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

Percentage Accurate: 77.3% → 100.0%

Time: 3.6s

Alternatives: 7

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: 77.3% 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

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 77.6%

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

   1. +-commutative 77.6%

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

   2. sub-neg 77.6%

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

   3. distribute-rgt-in 77.6%

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

   4. *-lft-identity 77.6%

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

   5. associate-+l+ 77.6%

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

   6. +-commutative 77.6%

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

   7. distribute-lft-neg-out 77.6%

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

   8. sub-neg 77.6%

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

   9. associate--l+ 88.3%

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

   10. associate-+l- 100.0%

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

   11. +-inverses 100.0%

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

   12. metadata-eval 100.0%

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

   13. *-commutative 100.0%

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

3. Simplified 100.0%

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

4. Final simplification 100.0%

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

Alternative 2: 98.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;1 - y \leq -5000000000 \lor \neg \left(1 - y \leq 1\right):\\ \;\;\;\;y \cdot \left(x + -1\right)\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= (- 1.0 y) -5000000000.0) (not (<= (- 1.0 y) 1.0)))
   (* y (+ x -1.0))
   (+ 1.0 (* x y))))

C

double code(double x, double y) {
	double tmp;
	if (((1.0 - y) <= -5000000000.0) || !((1.0 - y) <= 1.0)) {
		tmp = y * (x + -1.0);
	} else {
		tmp = 1.0 + (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 (((1.0d0 - y) <= (-5000000000.0d0)) .or. (.not. ((1.0d0 - y) <= 1.0d0))) then
        tmp = y * (x + (-1.0d0))
    else
        tmp = 1.0d0 + (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (((1.0 - y) <= -5000000000.0) || !((1.0 - y) <= 1.0)) {
		tmp = y * (x + -1.0);
	} else {
		tmp = 1.0 + (x * y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if ((1.0 - y) <= -5000000000.0) or not ((1.0 - y) <= 1.0):
		tmp = y * (x + -1.0)
	else:
		tmp = 1.0 + (x * y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((Float64(1.0 - y) <= -5000000000.0) || !(Float64(1.0 - y) <= 1.0))
		tmp = Float64(y * Float64(x + -1.0));
	else
		tmp = Float64(1.0 + Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (((1.0 - y) <= -5000000000.0) || ~(((1.0 - y) <= 1.0)))
		tmp = y * (x + -1.0);
	else
		tmp = 1.0 + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[N[(1.0 - y), $MachinePrecision], -5000000000.0], N[Not[LessEqual[N[(1.0 - y), $MachinePrecision], 1.0]], $MachinePrecision]], N[(y * N[(x + -1.0), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 1 y) < -5e9 or 1 < (-.f64 1 y)

   1. Initial program 99.0%

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

      1. +-commutative 99.0%

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

      2. sub-neg 99.0%

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

      3. distribute-rgt-in 99.0%

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

      4. *-lft-identity 99.0%

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

      5. associate-+l+ 99.0%

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

      6. +-commutative 99.0%

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

      7. distribute-lft-neg-out 99.0%

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

      8. sub-neg 99.0%

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

      9. associate--l+ 100.0%

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

      10. associate-+l- 100.0%

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

      11. +-inverses 100.0%

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

      12. metadata-eval 100.0%

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

      13. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 99.7%

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

   if -5e9 < (-.f64 1 y) < 1

   1. Initial program 55.9%

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

      1. +-commutative 55.9%

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

      2. sub-neg 55.9%

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

      3. distribute-rgt-in 56.0%

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

      4. *-lft-identity 56.0%

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

      5. associate-+l+ 56.0%

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

      6. +-commutative 56.0%

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

      7. distribute-lft-neg-out 56.0%

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

      8. sub-neg 56.0%

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

      9. associate--l+ 76.5%

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

      10. associate-+l- 100.0%

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

      11. +-inverses 100.0%

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

      12. metadata-eval 100.0%

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

      13. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 98.5%

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

      1. mul-1-neg 98.5%

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

      2. distribute-rgt-neg-in 98.5%

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

   6. Simplified 98.5%

      \[\leadsto 1 - \color{blue}{x \cdot \left(-y\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - y \leq -5000000000 \lor \neg \left(1 - y \leq 1\right):\\ \;\;\;\;y \cdot \left(x + -1\right)\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot y\\ \end{array} \]

Alternative 3: 86.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{-51} \lor \neg \left(y \leq 0.00018\right):\\ \;\;\;\;y \cdot \left(x + -1\right)\\ \mathbf{else}:\\ \;\;\;\;1 - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -7.5e-51) (not (<= y 0.00018))) (* y (+ x -1.0)) (- 1.0 y)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -7.5e-51) || !(y <= 0.00018)) {
		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 <= (-7.5d-51)) .or. (.not. (y <= 0.00018d0))) 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 <= -7.5e-51) || !(y <= 0.00018)) {
		tmp = y * (x + -1.0);
	} else {
		tmp = 1.0 - y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -7.5e-51) or not (y <= 0.00018):
		tmp = y * (x + -1.0)
	else:
		tmp = 1.0 - y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -7.5e-51) || !(y <= 0.00018))
		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 <= -7.5e-51) || ~((y <= 0.00018)))
		tmp = y * (x + -1.0);
	else
		tmp = 1.0 - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -7.5e-51], N[Not[LessEqual[y, 0.00018]], $MachinePrecision]], N[(y * N[(x + -1.0), $MachinePrecision]), $MachinePrecision], N[(1.0 - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.49999999999999976e-51 or 1.80000000000000011e-4 < y

   1. Initial program 96.8%

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

      1. +-commutative 96.8%

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

      2. sub-neg 96.8%

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

      3. distribute-rgt-in 96.8%

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

      4. *-lft-identity 96.8%

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

      5. associate-+l+ 96.8%

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

      6. +-commutative 96.8%

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

      7. distribute-lft-neg-out 96.8%

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

      8. sub-neg 96.8%

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

      9. associate--l+ 100.0%

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

      10. associate-+l- 100.0%

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

      11. +-inverses 100.0%

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

      12. metadata-eval 100.0%

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

      13. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 97.1%

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

   if -7.49999999999999976e-51 < y < 1.80000000000000011e-4

   1. Initial program 54.8%

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

      1. +-commutative 54.8%

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

      2. sub-neg 54.8%

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

      3. distribute-rgt-in 54.9%

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

      4. *-lft-identity 54.9%

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

      5. associate-+l+ 54.9%

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

      6. +-commutative 54.9%

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

      7. distribute-lft-neg-out 54.9%

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

      8. sub-neg 54.9%

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

      9. associate--l+ 74.5%

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

      10. associate-+l- 100.0%

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

      11. +-inverses 100.0%

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

      12. metadata-eval 100.0%

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

      13. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 78.8%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{-51} \lor \neg \left(y \leq 0.00018\right):\\ \;\;\;\;y \cdot \left(x + -1\right)\\ \mathbf{else}:\\ \;\;\;\;1 - y\\ \end{array} \]

Alternative 4: 62.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{-44} \lor \neg \left(y \leq 6.3 \cdot 10^{-18}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -2.9e-44) (not (<= y 6.3e-18))) (* x y) 1.0))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -2.9e-44) || !(y <= 6.3e-18)) {
		tmp = x * y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-2.9d-44)) .or. (.not. (y <= 6.3d-18))) then
        tmp = x * y
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -2.9e-44) || !(y <= 6.3e-18)) {
		tmp = x * y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -2.9e-44) or not (y <= 6.3e-18):
		tmp = x * y
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -2.9e-44) || !(y <= 6.3e-18))
		tmp = Float64(x * y);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -2.9e-44) || ~((y <= 6.3e-18)))
		tmp = x * y;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -2.9e-44], N[Not[LessEqual[y, 6.3e-18]], $MachinePrecision]], N[(x * y), $MachinePrecision], 1.0]

Derivation

1. Split input into 2 regimes

2. if y < -2.9000000000000001e-44 or 6.3000000000000004e-18 < y

   1. Initial program 96.6%

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

      1. +-commutative 96.6%

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

      2. sub-neg 96.6%

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

      3. distribute-rgt-in 96.6%

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

      4. *-lft-identity 96.6%

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

      5. associate-+l+ 96.6%

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

      6. +-commutative 96.6%

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

      7. distribute-lft-neg-out 96.6%

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

      8. sub-neg 96.6%

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

      9. associate--l+ 100.0%

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

      10. associate-+l- 100.0%

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

      11. +-inverses 100.0%

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

      12. metadata-eval 100.0%

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

      13. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 55.7%

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

      1. *-commutative 55.7%

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

   6. Simplified 55.7%

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

   if -2.9000000000000001e-44 < y < 6.3000000000000004e-18

   1. Initial program 54.4%

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

      1. +-commutative 54.4%

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

      2. sub-neg 54.4%

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

      3. distribute-rgt-in 54.4%

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

      4. *-lft-identity 54.4%

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

      5. associate-+l+ 54.4%

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

      6. +-commutative 54.4%

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

      7. distribute-lft-neg-out 54.4%

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

      8. sub-neg 54.4%

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

      9. associate--l+ 74.0%

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

      10. associate-+l- 100.0%

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

      11. +-inverses 100.0%

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

      12. metadata-eval 100.0%

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

      13. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 79.3%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{-44} \lor \neg \left(y \leq 6.3 \cdot 10^{-18}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 5: 86.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.4 \cdot 10^{+48} \lor \neg \left(x \leq 2.7 \cdot 10^{+48}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;1 - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -5.4e+48) (not (<= x 2.7e+48))) (* x y) (- 1.0 y)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -5.4e+48) || !(x <= 2.7e+48)) {
		tmp = x * y;
	} 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 ((x <= (-5.4d+48)) .or. (.not. (x <= 2.7d+48))) then
        tmp = x * y
    else
        tmp = 1.0d0 - y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -5.4e+48) || !(x <= 2.7e+48)) {
		tmp = x * y;
	} else {
		tmp = 1.0 - y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -5.4e+48) or not (x <= 2.7e+48):
		tmp = x * y
	else:
		tmp = 1.0 - y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -5.4e+48) || !(x <= 2.7e+48))
		tmp = Float64(x * y);
	else
		tmp = Float64(1.0 - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -5.4e+48) || ~((x <= 2.7e+48)))
		tmp = x * y;
	else
		tmp = 1.0 - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -5.4e+48], N[Not[LessEqual[x, 2.7e+48]], $MachinePrecision]], N[(x * y), $MachinePrecision], N[(1.0 - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.40000000000000007e48 or 2.70000000000000004e48 < x

   1. Initial program 57.5%

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

      1. +-commutative 57.5%

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

      2. sub-neg 57.5%

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

      3. distribute-rgt-in 57.5%

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

      4. *-lft-identity 57.5%

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

      5. associate-+l+ 57.5%

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

      6. +-commutative 57.5%

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

      7. distribute-lft-neg-out 57.5%

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

      8. sub-neg 57.5%

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

      9. associate--l+ 80.1%

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

      10. associate-+l- 100.0%

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

      11. +-inverses 100.0%

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

      12. metadata-eval 100.0%

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

      13. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 80.1%

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

      1. *-commutative 80.1%

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

   6. Simplified 80.1%

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

   if -5.40000000000000007e48 < x < 2.70000000000000004e48

   1. Initial program 95.6%

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

      1. +-commutative 95.6%

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

      2. sub-neg 95.6%

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

      3. distribute-rgt-in 95.6%

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

      4. *-lft-identity 95.6%

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

      5. associate-+l+ 95.6%

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

      6. +-commutative 95.6%

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

      7. distribute-lft-neg-out 95.6%

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

      8. sub-neg 95.6%

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

      9. associate--l+ 95.7%

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

      10. associate-+l- 100.0%

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

      11. +-inverses 100.0%

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

      12. metadata-eval 100.0%

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

      13. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 94.6%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.4 \cdot 10^{+48} \lor \neg \left(x \leq 2.7 \cdot 10^{+48}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;1 - y\\ \end{array} \]

Alternative 6: 61.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-5} \lor \neg \left(y \leq 1600000000\right):\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.4e-5) (not (<= y 1600000000.0))) (- y) 1.0))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.4e-5) || !(y <= 1600000000.0)) {
		tmp = -y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-1.4d-5)) .or. (.not. (y <= 1600000000.0d0))) then
        tmp = -y
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -1.4e-5) || !(y <= 1600000000.0)) {
		tmp = -y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.4e-5) or not (y <= 1600000000.0):
		tmp = -y
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.4e-5) || !(y <= 1600000000.0))
		tmp = Float64(-y);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -1.4e-5) || ~((y <= 1600000000.0)))
		tmp = -y;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1.4e-5], N[Not[LessEqual[y, 1600000000.0]], $MachinePrecision]], (-y), 1.0]

Derivation

1. Split input into 2 regimes

2. if y < -1.39999999999999998e-5 or 1.6e9 < y

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. sub-neg 99.8%

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

      3. distribute-rgt-in 99.8%

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

      4. *-lft-identity 99.8%

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

      5. associate-+l+ 99.8%

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

      6. +-commutative 99.8%

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

      7. distribute-lft-neg-out 99.8%

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

      8. sub-neg 99.8%

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

      9. associate--l+ 100.0%

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

      10. associate-+l- 100.0%

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

      11. +-inverses 100.0%

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

      12. metadata-eval 100.0%

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

      13. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 99.7%

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

   5. Taylor expanded in x around 0 46.2%

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

      1. neg-mul-1 46.2%

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

   7. Simplified 46.2%

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

   if -1.39999999999999998e-5 < y < 1.6e9

   1. Initial program 55.8%

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

      1. +-commutative 55.8%

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

      2. sub-neg 55.8%

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

      3. distribute-rgt-in 55.8%

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

      4. *-lft-identity 55.8%

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

      5. associate-+l+ 55.8%

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

      6. +-commutative 55.8%

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

      7. distribute-lft-neg-out 55.8%

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

      8. sub-neg 55.8%

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

      9. associate--l+ 76.9%

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

      10. associate-+l- 100.0%

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

      11. +-inverses 100.0%

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

      12. metadata-eval 100.0%

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

      13. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 73.3%

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

4. Final simplification 59.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-5} \lor \neg \left(y \leq 1600000000\right):\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 7: 38.7% 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 77.6%

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

   1. +-commutative 77.6%

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

   2. sub-neg 77.6%

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

   3. distribute-rgt-in 77.6%

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

   4. *-lft-identity 77.6%

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

   5. associate-+l+ 77.6%

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

   6. +-commutative 77.6%

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

   7. distribute-lft-neg-out 77.6%

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

   8. sub-neg 77.6%

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

   9. associate--l+ 88.3%

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

   10. associate-+l- 100.0%

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

   11. +-inverses 100.0%

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

   12. metadata-eval 100.0%

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

   13. *-commutative 100.0%

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

3. Simplified 100.0%

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

4. Taylor expanded in y around 0 38.3%

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

5. Final simplification 38.3%

   \[\leadsto 1 \]

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 2023314 
(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))))