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

Percentage Accurate: 78.3% → 100.0%

Time: 3.8s

Alternatives: 5

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: 78.3% 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

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 75.9%

   \[x + \left(1 - x\right) \cdot \left(1 - y\right) \]
2. Step-by-step derivation

   1. +-commutative 75.9%

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

   2. sub-neg 75.9%

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

   3. distribute-lft-in 75.9%

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

   4. +-commutative 75.9%

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

   5. *-rgt-identity 75.9%

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

   6. associate-+r- 75.9%

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

   7. associate-+l- 100.0%

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

   8. +-inverses 100.0%

      \[\leadsto \left(\left(1 - x\right) \cdot \left(-y\right) + 1\right) - \color{blue}{0} \]

   9. --rgt-identity 100.0%

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

   10. sub-neg 100.0%

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

   11. +-commutative 100.0%

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

   12. distribute-lft1-in 100.0%

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

   13. *-commutative 100.0%

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

   14. unsub-neg 100.0%

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

   15. associate-+l- 100.0%

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

   16. distribute-lft-neg-out 100.0%

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

   17. *-commutative 100.0%

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

   18. distribute-lft-neg-in 100.0%

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

   19. remove-double-neg 100.0%

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

   20. sub-neg 100.0%

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

   21. metadata-eval 100.0%

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

3. Simplified 100.0%

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

4. Final simplification 100.0%

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

Alternative 2: 62.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{+238}:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{+125}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq -2.75 \cdot 10^{+82}:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-22}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 0.0105:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -4.3e+238)
   (- y)
   (if (<= y -5.8e+125)
     (* x y)
     (if (<= y -2.75e+82)
       (- y)
       (if (<= y -3.6e-22) (* x y) (if (<= y 0.0105) 1.0 (- y)))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -4.3e+238) {
		tmp = -y;
	} else if (y <= -5.8e+125) {
		tmp = x * y;
	} else if (y <= -2.75e+82) {
		tmp = -y;
	} else if (y <= -3.6e-22) {
		tmp = x * y;
	} else if (y <= 0.0105) {
		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 <= (-4.3d+238)) then
        tmp = -y
    else if (y <= (-5.8d+125)) then
        tmp = x * y
    else if (y <= (-2.75d+82)) then
        tmp = -y
    else if (y <= (-3.6d-22)) then
        tmp = x * y
    else if (y <= 0.0105d0) 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 <= -4.3e+238) {
		tmp = -y;
	} else if (y <= -5.8e+125) {
		tmp = x * y;
	} else if (y <= -2.75e+82) {
		tmp = -y;
	} else if (y <= -3.6e-22) {
		tmp = x * y;
	} else if (y <= 0.0105) {
		tmp = 1.0;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -4.3e+238:
		tmp = -y
	elif y <= -5.8e+125:
		tmp = x * y
	elif y <= -2.75e+82:
		tmp = -y
	elif y <= -3.6e-22:
		tmp = x * y
	elif y <= 0.0105:
		tmp = 1.0
	else:
		tmp = -y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -4.3e+238)
		tmp = Float64(-y);
	elseif (y <= -5.8e+125)
		tmp = Float64(x * y);
	elseif (y <= -2.75e+82)
		tmp = Float64(-y);
	elseif (y <= -3.6e-22)
		tmp = Float64(x * y);
	elseif (y <= 0.0105)
		tmp = 1.0;
	else
		tmp = Float64(-y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -4.3e+238)
		tmp = -y;
	elseif (y <= -5.8e+125)
		tmp = x * y;
	elseif (y <= -2.75e+82)
		tmp = -y;
	elseif (y <= -3.6e-22)
		tmp = x * y;
	elseif (y <= 0.0105)
		tmp = 1.0;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -4.3e+238], (-y), If[LessEqual[y, -5.8e+125], N[(x * y), $MachinePrecision], If[LessEqual[y, -2.75e+82], (-y), If[LessEqual[y, -3.6e-22], N[(x * y), $MachinePrecision], If[LessEqual[y, 0.0105], 1.0, (-y)]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.29999999999999983e238 or -5.79999999999999986e125 < y < -2.74999999999999998e82 or 0.0105000000000000007 < y

   1. Initial program 99.9%

      \[x + \left(1 - x\right) \cdot \left(1 - y\right) \]
   2. Step-by-step derivation

      1. +-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. distribute-lft-in 99.9%

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

      4. +-commutative 99.9%

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

      5. *-rgt-identity 99.9%

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

      6. associate-+r- 99.9%

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

      7. associate-+l- 100.0%

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

      8. +-inverses 100.0%

         \[\leadsto \left(\left(1 - x\right) \cdot \left(-y\right) + 1\right) - \color{blue}{0} \]

      9. --rgt-identity 100.0%

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

      10. sub-neg 100.0%

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

      11. +-commutative 100.0%

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

      12. distribute-lft1-in 100.0%

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

      13. *-commutative 100.0%

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

      14. unsub-neg 100.0%

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

      15. associate-+l- 100.0%

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

      16. distribute-lft-neg-out 100.0%

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

      17. *-commutative 100.0%

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

      18. distribute-lft-neg-in 100.0%

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

      19. remove-double-neg 100.0%

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

      20. sub-neg 100.0%

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

      21. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 99.1%

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

   5. Taylor expanded in x around 0 69.2%

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

      1. mul-1-neg 69.2%

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

   7. Simplified 69.2%

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

   if -4.29999999999999983e238 < y < -5.79999999999999986e125 or -2.74999999999999998e82 < y < -3.5999999999999998e-22

   1. Initial program 95.8%

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

   2. Taylor expanded in x around -inf 67.4%

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

      1. *-commutative 67.4%

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

   4. Simplified 67.4%

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

   if -3.5999999999999998e-22 < y < 0.0105000000000000007

   1. Initial program 52.3%

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

   2. Taylor expanded in y around 0 76.4%

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

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{+238}:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{+125}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq -2.75 \cdot 10^{+82}:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq -3.6 \cdot 10^{-22}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 0.0105:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]

Alternative 3: 86.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{+31}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{+89}:\\ \;\;\;\;1 - y\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -5.8e+31) (* x y) (if (<= x 4.4e+89) (- 1.0 y) (* x y))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -5.8e+31) {
		tmp = x * y;
	} else if (x <= 4.4e+89) {
		tmp = 1.0 - y;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-5.8d+31)) then
        tmp = x * y
    else if (x <= 4.4d+89) then
        tmp = 1.0d0 - y
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -5.8e+31) {
		tmp = x * y;
	} else if (x <= 4.4e+89) {
		tmp = 1.0 - y;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -5.8e+31:
		tmp = x * y
	elif x <= 4.4e+89:
		tmp = 1.0 - y
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -5.8e+31)
		tmp = Float64(x * y);
	elseif (x <= 4.4e+89)
		tmp = Float64(1.0 - y);
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -5.8e+31)
		tmp = x * y;
	elseif (x <= 4.4e+89)
		tmp = 1.0 - y;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -5.8e+31], N[(x * y), $MachinePrecision], If[LessEqual[x, 4.4e+89], N[(1.0 - y), $MachinePrecision], N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -5.8000000000000001e31 or 4.4e89 < x

   1. Initial program 50.4%

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

   2. Taylor expanded in x around -inf 77.9%

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

      1. *-commutative 77.9%

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

   4. Simplified 77.9%

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

   if -5.8000000000000001e31 < x < 4.4e89

   1. Initial program 92.5%

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

   2. Taylor expanded in x around 0 95.2%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{+31}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{+89}:\\ \;\;\;\;1 - y\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 4: 61.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq 0.0105:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0) (- y) (if (<= y 0.0105) 1.0 (- y))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = -y;
	} else if (y <= 0.0105) {
		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 <= 0.0105d0) 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 <= 0.0105) {
		tmp = 1.0;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = -y
	elif y <= 0.0105:
		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 <= 0.0105)
		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 <= 0.0105)
		tmp = 1.0;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.0], (-y), If[LessEqual[y, 0.0105], 1.0, (-y)]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 0.0105000000000000007 < y

   1. Initial program 99.9%

      \[x + \left(1 - x\right) \cdot \left(1 - y\right) \]
   2. Step-by-step derivation

      1. +-commutative 99.9%

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

      2. sub-neg 99.9%

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

      3. distribute-lft-in 99.9%

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

      4. +-commutative 99.9%

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

      5. *-rgt-identity 99.9%

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

      6. associate-+r- 99.9%

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

      7. associate-+l- 100.0%

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

      8. +-inverses 100.0%

         \[\leadsto \left(\left(1 - x\right) \cdot \left(-y\right) + 1\right) - \color{blue}{0} \]

      9. --rgt-identity 100.0%

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

      10. sub-neg 100.0%

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

      11. +-commutative 100.0%

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

      12. distribute-lft1-in 100.0%

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

      13. *-commutative 100.0%

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

      14. unsub-neg 100.0%

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

      15. associate-+l- 100.0%

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

      16. distribute-lft-neg-out 100.0%

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

      17. *-commutative 100.0%

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

      18. distribute-lft-neg-in 100.0%

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

      19. remove-double-neg 100.0%

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

      20. sub-neg 100.0%

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

      21. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 98.2%

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

   5. Taylor expanded in x around 0 56.9%

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

      1. mul-1-neg 56.9%

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

   7. Simplified 56.9%

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

   if -1 < y < 0.0105000000000000007

   1. Initial program 51.5%

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

   2. Taylor expanded in y around 0 75.3%

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

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq 0.0105:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]

Alternative 5: 37.9% 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 75.9%

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

2. Taylor expanded in y around 0 38.7%

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

3. Final simplification 38.7%

   \[\leadsto 1 \]

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 2023297 
(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))))