)\right)} \]
          7. remove-double-negN/A

            \[\leadsto x \cdot \color{blue}{y} \]
          8. lower-*.f6480.5

            \[\leadsto \color{blue}{x \cdot y} \]
        5. Applied rewrites80.5%

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

        if -2.1999999999999999e48 < x < 9.5e15

        1. Initial program 96.9%

          \[x + \left(1 - x\right) \cdot \left(1 - y\right) \]
        2. Add Preprocessing
        3. Taylor expanded in x around 0

          \[\leadsto \color{blue}{1 - y} \]
        4. Step-by-step derivation
          1. lower--.f6497.4

            \[\leadsto \color{blue}{1 - y} \]
        5. Applied rewrites97.4%

          \[\leadsto \color{blue}{1 - y} \]
      3. Recombined 2 regimes into one program.
      4. Final simplification89.9%

        \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{+48}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+15}:\\ \;\;\;\;1 - y\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]
      5. Add Preprocessing

      Alternative 5: 63.0% accurate, 3.8× speedup?

      \[\begin{array}{l} \\ 1 - y \end{array} \]
      (FPCore (x y) :precision binary64 (- 1.0 y))
      double code(double x, double y) {
      	return 1.0 - y;
      }
      
      real(8) function code(x, y)
          real(8), intent (in) :: x
          real(8), intent (in) :: y
          code = 1.0d0 - y
      end function
      
      public static double code(double x, double y) {
      	return 1.0 - y;
      }
      
      def code(x, y):
      	return 1.0 - y
      
      function code(x, y)
      	return Float64(1.0 - y)
      end
      
      function tmp = code(x, y)
      	tmp = 1.0 - y;
      end
      
      code[x_, y_] := N[(1.0 - y), $MachinePrecision]
      
      \begin{array}{l}
      
      \\
      1 - y
      \end{array}
      
      Derivation
      1. Initial program 76.8%

        \[x + \left(1 - x\right) \cdot \left(1 - y\right) \]
      2. Add Preprocessing
      3. Taylor expanded in x around 0

        \[\leadsto \color{blue}{1 - y} \]
      4. Step-by-step derivation
        1. lower--.f6464.0

          \[\leadsto \color{blue}{1 - y} \]
      5. Applied rewrites64.0%

        \[\leadsto \color{blue}{1 - y} \]
      6. Add Preprocessing

      Alternative 6: 38.8% accurate, 15.0× speedup?

      \[\begin{array}{l} \\ 1 \end{array} \]
      (FPCore (x y) :precision binary64 1.0)
      double code(double x, double y) {
      	return 1.0;
      }
      
      real(8) function code(x, y)
          real(8), intent (in) :: x
          real(8), intent (in) :: y
          code = 1.0d0
      end function
      
      public static double code(double x, double y) {
      	return 1.0;
      }
      
      def code(x, y):
      	return 1.0
      
      function code(x, y)
      	return 1.0
      end
      
      function tmp = code(x, y)
      	tmp = 1.0;
      end
      
      code[x_, y_] := 1.0
      
      \begin{array}{l}
      
      \\
      1
      \end{array}
      
      Derivation
      1. Initial program 76.8%

        \[x + \left(1 - x\right) \cdot \left(1 - y\right) \]
      2. Add Preprocessing
      3. Taylor expanded in y around 0

        \[\leadsto \color{blue}{1} \]
      4. Step-by-step derivation
        1. Applied rewrites39.6%

          \[\leadsto \color{blue}{1} \]
        2. Add Preprocessing

        Developer Target 1: 100.0% accurate, 1.3× speedup?

        \[\begin{array}{l} \\ y \cdot x - \left(y - 1\right) \end{array} \]
        (FPCore (x y) :precision binary64 (- (* y x) (- y 1.0)))
        double code(double x, double y) {
        	return (y * x) - (y - 1.0);
        }
        
        real(8) function code(x, y)
            real(8), intent (in) :: x
            real(8), intent (in) :: y
            code = (y * x) - (y - 1.0d0)
        end function
        
        public static double code(double x, double y) {
        	return (y * x) - (y - 1.0);
        }
        
        def code(x, y):
        	return (y * x) - (y - 1.0)
        
        function code(x, y)
        	return Float64(Float64(y * x) - Float64(y - 1.0))
        end
        
        function tmp = code(x, y)
        	tmp = (y * x) - (y - 1.0);
        end
        
        code[x_, y_] := N[(N[(y * x), $MachinePrecision] - N[(y - 1.0), $MachinePrecision]), $MachinePrecision]
        
        \begin{array}{l}
        
        \\
        y \cdot x - \left(y - 1\right)
        \end{array}
        

        Reproduce

        ?
        herbie shell --seed 2024249 
        (FPCore (x y)
          :name "Graphics.Rendering.Chart.Plot.Vectors:renderPlotVectors from Chart-1.5.3"
          :precision binary64
        
          :alt
          (! :herbie-platform default (- (* y x) (- y 1)))
        
          (+ x (* (- 1.0 x) (- 1.0 y))))