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

Percentage Accurate: 78.1% → 100.0%

Time: 3.4s

Alternatives: 6

Speedup: 1.3×

Specification

Math

\[\begin{array}{l} \\ x + \left(1 - x\right) \cdot \left(1 - y\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (+ x (* (- 1.0 x) (- 1.0 y))))

C

double code(double x, double y) {
	return x + ((1.0 - x) * (1.0 - y));
}

Fortran

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

Java

public static double code(double x, double y) {
	return x + ((1.0 - x) * (1.0 - y));
}

Python

def code(x, y):
	return x + ((1.0 - x) * (1.0 - y))

Julia

function code(x, y)
	return Float64(x + Float64(Float64(1.0 - x) * Float64(1.0 - y)))
end

MATLAB

function tmp = code(x, y)
	tmp = x + ((1.0 - x) * (1.0 - y));
end

Wolfram

code[x_, y_] := N[(x + N[(N[(1.0 - x), $MachinePrecision] * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 78.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \left(1 - x\right) \cdot \left(1 - y\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (+ x (* (- 1.0 x) (- 1.0 y))))

C

double code(double x, double y) {
	return x + ((1.0 - x) * (1.0 - y));
}

Fortran

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

Java

public static double code(double x, double y) {
	return x + ((1.0 - x) * (1.0 - y));
}

Python

def code(x, y):
	return x + ((1.0 - x) * (1.0 - y))

Julia

function code(x, y)
	return Float64(x + Float64(Float64(1.0 - x) * Float64(1.0 - y)))
end

MATLAB

function tmp = code(x, y)
	tmp = x + ((1.0 - x) * (1.0 - y));
end

Wolfram

code[x_, y_] := N[(x + N[(N[(1.0 - x), $MachinePrecision] * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \left(1 + y \cdot x\right) - y \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (- (+ 1.0 (* y x)) y))

C

double code(double x, double y) {
	return (1.0 + (y * x)) - y;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (1.0d0 + (y * x)) - y
end function

Java

public static double code(double x, double y) {
	return (1.0 + (y * x)) - y;
}

Python

def code(x, y):
	return (1.0 + (y * x)) - y

Julia

function code(x, y)
	return Float64(Float64(1.0 + Float64(y * x)) - y)
end

MATLAB

function tmp = code(x, y)
	tmp = (1.0 + (y * x)) - y;
end

Wolfram

code[x_, y_] := N[(N[(1.0 + N[(y * x), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]

Derivation

1. Initial program 78.4%

   \[x + \left(1 - x\right) \cdot \left(1 - y\right) \]

2. Taylor expanded in x around -inf 100.0%

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

3. Final simplification 100.0%

   \[\leadsto \left(1 + y \cdot x\right) - y \]

Alternative 2: 62.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.35 \cdot 10^{-9}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-34}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.56 \cdot 10^{+40}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+302}:\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -3.35e-9)
   (* y x)
   (if (<= y 3.8e-34)
     1.0
     (if (<= y 1.56e+40) (* y x) (if (<= y 9e+302) (- y) (* y x))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -3.35e-9) {
		tmp = y * x;
	} else if (y <= 3.8e-34) {
		tmp = 1.0;
	} else if (y <= 1.56e+40) {
		tmp = y * x;
	} else if (y <= 9e+302) {
		tmp = -y;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-3.35d-9)) then
        tmp = y * x
    else if (y <= 3.8d-34) then
        tmp = 1.0d0
    else if (y <= 1.56d+40) then
        tmp = y * x
    else if (y <= 9d+302) then
        tmp = -y
    else
        tmp = y * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -3.35e-9) {
		tmp = y * x;
	} else if (y <= 3.8e-34) {
		tmp = 1.0;
	} else if (y <= 1.56e+40) {
		tmp = y * x;
	} else if (y <= 9e+302) {
		tmp = -y;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -3.35e-9:
		tmp = y * x
	elif y <= 3.8e-34:
		tmp = 1.0
	elif y <= 1.56e+40:
		tmp = y * x
	elif y <= 9e+302:
		tmp = -y
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -3.35e-9)
		tmp = Float64(y * x);
	elseif (y <= 3.8e-34)
		tmp = 1.0;
	elseif (y <= 1.56e+40)
		tmp = Float64(y * x);
	elseif (y <= 9e+302)
		tmp = Float64(-y);
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -3.35e-9)
		tmp = y * x;
	elseif (y <= 3.8e-34)
		tmp = 1.0;
	elseif (y <= 1.56e+40)
		tmp = y * x;
	elseif (y <= 9e+302)
		tmp = -y;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -3.35e-9], N[(y * x), $MachinePrecision], If[LessEqual[y, 3.8e-34], 1.0, If[LessEqual[y, 1.56e+40], N[(y * x), $MachinePrecision], If[LessEqual[y, 9e+302], (-y), N[(y * x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.34999999999999981e-9 or 3.8000000000000001e-34 < y < 1.56e40 or 9.0000000000000003e302 < y

   1. Initial program 95.9%

      \[x + \left(1 - x\right) \cdot \left(1 - y\right) \]

   2. Taylor expanded in x around inf 56.1%

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

      1. mul-1-neg 56.1%

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

      2. unsub-neg 56.1%

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

      3. sub-neg 56.1%

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

      4. associate--r+ 59.8%

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

      5. metadata-eval 59.8%

         \[\leadsto \left(\color{blue}{0} - \left(-y\right)\right) \cdot x \]

      6. neg-sub0 59.8%

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

      7. remove-double-neg 59.8%

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

   4. Simplified 59.8%

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

   if -3.34999999999999981e-9 < y < 3.8000000000000001e-34

   1. Initial program 57.8%

      \[x + \left(1 - x\right) \cdot \left(1 - y\right) \]

   2. Taylor expanded in y around 0 79.7%

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

   if 1.56e40 < y < 9.0000000000000003e302

   1. Initial program 100.0%

      \[x + \left(1 - x\right) \cdot \left(1 - y\right) \]

   2. Taylor expanded in y around inf 100.0%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(1 - x\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 100.0%

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

      2. distribute-rgt-neg-in 100.0%

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

      3. sub-neg 100.0%

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

      4. distribute-neg-in 100.0%

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

      5. metadata-eval 100.0%

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

      6. remove-double-neg 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in x around 0 56.5%

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

      1. neg-mul-1 56.5%

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

   7. Simplified 56.5%

      \[\leadsto \color{blue}{-y} \]
3. Recombined 3 regimes into one program.

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.35 \cdot 10^{-9}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-34}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.56 \cdot 10^{+40}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+302}:\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 3: 86.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -58000 \lor \neg \left(y \leq 9.8 \cdot 10^{-34}\right):\\ \;\;\;\;y \cdot \left(x + -1\right)\\ \mathbf{else}:\\ \;\;\;\;1 - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -58000.0) (not (<= y 9.8e-34))) (* y (+ x -1.0)) (- 1.0 y)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -58000.0) || !(y <= 9.8e-34)) {
		tmp = y * (x + -1.0);
	} else {
		tmp = 1.0 - y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-58000.0d0)) .or. (.not. (y <= 9.8d-34))) then
        tmp = y * (x + (-1.0d0))
    else
        tmp = 1.0d0 - y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -58000.0) || !(y <= 9.8e-34)) {
		tmp = y * (x + -1.0);
	} else {
		tmp = 1.0 - y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -58000.0) or not (y <= 9.8e-34):
		tmp = y * (x + -1.0)
	else:
		tmp = 1.0 - y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -58000.0) || !(y <= 9.8e-34))
		tmp = Float64(y * Float64(x + -1.0));
	else
		tmp = Float64(1.0 - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -58000.0) || ~((y <= 9.8e-34)))
		tmp = y * (x + -1.0);
	else
		tmp = 1.0 - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -58000.0], N[Not[LessEqual[y, 9.8e-34]], $MachinePrecision]], N[(y * N[(x + -1.0), $MachinePrecision]), $MachinePrecision], N[(1.0 - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -58000 or 9.79999999999999925e-34 < y

   1. Initial program 97.3%

      \[x + \left(1 - x\right) \cdot \left(1 - y\right) \]

   2. Taylor expanded in y around inf 98.5%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(1 - x\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 98.5%

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

      2. distribute-rgt-neg-in 98.5%

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

      3. sub-neg 98.5%

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

      4. distribute-neg-in 98.5%

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

      5. metadata-eval 98.5%

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

      6. remove-double-neg 98.5%

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

   4. Simplified 98.5%

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

   if -58000 < y < 9.79999999999999925e-34

   1. Initial program 58.9%

      \[x + \left(1 - x\right) \cdot \left(1 - y\right) \]

   2. Taylor expanded in x around 0 80.1%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -58000 \lor \neg \left(y \leq 9.8 \cdot 10^{-34}\right):\\ \;\;\;\;y \cdot \left(x + -1\right)\\ \mathbf{else}:\\ \;\;\;\;1 - y\\ \end{array} \]

Alternative 4: 86.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -440:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+51}:\\ \;\;\;\;1 - y\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -440.0) (* y x) (if (<= x 7.5e+51) (- 1.0 y) (* y x))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -440.0) {
		tmp = y * x;
	} else if (x <= 7.5e+51) {
		tmp = 1.0 - y;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-440.0d0)) then
        tmp = y * x
    else if (x <= 7.5d+51) then
        tmp = 1.0d0 - y
    else
        tmp = y * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -440.0) {
		tmp = y * x;
	} else if (x <= 7.5e+51) {
		tmp = 1.0 - y;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -440.0:
		tmp = y * x
	elif x <= 7.5e+51:
		tmp = 1.0 - y
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -440.0)
		tmp = Float64(y * x);
	elseif (x <= 7.5e+51)
		tmp = Float64(1.0 - y);
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -440.0)
		tmp = y * x;
	elseif (x <= 7.5e+51)
		tmp = 1.0 - y;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -440.0], N[(y * x), $MachinePrecision], If[LessEqual[x, 7.5e+51], N[(1.0 - y), $MachinePrecision], N[(y * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -440 or 7.4999999999999999e51 < x

   1. Initial program 57.9%

      \[x + \left(1 - x\right) \cdot \left(1 - y\right) \]

   2. Taylor expanded in x around inf 56.5%

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

      1. mul-1-neg 56.5%

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

      2. unsub-neg 56.5%

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

      3. sub-neg 56.5%

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

      4. associate--r+ 79.0%

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

      5. metadata-eval 79.0%

         \[\leadsto \left(\color{blue}{0} - \left(-y\right)\right) \cdot x \]

      6. neg-sub0 79.0%

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

      7. remove-double-neg 79.0%

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

   4. Simplified 79.0%

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

   if -440 < x < 7.4999999999999999e51

   1. Initial program 95.2%

      \[x + \left(1 - x\right) \cdot \left(1 - y\right) \]

   2. Taylor expanded in x around 0 96.0%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -440:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+51}:\\ \;\;\;\;1 - y\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]

Alternative 5: 61.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-10}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0) (- y) (if (<= y 1.7e-10) 1.0 (- y))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = -y;
	} else if (y <= 1.7e-10) {
		tmp = 1.0;
	} else {
		tmp = -y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-1.0d0)) then
        tmp = -y
    else if (y <= 1.7d-10) then
        tmp = 1.0d0
    else
        tmp = -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = -y;
	} else if (y <= 1.7e-10) {
		tmp = 1.0;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = -y
	elif y <= 1.7e-10:
		tmp = 1.0
	else:
		tmp = -y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.0)
		tmp = Float64(-y);
	elseif (y <= 1.7e-10)
		tmp = 1.0;
	else
		tmp = Float64(-y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.0)
		tmp = -y;
	elseif (y <= 1.7e-10)
		tmp = 1.0;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.0], (-y), If[LessEqual[y, 1.7e-10], 1.0, (-y)]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 1.70000000000000007e-10 < y

   1. Initial program 99.6%

      \[x + \left(1 - x\right) \cdot \left(1 - y\right) \]

   2. Taylor expanded in y around inf 97.8%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot \left(1 - x\right)\right)} \]
   3. Step-by-step derivation

      1. mul-1-neg 97.8%

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

      2. distribute-rgt-neg-in 97.8%

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

      3. sub-neg 97.8%

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

      4. distribute-neg-in 97.8%

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

      5. metadata-eval 97.8%

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

      6. remove-double-neg 97.8%

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

   4. Simplified 97.8%

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

   5. Taylor expanded in x around 0 45.8%

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

      1. neg-mul-1 45.8%

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

   7. Simplified 45.8%

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

   if -1 < y < 1.70000000000000007e-10

   1. Initial program 57.0%

      \[x + \left(1 - x\right) \cdot \left(1 - y\right) \]

   2. Taylor expanded in y around 0 76.9%

      \[\leadsto \color{blue}{1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-10}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]

Alternative 6: 38.1% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ 1 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 1.0)

C

double code(double x, double y) {
	return 1.0;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 1.0d0
end function

Java

public static double code(double x, double y) {
	return 1.0;
}

Python

def code(x, y):
	return 1.0

Julia

function code(x, y)
	return 1.0
end

MATLAB

function tmp = code(x, y)
	tmp = 1.0;
end

Wolfram

code[x_, y_] := 1.0

Derivation

1. Initial program 78.4%

   \[x + \left(1 - x\right) \cdot \left(1 - y\right) \]

2. Taylor expanded in y around 0 39.7%

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

3. Final simplification 39.7%

   \[\leadsto 1 \]

Developer target: 100.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ y \cdot x - \left(y - 1\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (- (* y x) (- y 1.0)))

C

double code(double x, double y) {
	return (y * x) - (y - 1.0);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (y * x) - (y - 1.0d0)
end function

Java

public static double code(double x, double y) {
	return (y * x) - (y - 1.0);
}

Python

def code(x, y):
	return (y * x) - (y - 1.0)

Julia

function code(x, y)
	return Float64(Float64(y * x) - Float64(y - 1.0))
end

MATLAB

function tmp = code(x, y)
	tmp = (y * x) - (y - 1.0);
end

Wolfram

code[x_, y_] := N[(N[(y * x), $MachinePrecision] - N[(y - 1.0), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2023171 
(FPCore (x y)
  :name "Graphics.Rendering.Chart.Plot.Vectors:renderPlotVectors from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (- (* y x) (- y 1.0))

  (+ x (* (- 1.0 x) (- 1.0 y))))