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

Percentage Accurate: 78.8% → 100.0%
Time: 4.2s
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: 78.8% 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?

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

\\
\mathsf{fma}\left(y, x, 1 - y\right)
\end{array}
Derivation
  1. Initial program 82.0%

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

    \[\leadsto \color{blue}{\left(1 + x \cdot \left(1 + -1 \cdot \left(1 - y\right)\right)\right) - y} \]
  4. Applied rewrites100.0%

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

Alternative 2: 88.9% accurate, 0.3× speedup?

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + \left(1 - x\right) \cdot \left(1 - y\right)\\ \mathbf{if}\;t\_0 \leq 0 \lor \neg \left(t\_0 \leq 10000000000000\right):\\ \;\;\;\;\left(-1 + x\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;1 - y\\ \end{array} \end{array} \]
(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ x (* (- 1.0 x) (- 1.0 y)))))
   (if (or (<= t_0 0.0) (not (<= t_0 10000000000000.0)))
     (* (+ -1.0 x) y)
     (- 1.0 y))))
double code(double x, double y) {
	double t_0 = x + ((1.0 - x) * (1.0 - y));
	double tmp;
	if ((t_0 <= 0.0) || !(t_0 <= 10000000000000.0)) {
		tmp = (-1.0 + x) * y;
	} else {
		tmp = 1.0 - y;
	}
	return tmp;
}
real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x + ((1.0d0 - x) * (1.0d0 - y))
    if ((t_0 <= 0.0d0) .or. (.not. (t_0 <= 10000000000000.0d0))) then
        tmp = ((-1.0d0) + x) * y
    else
        tmp = 1.0d0 - y
    end if
    code = tmp
end function
public static double code(double x, double y) {
	double t_0 = x + ((1.0 - x) * (1.0 - y));
	double tmp;
	if ((t_0 <= 0.0) || !(t_0 <= 10000000000000.0)) {
		tmp = (-1.0 + x) * y;
	} else {
		tmp = 1.0 - y;
	}
	return tmp;
}
def code(x, y):
	t_0 = x + ((1.0 - x) * (1.0 - y))
	tmp = 0
	if (t_0 <= 0.0) or not (t_0 <= 10000000000000.0):
		tmp = (-1.0 + x) * y
	else:
		tmp = 1.0 - y
	return tmp
function code(x, y)
	t_0 = Float64(x + Float64(Float64(1.0 - x) * Float64(1.0 - y)))
	tmp = 0.0
	if ((t_0 <= 0.0) || !(t_0 <= 10000000000000.0))
		tmp = Float64(Float64(-1.0 + x) * y);
	else
		tmp = Float64(1.0 - y);
	end
	return tmp
end
function tmp_2 = code(x, y)
	t_0 = x + ((1.0 - x) * (1.0 - y));
	tmp = 0.0;
	if ((t_0 <= 0.0) || ~((t_0 <= 10000000000000.0)))
		tmp = (-1.0 + x) * y;
	else
		tmp = 1.0 - y;
	end
	tmp_2 = tmp;
end
code[x_, y_] := Block[{t$95$0 = N[(x + N[(N[(1.0 - x), $MachinePrecision] * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, 0.0], N[Not[LessEqual[t$95$0, 10000000000000.0]], $MachinePrecision]], N[(N[(-1.0 + x), $MachinePrecision] * y), $MachinePrecision], N[(1.0 - y), $MachinePrecision]]]
\begin{array}{l}

\\
\begin{array}{l}
t_0 := x + \left(1 - x\right) \cdot \left(1 - y\right)\\
\mathbf{if}\;t\_0 \leq 0 \lor \neg \left(t\_0 \leq 10000000000000\right):\\
\;\;\;\;\left(-1 + x\right) \cdot y\\

\mathbf{else}:\\
\;\;\;\;1 - y\\


\end{array}
\end{array}
Derivation
  1. Split input into 2 regimes
  2. if (+.f64 x (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) y))) < 0.0 or 1e13 < (+.f64 x (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) y)))

    1. Initial program 73.4%

      \[x + \left(1 - x\right) \cdot \left(1 - y\right) \]
    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. *-lft-identityN/A

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

        \[\leadsto \left(\mathsf{neg}\left(\left(1 - \color{blue}{\left(\mathsf{neg}\left(-1\right)\right)} \cdot x\right)\right)\right) \cdot y \]
      7. fp-cancel-sign-sub-invN/A

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

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

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

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

        \[\leadsto \left(-1 + \color{blue}{x}\right) \cdot y \]
      12. lower-+.f6488.5

        \[\leadsto \color{blue}{\left(-1 + x\right)} \cdot y \]
    5. Applied rewrites88.5%

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

    if 0.0 < (+.f64 x (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) y))) < 1e13

    1. Initial program 100.0%

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

      \[\leadsto \color{blue}{1 - y} \]
    4. Step-by-step derivation
      1. lower--.f6499.9

        \[\leadsto \color{blue}{1 - y} \]
    5. Applied rewrites99.9%

      \[\leadsto \color{blue}{1 - y} \]
  3. Recombined 2 regimes into one program.
  4. Final simplification92.2%

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(1 - x\right) \cdot \left(1 - y\right) \leq 0 \lor \neg \left(x + \left(1 - x\right) \cdot \left(1 - y\right) \leq 10000000000000\right):\\ \;\;\;\;\left(-1 + x\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;1 - y\\ \end{array} \]
  5. Add Preprocessing

Alternative 3: 87.2% accurate, 0.8× speedup?

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+24} \lor \neg \left(x \leq 480000\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;1 - y\\ \end{array} \end{array} \]
(FPCore (x y)
 :precision binary64
 (if (or (<= x -1.5e+24) (not (<= x 480000.0))) (* y x) (- 1.0 y)))
double code(double x, double y) {
	double tmp;
	if ((x <= -1.5e+24) || !(x <= 480000.0)) {
		tmp = y * x;
	} else {
		tmp = 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 <= (-1.5d+24)) .or. (.not. (x <= 480000.0d0))) then
        tmp = y * x
    else
        tmp = 1.0d0 - y
    end if
    code = tmp
end function
public static double code(double x, double y) {
	double tmp;
	if ((x <= -1.5e+24) || !(x <= 480000.0)) {
		tmp = y * x;
	} else {
		tmp = 1.0 - y;
	}
	return tmp;
}
def code(x, y):
	tmp = 0
	if (x <= -1.5e+24) or not (x <= 480000.0):
		tmp = y * x
	else:
		tmp = 1.0 - y
	return tmp
function code(x, y)
	tmp = 0.0
	if ((x <= -1.5e+24) || !(x <= 480000.0))
		tmp = Float64(y * x);
	else
		tmp = Float64(1.0 - y);
	end
	return tmp
end
function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -1.5e+24) || ~((x <= 480000.0)))
		tmp = y * x;
	else
		tmp = 1.0 - y;
	end
	tmp_2 = tmp;
end
code[x_, y_] := If[Or[LessEqual[x, -1.5e+24], N[Not[LessEqual[x, 480000.0]], $MachinePrecision]], N[(y * x), $MachinePrecision], N[(1.0 - y), $MachinePrecision]]
\begin{array}{l}

\\
\begin{array}{l}
\mathbf{if}\;x \leq -1.5 \cdot 10^{+24} \lor \neg \left(x \leq 480000\right):\\
\;\;\;\;y \cdot x\\

\mathbf{else}:\\
\;\;\;\;1 - y\\


\end{array}
\end{array}
Derivation
  1. Split input into 2 regimes
  2. if x < -1.49999999999999997e24 or 4.8e5 < x

    1. Initial program 57.5%

      \[x + \left(1 - x\right) \cdot \left(1 - y\right) \]
    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. fp-cancel-sign-sub-invN/A

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

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

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

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

        \[\leadsto x \cdot \left(\color{blue}{0} + y\right) \]
      6. +-lft-identityN/A

        \[\leadsto x \cdot \color{blue}{y} \]
      7. *-commutativeN/A

        \[\leadsto \color{blue}{y \cdot x} \]
      8. lower-*.f6482.0

        \[\leadsto \color{blue}{y \cdot x} \]
    5. Applied rewrites82.0%

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

    if -1.49999999999999997e24 < x < 4.8e5

    1. Initial program 99.3%

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

      \[\leadsto \color{blue}{1 - y} \]
    4. Step-by-step derivation
      1. lower--.f6498.7

        \[\leadsto \color{blue}{1 - y} \]
    5. Applied rewrites98.7%

      \[\leadsto \color{blue}{1 - y} \]
  3. Recombined 2 regimes into one program.
  4. Final simplification91.8%

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+24} \lor \neg \left(x \leq 480000\right):\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;1 - y\\ \end{array} \]
  5. Add Preprocessing

Alternative 4: 61.2% accurate, 1.0× speedup?

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 245000\right):\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]
(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.0) (not (<= y 245000.0))) (- y) 1.0))
double code(double x, double y) {
	double tmp;
	if ((y <= -1.0) || !(y <= 245000.0)) {
		tmp = -y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}
real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-1.0d0)) .or. (.not. (y <= 245000.0d0))) then
        tmp = -y
    else
        tmp = 1.0d0
    end if
    code = tmp
end function
public static double code(double x, double y) {
	double tmp;
	if ((y <= -1.0) || !(y <= 245000.0)) {
		tmp = -y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}
def code(x, y):
	tmp = 0
	if (y <= -1.0) or not (y <= 245000.0):
		tmp = -y
	else:
		tmp = 1.0
	return tmp
function code(x, y)
	tmp = 0.0
	if ((y <= -1.0) || !(y <= 245000.0))
		tmp = Float64(-y);
	else
		tmp = 1.0;
	end
	return tmp
end
function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -1.0) || ~((y <= 245000.0)))
		tmp = -y;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end
code[x_, y_] := If[Or[LessEqual[y, -1.0], N[Not[LessEqual[y, 245000.0]], $MachinePrecision]], (-y), 1.0]
\begin{array}{l}

\\
\begin{array}{l}
\mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 245000\right):\\
\;\;\;\;-y\\

\mathbf{else}:\\
\;\;\;\;1\\


\end{array}
\end{array}
Derivation
  1. Split input into 2 regimes
  2. if y < -1 or 245000 < y

    1. Initial program 100.0%

      \[x + \left(1 - x\right) \cdot \left(1 - y\right) \]
    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. *-lft-identityN/A

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

        \[\leadsto \left(\mathsf{neg}\left(\left(1 - \color{blue}{\left(\mathsf{neg}\left(-1\right)\right)} \cdot x\right)\right)\right) \cdot y \]
      7. fp-cancel-sign-sub-invN/A

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

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

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

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

        \[\leadsto \left(-1 + \color{blue}{x}\right) \cdot y \]
      12. lower-+.f6499.8

        \[\leadsto \color{blue}{\left(-1 + x\right)} \cdot y \]
    5. Applied rewrites99.8%

      \[\leadsto \color{blue}{\left(-1 + x\right) \cdot y} \]
    6. Taylor expanded in x around 0

      \[\leadsto -1 \cdot \color{blue}{y} \]
    7. Step-by-step derivation
      1. Applied rewrites53.6%

        \[\leadsto -y \]

      if -1 < y < 245000

      1. Initial program 64.9%

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

        \[\leadsto \color{blue}{\left(1 + x \cdot \left(1 + -1 \cdot \left(1 - y\right)\right)\right) - y} \]
      4. Applied rewrites100.0%

        \[\leadsto \color{blue}{\mathsf{fma}\left(y, x, 1 - y\right)} \]
      5. Taylor expanded in y around 0

        \[\leadsto \color{blue}{1} \]
      6. Step-by-step derivation
        1. Applied rewrites75.0%

          \[\leadsto \color{blue}{1} \]
      7. Recombined 2 regimes into one program.
      8. Final simplification64.5%

        \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 245000\right):\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
      9. Add Preprocessing

      Alternative 5: 62.2% 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 82.0%

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

        \[\leadsto \color{blue}{1 - y} \]
      4. Step-by-step derivation
        1. lower--.f6466.1

          \[\leadsto \color{blue}{1 - y} \]
      5. Applied rewrites66.1%

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

      Alternative 6: 37.0% 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 82.0%

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

        \[\leadsto \color{blue}{\left(1 + x \cdot \left(1 + -1 \cdot \left(1 - y\right)\right)\right) - y} \]
      4. Applied rewrites100.0%

        \[\leadsto \color{blue}{\mathsf{fma}\left(y, x, 1 - y\right)} \]
      5. Taylor expanded in y around 0

        \[\leadsto \color{blue}{1} \]
      6. Step-by-step derivation
        1. Applied rewrites39.7%

          \[\leadsto \color{blue}{1} \]
        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 2024326 
        (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))))