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

Percentage Accurate: 77.7% → 100.0%

Time: 3.2s

Alternatives: 7

Speedup: 1.3×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 77.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 81.7%

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

   1. +-commutative 81.7%

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

   2. sub-neg 81.7%

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

   3. distribute-rgt-in 81.7%

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

   4. *-lft-identity 81.7%

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

   5. associate-+l+ 81.7%

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

   6. +-commutative 81.7%

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

   7. distribute-lft-neg-out 81.7%

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

   8. sub-neg 81.7%

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

   9. associate--l+ 91.6%

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

   10. associate-+l- 100.0%

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

   11. +-inverses 100.0%

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

   12. metadata-eval 100.0%

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

   13. *-commutative 100.0%

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

3. Simplified 100.0%

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

4. Final simplification 100.0%

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

Alternative 2: 62.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+109}:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq -2.25 \cdot 10^{+46}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq -220000:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{-24}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 3.65 \cdot 10^{-22}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+106} \lor \neg \left(y \leq 4.5 \cdot 10^{+216}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -7.5e+109)
   (- y)
   (if (<= y -2.25e+46)
     (* x y)
     (if (<= y -220000.0)
       (- y)
       (if (<= y -1.25e-24)
         (* x y)
         (if (<= y 3.65e-22)
           1.0
           (if (or (<= y 7.8e+106) (not (<= y 4.5e+216))) (* x y) (- y))))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -7.5e+109) {
		tmp = -y;
	} else if (y <= -2.25e+46) {
		tmp = x * y;
	} else if (y <= -220000.0) {
		tmp = -y;
	} else if (y <= -1.25e-24) {
		tmp = x * y;
	} else if (y <= 3.65e-22) {
		tmp = 1.0;
	} else if ((y <= 7.8e+106) || !(y <= 4.5e+216)) {
		tmp = x * y;
	} else {
		tmp = -y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-7.5d+109)) then
        tmp = -y
    else if (y <= (-2.25d+46)) then
        tmp = x * y
    else if (y <= (-220000.0d0)) then
        tmp = -y
    else if (y <= (-1.25d-24)) then
        tmp = x * y
    else if (y <= 3.65d-22) then
        tmp = 1.0d0
    else if ((y <= 7.8d+106) .or. (.not. (y <= 4.5d+216))) then
        tmp = x * y
    else
        tmp = -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -7.5e+109) {
		tmp = -y;
	} else if (y <= -2.25e+46) {
		tmp = x * y;
	} else if (y <= -220000.0) {
		tmp = -y;
	} else if (y <= -1.25e-24) {
		tmp = x * y;
	} else if (y <= 3.65e-22) {
		tmp = 1.0;
	} else if ((y <= 7.8e+106) || !(y <= 4.5e+216)) {
		tmp = x * y;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -7.5e+109:
		tmp = -y
	elif y <= -2.25e+46:
		tmp = x * y
	elif y <= -220000.0:
		tmp = -y
	elif y <= -1.25e-24:
		tmp = x * y
	elif y <= 3.65e-22:
		tmp = 1.0
	elif (y <= 7.8e+106) or not (y <= 4.5e+216):
		tmp = x * y
	else:
		tmp = -y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -7.5e+109)
		tmp = Float64(-y);
	elseif (y <= -2.25e+46)
		tmp = Float64(x * y);
	elseif (y <= -220000.0)
		tmp = Float64(-y);
	elseif (y <= -1.25e-24)
		tmp = Float64(x * y);
	elseif (y <= 3.65e-22)
		tmp = 1.0;
	elseif ((y <= 7.8e+106) || !(y <= 4.5e+216))
		tmp = Float64(x * y);
	else
		tmp = Float64(-y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -7.5e+109)
		tmp = -y;
	elseif (y <= -2.25e+46)
		tmp = x * y;
	elseif (y <= -220000.0)
		tmp = -y;
	elseif (y <= -1.25e-24)
		tmp = x * y;
	elseif (y <= 3.65e-22)
		tmp = 1.0;
	elseif ((y <= 7.8e+106) || ~((y <= 4.5e+216)))
		tmp = x * y;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -7.5e+109], (-y), If[LessEqual[y, -2.25e+46], N[(x * y), $MachinePrecision], If[LessEqual[y, -220000.0], (-y), If[LessEqual[y, -1.25e-24], N[(x * y), $MachinePrecision], If[LessEqual[y, 3.65e-22], 1.0, If[Or[LessEqual[y, 7.8e+106], N[Not[LessEqual[y, 4.5e+216]], $MachinePrecision]], N[(x * y), $MachinePrecision], (-y)]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.50000000000000018e109 or -2.25000000000000005e46 < y < -2.2e5 or 7.79999999999999937e106 < y < 4.50000000000000025e216

   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. sub-neg 100.0%

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

      3. distribute-rgt-in 100.0%

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

      4. *-lft-identity 100.0%

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

      5. associate-+l+ 100.0%

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

      6. +-commutative 100.0%

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

      7. distribute-lft-neg-out 100.0%

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

      8. sub-neg 100.0%

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

      9. associate--l+ 100.0%

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

      10. associate-+l- 100.0%

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

      11. +-inverses 100.0%

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

      12. metadata-eval 100.0%

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

      13. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 99.1%

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

   5. Taylor expanded in x around 0 63.9%

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

      1. mul-1-neg 63.9%

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

   7. Simplified 63.9%

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

   if -7.50000000000000018e109 < y < -2.25000000000000005e46 or -2.2e5 < y < -1.24999999999999995e-24 or 3.65000000000000014e-22 < y < 7.79999999999999937e106 or 4.50000000000000025e216 < y

   1. Initial program 91.0%

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

      1. +-commutative 91.0%

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

      2. sub-neg 91.0%

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

      3. distribute-rgt-in 91.1%

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

      4. *-lft-identity 91.1%

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

      5. associate-+l+ 91.1%

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

      6. +-commutative 91.1%

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

      7. distribute-lft-neg-out 91.1%

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

      8. sub-neg 91.1%

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

      9. associate--l+ 100.0%

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

      10. associate-+l- 100.0%

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

      11. +-inverses 100.0%

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

      12. metadata-eval 100.0%

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

      13. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 72.2%

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

      1. *-commutative 72.2%

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

   6. Simplified 72.2%

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

   if -1.24999999999999995e-24 < y < 3.65000000000000014e-22

   1. Initial program 63.2%

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

      1. +-commutative 63.2%

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

      2. sub-neg 63.2%

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

      3. distribute-rgt-in 63.2%

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

      4. *-lft-identity 63.2%

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

      5. associate-+l+ 63.2%

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

      6. +-commutative 63.2%

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

      7. distribute-lft-neg-out 63.2%

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

      8. sub-neg 63.2%

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

      9. associate--l+ 80.6%

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

      10. associate-+l- 100.0%

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

      11. +-inverses 100.0%

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

      12. metadata-eval 100.0%

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

      13. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 81.7%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+109}:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq -2.25 \cdot 10^{+46}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq -220000:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{-24}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 3.65 \cdot 10^{-22}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+106} \lor \neg \left(y \leq 4.5 \cdot 10^{+216}\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]

Alternative 3: 98.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{+20} \lor \neg \left(x \leq 1\right):\\ \;\;\;\;1 + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;1 - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -2.6e+20) (not (<= x 1.0))) (+ 1.0 (* x y)) (- 1.0 y)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -2.6e+20) || !(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 <= (-2.6d+20)) .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 <= -2.6e+20) || !(x <= 1.0)) {
		tmp = 1.0 + (x * y);
	} else {
		tmp = 1.0 - y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -2.6e+20) 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 <= -2.6e+20) || !(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 <= -2.6e+20) || ~((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, -2.6e+20], 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 < -2.6e20 or 1 < x

   1. Initial program 60.6%

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

      1. +-commutative 60.6%

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

      2. sub-neg 60.6%

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

      3. distribute-rgt-in 60.6%

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

      4. *-lft-identity 60.6%

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

      5. associate-+l+ 60.6%

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

      6. +-commutative 60.6%

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

      7. distribute-lft-neg-out 60.6%

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

      8. sub-neg 60.6%

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

      9. associate--l+ 82.3%

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

      10. associate-+l- 100.0%

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

      11. +-inverses 100.0%

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

      12. metadata-eval 100.0%

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

      13. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 99.9%

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

      1. mul-1-neg 99.9%

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

      2. distribute-rgt-neg-in 99.9%

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

   6. Simplified 99.9%

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

   if -2.6e20 < x < 1

   1. Initial program 99.3%

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

      1. +-commutative 99.3%

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

      2. sub-neg 99.3%

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

      3. distribute-rgt-in 99.3%

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

      4. *-lft-identity 99.3%

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

      5. associate-+l+ 99.3%

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

      6. +-commutative 99.3%

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

      7. distribute-lft-neg-out 99.3%

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

      8. sub-neg 99.3%

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

      9. associate--l+ 99.3%

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

      10. associate-+l- 100.0%

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

      11. +-inverses 100.0%

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

      12. metadata-eval 100.0%

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

      13. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 98.8%

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

4. Final simplification 99.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{+20} \lor \neg \left(x \leq 1\right):\\ \;\;\;\;1 + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;1 - y\\ \end{array} \]

Alternative 4: 86.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.8 \cdot 10^{+20}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-25}:\\ \;\;\;\;1 - y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -7.8e+20) (* x y) (if (<= x 1.2e-25) (- 1.0 y) (* y (+ x -1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -7.8e+20) {
		tmp = x * y;
	} else if (x <= 1.2e-25) {
		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 <= (-7.8d+20)) then
        tmp = x * y
    else if (x <= 1.2d-25) 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 <= -7.8e+20) {
		tmp = x * y;
	} else if (x <= 1.2e-25) {
		tmp = 1.0 - y;
	} else {
		tmp = y * (x + -1.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -7.8e+20:
		tmp = x * y
	elif x <= 1.2e-25:
		tmp = 1.0 - y
	else:
		tmp = y * (x + -1.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -7.8e+20)
		tmp = Float64(x * y);
	elseif (x <= 1.2e-25)
		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 <= -7.8e+20)
		tmp = x * y;
	elseif (x <= 1.2e-25)
		tmp = 1.0 - y;
	else
		tmp = y * (x + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -7.8e+20], N[(x * y), $MachinePrecision], If[LessEqual[x, 1.2e-25], N[(1.0 - y), $MachinePrecision], N[(y * N[(x + -1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.8e20

   1. Initial program 56.1%

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

      1. +-commutative 56.1%

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

      2. sub-neg 56.1%

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

      3. distribute-rgt-in 56.1%

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

      4. *-lft-identity 56.1%

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

      5. associate-+l+ 56.1%

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

      6. +-commutative 56.1%

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

      7. distribute-lft-neg-out 56.1%

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

      8. sub-neg 56.1%

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

      9. associate--l+ 88.6%

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

      10. associate-+l- 100.0%

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

      11. +-inverses 100.0%

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

      12. metadata-eval 100.0%

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

      13. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 88.6%

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

      1. *-commutative 88.6%

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

   6. Simplified 88.6%

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

   if -7.8e20 < x < 1.20000000000000005e-25

   1. Initial program 99.3%

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

      1. +-commutative 99.3%

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

      2. sub-neg 99.3%

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

      3. distribute-rgt-in 99.3%

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

      4. *-lft-identity 99.3%

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

      5. associate-+l+ 99.3%

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

      6. +-commutative 99.3%

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

      7. distribute-lft-neg-out 99.3%

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

      8. sub-neg 99.3%

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

      9. associate--l+ 99.3%

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

      10. associate-+l- 100.0%

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

      11. +-inverses 100.0%

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

      12. metadata-eval 100.0%

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

      13. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 100.0%

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

   if 1.20000000000000005e-25 < x

   1. Initial program 66.2%

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

      1. +-commutative 66.2%

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

      2. sub-neg 66.2%

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

      3. distribute-rgt-in 66.2%

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

      4. *-lft-identity 66.2%

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

      5. associate-+l+ 66.2%

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

      6. +-commutative 66.2%

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

      7. distribute-lft-neg-out 66.2%

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

      8. sub-neg 66.2%

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

      9. associate--l+ 78.6%

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

      10. associate-+l- 100.0%

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

      11. +-inverses 100.0%

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

      12. metadata-eval 100.0%

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

      13. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 77.3%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.8 \cdot 10^{+20}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-25}:\\ \;\;\;\;1 - y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x + -1\right)\\ \end{array} \]

Alternative 5: 87.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{+20} \lor \neg \left(x \leq 36000000000\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;1 - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -2.6e+20) (not (<= x 36000000000.0))) (* x y) (- 1.0 y)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -2.6e+20) || !(x <= 36000000000.0)) {
		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 <= (-2.6d+20)) .or. (.not. (x <= 36000000000.0d0))) 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 <= -2.6e+20) || !(x <= 36000000000.0)) {
		tmp = x * y;
	} else {
		tmp = 1.0 - y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -2.6e+20) or not (x <= 36000000000.0):
		tmp = x * y
	else:
		tmp = 1.0 - y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -2.6e+20) || !(x <= 36000000000.0))
		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 <= -2.6e+20) || ~((x <= 36000000000.0)))
		tmp = x * y;
	else
		tmp = 1.0 - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -2.6e+20], N[Not[LessEqual[x, 36000000000.0]], $MachinePrecision]], N[(x * y), $MachinePrecision], N[(1.0 - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.6e20 or 3.6e10 < x

   1. Initial program 60.2%

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

      1. +-commutative 60.2%

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

      2. sub-neg 60.2%

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

      3. distribute-rgt-in 60.2%

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

      4. *-lft-identity 60.2%

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

      5. associate-+l+ 60.2%

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

      6. +-commutative 60.2%

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

      7. distribute-lft-neg-out 60.2%

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

      8. sub-neg 60.2%

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

      9. associate--l+ 82.1%

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

      10. associate-+l- 100.0%

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

      11. +-inverses 100.0%

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

      12. metadata-eval 100.0%

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

      13. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 82.0%

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

      1. *-commutative 82.0%

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

   6. Simplified 82.0%

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

   if -2.6e20 < x < 3.6e10

   1. Initial program 99.3%

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

      1. +-commutative 99.3%

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

      2. sub-neg 99.3%

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

      3. distribute-rgt-in 99.3%

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

      4. *-lft-identity 99.3%

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

      5. associate-+l+ 99.3%

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

      6. +-commutative 99.3%

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

      7. distribute-lft-neg-out 99.3%

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

      8. sub-neg 99.3%

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

      9. associate--l+ 99.3%

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

      10. associate-+l- 100.0%

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

      11. +-inverses 100.0%

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

      12. metadata-eval 100.0%

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

      13. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 98.9%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{+20} \lor \neg \left(x \leq 36000000000\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;1 - y\\ \end{array} \]

Alternative 6: 61.2% accurate, 1.5× 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 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. sub-neg 100.0%

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

      3. distribute-rgt-in 100.0%

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

      4. *-lft-identity 100.0%

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

      5. associate-+l+ 100.0%

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

      6. +-commutative 100.0%

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

      7. distribute-lft-neg-out 100.0%

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

      8. sub-neg 100.0%

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

      9. associate--l+ 100.0%

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

      10. associate-+l- 100.0%

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

      11. +-inverses 100.0%

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

      12. metadata-eval 100.0%

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

      13. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 98.8%

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

   5. Taylor expanded in x around 0 49.4%

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

      1. mul-1-neg 49.4%

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

   7. Simplified 49.4%

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

   if -1 < y < 1

   1. Initial program 61.4%

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

      1. +-commutative 61.4%

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

      2. sub-neg 61.4%

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

      3. distribute-rgt-in 61.4%

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

      4. *-lft-identity 61.4%

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

      5. associate-+l+ 61.4%

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

      6. +-commutative 61.4%

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

      7. distribute-lft-neg-out 61.4%

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

      8. sub-neg 61.4%

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

      9. associate--l+ 82.2%

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

      10. associate-+l- 100.0%

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

      11. +-inverses 100.0%

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

      12. metadata-eval 100.0%

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

      13. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 76.9%

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

4. Final simplification 62.4%

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

Alternative 7: 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 81.7%

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

   1. +-commutative 81.7%

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

   2. sub-neg 81.7%

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

   3. distribute-rgt-in 81.7%

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

   4. *-lft-identity 81.7%

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

   5. associate-+l+ 81.7%

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

   6. +-commutative 81.7%

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

   7. distribute-lft-neg-out 81.7%

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

   8. sub-neg 81.7%

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

   9. associate--l+ 91.6%

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

   10. associate-+l- 100.0%

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

   11. +-inverses 100.0%

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

   12. metadata-eval 100.0%

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

   13. *-commutative 100.0%

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

3. Simplified 100.0%

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

4. Taylor expanded in y around 0 37.9%

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

5. Final simplification 37.9%

   \[\leadsto 1 \]

Developer target: 100.0% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023308 
(FPCore (x y)
  :name "Graphics.Rendering.Chart.Plot.Vectors:renderPlotVectors from Chart-1.5.3"
  :precision binary64

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

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