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

Percentage Accurate: 76.8% → 100.0%

Time: 4.8s

Alternatives: 8

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: 76.8% 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

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 79.1%

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

   1. +-commutative 79.1%

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

   2. remove-double-neg 79.1%

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

   3. unsub-neg 79.1%

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

   4. sub-neg 79.1%

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

   5. +-commutative 79.1%

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

   6. distribute-rgt-in 79.1%

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

   7. *-lft-identity 79.1%

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

   8. associate--l+ 89.8%

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

   9. associate--l- 100.0%

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

   10. sub-neg 100.0%

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

   11. +-inverses 100.0%

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

   12. metadata-eval 100.0%

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

   13. +-commutative 100.0%

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

   14. distribute-lft-neg-out 100.0%

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

   15. distribute-rgt-neg-in 100.0%

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

   16. neg-sub0 100.0%

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

   17. associate--r- 100.0%

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

   18. metadata-eval 100.0%

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

   19. +-commutative 100.0%

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

3. Simplified 100.0%

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

   1. distribute-lft-in 100.0%

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

   2. *-commutative 100.0%

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

   3. mul-1-neg 100.0%

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

6. Applied egg-rr 100.0%

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

7. Taylor expanded in x around 0 100.0%

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

Alternative 2: 62.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{+19}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{-67}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{-113}:\\ \;\;\;\;-y\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{-164}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -8.6 \cdot 10^{-214}:\\ \;\;\;\;-y\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{-262}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2.8e+19)
   (* x y)
   (if (<= x -2.5e-67)
     1.0
     (if (<= x -5.2e-113)
       (- y)
       (if (<= x -5.2e-164)
         1.0
         (if (<= x -8.6e-214)
           (- y)
           (if (<= x -3.2e-262) 1.0 (if (<= x 1.0) (- y) (* x y)))))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.8e+19) {
		tmp = x * y;
	} else if (x <= -2.5e-67) {
		tmp = 1.0;
	} else if (x <= -5.2e-113) {
		tmp = -y;
	} else if (x <= -5.2e-164) {
		tmp = 1.0;
	} else if (x <= -8.6e-214) {
		tmp = -y;
	} else if (x <= -3.2e-262) {
		tmp = 1.0;
	} else if (x <= 1.0) {
		tmp = -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 <= (-2.8d+19)) then
        tmp = x * y
    else if (x <= (-2.5d-67)) then
        tmp = 1.0d0
    else if (x <= (-5.2d-113)) then
        tmp = -y
    else if (x <= (-5.2d-164)) then
        tmp = 1.0d0
    else if (x <= (-8.6d-214)) then
        tmp = -y
    else if (x <= (-3.2d-262)) then
        tmp = 1.0d0
    else if (x <= 1.0d0) then
        tmp = -y
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -2.8e+19) {
		tmp = x * y;
	} else if (x <= -2.5e-67) {
		tmp = 1.0;
	} else if (x <= -5.2e-113) {
		tmp = -y;
	} else if (x <= -5.2e-164) {
		tmp = 1.0;
	} else if (x <= -8.6e-214) {
		tmp = -y;
	} else if (x <= -3.2e-262) {
		tmp = 1.0;
	} else if (x <= 1.0) {
		tmp = -y;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2.8e+19:
		tmp = x * y
	elif x <= -2.5e-67:
		tmp = 1.0
	elif x <= -5.2e-113:
		tmp = -y
	elif x <= -5.2e-164:
		tmp = 1.0
	elif x <= -8.6e-214:
		tmp = -y
	elif x <= -3.2e-262:
		tmp = 1.0
	elif x <= 1.0:
		tmp = -y
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2.8e+19)
		tmp = Float64(x * y);
	elseif (x <= -2.5e-67)
		tmp = 1.0;
	elseif (x <= -5.2e-113)
		tmp = Float64(-y);
	elseif (x <= -5.2e-164)
		tmp = 1.0;
	elseif (x <= -8.6e-214)
		tmp = Float64(-y);
	elseif (x <= -3.2e-262)
		tmp = 1.0;
	elseif (x <= 1.0)
		tmp = Float64(-y);
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2.8e+19)
		tmp = x * y;
	elseif (x <= -2.5e-67)
		tmp = 1.0;
	elseif (x <= -5.2e-113)
		tmp = -y;
	elseif (x <= -5.2e-164)
		tmp = 1.0;
	elseif (x <= -8.6e-214)
		tmp = -y;
	elseif (x <= -3.2e-262)
		tmp = 1.0;
	elseif (x <= 1.0)
		tmp = -y;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2.8e+19], N[(x * y), $MachinePrecision], If[LessEqual[x, -2.5e-67], 1.0, If[LessEqual[x, -5.2e-113], (-y), If[LessEqual[x, -5.2e-164], 1.0, If[LessEqual[x, -8.6e-214], (-y), If[LessEqual[x, -3.2e-262], 1.0, If[LessEqual[x, 1.0], (-y), N[(x * y), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.8e19 or 1 < x

   1. Initial program 60.8%

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

      1. +-commutative 60.8%

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

      2. remove-double-neg 60.8%

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

      3. unsub-neg 60.8%

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

      4. sub-neg 60.8%

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

      5. +-commutative 60.8%

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

      6. distribute-rgt-in 60.8%

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

      7. *-lft-identity 60.8%

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

      8. associate--l+ 81.3%

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

      9. associate--l- 100.0%

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

      10. sub-neg 100.0%

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

      11. +-inverses 100.0%

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

      12. metadata-eval 100.0%

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

      13. +-commutative 100.0%

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

      14. distribute-lft-neg-out 100.0%

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

      15. distribute-rgt-neg-in 100.0%

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

      16. neg-sub0 100.0%

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

      17. associate--r- 100.0%

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

      18. metadata-eval 100.0%

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

      19. +-commutative 100.0%

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

   3. Simplified 100.0%

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

      1. distribute-lft-in 100.0%

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

      2. *-commutative 100.0%

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

      3. mul-1-neg 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in x around 0 100.0%

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

   8. Taylor expanded in x around inf 79.2%

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

   9. Taylor expanded in x around inf 77.9%

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

       1. *-commutative 77.9%

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

   11. Simplified 77.9%

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

   if -2.8e19 < x < -2.4999999999999999e-67 or -5.1999999999999998e-113 < x < -5.2000000000000003e-164 or -8.5999999999999999e-214 < x < -3.2e-262

   1. Initial program 97.3%

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

      1. +-commutative 97.3%

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

      2. remove-double-neg 97.3%

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

      3. unsub-neg 97.3%

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

      4. sub-neg 97.3%

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

      5. +-commutative 97.3%

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

      6. distribute-rgt-in 97.4%

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

      7. *-lft-identity 97.4%

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

      8. associate--l+ 97.4%

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

      9. associate--l- 100.0%

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

      10. sub-neg 100.0%

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

      11. +-inverses 100.0%

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

      12. metadata-eval 100.0%

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

      13. +-commutative 100.0%

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

      14. distribute-lft-neg-out 100.0%

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

      15. distribute-rgt-neg-in 100.0%

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

      16. neg-sub0 100.0%

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

      17. associate--r- 100.0%

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

      18. metadata-eval 100.0%

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

      19. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 68.6%

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

   if -2.4999999999999999e-67 < x < -5.1999999999999998e-113 or -5.2000000000000003e-164 < x < -8.5999999999999999e-214 or -3.2e-262 < x < 1

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. remove-double-neg 100.0%

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

      3. unsub-neg 100.0%

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

      4. sub-neg 100.0%

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

      5. +-commutative 100.0%

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

      6. distribute-rgt-in 100.0%

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

      7. *-lft-identity 100.0%

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

      8. associate--l+ 100.0%

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

      9. associate--l- 100.0%

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

      10. sub-neg 100.0%

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

      11. +-inverses 100.0%

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

      12. metadata-eval 100.0%

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

      13. +-commutative 100.0%

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

      14. distribute-lft-neg-out 100.0%

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

      15. distribute-rgt-neg-in 100.0%

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

      16. neg-sub0 100.0%

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

      17. associate--r- 100.0%

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

      18. metadata-eval 100.0%

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

      19. +-commutative 100.0%

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

   3. Simplified 100.0%

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

      1. distribute-lft-in 100.0%

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

      2. *-commutative 100.0%

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

      3. mul-1-neg 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in x around 0 100.0%

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

   8. Taylor expanded in x around inf 64.6%

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

   9. Taylor expanded in x around 0 64.2%

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

       1. neg-mul-1 64.2%

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

   11. Simplified 64.2%

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

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{+19}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{-67}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{-113}:\\ \;\;\;\;-y\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{-164}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -8.6 \cdot 10^{-214}:\\ \;\;\;\;-y\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{-262}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 97.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;1 - y \leq -5 \cdot 10^{+27} \lor \neg \left(1 - y \leq 1\right):\\ \;\;\;\;x \cdot y - y\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= (- 1.0 y) -5e+27) (not (<= (- 1.0 y) 1.0)))
   (- (* x y) y)
   (+ 1.0 (* x y))))

C

double code(double x, double y) {
	double tmp;
	if (((1.0 - y) <= -5e+27) || !((1.0 - y) <= 1.0)) {
		tmp = (x * y) - y;
	} 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) <= (-5d+27)) .or. (.not. ((1.0d0 - y) <= 1.0d0))) then
        tmp = (x * y) - y
    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) <= -5e+27) || !((1.0 - y) <= 1.0)) {
		tmp = (x * y) - y;
	} else {
		tmp = 1.0 + (x * y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if ((1.0 - y) <= -5e+27) or not ((1.0 - y) <= 1.0):
		tmp = (x * y) - y
	else:
		tmp = 1.0 + (x * y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((Float64(1.0 - y) <= -5e+27) || !(Float64(1.0 - y) <= 1.0))
		tmp = Float64(Float64(x * y) - y);
	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) <= -5e+27) || ~(((1.0 - y) <= 1.0)))
		tmp = (x * y) - y;
	else
		tmp = 1.0 + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[N[(1.0 - y), $MachinePrecision], -5e+27], N[Not[LessEqual[N[(1.0 - y), $MachinePrecision], 1.0]], $MachinePrecision]], N[(N[(x * y), $MachinePrecision] - y), $MachinePrecision], N[(1.0 + N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 #s(literal 1 binary64) y) < -4.99999999999999979e27 or 1 < (-.f64 #s(literal 1 binary64) y)

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. remove-double-neg 100.0%

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

      3. unsub-neg 100.0%

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

      4. sub-neg 100.0%

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

      5. +-commutative 100.0%

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

      6. distribute-rgt-in 100.0%

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

      7. *-lft-identity 100.0%

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

      8. associate--l+ 100.0%

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

      9. associate--l- 100.0%

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

      10. sub-neg 100.0%

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

      11. +-inverses 100.0%

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

      12. metadata-eval 100.0%

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

      13. +-commutative 100.0%

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

      14. distribute-lft-neg-out 100.0%

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

      15. distribute-rgt-neg-in 100.0%

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

      16. neg-sub0 100.0%

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

      17. associate--r- 100.0%

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

      18. metadata-eval 100.0%

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

      19. +-commutative 100.0%

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

   3. Simplified 100.0%

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

      1. distribute-lft-in 100.0%

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

      2. *-commutative 100.0%

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

      3. mul-1-neg 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in x around 0 100.0%

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

   8. Taylor expanded in x around inf 98.3%

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

   if -4.99999999999999979e27 < (-.f64 #s(literal 1 binary64) y) < 1

   1. Initial program 55.0%

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

      1. +-commutative 55.0%

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

      2. remove-double-neg 55.0%

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

      3. unsub-neg 55.0%

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

      4. sub-neg 55.0%

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

      5. +-commutative 55.0%

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

      6. distribute-rgt-in 55.0%

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

      7. *-lft-identity 55.0%

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

      8. associate--l+ 78.1%

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

      9. associate--l- 100.0%

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

      10. sub-neg 100.0%

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

      11. +-inverses 100.0%

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

      12. metadata-eval 100.0%

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

      13. +-commutative 100.0%

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

      14. distribute-lft-neg-out 100.0%

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

      15. distribute-rgt-neg-in 100.0%

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

      16. neg-sub0 100.0%

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

      17. associate--r- 100.0%

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

      18. metadata-eval 100.0%

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

      19. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 98.3%

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

      1. *-commutative 98.3%

         \[\leadsto 1 + \color{blue}{y \cdot x} \]

   7. Simplified 98.3%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - y \leq -5 \cdot 10^{+27} \lor \neg \left(1 - y \leq 1\right):\\ \;\;\;\;x \cdot y - y\\ \mathbf{else}:\\ \;\;\;\;1 + x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 97.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -360000000000 \lor \neg \left(x \leq 5.8 \cdot 10^{-36}\right):\\ \;\;\;\;1 + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;1 - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -360000000000.0) (not (<= x 5.8e-36)))
   (+ 1.0 (* x y))
   (- 1.0 y)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -360000000000.0) || !(x <= 5.8e-36)) {
		tmp = 1.0 + (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 <= (-360000000000.0d0)) .or. (.not. (x <= 5.8d-36))) then
        tmp = 1.0d0 + (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 <= -360000000000.0) || !(x <= 5.8e-36)) {
		tmp = 1.0 + (x * y);
	} else {
		tmp = 1.0 - y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -360000000000.0) or not (x <= 5.8e-36):
		tmp = 1.0 + (x * y)
	else:
		tmp = 1.0 - y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -360000000000.0) || !(x <= 5.8e-36))
		tmp = Float64(1.0 + 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 <= -360000000000.0) || ~((x <= 5.8e-36)))
		tmp = 1.0 + (x * y);
	else
		tmp = 1.0 - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -360000000000.0], N[Not[LessEqual[x, 5.8e-36]], $MachinePrecision]], N[(1.0 + N[(x * y), $MachinePrecision]), $MachinePrecision], N[(1.0 - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.6e11 or 5.80000000000000026e-36 < x

   1. Initial program 62.0%

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

      1. +-commutative 62.0%

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

      2. remove-double-neg 62.0%

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

      3. unsub-neg 62.0%

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

      4. sub-neg 62.0%

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

      5. +-commutative 62.0%

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

      6. distribute-rgt-in 62.1%

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

      7. *-lft-identity 62.1%

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

      8. associate--l+ 81.5%

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

      9. associate--l- 100.0%

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

      10. sub-neg 100.0%

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

      11. +-inverses 100.0%

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

      12. metadata-eval 100.0%

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

      13. +-commutative 100.0%

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

      14. distribute-lft-neg-out 100.0%

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

      15. distribute-rgt-neg-in 100.0%

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

      16. neg-sub0 100.0%

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

      17. associate--r- 100.0%

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

      18. metadata-eval 100.0%

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

      19. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 95.9%

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

      1. *-commutative 95.9%

         \[\leadsto 1 + \color{blue}{y \cdot x} \]

   7. Simplified 95.9%

      \[\leadsto 1 + \color{blue}{y \cdot x} \]

   if -3.6e11 < x < 5.80000000000000026e-36

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. remove-double-neg 100.0%

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

      3. unsub-neg 100.0%

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

      4. sub-neg 100.0%

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

      5. +-commutative 100.0%

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

      6. distribute-rgt-in 100.0%

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

      7. *-lft-identity 100.0%

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

      8. associate--l+ 100.0%

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

      9. associate--l- 100.0%

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

      10. sub-neg 100.0%

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

      11. +-inverses 100.0%

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

      12. metadata-eval 100.0%

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

      13. +-commutative 100.0%

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

      14. distribute-lft-neg-out 100.0%

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

      15. distribute-rgt-neg-in 100.0%

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

      16. neg-sub0 100.0%

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

      17. associate--r- 100.0%

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

      18. metadata-eval 100.0%

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

      19. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 98.2%

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

      1. neg-mul-1 98.2%

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

      2. unsub-neg 98.2%

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

   7. Simplified 98.2%

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

4. Final simplification 96.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -360000000000 \lor \neg \left(x \leq 5.8 \cdot 10^{-36}\right):\\ \;\;\;\;1 + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;1 - y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 86.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+58} \lor \neg \left(x \leq 1.9 \cdot 10^{+34}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;1 - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -1.3e+58) (not (<= x 1.9e+34))) (* x y) (- 1.0 y)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -1.3e+58) || !(x <= 1.9e+34)) {
		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 <= (-1.3d+58)) .or. (.not. (x <= 1.9d+34))) 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 <= -1.3e+58) || !(x <= 1.9e+34)) {
		tmp = x * y;
	} else {
		tmp = 1.0 - y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -1.3e+58) or not (x <= 1.9e+34):
		tmp = x * y
	else:
		tmp = 1.0 - y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -1.3e+58) || !(x <= 1.9e+34))
		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 <= -1.3e+58) || ~((x <= 1.9e+34)))
		tmp = x * y;
	else
		tmp = 1.0 - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -1.3e+58], N[Not[LessEqual[x, 1.9e+34]], $MachinePrecision]], N[(x * y), $MachinePrecision], N[(1.0 - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.29999999999999994e58 or 1.9000000000000001e34 < x

   1. Initial program 59.9%

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

      1. +-commutative 59.9%

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

      2. remove-double-neg 59.9%

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

      3. unsub-neg 59.9%

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

      4. sub-neg 59.9%

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

      5. +-commutative 59.9%

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

      6. distribute-rgt-in 59.9%

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

      7. *-lft-identity 59.9%

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

      8. associate--l+ 82.2%

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

      9. associate--l- 100.0%

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

      10. sub-neg 100.0%

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

      11. +-inverses 100.0%

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

      12. metadata-eval 100.0%

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

      13. +-commutative 100.0%

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

      14. distribute-lft-neg-out 100.0%

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

      15. distribute-rgt-neg-in 100.0%

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

      16. neg-sub0 100.0%

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

      17. associate--r- 100.0%

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

      18. metadata-eval 100.0%

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

      19. +-commutative 100.0%

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

   3. Simplified 100.0%

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

      1. distribute-lft-in 100.0%

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

      2. *-commutative 100.0%

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

      3. mul-1-neg 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in x around 0 100.0%

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

   8. Taylor expanded in x around inf 82.2%

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

   9. Taylor expanded in x around inf 82.2%

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

       1. *-commutative 82.2%

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

   11. Simplified 82.2%

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

   if -1.29999999999999994e58 < x < 1.9000000000000001e34

   1. Initial program 95.7%

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

      1. +-commutative 95.7%

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

      2. remove-double-neg 95.7%

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

      3. unsub-neg 95.7%

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

      4. sub-neg 95.7%

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

      5. +-commutative 95.7%

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

      6. distribute-rgt-in 95.7%

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

      7. *-lft-identity 95.7%

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

      8. associate--l+ 96.5%

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

      9. associate--l- 100.0%

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

      10. sub-neg 100.0%

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

      11. +-inverses 100.0%

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

      12. metadata-eval 100.0%

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

      13. +-commutative 100.0%

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

      14. distribute-lft-neg-out 100.0%

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

      15. distribute-rgt-neg-in 100.0%

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

      16. neg-sub0 100.0%

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

      17. associate--r- 100.0%

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

      18. metadata-eval 100.0%

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

      19. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 92.0%

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

      1. neg-mul-1 92.0%

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

      2. unsub-neg 92.0%

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

   7. Simplified 92.0%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{+58} \lor \neg \left(x \leq 1.9 \cdot 10^{+34}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;1 - y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 59.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+66} \lor \neg \left(y \leq 1.45 \cdot 10^{-18}\right):\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -4.4e+66) (not (<= y 1.45e-18))) (- y) 1.0))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -4.4e+66) || !(y <= 1.45e-18)) {
		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 <= (-4.4d+66)) .or. (.not. (y <= 1.45d-18))) 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 <= -4.4e+66) || !(y <= 1.45e-18)) {
		tmp = -y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -4.4e+66) or not (y <= 1.45e-18):
		tmp = -y
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -4.4e+66) || !(y <= 1.45e-18))
		tmp = Float64(-y);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -4.4e+66) || ~((y <= 1.45e-18)))
		tmp = -y;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -4.4e+66], N[Not[LessEqual[y, 1.45e-18]], $MachinePrecision]], (-y), 1.0]

Derivation

1. Split input into 2 regimes

2. if y < -4.3999999999999997e66 or 1.45e-18 < y

   1. Initial program 99.2%

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

      1. +-commutative 99.2%

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

      2. remove-double-neg 99.2%

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

      3. unsub-neg 99.2%

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

      4. sub-neg 99.2%

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

      5. +-commutative 99.2%

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

      6. distribute-rgt-in 99.2%

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

      7. *-lft-identity 99.2%

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

      8. associate--l+ 99.9%

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

      9. associate--l- 100.0%

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

      10. sub-neg 100.0%

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

      11. +-inverses 100.0%

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

      12. metadata-eval 100.0%

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

      13. +-commutative 100.0%

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

      14. distribute-lft-neg-out 100.0%

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

      15. distribute-rgt-neg-in 100.0%

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

      16. neg-sub0 100.0%

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

      17. associate--r- 100.0%

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

      18. metadata-eval 100.0%

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

      19. +-commutative 100.0%

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

   3. Simplified 100.0%

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

      1. distribute-lft-in 100.0%

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

      2. *-commutative 100.0%

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

      3. mul-1-neg 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in x around 0 100.0%

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

   8. Taylor expanded in x around inf 99.1%

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

   9. Taylor expanded in x around 0 45.0%

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

       1. neg-mul-1 45.0%

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

   11. Simplified 45.0%

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

   if -4.3999999999999997e66 < y < 1.45e-18

   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. remove-double-neg 55.9%

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

      3. unsub-neg 55.9%

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

      4. sub-neg 55.9%

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

      5. +-commutative 55.9%

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

      6. distribute-rgt-in 55.9%

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

      7. *-lft-identity 55.9%

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

      8. associate--l+ 78.2%

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

      9. associate--l- 100.0%

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

      10. sub-neg 100.0%

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

      11. +-inverses 100.0%

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

      12. metadata-eval 100.0%

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

      13. +-commutative 100.0%

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

      14. distribute-lft-neg-out 100.0%

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

      15. distribute-rgt-neg-in 100.0%

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

      16. neg-sub0 100.0%

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

      17. associate--r- 100.0%

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

      18. metadata-eval 100.0%

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

      19. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 70.1%

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

4. Final simplification 56.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+66} \lor \neg \left(y \leq 1.45 \cdot 10^{-18}\right):\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 100.0% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 79.1%

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

   1. +-commutative 79.1%

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

   2. remove-double-neg 79.1%

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

   3. unsub-neg 79.1%

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

   4. sub-neg 79.1%

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

   5. +-commutative 79.1%

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

   6. distribute-rgt-in 79.1%

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

   7. *-lft-identity 79.1%

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

   8. associate--l+ 89.8%

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

   9. associate--l- 100.0%

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

   10. sub-neg 100.0%

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

   11. +-inverses 100.0%

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

   12. metadata-eval 100.0%

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

   13. +-commutative 100.0%

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

   14. distribute-lft-neg-out 100.0%

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

   15. distribute-rgt-neg-in 100.0%

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

   16. neg-sub0 100.0%

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

   17. associate--r- 100.0%

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

   18. metadata-eval 100.0%

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

   19. +-commutative 100.0%

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

3. Simplified 100.0%

   \[\leadsto \color{blue}{1 + y \cdot \left(x + -1\right)} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 8: 38.6% 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 79.1%

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

   1. +-commutative 79.1%

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

   2. remove-double-neg 79.1%

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

   3. unsub-neg 79.1%

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

   4. sub-neg 79.1%

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

   5. +-commutative 79.1%

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

   6. distribute-rgt-in 79.1%

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

   7. *-lft-identity 79.1%

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

   8. associate--l+ 89.8%

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

   9. associate--l- 100.0%

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

   10. sub-neg 100.0%

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

   11. +-inverses 100.0%

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

   12. metadata-eval 100.0%

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

   13. +-commutative 100.0%

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

   14. distribute-lft-neg-out 100.0%

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

   15. distribute-rgt-neg-in 100.0%

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

   16. neg-sub0 100.0%

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

   17. associate--r- 100.0%

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

   18. metadata-eval 100.0%

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

   19. +-commutative 100.0%

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

3. Simplified 100.0%

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

5. Taylor expanded in y around 0 34.2%

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

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 2024107 
(FPCore (x y)
  :name "Graphics.Rendering.Chart.Plot.Vectors:renderPlotVectors from Chart-1.5.3"
  :precision binary64

  :alt
  (- (* y x) (- y 1.0))

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