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

Percentage Accurate: 78.5% → 100.0%

Time: 5.0s

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: 78.5% 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 78.4%

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

   1. +-commutative 78.4%

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

   2. remove-double-neg 78.4%

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

   3. unsub-neg 78.4%

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

   4. sub-neg 78.4%

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

   5. +-commutative 78.4%

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

   6. distribute-rgt-in 78.4%

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

   7. *-lft-identity 78.4%

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

   8. associate--l+ 90.6%

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

   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: 61.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.72 \cdot 10^{+80}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-75}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.72e+80)
   (* x y)
   (if (<= x 2.9e-75) 1.0 (if (<= x 1.0) (- y) (* x y)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.72e+80) {
		tmp = x * y;
	} else if (x <= 2.9e-75) {
		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 <= (-1.72d+80)) then
        tmp = x * y
    else if (x <= 2.9d-75) 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 <= -1.72e+80) {
		tmp = x * y;
	} else if (x <= 2.9e-75) {
		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 <= -1.72e+80:
		tmp = x * y
	elif x <= 2.9e-75:
		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 <= -1.72e+80)
		tmp = Float64(x * y);
	elseif (x <= 2.9e-75)
		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 <= -1.72e+80)
		tmp = x * y;
	elseif (x <= 2.9e-75)
		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, -1.72e+80], N[(x * y), $MachinePrecision], If[LessEqual[x, 2.9e-75], 1.0, If[LessEqual[x, 1.0], (-y), N[(x * y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.7200000000000001e80 or 1 < x

   1. Initial program 55.6%

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

      1. +-commutative 55.6%

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

      2. remove-double-neg 55.6%

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

      3. unsub-neg 55.6%

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

      4. sub-neg 55.6%

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

      5. +-commutative 55.6%

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

      6. distribute-rgt-in 55.6%

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

      7. *-lft-identity 55.6%

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

      8. associate--l+ 84.1%

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

      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. 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 84.1%

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

      1. *-commutative 84.1%

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

   10. Simplified 84.1%

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

   if -1.7200000000000001e80 < x < 2.9000000000000002e-75

   1. Initial program 94.8%

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

      1. +-commutative 94.8%

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

      2. remove-double-neg 94.8%

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

      3. unsub-neg 94.8%

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

      4. sub-neg 94.8%

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

      5. +-commutative 94.8%

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

      6. distribute-rgt-in 94.8%

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

      7. *-lft-identity 94.8%

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

      8. associate--l+ 94.9%

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

      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. Taylor expanded in y around 0 58.2%

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

   if 2.9000000000000002e-75 < 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 y around inf 69.9%

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

   9. Taylor expanded in x around 0 64.3%

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

       1. mul-1-neg 64.3%

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

   11. Simplified 64.3%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.72 \cdot 10^{+80}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-75}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.9% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if x < -1 or 1 < x

   1. Initial program 55.5%

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

      1. +-commutative 55.5%

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

      2. remove-double-neg 55.5%

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

      3. unsub-neg 55.5%

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

      4. sub-neg 55.5%

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

      5. +-commutative 55.5%

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

      6. distribute-rgt-in 55.5%

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

      7. *-lft-identity 55.5%

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

      8. associate--l+ 80.6%

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

      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 99.1%

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

      1. *-commutative 99.1%

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

   7. Simplified 99.1%

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

   if -1 < 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. Taylor expanded in x around 0 98.7%

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

      1. neg-mul-1 98.7%

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

      2. unsub-neg 98.7%

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

   7. Simplified 98.7%

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

4. Final simplification 98.9%

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

Alternative 4: 86.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{+80}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-11}:\\ \;\;\;\;1 - y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.8e+80) (* x y) (if (<= x 1.5e-11) (- 1.0 y) (* y (+ x -1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.8e+80) {
		tmp = x * y;
	} else if (x <= 1.5e-11) {
		tmp = 1.0 - y;
	} else {
		tmp = y * (x + -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 (x <= (-1.8d+80)) then
        tmp = x * y
    else if (x <= 1.5d-11) then
        tmp = 1.0d0 - y
    else
        tmp = y * (x + (-1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -1.8e+80) {
		tmp = x * y;
	} else if (x <= 1.5e-11) {
		tmp = 1.0 - y;
	} else {
		tmp = y * (x + -1.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.8e+80:
		tmp = x * y
	elif x <= 1.5e-11:
		tmp = 1.0 - y
	else:
		tmp = y * (x + -1.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.8e+80)
		tmp = Float64(x * y);
	elseif (x <= 1.5e-11)
		tmp = Float64(1.0 - y);
	else
		tmp = Float64(y * Float64(x + -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.8e+80)
		tmp = x * y;
	elseif (x <= 1.5e-11)
		tmp = 1.0 - y;
	else
		tmp = y * (x + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.8e+80], N[(x * y), $MachinePrecision], If[LessEqual[x, 1.5e-11], N[(1.0 - y), $MachinePrecision], N[(y * N[(x + -1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.79999999999999997e80

   1. Initial program 52.3%

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

      1. +-commutative 52.3%

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

      2. remove-double-neg 52.3%

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

      3. unsub-neg 52.3%

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

      4. sub-neg 52.3%

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

      5. +-commutative 52.3%

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

      6. distribute-rgt-in 52.3%

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

      7. *-lft-identity 52.3%

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

      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. Taylor expanded in x around inf 89.8%

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

      1. *-commutative 89.8%

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

   10. Simplified 89.8%

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

   if -1.79999999999999997e80 < x < 1.5e-11

   1. Initial program 95.3%

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

      1. +-commutative 95.3%

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

      2. remove-double-neg 95.3%

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

      3. unsub-neg 95.3%

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

      4. sub-neg 95.3%

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

      5. +-commutative 95.3%

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

      6. distribute-rgt-in 95.3%

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

      7. *-lft-identity 95.3%

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

      8. associate--l+ 95.4%

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

      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 x around 0 95.3%

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

      1. neg-mul-1 95.3%

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

      2. unsub-neg 95.3%

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

   7. Simplified 95.3%

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

   if 1.5e-11 < x

   1. Initial program 60.5%

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

      1. +-commutative 60.5%

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

      2. remove-double-neg 60.5%

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

      3. unsub-neg 60.5%

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

      4. sub-neg 60.5%

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

      5. +-commutative 60.5%

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

      6. distribute-rgt-in 60.6%

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

      7. *-lft-identity 60.6%

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

      8. associate--l+ 80.0%

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

      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 y around inf 80.0%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{+80}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-11}:\\ \;\;\;\;1 - y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 86.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{+80} \lor \neg \left(x \leq 5500000000000\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;1 - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -1.65e+80) (not (<= x 5500000000000.0))) (* x y) (- 1.0 y)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -1.65e+80) || !(x <= 5500000000000.0)) {
		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 <= (-1.65d+80)) .or. (.not. (x <= 5500000000000.0d0))) 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 <= -1.65e+80) || !(x <= 5500000000000.0)) {
		tmp = x * y;
	} else {
		tmp = 1.0 - y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -1.65e+80) or not (x <= 5500000000000.0):
		tmp = x * y
	else:
		tmp = 1.0 - y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -1.65e+80) || !(x <= 5500000000000.0))
		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 <= -1.65e+80) || ~((x <= 5500000000000.0)))
		tmp = x * y;
	else
		tmp = 1.0 - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -1.65e+80], N[Not[LessEqual[x, 5500000000000.0]], $MachinePrecision]], N[(x * y), $MachinePrecision], N[(1.0 - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.64999999999999995e80 or 5.5e12 < x

   1. Initial program 55.6%

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

      1. +-commutative 55.6%

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

      2. remove-double-neg 55.6%

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

      3. unsub-neg 55.6%

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

      4. sub-neg 55.6%

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

      5. +-commutative 55.6%

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

      6. distribute-rgt-in 55.6%

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

      7. *-lft-identity 55.6%

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

      8. associate--l+ 84.1%

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

      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. 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 84.1%

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

      1. *-commutative 84.1%

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

   10. Simplified 84.1%

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

   if -1.64999999999999995e80 < x < 5.5e12

   1. Initial program 95.4%

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

      1. +-commutative 95.4%

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

      2. remove-double-neg 95.4%

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

      3. unsub-neg 95.4%

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

      4. sub-neg 95.4%

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

      5. +-commutative 95.4%

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

      6. distribute-rgt-in 95.4%

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

      7. *-lft-identity 95.4%

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

      8. associate--l+ 95.5%

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

      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 94.8%

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

      1. neg-mul-1 94.8%

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

      2. unsub-neg 94.8%

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

   7. Simplified 94.8%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{+80} \lor \neg \left(x \leq 5500000000000\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;1 - y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 60.6% accurate, 0.7× speedup

Math

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

FPCore

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

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.0) || !(y <= 1.0)) {
		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 <= (-1.0d0)) .or. (.not. (y <= 1.0d0))) 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 <= -1.0) || !(y <= 1.0)) {
		tmp = -y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if y < -1 or 1 < y

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. remove-double-neg 99.9%

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

      3. unsub-neg 99.9%

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

      4. sub-neg 99.9%

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

      5. +-commutative 99.9%

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

      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 y around inf 98.8%

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

   9. Taylor expanded in x around 0 47.6%

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

       1. mul-1-neg 47.6%

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

   11. Simplified 47.6%

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

   if -1 < y < 1

   1. Initial program 58.5%

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

      1. +-commutative 58.5%

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

      2. remove-double-neg 58.5%

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

      3. unsub-neg 58.5%

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

      4. sub-neg 58.5%

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

      5. +-commutative 58.5%

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

      6. distribute-rgt-in 58.5%

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

      7. *-lft-identity 58.5%

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

      8. associate--l+ 81.9%

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

      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. Taylor expanded in y around 0 72.7%

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

4. Final simplification 60.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
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 78.4%

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

   1. +-commutative 78.4%

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

   2. remove-double-neg 78.4%

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

   3. unsub-neg 78.4%

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

   4. sub-neg 78.4%

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

   5. +-commutative 78.4%

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

   6. distribute-rgt-in 78.4%

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

   7. *-lft-identity 78.4%

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

   8. associate--l+ 90.6%

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

   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: 37.1% accurate, 9.0× speedup

Math

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

FPCore

(FPCore (x y) :precision binary64 1.0)

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return 1.0

Julia

function code(x, y)
	return 1.0
end

MATLAB

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

Wolfram

code[x_, y_] := 1.0

Derivation

1. Initial program 78.4%

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

   1. +-commutative 78.4%

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

   2. remove-double-neg 78.4%

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

   3. unsub-neg 78.4%

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

   4. sub-neg 78.4%

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

   5. +-commutative 78.4%

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

   6. distribute-rgt-in 78.4%

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

   7. *-lft-identity 78.4%

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

   8. associate--l+ 90.6%

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

   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 39.1%

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

Developer Target 1: 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 2024146 
(FPCore (x y)
  :name "Graphics.Rendering.Chart.Plot.Vectors:renderPlotVectors from Chart-1.5.3"
  :precision binary64

  :alt
  (! :herbie-platform default (- (* y x) (- y 1)))

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