Diagrams.TwoD.Arc:bezierFromSweepQ1 from diagrams-lib-1.3.0.3

Percentage Accurate: 93.9% → 99.8%

Time: 8.4s

Alternatives: 16

Speedup: 1.0×

• 25.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (* (- 1.0 x) (- 3.0 x)) (* y 3.0)))

C

double code(double x, double y) {
	return ((1.0 - x) * (3.0 - x)) / (y * 3.0);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = ((1.0d0 - x) * (3.0d0 - x)) / (y * 3.0d0)
end function

Java

public static double code(double x, double y) {
	return ((1.0 - x) * (3.0 - x)) / (y * 3.0);
}

Python

def code(x, y):
	return ((1.0 - x) * (3.0 - x)) / (y * 3.0)

Julia

function code(x, y)
	return Float64(Float64(Float64(1.0 - x) * Float64(3.0 - x)) / Float64(y * 3.0))
end

MATLAB

function tmp = code(x, y)
	tmp = ((1.0 - x) * (3.0 - x)) / (y * 3.0);
end

Wolfram

code[x_, y_] := N[(N[(N[(1.0 - x), $MachinePrecision] * N[(3.0 - x), $MachinePrecision]), $MachinePrecision] / N[(y * 3.0), $MachinePrecision]), $MachinePrecision]

Initial Program: 93.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (* (- 1.0 x) (- 3.0 x)) (* y 3.0)))

C

double code(double x, double y) {
	return ((1.0 - x) * (3.0 - x)) / (y * 3.0);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = ((1.0d0 - x) * (3.0d0 - x)) / (y * 3.0d0)
end function

Java

public static double code(double x, double y) {
	return ((1.0 - x) * (3.0 - x)) / (y * 3.0);
}

Python

def code(x, y):
	return ((1.0 - x) * (3.0 - x)) / (y * 3.0)

Julia

function code(x, y)
	return Float64(Float64(Float64(1.0 - x) * Float64(3.0 - x)) / Float64(y * 3.0))
end

MATLAB

function tmp = code(x, y)
	tmp = ((1.0 - x) * (3.0 - x)) / (y * 3.0);
end

Wolfram

code[x_, y_] := N[(N[(N[(1.0 - x), $MachinePrecision] * N[(3.0 - x), $MachinePrecision]), $MachinePrecision] / N[(y * 3.0), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{1 - x}{y} \cdot \frac{3 - x}{3} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* (/ (- 1.0 x) y) (/ (- 3.0 x) 3.0)))

C

double code(double x, double y) {
	return ((1.0 - x) / y) * ((3.0 - x) / 3.0);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = ((1.0d0 - x) / y) * ((3.0d0 - x) / 3.0d0)
end function

Java

public static double code(double x, double y) {
	return ((1.0 - x) / y) * ((3.0 - x) / 3.0);
}

Python

def code(x, y):
	return ((1.0 - x) / y) * ((3.0 - x) / 3.0)

Julia

function code(x, y)
	return Float64(Float64(Float64(1.0 - x) / y) * Float64(Float64(3.0 - x) / 3.0))
end

MATLAB

function tmp = code(x, y)
	tmp = ((1.0 - x) / y) * ((3.0 - x) / 3.0);
end

Wolfram

code[x_, y_] := N[(N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision] * N[(N[(3.0 - x), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 93.8%

   \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
2. Step-by-step derivation

   1. times-frac 99.9%

      \[\leadsto \color{blue}{\frac{1 - x}{y} \cdot \frac{3 - x}{3}} \]

3. Simplified 99.9%

   \[\leadsto \color{blue}{\frac{1 - x}{y} \cdot \frac{3 - x}{3}} \]

4. Final simplification 99.9%

   \[\leadsto \frac{1 - x}{y} \cdot \frac{3 - x}{3} \]

Alternative 2: 98.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.8 \lor \neg \left(x \leq 3\right):\\ \;\;\;\;-0.3333333333333333 \cdot \left(x \cdot \frac{1 - x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot -1.3333333333333333 + 1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -3.8) (not (<= x 3.0)))
   (* -0.3333333333333333 (* x (/ (- 1.0 x) y)))
   (/ (+ (* x -1.3333333333333333) 1.0) y)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -3.8) || !(x <= 3.0)) {
		tmp = -0.3333333333333333 * (x * ((1.0 - x) / y));
	} else {
		tmp = ((x * -1.3333333333333333) + 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 <= (-3.8d0)) .or. (.not. (x <= 3.0d0))) then
        tmp = (-0.3333333333333333d0) * (x * ((1.0d0 - x) / y))
    else
        tmp = ((x * (-1.3333333333333333d0)) + 1.0d0) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -3.8) || !(x <= 3.0)) {
		tmp = -0.3333333333333333 * (x * ((1.0 - x) / y));
	} else {
		tmp = ((x * -1.3333333333333333) + 1.0) / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -3.8) or not (x <= 3.0):
		tmp = -0.3333333333333333 * (x * ((1.0 - x) / y))
	else:
		tmp = ((x * -1.3333333333333333) + 1.0) / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -3.8) || !(x <= 3.0))
		tmp = Float64(-0.3333333333333333 * Float64(x * Float64(Float64(1.0 - x) / y)));
	else
		tmp = Float64(Float64(Float64(x * -1.3333333333333333) + 1.0) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -3.8) || ~((x <= 3.0)))
		tmp = -0.3333333333333333 * (x * ((1.0 - x) / y));
	else
		tmp = ((x * -1.3333333333333333) + 1.0) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -3.8], N[Not[LessEqual[x, 3.0]], $MachinePrecision]], N[(-0.3333333333333333 * N[(x * N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * -1.3333333333333333), $MachinePrecision] + 1.0), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.7999999999999998 or 3 < x

   1. Initial program 87.3%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   2. Step-by-step derivation

      1. *-commutative 87.3%

         \[\leadsto \frac{\color{blue}{\left(3 - x\right) \cdot \left(1 - x\right)}}{y \cdot 3} \]

      2. associate-*l/ 99.7%

         \[\leadsto \color{blue}{\frac{3 - x}{y \cdot 3} \cdot \left(1 - x\right)} \]

      3. *-commutative 99.7%

         \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{3 - x}{y \cdot 3}} \]

      4. associate-/l/ 99.7%

         \[\leadsto \left(1 - x\right) \cdot \color{blue}{\frac{\frac{3 - x}{3}}{y}} \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{\frac{x + -3}{-3}}{y}} \]

   4. Taylor expanded in x around inf 98.9%

      \[\leadsto \left(1 - x\right) \cdot \color{blue}{\left(-0.3333333333333333 \cdot \frac{x}{y}\right)} \]
   5. Step-by-step derivation

      1. associate-*r/ 98.8%

         \[\leadsto \left(1 - x\right) \cdot \color{blue}{\frac{-0.3333333333333333 \cdot x}{y}} \]

      2. clear-num 98.8%

         \[\leadsto \left(1 - x\right) \cdot \color{blue}{\frac{1}{\frac{y}{-0.3333333333333333 \cdot x}}} \]

      3. un-div-inv 98.9%

         \[\leadsto \color{blue}{\frac{1 - x}{\frac{y}{-0.3333333333333333 \cdot x}}} \]

      4. *-un-lft-identity 98.9%

         \[\leadsto \frac{1 - x}{\frac{\color{blue}{1 \cdot y}}{-0.3333333333333333 \cdot x}} \]

      5. times-frac 99.0%

         \[\leadsto \frac{1 - x}{\color{blue}{\frac{1}{-0.3333333333333333} \cdot \frac{y}{x}}} \]

      6. metadata-eval 99.0%

         \[\leadsto \frac{1 - x}{\color{blue}{-3} \cdot \frac{y}{x}} \]

   6. Applied egg-rr 99.0%

      \[\leadsto \color{blue}{\frac{1 - x}{-3 \cdot \frac{y}{x}}} \]
   7. Step-by-step derivation

      1. associate-/r* 98.9%

         \[\leadsto \color{blue}{\frac{\frac{1 - x}{-3}}{\frac{y}{x}}} \]

      2. div-sub 98.9%

         \[\leadsto \frac{\color{blue}{\frac{1}{-3} - \frac{x}{-3}}}{\frac{y}{x}} \]

      3. metadata-eval 98.9%

         \[\leadsto \frac{\color{blue}{-0.3333333333333333} - \frac{x}{-3}}{\frac{y}{x}} \]

      4. metadata-eval 98.9%

         \[\leadsto \frac{-0.3333333333333333 - \frac{x}{\color{blue}{\frac{1}{-0.3333333333333333}}}}{\frac{y}{x}} \]

      5. associate-/l* 98.9%

         \[\leadsto \frac{-0.3333333333333333 - \color{blue}{\frac{x \cdot -0.3333333333333333}{1}}}{\frac{y}{x}} \]

      6. /-rgt-identity 98.9%

         \[\leadsto \frac{-0.3333333333333333 - \color{blue}{x \cdot -0.3333333333333333}}{\frac{y}{x}} \]

      7. cancel-sign-sub-inv 98.9%

         \[\leadsto \frac{\color{blue}{-0.3333333333333333 + \left(-x\right) \cdot -0.3333333333333333}}{\frac{y}{x}} \]

      8. metadata-eval 98.9%

         \[\leadsto \frac{\color{blue}{1 \cdot -0.3333333333333333} + \left(-x\right) \cdot -0.3333333333333333}{\frac{y}{x}} \]

      9. distribute-rgt-in 98.9%

         \[\leadsto \frac{\color{blue}{-0.3333333333333333 \cdot \left(1 + \left(-x\right)\right)}}{\frac{y}{x}} \]

      10. sub-neg 98.9%

          \[\leadsto \frac{-0.3333333333333333 \cdot \color{blue}{\left(1 - x\right)}}{\frac{y}{x}} \]

      11. *-commutative 98.9%

          \[\leadsto \frac{\color{blue}{\left(1 - x\right) \cdot -0.3333333333333333}}{\frac{y}{x}} \]

      12. associate-/r/ 98.8%

          \[\leadsto \color{blue}{\frac{\left(1 - x\right) \cdot -0.3333333333333333}{y} \cdot x} \]

      13. *-commutative 98.8%

          \[\leadsto \frac{\color{blue}{-0.3333333333333333 \cdot \left(1 - x\right)}}{y} \cdot x \]

      14. sub-neg 98.8%

          \[\leadsto \frac{-0.3333333333333333 \cdot \color{blue}{\left(1 + \left(-x\right)\right)}}{y} \cdot x \]

      15. distribute-rgt-in 98.8%

          \[\leadsto \frac{\color{blue}{1 \cdot -0.3333333333333333 + \left(-x\right) \cdot -0.3333333333333333}}{y} \cdot x \]

      16. metadata-eval 98.8%

          \[\leadsto \frac{\color{blue}{-0.3333333333333333} + \left(-x\right) \cdot -0.3333333333333333}{y} \cdot x \]

      17. cancel-sign-sub-inv 98.8%

          \[\leadsto \frac{\color{blue}{-0.3333333333333333 - x \cdot -0.3333333333333333}}{y} \cdot x \]

      18. metadata-eval 98.8%

          \[\leadsto \frac{\color{blue}{\frac{1}{-3}} - x \cdot -0.3333333333333333}{y} \cdot x \]

      19. /-rgt-identity 98.8%

          \[\leadsto \frac{\frac{1}{-3} - \color{blue}{\frac{x \cdot -0.3333333333333333}{1}}}{y} \cdot x \]

      20. associate-/l* 98.9%

          \[\leadsto \frac{\frac{1}{-3} - \color{blue}{\frac{x}{\frac{1}{-0.3333333333333333}}}}{y} \cdot x \]

      21. metadata-eval 98.9%

          \[\leadsto \frac{\frac{1}{-3} - \frac{x}{\color{blue}{-3}}}{y} \cdot x \]

      22. div-sub 98.9%

          \[\leadsto \frac{\color{blue}{\frac{1 - x}{-3}}}{y} \cdot x \]

      23. associate-/r* 98.9%

          \[\leadsto \color{blue}{\frac{1 - x}{-3 \cdot y}} \cdot x \]

      24. *-commutative 98.9%

          \[\leadsto \color{blue}{x \cdot \frac{1 - x}{-3 \cdot y}} \]

   8. Simplified 98.9%

      \[\leadsto \color{blue}{x \cdot \frac{1 - x}{y \cdot -3}} \]

   9. Taylor expanded in y around 0 86.4%

      \[\leadsto \color{blue}{-0.3333333333333333 \cdot \frac{x \cdot \left(1 - x\right)}{y}} \]
   10. Step-by-step derivation

       1. associate-*r/ 98.9%

          \[\leadsto -0.3333333333333333 \cdot \color{blue}{\left(x \cdot \frac{1 - x}{y}\right)} \]

   11. Simplified 98.9%

       \[\leadsto \color{blue}{-0.3333333333333333 \cdot \left(x \cdot \frac{1 - x}{y}\right)} \]

   if -3.7999999999999998 < x < 3

   1. Initial program 99.5%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   2. Step-by-step derivation

      1. *-commutative 99.5%

         \[\leadsto \frac{\color{blue}{\left(3 - x\right) \cdot \left(1 - x\right)}}{y \cdot 3} \]

      2. associate-*l/ 99.6%

         \[\leadsto \color{blue}{\frac{3 - x}{y \cdot 3} \cdot \left(1 - x\right)} \]

      3. *-commutative 99.6%

         \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{3 - x}{y \cdot 3}} \]

      4. associate-/l/ 100.0%

         \[\leadsto \left(1 - x\right) \cdot \color{blue}{\frac{\frac{3 - x}{3}}{y}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{\frac{x + -3}{-3}}{y}} \]

   4. Taylor expanded in x around 0 98.4%

      \[\leadsto \color{blue}{-1.3333333333333333 \cdot \frac{x}{y} + \frac{1}{y}} \]

   5. Taylor expanded in y around 0 98.4%

      \[\leadsto \color{blue}{\frac{1 + -1.3333333333333333 \cdot x}{y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.8 \lor \neg \left(x \leq 3\right):\\ \;\;\;\;-0.3333333333333333 \cdot \left(x \cdot \frac{1 - x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot -1.3333333333333333 + 1}{y}\\ \end{array} \]

Alternative 3: 98.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.3 \lor \neg \left(x \leq 1.3\right):\\ \;\;\;\;\frac{x}{y} \cdot \frac{x - 3}{3}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot -1.3333333333333333 + 1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -2.3) (not (<= x 1.3)))
   (* (/ x y) (/ (- x 3.0) 3.0))
   (/ (+ (* x -1.3333333333333333) 1.0) y)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -2.3) || !(x <= 1.3)) {
		tmp = (x / y) * ((x - 3.0) / 3.0);
	} else {
		tmp = ((x * -1.3333333333333333) + 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 <= (-2.3d0)) .or. (.not. (x <= 1.3d0))) then
        tmp = (x / y) * ((x - 3.0d0) / 3.0d0)
    else
        tmp = ((x * (-1.3333333333333333d0)) + 1.0d0) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -2.3) || !(x <= 1.3)) {
		tmp = (x / y) * ((x - 3.0) / 3.0);
	} else {
		tmp = ((x * -1.3333333333333333) + 1.0) / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -2.3) or not (x <= 1.3):
		tmp = (x / y) * ((x - 3.0) / 3.0)
	else:
		tmp = ((x * -1.3333333333333333) + 1.0) / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -2.3) || !(x <= 1.3))
		tmp = Float64(Float64(x / y) * Float64(Float64(x - 3.0) / 3.0));
	else
		tmp = Float64(Float64(Float64(x * -1.3333333333333333) + 1.0) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -2.3) || ~((x <= 1.3)))
		tmp = (x / y) * ((x - 3.0) / 3.0);
	else
		tmp = ((x * -1.3333333333333333) + 1.0) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -2.3], N[Not[LessEqual[x, 1.3]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] * N[(N[(x - 3.0), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * -1.3333333333333333), $MachinePrecision] + 1.0), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.2999999999999998 or 1.30000000000000004 < x

   1. Initial program 87.4%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   2. Step-by-step derivation

      1. times-frac 99.7%

         \[\leadsto \color{blue}{\frac{1 - x}{y} \cdot \frac{3 - x}{3}} \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\frac{1 - x}{y} \cdot \frac{3 - x}{3}} \]

   4. Taylor expanded in x around inf 98.4%

      \[\leadsto \color{blue}{\left(-1 \cdot \frac{x}{y}\right)} \cdot \frac{3 - x}{3} \]
   5. Step-by-step derivation

      1. neg-mul-1 98.1%

         \[\leadsto -0.3333333333333333 \cdot \left(x \cdot \color{blue}{\left(-\frac{x}{y}\right)}\right) \]

      2. distribute-neg-frac 98.1%

         \[\leadsto -0.3333333333333333 \cdot \left(x \cdot \color{blue}{\frac{-x}{y}}\right) \]

   6. Simplified 98.4%

      \[\leadsto \color{blue}{\frac{-x}{y}} \cdot \frac{3 - x}{3} \]

   if -2.2999999999999998 < x < 1.30000000000000004

   1. Initial program 99.5%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   2. Step-by-step derivation

      1. *-commutative 99.5%

         \[\leadsto \frac{\color{blue}{\left(3 - x\right) \cdot \left(1 - x\right)}}{y \cdot 3} \]

      2. associate-*l/ 99.6%

         \[\leadsto \color{blue}{\frac{3 - x}{y \cdot 3} \cdot \left(1 - x\right)} \]

      3. *-commutative 99.6%

         \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{3 - x}{y \cdot 3}} \]

      4. associate-/l/ 100.0%

         \[\leadsto \left(1 - x\right) \cdot \color{blue}{\frac{\frac{3 - x}{3}}{y}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{\frac{x + -3}{-3}}{y}} \]

   4. Taylor expanded in x around 0 99.0%

      \[\leadsto \color{blue}{-1.3333333333333333 \cdot \frac{x}{y} + \frac{1}{y}} \]

   5. Taylor expanded in y around 0 99.0%

      \[\leadsto \color{blue}{\frac{1 + -1.3333333333333333 \cdot x}{y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3 \lor \neg \left(x \leq 1.3\right):\\ \;\;\;\;\frac{x}{y} \cdot \frac{x - 3}{3}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot -1.3333333333333333 + 1}{y}\\ \end{array} \]

Alternative 4: 98.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.8:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{x}{\frac{y}{1 - x}}\\ \mathbf{elif}\;x \leq 3:\\ \;\;\;\;\frac{x \cdot -1.3333333333333333 + 1}{y}\\ \mathbf{else}:\\ \;\;\;\;-0.3333333333333333 \cdot \left(x \cdot \frac{1 - x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -3.8)
   (* -0.3333333333333333 (/ x (/ y (- 1.0 x))))
   (if (<= x 3.0)
     (/ (+ (* x -1.3333333333333333) 1.0) y)
     (* -0.3333333333333333 (* x (/ (- 1.0 x) y))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -3.8) {
		tmp = -0.3333333333333333 * (x / (y / (1.0 - x)));
	} else if (x <= 3.0) {
		tmp = ((x * -1.3333333333333333) + 1.0) / y;
	} else {
		tmp = -0.3333333333333333 * (x * ((1.0 - x) / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-3.8d0)) then
        tmp = (-0.3333333333333333d0) * (x / (y / (1.0d0 - x)))
    else if (x <= 3.0d0) then
        tmp = ((x * (-1.3333333333333333d0)) + 1.0d0) / y
    else
        tmp = (-0.3333333333333333d0) * (x * ((1.0d0 - x) / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -3.8) {
		tmp = -0.3333333333333333 * (x / (y / (1.0 - x)));
	} else if (x <= 3.0) {
		tmp = ((x * -1.3333333333333333) + 1.0) / y;
	} else {
		tmp = -0.3333333333333333 * (x * ((1.0 - x) / y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -3.8:
		tmp = -0.3333333333333333 * (x / (y / (1.0 - x)))
	elif x <= 3.0:
		tmp = ((x * -1.3333333333333333) + 1.0) / y
	else:
		tmp = -0.3333333333333333 * (x * ((1.0 - x) / y))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -3.8)
		tmp = Float64(-0.3333333333333333 * Float64(x / Float64(y / Float64(1.0 - x))));
	elseif (x <= 3.0)
		tmp = Float64(Float64(Float64(x * -1.3333333333333333) + 1.0) / y);
	else
		tmp = Float64(-0.3333333333333333 * Float64(x * Float64(Float64(1.0 - x) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -3.8)
		tmp = -0.3333333333333333 * (x / (y / (1.0 - x)));
	elseif (x <= 3.0)
		tmp = ((x * -1.3333333333333333) + 1.0) / y;
	else
		tmp = -0.3333333333333333 * (x * ((1.0 - x) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -3.8], N[(-0.3333333333333333 * N[(x / N[(y / N[(1.0 - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.0], N[(N[(N[(x * -1.3333333333333333), $MachinePrecision] + 1.0), $MachinePrecision] / y), $MachinePrecision], N[(-0.3333333333333333 * N[(x * N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.7999999999999998

   1. Initial program 87.0%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   2. Step-by-step derivation

      1. *-commutative 87.0%

         \[\leadsto \frac{\color{blue}{\left(3 - x\right) \cdot \left(1 - x\right)}}{y \cdot 3} \]

      2. associate-*l/ 99.8%

         \[\leadsto \color{blue}{\frac{3 - x}{y \cdot 3} \cdot \left(1 - x\right)} \]

      3. *-commutative 99.8%

         \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{3 - x}{y \cdot 3}} \]

      4. associate-/l/ 99.7%

         \[\leadsto \left(1 - x\right) \cdot \color{blue}{\frac{\frac{3 - x}{3}}{y}} \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{\frac{x + -3}{-3}}{y}} \]

   4. Taylor expanded in x around inf 98.6%

      \[\leadsto \left(1 - x\right) \cdot \color{blue}{\left(-0.3333333333333333 \cdot \frac{x}{y}\right)} \]

   5. Taylor expanded in y around 0 85.9%

      \[\leadsto \color{blue}{-0.3333333333333333 \cdot \frac{x \cdot \left(1 - x\right)}{y}} \]
   6. Step-by-step derivation

      1. associate-/l* 98.8%

         \[\leadsto -0.3333333333333333 \cdot \color{blue}{\frac{x}{\frac{y}{1 - x}}} \]

   7. Simplified 98.8%

      \[\leadsto \color{blue}{-0.3333333333333333 \cdot \frac{x}{\frac{y}{1 - x}}} \]

   if -3.7999999999999998 < x < 3

   1. Initial program 99.5%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   2. Step-by-step derivation

      1. *-commutative 99.5%

         \[\leadsto \frac{\color{blue}{\left(3 - x\right) \cdot \left(1 - x\right)}}{y \cdot 3} \]

      2. associate-*l/ 99.6%

         \[\leadsto \color{blue}{\frac{3 - x}{y \cdot 3} \cdot \left(1 - x\right)} \]

      3. *-commutative 99.6%

         \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{3 - x}{y \cdot 3}} \]

      4. associate-/l/ 100.0%

         \[\leadsto \left(1 - x\right) \cdot \color{blue}{\frac{\frac{3 - x}{3}}{y}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{\frac{x + -3}{-3}}{y}} \]

   4. Taylor expanded in x around 0 98.4%

      \[\leadsto \color{blue}{-1.3333333333333333 \cdot \frac{x}{y} + \frac{1}{y}} \]

   5. Taylor expanded in y around 0 98.4%

      \[\leadsto \color{blue}{\frac{1 + -1.3333333333333333 \cdot x}{y}} \]

   if 3 < x

   1. Initial program 87.5%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   2. Step-by-step derivation

      1. *-commutative 87.5%

         \[\leadsto \frac{\color{blue}{\left(3 - x\right) \cdot \left(1 - x\right)}}{y \cdot 3} \]

      2. associate-*l/ 99.6%

         \[\leadsto \color{blue}{\frac{3 - x}{y \cdot 3} \cdot \left(1 - x\right)} \]

      3. *-commutative 99.6%

         \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{3 - x}{y \cdot 3}} \]

      4. associate-/l/ 99.7%

         \[\leadsto \left(1 - x\right) \cdot \color{blue}{\frac{\frac{3 - x}{3}}{y}} \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{\frac{x + -3}{-3}}{y}} \]

   4. Taylor expanded in x around inf 99.1%

      \[\leadsto \left(1 - x\right) \cdot \color{blue}{\left(-0.3333333333333333 \cdot \frac{x}{y}\right)} \]
   5. Step-by-step derivation

      1. associate-*r/ 99.0%

         \[\leadsto \left(1 - x\right) \cdot \color{blue}{\frac{-0.3333333333333333 \cdot x}{y}} \]

      2. clear-num 99.0%

         \[\leadsto \left(1 - x\right) \cdot \color{blue}{\frac{1}{\frac{y}{-0.3333333333333333 \cdot x}}} \]

      3. un-div-inv 99.0%

         \[\leadsto \color{blue}{\frac{1 - x}{\frac{y}{-0.3333333333333333 \cdot x}}} \]

      4. *-un-lft-identity 99.0%

         \[\leadsto \frac{1 - x}{\frac{\color{blue}{1 \cdot y}}{-0.3333333333333333 \cdot x}} \]

      5. times-frac 99.1%

         \[\leadsto \frac{1 - x}{\color{blue}{\frac{1}{-0.3333333333333333} \cdot \frac{y}{x}}} \]

      6. metadata-eval 99.1%

         \[\leadsto \frac{1 - x}{\color{blue}{-3} \cdot \frac{y}{x}} \]

   6. Applied egg-rr 99.1%

      \[\leadsto \color{blue}{\frac{1 - x}{-3 \cdot \frac{y}{x}}} \]
   7. Step-by-step derivation

      1. associate-/r* 99.1%

         \[\leadsto \color{blue}{\frac{\frac{1 - x}{-3}}{\frac{y}{x}}} \]

      2. div-sub 99.1%

         \[\leadsto \frac{\color{blue}{\frac{1}{-3} - \frac{x}{-3}}}{\frac{y}{x}} \]

      3. metadata-eval 99.1%

         \[\leadsto \frac{\color{blue}{-0.3333333333333333} - \frac{x}{-3}}{\frac{y}{x}} \]

      4. metadata-eval 99.1%

         \[\leadsto \frac{-0.3333333333333333 - \frac{x}{\color{blue}{\frac{1}{-0.3333333333333333}}}}{\frac{y}{x}} \]

      5. associate-/l* 99.0%

         \[\leadsto \frac{-0.3333333333333333 - \color{blue}{\frac{x \cdot -0.3333333333333333}{1}}}{\frac{y}{x}} \]

      6. /-rgt-identity 99.0%

         \[\leadsto \frac{-0.3333333333333333 - \color{blue}{x \cdot -0.3333333333333333}}{\frac{y}{x}} \]

      7. cancel-sign-sub-inv 99.0%

         \[\leadsto \frac{\color{blue}{-0.3333333333333333 + \left(-x\right) \cdot -0.3333333333333333}}{\frac{y}{x}} \]

      8. metadata-eval 99.0%

         \[\leadsto \frac{\color{blue}{1 \cdot -0.3333333333333333} + \left(-x\right) \cdot -0.3333333333333333}{\frac{y}{x}} \]

      9. distribute-rgt-in 99.0%

         \[\leadsto \frac{\color{blue}{-0.3333333333333333 \cdot \left(1 + \left(-x\right)\right)}}{\frac{y}{x}} \]

      10. sub-neg 99.0%

          \[\leadsto \frac{-0.3333333333333333 \cdot \color{blue}{\left(1 - x\right)}}{\frac{y}{x}} \]

      11. *-commutative 99.0%

          \[\leadsto \frac{\color{blue}{\left(1 - x\right) \cdot -0.3333333333333333}}{\frac{y}{x}} \]

      12. associate-/r/ 99.0%

          \[\leadsto \color{blue}{\frac{\left(1 - x\right) \cdot -0.3333333333333333}{y} \cdot x} \]

      13. *-commutative 99.0%

          \[\leadsto \frac{\color{blue}{-0.3333333333333333 \cdot \left(1 - x\right)}}{y} \cdot x \]

      14. sub-neg 99.0%

          \[\leadsto \frac{-0.3333333333333333 \cdot \color{blue}{\left(1 + \left(-x\right)\right)}}{y} \cdot x \]

      15. distribute-rgt-in 99.0%

          \[\leadsto \frac{\color{blue}{1 \cdot -0.3333333333333333 + \left(-x\right) \cdot -0.3333333333333333}}{y} \cdot x \]

      16. metadata-eval 99.0%

          \[\leadsto \frac{\color{blue}{-0.3333333333333333} + \left(-x\right) \cdot -0.3333333333333333}{y} \cdot x \]

      17. cancel-sign-sub-inv 99.0%

          \[\leadsto \frac{\color{blue}{-0.3333333333333333 - x \cdot -0.3333333333333333}}{y} \cdot x \]

      18. metadata-eval 99.0%

          \[\leadsto \frac{\color{blue}{\frac{1}{-3}} - x \cdot -0.3333333333333333}{y} \cdot x \]

      19. /-rgt-identity 99.0%

          \[\leadsto \frac{\frac{1}{-3} - \color{blue}{\frac{x \cdot -0.3333333333333333}{1}}}{y} \cdot x \]

      20. associate-/l* 99.1%

          \[\leadsto \frac{\frac{1}{-3} - \color{blue}{\frac{x}{\frac{1}{-0.3333333333333333}}}}{y} \cdot x \]

      21. metadata-eval 99.1%

          \[\leadsto \frac{\frac{1}{-3} - \frac{x}{\color{blue}{-3}}}{y} \cdot x \]

      22. div-sub 99.1%

          \[\leadsto \frac{\color{blue}{\frac{1 - x}{-3}}}{y} \cdot x \]

      23. associate-/r* 99.0%

          \[\leadsto \color{blue}{\frac{1 - x}{-3 \cdot y}} \cdot x \]

      24. *-commutative 99.0%

          \[\leadsto \color{blue}{x \cdot \frac{1 - x}{-3 \cdot y}} \]

   8. Simplified 99.0%

      \[\leadsto \color{blue}{x \cdot \frac{1 - x}{y \cdot -3}} \]

   9. Taylor expanded in y around 0 86.9%

      \[\leadsto \color{blue}{-0.3333333333333333 \cdot \frac{x \cdot \left(1 - x\right)}{y}} \]
   10. Step-by-step derivation

       1. associate-*r/ 99.2%

          \[\leadsto -0.3333333333333333 \cdot \color{blue}{\left(x \cdot \frac{1 - x}{y}\right)} \]

   11. Simplified 99.2%

       \[\leadsto \color{blue}{-0.3333333333333333 \cdot \left(x \cdot \frac{1 - x}{y}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.8:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{x}{\frac{y}{1 - x}}\\ \mathbf{elif}\;x \leq 3:\\ \;\;\;\;\frac{x \cdot -1.3333333333333333 + 1}{y}\\ \mathbf{else}:\\ \;\;\;\;-0.3333333333333333 \cdot \left(x \cdot \frac{1 - x}{y}\right)\\ \end{array} \]

Alternative 5: 98.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.8:\\ \;\;\;\;x \cdot \frac{1 - x}{y \cdot -3}\\ \mathbf{elif}\;x \leq 3:\\ \;\;\;\;\frac{x \cdot -1.3333333333333333 + 1}{y}\\ \mathbf{else}:\\ \;\;\;\;-0.3333333333333333 \cdot \left(x \cdot \frac{1 - x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -3.8)
   (* x (/ (- 1.0 x) (* y -3.0)))
   (if (<= x 3.0)
     (/ (+ (* x -1.3333333333333333) 1.0) y)
     (* -0.3333333333333333 (* x (/ (- 1.0 x) y))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -3.8) {
		tmp = x * ((1.0 - x) / (y * -3.0));
	} else if (x <= 3.0) {
		tmp = ((x * -1.3333333333333333) + 1.0) / y;
	} else {
		tmp = -0.3333333333333333 * (x * ((1.0 - x) / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-3.8d0)) then
        tmp = x * ((1.0d0 - x) / (y * (-3.0d0)))
    else if (x <= 3.0d0) then
        tmp = ((x * (-1.3333333333333333d0)) + 1.0d0) / y
    else
        tmp = (-0.3333333333333333d0) * (x * ((1.0d0 - x) / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -3.8) {
		tmp = x * ((1.0 - x) / (y * -3.0));
	} else if (x <= 3.0) {
		tmp = ((x * -1.3333333333333333) + 1.0) / y;
	} else {
		tmp = -0.3333333333333333 * (x * ((1.0 - x) / y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -3.8:
		tmp = x * ((1.0 - x) / (y * -3.0))
	elif x <= 3.0:
		tmp = ((x * -1.3333333333333333) + 1.0) / y
	else:
		tmp = -0.3333333333333333 * (x * ((1.0 - x) / y))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -3.8)
		tmp = Float64(x * Float64(Float64(1.0 - x) / Float64(y * -3.0)));
	elseif (x <= 3.0)
		tmp = Float64(Float64(Float64(x * -1.3333333333333333) + 1.0) / y);
	else
		tmp = Float64(-0.3333333333333333 * Float64(x * Float64(Float64(1.0 - x) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -3.8)
		tmp = x * ((1.0 - x) / (y * -3.0));
	elseif (x <= 3.0)
		tmp = ((x * -1.3333333333333333) + 1.0) / y;
	else
		tmp = -0.3333333333333333 * (x * ((1.0 - x) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -3.8], N[(x * N[(N[(1.0 - x), $MachinePrecision] / N[(y * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.0], N[(N[(N[(x * -1.3333333333333333), $MachinePrecision] + 1.0), $MachinePrecision] / y), $MachinePrecision], N[(-0.3333333333333333 * N[(x * N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.7999999999999998

   1. Initial program 87.0%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   2. Step-by-step derivation

      1. *-commutative 87.0%

         \[\leadsto \frac{\color{blue}{\left(3 - x\right) \cdot \left(1 - x\right)}}{y \cdot 3} \]

      2. associate-*l/ 99.8%

         \[\leadsto \color{blue}{\frac{3 - x}{y \cdot 3} \cdot \left(1 - x\right)} \]

      3. *-commutative 99.8%

         \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{3 - x}{y \cdot 3}} \]

      4. associate-/l/ 99.7%

         \[\leadsto \left(1 - x\right) \cdot \color{blue}{\frac{\frac{3 - x}{3}}{y}} \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{\frac{x + -3}{-3}}{y}} \]

   4. Taylor expanded in x around inf 98.6%

      \[\leadsto \left(1 - x\right) \cdot \color{blue}{\left(-0.3333333333333333 \cdot \frac{x}{y}\right)} \]
   5. Step-by-step derivation

      1. associate-*r/ 98.6%

         \[\leadsto \left(1 - x\right) \cdot \color{blue}{\frac{-0.3333333333333333 \cdot x}{y}} \]

      2. clear-num 98.7%

         \[\leadsto \left(1 - x\right) \cdot \color{blue}{\frac{1}{\frac{y}{-0.3333333333333333 \cdot x}}} \]

      3. un-div-inv 98.8%

         \[\leadsto \color{blue}{\frac{1 - x}{\frac{y}{-0.3333333333333333 \cdot x}}} \]

      4. *-un-lft-identity 98.8%

         \[\leadsto \frac{1 - x}{\frac{\color{blue}{1 \cdot y}}{-0.3333333333333333 \cdot x}} \]

      5. times-frac 98.9%

         \[\leadsto \frac{1 - x}{\color{blue}{\frac{1}{-0.3333333333333333} \cdot \frac{y}{x}}} \]

      6. metadata-eval 98.9%

         \[\leadsto \frac{1 - x}{\color{blue}{-3} \cdot \frac{y}{x}} \]

   6. Applied egg-rr 98.9%

      \[\leadsto \color{blue}{\frac{1 - x}{-3 \cdot \frac{y}{x}}} \]
   7. Step-by-step derivation

      1. associate-/r* 98.8%

         \[\leadsto \color{blue}{\frac{\frac{1 - x}{-3}}{\frac{y}{x}}} \]

      2. div-sub 98.8%

         \[\leadsto \frac{\color{blue}{\frac{1}{-3} - \frac{x}{-3}}}{\frac{y}{x}} \]

      3. metadata-eval 98.8%

         \[\leadsto \frac{\color{blue}{-0.3333333333333333} - \frac{x}{-3}}{\frac{y}{x}} \]

      4. metadata-eval 98.8%

         \[\leadsto \frac{-0.3333333333333333 - \frac{x}{\color{blue}{\frac{1}{-0.3333333333333333}}}}{\frac{y}{x}} \]

      5. associate-/l* 98.7%

         \[\leadsto \frac{-0.3333333333333333 - \color{blue}{\frac{x \cdot -0.3333333333333333}{1}}}{\frac{y}{x}} \]

      6. /-rgt-identity 98.7%

         \[\leadsto \frac{-0.3333333333333333 - \color{blue}{x \cdot -0.3333333333333333}}{\frac{y}{x}} \]

      7. cancel-sign-sub-inv 98.7%

         \[\leadsto \frac{\color{blue}{-0.3333333333333333 + \left(-x\right) \cdot -0.3333333333333333}}{\frac{y}{x}} \]

      8. metadata-eval 98.7%

         \[\leadsto \frac{\color{blue}{1 \cdot -0.3333333333333333} + \left(-x\right) \cdot -0.3333333333333333}{\frac{y}{x}} \]

      9. distribute-rgt-in 98.7%

         \[\leadsto \frac{\color{blue}{-0.3333333333333333 \cdot \left(1 + \left(-x\right)\right)}}{\frac{y}{x}} \]

      10. sub-neg 98.7%

          \[\leadsto \frac{-0.3333333333333333 \cdot \color{blue}{\left(1 - x\right)}}{\frac{y}{x}} \]

      11. *-commutative 98.7%

          \[\leadsto \frac{\color{blue}{\left(1 - x\right) \cdot -0.3333333333333333}}{\frac{y}{x}} \]

      12. associate-/r/ 98.6%

          \[\leadsto \color{blue}{\frac{\left(1 - x\right) \cdot -0.3333333333333333}{y} \cdot x} \]

      13. *-commutative 98.6%

          \[\leadsto \frac{\color{blue}{-0.3333333333333333 \cdot \left(1 - x\right)}}{y} \cdot x \]

      14. sub-neg 98.6%

          \[\leadsto \frac{-0.3333333333333333 \cdot \color{blue}{\left(1 + \left(-x\right)\right)}}{y} \cdot x \]

      15. distribute-rgt-in 98.6%

          \[\leadsto \frac{\color{blue}{1 \cdot -0.3333333333333333 + \left(-x\right) \cdot -0.3333333333333333}}{y} \cdot x \]

      16. metadata-eval 98.6%

          \[\leadsto \frac{\color{blue}{-0.3333333333333333} + \left(-x\right) \cdot -0.3333333333333333}{y} \cdot x \]

      17. cancel-sign-sub-inv 98.6%

          \[\leadsto \frac{\color{blue}{-0.3333333333333333 - x \cdot -0.3333333333333333}}{y} \cdot x \]

      18. metadata-eval 98.6%

          \[\leadsto \frac{\color{blue}{\frac{1}{-3}} - x \cdot -0.3333333333333333}{y} \cdot x \]

      19. /-rgt-identity 98.6%

          \[\leadsto \frac{\frac{1}{-3} - \color{blue}{\frac{x \cdot -0.3333333333333333}{1}}}{y} \cdot x \]

      20. associate-/l* 98.8%

          \[\leadsto \frac{\frac{1}{-3} - \color{blue}{\frac{x}{\frac{1}{-0.3333333333333333}}}}{y} \cdot x \]

      21. metadata-eval 98.8%

          \[\leadsto \frac{\frac{1}{-3} - \frac{x}{\color{blue}{-3}}}{y} \cdot x \]

      22. div-sub 98.8%

          \[\leadsto \frac{\color{blue}{\frac{1 - x}{-3}}}{y} \cdot x \]

      23. associate-/r* 98.9%

          \[\leadsto \color{blue}{\frac{1 - x}{-3 \cdot y}} \cdot x \]

      24. *-commutative 98.9%

          \[\leadsto \color{blue}{x \cdot \frac{1 - x}{-3 \cdot y}} \]

   8. Simplified 98.9%

      \[\leadsto \color{blue}{x \cdot \frac{1 - x}{y \cdot -3}} \]

   if -3.7999999999999998 < x < 3

   1. Initial program 99.5%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   2. Step-by-step derivation

      1. *-commutative 99.5%

         \[\leadsto \frac{\color{blue}{\left(3 - x\right) \cdot \left(1 - x\right)}}{y \cdot 3} \]

      2. associate-*l/ 99.6%

         \[\leadsto \color{blue}{\frac{3 - x}{y \cdot 3} \cdot \left(1 - x\right)} \]

      3. *-commutative 99.6%

         \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{3 - x}{y \cdot 3}} \]

      4. associate-/l/ 100.0%

         \[\leadsto \left(1 - x\right) \cdot \color{blue}{\frac{\frac{3 - x}{3}}{y}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{\frac{x + -3}{-3}}{y}} \]

   4. Taylor expanded in x around 0 98.4%

      \[\leadsto \color{blue}{-1.3333333333333333 \cdot \frac{x}{y} + \frac{1}{y}} \]

   5. Taylor expanded in y around 0 98.4%

      \[\leadsto \color{blue}{\frac{1 + -1.3333333333333333 \cdot x}{y}} \]

   if 3 < x

   1. Initial program 87.5%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   2. Step-by-step derivation

      1. *-commutative 87.5%

         \[\leadsto \frac{\color{blue}{\left(3 - x\right) \cdot \left(1 - x\right)}}{y \cdot 3} \]

      2. associate-*l/ 99.6%

         \[\leadsto \color{blue}{\frac{3 - x}{y \cdot 3} \cdot \left(1 - x\right)} \]

      3. *-commutative 99.6%

         \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{3 - x}{y \cdot 3}} \]

      4. associate-/l/ 99.7%

         \[\leadsto \left(1 - x\right) \cdot \color{blue}{\frac{\frac{3 - x}{3}}{y}} \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{\frac{x + -3}{-3}}{y}} \]

   4. Taylor expanded in x around inf 99.1%

      \[\leadsto \left(1 - x\right) \cdot \color{blue}{\left(-0.3333333333333333 \cdot \frac{x}{y}\right)} \]
   5. Step-by-step derivation

      1. associate-*r/ 99.0%

         \[\leadsto \left(1 - x\right) \cdot \color{blue}{\frac{-0.3333333333333333 \cdot x}{y}} \]

      2. clear-num 99.0%

         \[\leadsto \left(1 - x\right) \cdot \color{blue}{\frac{1}{\frac{y}{-0.3333333333333333 \cdot x}}} \]

      3. un-div-inv 99.0%

         \[\leadsto \color{blue}{\frac{1 - x}{\frac{y}{-0.3333333333333333 \cdot x}}} \]

      4. *-un-lft-identity 99.0%

         \[\leadsto \frac{1 - x}{\frac{\color{blue}{1 \cdot y}}{-0.3333333333333333 \cdot x}} \]

      5. times-frac 99.1%

         \[\leadsto \frac{1 - x}{\color{blue}{\frac{1}{-0.3333333333333333} \cdot \frac{y}{x}}} \]

      6. metadata-eval 99.1%

         \[\leadsto \frac{1 - x}{\color{blue}{-3} \cdot \frac{y}{x}} \]

   6. Applied egg-rr 99.1%

      \[\leadsto \color{blue}{\frac{1 - x}{-3 \cdot \frac{y}{x}}} \]
   7. Step-by-step derivation

      1. associate-/r* 99.1%

         \[\leadsto \color{blue}{\frac{\frac{1 - x}{-3}}{\frac{y}{x}}} \]

      2. div-sub 99.1%

         \[\leadsto \frac{\color{blue}{\frac{1}{-3} - \frac{x}{-3}}}{\frac{y}{x}} \]

      3. metadata-eval 99.1%

         \[\leadsto \frac{\color{blue}{-0.3333333333333333} - \frac{x}{-3}}{\frac{y}{x}} \]

      4. metadata-eval 99.1%

         \[\leadsto \frac{-0.3333333333333333 - \frac{x}{\color{blue}{\frac{1}{-0.3333333333333333}}}}{\frac{y}{x}} \]

      5. associate-/l* 99.0%

         \[\leadsto \frac{-0.3333333333333333 - \color{blue}{\frac{x \cdot -0.3333333333333333}{1}}}{\frac{y}{x}} \]

      6. /-rgt-identity 99.0%

         \[\leadsto \frac{-0.3333333333333333 - \color{blue}{x \cdot -0.3333333333333333}}{\frac{y}{x}} \]

      7. cancel-sign-sub-inv 99.0%

         \[\leadsto \frac{\color{blue}{-0.3333333333333333 + \left(-x\right) \cdot -0.3333333333333333}}{\frac{y}{x}} \]

      8. metadata-eval 99.0%

         \[\leadsto \frac{\color{blue}{1 \cdot -0.3333333333333333} + \left(-x\right) \cdot -0.3333333333333333}{\frac{y}{x}} \]

      9. distribute-rgt-in 99.0%

         \[\leadsto \frac{\color{blue}{-0.3333333333333333 \cdot \left(1 + \left(-x\right)\right)}}{\frac{y}{x}} \]

      10. sub-neg 99.0%

          \[\leadsto \frac{-0.3333333333333333 \cdot \color{blue}{\left(1 - x\right)}}{\frac{y}{x}} \]

      11. *-commutative 99.0%

          \[\leadsto \frac{\color{blue}{\left(1 - x\right) \cdot -0.3333333333333333}}{\frac{y}{x}} \]

      12. associate-/r/ 99.0%

          \[\leadsto \color{blue}{\frac{\left(1 - x\right) \cdot -0.3333333333333333}{y} \cdot x} \]

      13. *-commutative 99.0%

          \[\leadsto \frac{\color{blue}{-0.3333333333333333 \cdot \left(1 - x\right)}}{y} \cdot x \]

      14. sub-neg 99.0%

          \[\leadsto \frac{-0.3333333333333333 \cdot \color{blue}{\left(1 + \left(-x\right)\right)}}{y} \cdot x \]

      15. distribute-rgt-in 99.0%

          \[\leadsto \frac{\color{blue}{1 \cdot -0.3333333333333333 + \left(-x\right) \cdot -0.3333333333333333}}{y} \cdot x \]

      16. metadata-eval 99.0%

          \[\leadsto \frac{\color{blue}{-0.3333333333333333} + \left(-x\right) \cdot -0.3333333333333333}{y} \cdot x \]

      17. cancel-sign-sub-inv 99.0%

          \[\leadsto \frac{\color{blue}{-0.3333333333333333 - x \cdot -0.3333333333333333}}{y} \cdot x \]

      18. metadata-eval 99.0%

          \[\leadsto \frac{\color{blue}{\frac{1}{-3}} - x \cdot -0.3333333333333333}{y} \cdot x \]

      19. /-rgt-identity 99.0%

          \[\leadsto \frac{\frac{1}{-3} - \color{blue}{\frac{x \cdot -0.3333333333333333}{1}}}{y} \cdot x \]

      20. associate-/l* 99.1%

          \[\leadsto \frac{\frac{1}{-3} - \color{blue}{\frac{x}{\frac{1}{-0.3333333333333333}}}}{y} \cdot x \]

      21. metadata-eval 99.1%

          \[\leadsto \frac{\frac{1}{-3} - \frac{x}{\color{blue}{-3}}}{y} \cdot x \]

      22. div-sub 99.1%

          \[\leadsto \frac{\color{blue}{\frac{1 - x}{-3}}}{y} \cdot x \]

      23. associate-/r* 99.0%

          \[\leadsto \color{blue}{\frac{1 - x}{-3 \cdot y}} \cdot x \]

      24. *-commutative 99.0%

          \[\leadsto \color{blue}{x \cdot \frac{1 - x}{-3 \cdot y}} \]

   8. Simplified 99.0%

      \[\leadsto \color{blue}{x \cdot \frac{1 - x}{y \cdot -3}} \]

   9. Taylor expanded in y around 0 86.9%

      \[\leadsto \color{blue}{-0.3333333333333333 \cdot \frac{x \cdot \left(1 - x\right)}{y}} \]
   10. Step-by-step derivation

       1. associate-*r/ 99.2%

          \[\leadsto -0.3333333333333333 \cdot \color{blue}{\left(x \cdot \frac{1 - x}{y}\right)} \]

   11. Simplified 99.2%

       \[\leadsto \color{blue}{-0.3333333333333333 \cdot \left(x \cdot \frac{1 - x}{y}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.8:\\ \;\;\;\;x \cdot \frac{1 - x}{y \cdot -3}\\ \mathbf{elif}\;x \leq 3:\\ \;\;\;\;\frac{x \cdot -1.3333333333333333 + 1}{y}\\ \mathbf{else}:\\ \;\;\;\;-0.3333333333333333 \cdot \left(x \cdot \frac{1 - x}{y}\right)\\ \end{array} \]

Alternative 6: 98.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.8:\\ \;\;\;\;x \cdot \frac{1 - x}{y \cdot -3}\\ \mathbf{elif}\;x \leq 3:\\ \;\;\;\;\frac{x \cdot -1.3333333333333333 + 1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1 - x}{y}}{\frac{-3}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -3.8)
   (* x (/ (- 1.0 x) (* y -3.0)))
   (if (<= x 3.0)
     (/ (+ (* x -1.3333333333333333) 1.0) y)
     (/ (/ (- 1.0 x) y) (/ -3.0 x)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -3.8) {
		tmp = x * ((1.0 - x) / (y * -3.0));
	} else if (x <= 3.0) {
		tmp = ((x * -1.3333333333333333) + 1.0) / y;
	} else {
		tmp = ((1.0 - x) / y) / (-3.0 / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-3.8d0)) then
        tmp = x * ((1.0d0 - x) / (y * (-3.0d0)))
    else if (x <= 3.0d0) then
        tmp = ((x * (-1.3333333333333333d0)) + 1.0d0) / y
    else
        tmp = ((1.0d0 - x) / y) / ((-3.0d0) / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -3.8) {
		tmp = x * ((1.0 - x) / (y * -3.0));
	} else if (x <= 3.0) {
		tmp = ((x * -1.3333333333333333) + 1.0) / y;
	} else {
		tmp = ((1.0 - x) / y) / (-3.0 / x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -3.8:
		tmp = x * ((1.0 - x) / (y * -3.0))
	elif x <= 3.0:
		tmp = ((x * -1.3333333333333333) + 1.0) / y
	else:
		tmp = ((1.0 - x) / y) / (-3.0 / x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -3.8)
		tmp = Float64(x * Float64(Float64(1.0 - x) / Float64(y * -3.0)));
	elseif (x <= 3.0)
		tmp = Float64(Float64(Float64(x * -1.3333333333333333) + 1.0) / y);
	else
		tmp = Float64(Float64(Float64(1.0 - x) / y) / Float64(-3.0 / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -3.8)
		tmp = x * ((1.0 - x) / (y * -3.0));
	elseif (x <= 3.0)
		tmp = ((x * -1.3333333333333333) + 1.0) / y;
	else
		tmp = ((1.0 - x) / y) / (-3.0 / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -3.8], N[(x * N[(N[(1.0 - x), $MachinePrecision] / N[(y * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.0], N[(N[(N[(x * -1.3333333333333333), $MachinePrecision] + 1.0), $MachinePrecision] / y), $MachinePrecision], N[(N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision] / N[(-3.0 / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.7999999999999998

   1. Initial program 87.0%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   2. Step-by-step derivation

      1. *-commutative 87.0%

         \[\leadsto \frac{\color{blue}{\left(3 - x\right) \cdot \left(1 - x\right)}}{y \cdot 3} \]

      2. associate-*l/ 99.8%

         \[\leadsto \color{blue}{\frac{3 - x}{y \cdot 3} \cdot \left(1 - x\right)} \]

      3. *-commutative 99.8%

         \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{3 - x}{y \cdot 3}} \]

      4. associate-/l/ 99.7%

         \[\leadsto \left(1 - x\right) \cdot \color{blue}{\frac{\frac{3 - x}{3}}{y}} \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{\frac{x + -3}{-3}}{y}} \]

   4. Taylor expanded in x around inf 98.6%

      \[\leadsto \left(1 - x\right) \cdot \color{blue}{\left(-0.3333333333333333 \cdot \frac{x}{y}\right)} \]
   5. Step-by-step derivation

      1. associate-*r/ 98.6%

         \[\leadsto \left(1 - x\right) \cdot \color{blue}{\frac{-0.3333333333333333 \cdot x}{y}} \]

      2. clear-num 98.7%

         \[\leadsto \left(1 - x\right) \cdot \color{blue}{\frac{1}{\frac{y}{-0.3333333333333333 \cdot x}}} \]

      3. un-div-inv 98.8%

         \[\leadsto \color{blue}{\frac{1 - x}{\frac{y}{-0.3333333333333333 \cdot x}}} \]

      4. *-un-lft-identity 98.8%

         \[\leadsto \frac{1 - x}{\frac{\color{blue}{1 \cdot y}}{-0.3333333333333333 \cdot x}} \]

      5. times-frac 98.9%

         \[\leadsto \frac{1 - x}{\color{blue}{\frac{1}{-0.3333333333333333} \cdot \frac{y}{x}}} \]

      6. metadata-eval 98.9%

         \[\leadsto \frac{1 - x}{\color{blue}{-3} \cdot \frac{y}{x}} \]

   6. Applied egg-rr 98.9%

      \[\leadsto \color{blue}{\frac{1 - x}{-3 \cdot \frac{y}{x}}} \]
   7. Step-by-step derivation

      1. associate-/r* 98.8%

         \[\leadsto \color{blue}{\frac{\frac{1 - x}{-3}}{\frac{y}{x}}} \]

      2. div-sub 98.8%

         \[\leadsto \frac{\color{blue}{\frac{1}{-3} - \frac{x}{-3}}}{\frac{y}{x}} \]

      3. metadata-eval 98.8%

         \[\leadsto \frac{\color{blue}{-0.3333333333333333} - \frac{x}{-3}}{\frac{y}{x}} \]

      4. metadata-eval 98.8%

         \[\leadsto \frac{-0.3333333333333333 - \frac{x}{\color{blue}{\frac{1}{-0.3333333333333333}}}}{\frac{y}{x}} \]

      5. associate-/l* 98.7%

         \[\leadsto \frac{-0.3333333333333333 - \color{blue}{\frac{x \cdot -0.3333333333333333}{1}}}{\frac{y}{x}} \]

      6. /-rgt-identity 98.7%

         \[\leadsto \frac{-0.3333333333333333 - \color{blue}{x \cdot -0.3333333333333333}}{\frac{y}{x}} \]

      7. cancel-sign-sub-inv 98.7%

         \[\leadsto \frac{\color{blue}{-0.3333333333333333 + \left(-x\right) \cdot -0.3333333333333333}}{\frac{y}{x}} \]

      8. metadata-eval 98.7%

         \[\leadsto \frac{\color{blue}{1 \cdot -0.3333333333333333} + \left(-x\right) \cdot -0.3333333333333333}{\frac{y}{x}} \]

      9. distribute-rgt-in 98.7%

         \[\leadsto \frac{\color{blue}{-0.3333333333333333 \cdot \left(1 + \left(-x\right)\right)}}{\frac{y}{x}} \]

      10. sub-neg 98.7%

          \[\leadsto \frac{-0.3333333333333333 \cdot \color{blue}{\left(1 - x\right)}}{\frac{y}{x}} \]

      11. *-commutative 98.7%

          \[\leadsto \frac{\color{blue}{\left(1 - x\right) \cdot -0.3333333333333333}}{\frac{y}{x}} \]

      12. associate-/r/ 98.6%

          \[\leadsto \color{blue}{\frac{\left(1 - x\right) \cdot -0.3333333333333333}{y} \cdot x} \]

      13. *-commutative 98.6%

          \[\leadsto \frac{\color{blue}{-0.3333333333333333 \cdot \left(1 - x\right)}}{y} \cdot x \]

      14. sub-neg 98.6%

          \[\leadsto \frac{-0.3333333333333333 \cdot \color{blue}{\left(1 + \left(-x\right)\right)}}{y} \cdot x \]

      15. distribute-rgt-in 98.6%

          \[\leadsto \frac{\color{blue}{1 \cdot -0.3333333333333333 + \left(-x\right) \cdot -0.3333333333333333}}{y} \cdot x \]

      16. metadata-eval 98.6%

          \[\leadsto \frac{\color{blue}{-0.3333333333333333} + \left(-x\right) \cdot -0.3333333333333333}{y} \cdot x \]

      17. cancel-sign-sub-inv 98.6%

          \[\leadsto \frac{\color{blue}{-0.3333333333333333 - x \cdot -0.3333333333333333}}{y} \cdot x \]

      18. metadata-eval 98.6%

          \[\leadsto \frac{\color{blue}{\frac{1}{-3}} - x \cdot -0.3333333333333333}{y} \cdot x \]

      19. /-rgt-identity 98.6%

          \[\leadsto \frac{\frac{1}{-3} - \color{blue}{\frac{x \cdot -0.3333333333333333}{1}}}{y} \cdot x \]

      20. associate-/l* 98.8%

          \[\leadsto \frac{\frac{1}{-3} - \color{blue}{\frac{x}{\frac{1}{-0.3333333333333333}}}}{y} \cdot x \]

      21. metadata-eval 98.8%

          \[\leadsto \frac{\frac{1}{-3} - \frac{x}{\color{blue}{-3}}}{y} \cdot x \]

      22. div-sub 98.8%

          \[\leadsto \frac{\color{blue}{\frac{1 - x}{-3}}}{y} \cdot x \]

      23. associate-/r* 98.9%

          \[\leadsto \color{blue}{\frac{1 - x}{-3 \cdot y}} \cdot x \]

      24. *-commutative 98.9%

          \[\leadsto \color{blue}{x \cdot \frac{1 - x}{-3 \cdot y}} \]

   8. Simplified 98.9%

      \[\leadsto \color{blue}{x \cdot \frac{1 - x}{y \cdot -3}} \]

   if -3.7999999999999998 < x < 3

   1. Initial program 99.5%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   2. Step-by-step derivation

      1. *-commutative 99.5%

         \[\leadsto \frac{\color{blue}{\left(3 - x\right) \cdot \left(1 - x\right)}}{y \cdot 3} \]

      2. associate-*l/ 99.6%

         \[\leadsto \color{blue}{\frac{3 - x}{y \cdot 3} \cdot \left(1 - x\right)} \]

      3. *-commutative 99.6%

         \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{3 - x}{y \cdot 3}} \]

      4. associate-/l/ 100.0%

         \[\leadsto \left(1 - x\right) \cdot \color{blue}{\frac{\frac{3 - x}{3}}{y}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{\frac{x + -3}{-3}}{y}} \]

   4. Taylor expanded in x around 0 98.4%

      \[\leadsto \color{blue}{-1.3333333333333333 \cdot \frac{x}{y} + \frac{1}{y}} \]

   5. Taylor expanded in y around 0 98.4%

      \[\leadsto \color{blue}{\frac{1 + -1.3333333333333333 \cdot x}{y}} \]

   if 3 < x

   1. Initial program 87.5%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   2. Step-by-step derivation

      1. *-commutative 87.5%

         \[\leadsto \frac{\color{blue}{\left(3 - x\right) \cdot \left(1 - x\right)}}{y \cdot 3} \]

      2. associate-*l/ 99.6%

         \[\leadsto \color{blue}{\frac{3 - x}{y \cdot 3} \cdot \left(1 - x\right)} \]

      3. *-commutative 99.6%

         \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{3 - x}{y \cdot 3}} \]

      4. associate-/l/ 99.7%

         \[\leadsto \left(1 - x\right) \cdot \color{blue}{\frac{\frac{3 - x}{3}}{y}} \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{\frac{x + -3}{-3}}{y}} \]
   4. Step-by-step derivation

      1. associate-*r/ 87.6%

         \[\leadsto \color{blue}{\frac{\left(1 - x\right) \cdot \frac{x + -3}{-3}}{y}} \]

      2. *-commutative 87.6%

         \[\leadsto \frac{\color{blue}{\frac{x + -3}{-3} \cdot \left(1 - x\right)}}{y} \]

      3. frac-2neg 87.6%

         \[\leadsto \frac{\color{blue}{\frac{-\left(x + -3\right)}{--3}} \cdot \left(1 - x\right)}{y} \]

      4. +-commutative 87.6%

         \[\leadsto \frac{\frac{-\color{blue}{\left(-3 + x\right)}}{--3} \cdot \left(1 - x\right)}{y} \]

      5. distribute-neg-in 87.6%

         \[\leadsto \frac{\frac{\color{blue}{\left(--3\right) + \left(-x\right)}}{--3} \cdot \left(1 - x\right)}{y} \]

      6. metadata-eval 87.6%

         \[\leadsto \frac{\frac{\color{blue}{3} + \left(-x\right)}{--3} \cdot \left(1 - x\right)}{y} \]

      7. sub-neg 87.6%

         \[\leadsto \frac{\frac{\color{blue}{3 - x}}{--3} \cdot \left(1 - x\right)}{y} \]

      8. metadata-eval 87.6%

         \[\leadsto \frac{\frac{3 - x}{\color{blue}{3}} \cdot \left(1 - x\right)}{y} \]

      9. associate-*r/ 99.7%

         \[\leadsto \color{blue}{\frac{3 - x}{3} \cdot \frac{1 - x}{y}} \]

      10. clear-num 99.7%

          \[\leadsto \color{blue}{\frac{1}{\frac{3}{3 - x}}} \cdot \frac{1 - x}{y} \]

      11. associate-*l/ 99.7%

          \[\leadsto \color{blue}{\frac{1 \cdot \frac{1 - x}{y}}{\frac{3}{3 - x}}} \]

      12. *-un-lft-identity 99.7%

          \[\leadsto \frac{\color{blue}{\frac{1 - x}{y}}}{\frac{3}{3 - x}} \]

      13. metadata-eval 99.7%

          \[\leadsto \frac{\frac{1 - x}{y}}{\frac{\color{blue}{--3}}{3 - x}} \]

      14. sub-neg 99.7%

          \[\leadsto \frac{\frac{1 - x}{y}}{\frac{--3}{\color{blue}{3 + \left(-x\right)}}} \]

      15. metadata-eval 99.7%

          \[\leadsto \frac{\frac{1 - x}{y}}{\frac{--3}{\color{blue}{\left(--3\right)} + \left(-x\right)}} \]

      16. distribute-neg-in 99.7%

          \[\leadsto \frac{\frac{1 - x}{y}}{\frac{--3}{\color{blue}{-\left(-3 + x\right)}}} \]

      17. +-commutative 99.7%

          \[\leadsto \frac{\frac{1 - x}{y}}{\frac{--3}{-\color{blue}{\left(x + -3\right)}}} \]

      18. frac-2neg 99.7%

          \[\leadsto \frac{\frac{1 - x}{y}}{\color{blue}{\frac{-3}{x + -3}}} \]

   5. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\frac{\frac{1 - x}{y}}{\frac{-3}{x + -3}}} \]

   6. Taylor expanded in x around inf 99.2%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.8:\\ \;\;\;\;x \cdot \frac{1 - x}{y \cdot -3}\\ \mathbf{elif}\;x \leq 3:\\ \;\;\;\;\frac{x \cdot -1.3333333333333333 + 1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1 - x}{y}}{\frac{-3}{x}}\\ \end{array} \]

Alternative 7: 98.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.6 \lor \neg \left(x \leq 3\right):\\ \;\;\;\;-0.3333333333333333 \cdot \left(x \cdot \frac{-x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot -1.3333333333333333 + 1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -4.6) (not (<= x 3.0)))
   (* -0.3333333333333333 (* x (/ (- x) y)))
   (/ (+ (* x -1.3333333333333333) 1.0) y)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -4.6) || !(x <= 3.0)) {
		tmp = -0.3333333333333333 * (x * (-x / y));
	} else {
		tmp = ((x * -1.3333333333333333) + 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 <= (-4.6d0)) .or. (.not. (x <= 3.0d0))) then
        tmp = (-0.3333333333333333d0) * (x * (-x / y))
    else
        tmp = ((x * (-1.3333333333333333d0)) + 1.0d0) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -4.6) || !(x <= 3.0)) {
		tmp = -0.3333333333333333 * (x * (-x / y));
	} else {
		tmp = ((x * -1.3333333333333333) + 1.0) / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -4.6) or not (x <= 3.0):
		tmp = -0.3333333333333333 * (x * (-x / y))
	else:
		tmp = ((x * -1.3333333333333333) + 1.0) / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -4.6) || !(x <= 3.0))
		tmp = Float64(-0.3333333333333333 * Float64(x * Float64(Float64(-x) / y)));
	else
		tmp = Float64(Float64(Float64(x * -1.3333333333333333) + 1.0) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -4.6) || ~((x <= 3.0)))
		tmp = -0.3333333333333333 * (x * (-x / y));
	else
		tmp = ((x * -1.3333333333333333) + 1.0) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -4.6], N[Not[LessEqual[x, 3.0]], $MachinePrecision]], N[(-0.3333333333333333 * N[(x * N[((-x) / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * -1.3333333333333333), $MachinePrecision] + 1.0), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.5999999999999996 or 3 < x

   1. Initial program 87.3%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   2. Step-by-step derivation

      1. *-commutative 87.3%

         \[\leadsto \frac{\color{blue}{\left(3 - x\right) \cdot \left(1 - x\right)}}{y \cdot 3} \]

      2. associate-*l/ 99.7%

         \[\leadsto \color{blue}{\frac{3 - x}{y \cdot 3} \cdot \left(1 - x\right)} \]

      3. *-commutative 99.7%

         \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{3 - x}{y \cdot 3}} \]

      4. associate-/l/ 99.7%

         \[\leadsto \left(1 - x\right) \cdot \color{blue}{\frac{\frac{3 - x}{3}}{y}} \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{\frac{x + -3}{-3}}{y}} \]

   4. Taylor expanded in x around inf 98.9%

      \[\leadsto \left(1 - x\right) \cdot \color{blue}{\left(-0.3333333333333333 \cdot \frac{x}{y}\right)} \]
   5. Step-by-step derivation

      1. associate-*r/ 98.8%

         \[\leadsto \left(1 - x\right) \cdot \color{blue}{\frac{-0.3333333333333333 \cdot x}{y}} \]

      2. clear-num 98.8%

         \[\leadsto \left(1 - x\right) \cdot \color{blue}{\frac{1}{\frac{y}{-0.3333333333333333 \cdot x}}} \]

      3. un-div-inv 98.9%

         \[\leadsto \color{blue}{\frac{1 - x}{\frac{y}{-0.3333333333333333 \cdot x}}} \]

      4. *-un-lft-identity 98.9%

         \[\leadsto \frac{1 - x}{\frac{\color{blue}{1 \cdot y}}{-0.3333333333333333 \cdot x}} \]

      5. times-frac 99.0%

         \[\leadsto \frac{1 - x}{\color{blue}{\frac{1}{-0.3333333333333333} \cdot \frac{y}{x}}} \]

      6. metadata-eval 99.0%

         \[\leadsto \frac{1 - x}{\color{blue}{-3} \cdot \frac{y}{x}} \]

   6. Applied egg-rr 99.0%

      \[\leadsto \color{blue}{\frac{1 - x}{-3 \cdot \frac{y}{x}}} \]
   7. Step-by-step derivation

      1. associate-/r* 98.9%

         \[\leadsto \color{blue}{\frac{\frac{1 - x}{-3}}{\frac{y}{x}}} \]

      2. div-sub 98.9%

         \[\leadsto \frac{\color{blue}{\frac{1}{-3} - \frac{x}{-3}}}{\frac{y}{x}} \]

      3. metadata-eval 98.9%

         \[\leadsto \frac{\color{blue}{-0.3333333333333333} - \frac{x}{-3}}{\frac{y}{x}} \]

      4. metadata-eval 98.9%

         \[\leadsto \frac{-0.3333333333333333 - \frac{x}{\color{blue}{\frac{1}{-0.3333333333333333}}}}{\frac{y}{x}} \]

      5. associate-/l* 98.9%

         \[\leadsto \frac{-0.3333333333333333 - \color{blue}{\frac{x \cdot -0.3333333333333333}{1}}}{\frac{y}{x}} \]

      6. /-rgt-identity 98.9%

         \[\leadsto \frac{-0.3333333333333333 - \color{blue}{x \cdot -0.3333333333333333}}{\frac{y}{x}} \]

      7. cancel-sign-sub-inv 98.9%

         \[\leadsto \frac{\color{blue}{-0.3333333333333333 + \left(-x\right) \cdot -0.3333333333333333}}{\frac{y}{x}} \]

      8. metadata-eval 98.9%

         \[\leadsto \frac{\color{blue}{1 \cdot -0.3333333333333333} + \left(-x\right) \cdot -0.3333333333333333}{\frac{y}{x}} \]

      9. distribute-rgt-in 98.9%

         \[\leadsto \frac{\color{blue}{-0.3333333333333333 \cdot \left(1 + \left(-x\right)\right)}}{\frac{y}{x}} \]

      10. sub-neg 98.9%

          \[\leadsto \frac{-0.3333333333333333 \cdot \color{blue}{\left(1 - x\right)}}{\frac{y}{x}} \]

      11. *-commutative 98.9%

          \[\leadsto \frac{\color{blue}{\left(1 - x\right) \cdot -0.3333333333333333}}{\frac{y}{x}} \]

      12. associate-/r/ 98.8%

          \[\leadsto \color{blue}{\frac{\left(1 - x\right) \cdot -0.3333333333333333}{y} \cdot x} \]

      13. *-commutative 98.8%

          \[\leadsto \frac{\color{blue}{-0.3333333333333333 \cdot \left(1 - x\right)}}{y} \cdot x \]

      14. sub-neg 98.8%

          \[\leadsto \frac{-0.3333333333333333 \cdot \color{blue}{\left(1 + \left(-x\right)\right)}}{y} \cdot x \]

      15. distribute-rgt-in 98.8%

          \[\leadsto \frac{\color{blue}{1 \cdot -0.3333333333333333 + \left(-x\right) \cdot -0.3333333333333333}}{y} \cdot x \]

      16. metadata-eval 98.8%

          \[\leadsto \frac{\color{blue}{-0.3333333333333333} + \left(-x\right) \cdot -0.3333333333333333}{y} \cdot x \]

      17. cancel-sign-sub-inv 98.8%

          \[\leadsto \frac{\color{blue}{-0.3333333333333333 - x \cdot -0.3333333333333333}}{y} \cdot x \]

      18. metadata-eval 98.8%

          \[\leadsto \frac{\color{blue}{\frac{1}{-3}} - x \cdot -0.3333333333333333}{y} \cdot x \]

      19. /-rgt-identity 98.8%

          \[\leadsto \frac{\frac{1}{-3} - \color{blue}{\frac{x \cdot -0.3333333333333333}{1}}}{y} \cdot x \]

      20. associate-/l* 98.9%

          \[\leadsto \frac{\frac{1}{-3} - \color{blue}{\frac{x}{\frac{1}{-0.3333333333333333}}}}{y} \cdot x \]

      21. metadata-eval 98.9%

          \[\leadsto \frac{\frac{1}{-3} - \frac{x}{\color{blue}{-3}}}{y} \cdot x \]

      22. div-sub 98.9%

          \[\leadsto \frac{\color{blue}{\frac{1 - x}{-3}}}{y} \cdot x \]

      23. associate-/r* 98.9%

          \[\leadsto \color{blue}{\frac{1 - x}{-3 \cdot y}} \cdot x \]

      24. *-commutative 98.9%

          \[\leadsto \color{blue}{x \cdot \frac{1 - x}{-3 \cdot y}} \]

   8. Simplified 98.9%

      \[\leadsto \color{blue}{x \cdot \frac{1 - x}{y \cdot -3}} \]

   9. Taylor expanded in y around 0 86.4%

      \[\leadsto \color{blue}{-0.3333333333333333 \cdot \frac{x \cdot \left(1 - x\right)}{y}} \]
   10. Step-by-step derivation

       1. associate-*r/ 98.9%

          \[\leadsto -0.3333333333333333 \cdot \color{blue}{\left(x \cdot \frac{1 - x}{y}\right)} \]

   11. Simplified 98.9%

       \[\leadsto \color{blue}{-0.3333333333333333 \cdot \left(x \cdot \frac{1 - x}{y}\right)} \]

   12. Taylor expanded in x around inf 98.9%

       \[\leadsto -0.3333333333333333 \cdot \left(x \cdot \color{blue}{\left(-1 \cdot \frac{x}{y}\right)}\right) \]
   13. Step-by-step derivation

       1. neg-mul-1 98.9%

          \[\leadsto -0.3333333333333333 \cdot \left(x \cdot \color{blue}{\left(-\frac{x}{y}\right)}\right) \]

       2. distribute-neg-frac 98.9%

          \[\leadsto -0.3333333333333333 \cdot \left(x \cdot \color{blue}{\frac{-x}{y}}\right) \]

   14. Simplified 98.9%

       \[\leadsto -0.3333333333333333 \cdot \left(x \cdot \color{blue}{\frac{-x}{y}}\right) \]

   if -4.5999999999999996 < x < 3

   1. Initial program 99.5%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   2. Step-by-step derivation

      1. *-commutative 99.5%

         \[\leadsto \frac{\color{blue}{\left(3 - x\right) \cdot \left(1 - x\right)}}{y \cdot 3} \]

      2. associate-*l/ 99.6%

         \[\leadsto \color{blue}{\frac{3 - x}{y \cdot 3} \cdot \left(1 - x\right)} \]

      3. *-commutative 99.6%

         \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{3 - x}{y \cdot 3}} \]

      4. associate-/l/ 100.0%

         \[\leadsto \left(1 - x\right) \cdot \color{blue}{\frac{\frac{3 - x}{3}}{y}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{\frac{x + -3}{-3}}{y}} \]

   4. Taylor expanded in x around 0 98.4%

      \[\leadsto \color{blue}{-1.3333333333333333 \cdot \frac{x}{y} + \frac{1}{y}} \]

   5. Taylor expanded in y around 0 98.4%

      \[\leadsto \color{blue}{\frac{1 + -1.3333333333333333 \cdot x}{y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.6 \lor \neg \left(x \leq 3\right):\\ \;\;\;\;-0.3333333333333333 \cdot \left(x \cdot \frac{-x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot -1.3333333333333333 + 1}{y}\\ \end{array} \]

Alternative 8: 97.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.8 \lor \neg \left(x \leq 3\right):\\ \;\;\;\;x \cdot \left(0.3333333333333333 \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1 - x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -3.8) (not (<= x 3.0)))
   (* x (* 0.3333333333333333 (/ x y)))
   (/ (- 1.0 x) y)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -3.8) || !(x <= 3.0)) {
		tmp = x * (0.3333333333333333 * (x / y));
	} else {
		tmp = (1.0 - x) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-3.8d0)) .or. (.not. (x <= 3.0d0))) then
        tmp = x * (0.3333333333333333d0 * (x / y))
    else
        tmp = (1.0d0 - x) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -3.8) || !(x <= 3.0)) {
		tmp = x * (0.3333333333333333 * (x / y));
	} else {
		tmp = (1.0 - x) / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -3.8) or not (x <= 3.0):
		tmp = x * (0.3333333333333333 * (x / y))
	else:
		tmp = (1.0 - x) / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -3.8) || !(x <= 3.0))
		tmp = Float64(x * Float64(0.3333333333333333 * Float64(x / y)));
	else
		tmp = Float64(Float64(1.0 - x) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -3.8) || ~((x <= 3.0)))
		tmp = x * (0.3333333333333333 * (x / y));
	else
		tmp = (1.0 - x) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -3.8], N[Not[LessEqual[x, 3.0]], $MachinePrecision]], N[(x * N[(0.3333333333333333 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.7999999999999998 or 3 < x

   1. Initial program 87.3%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   2. Step-by-step derivation

      1. *-commutative 87.3%

         \[\leadsto \frac{\color{blue}{\left(3 - x\right) \cdot \left(1 - x\right)}}{y \cdot 3} \]

      2. associate-*l/ 99.7%

         \[\leadsto \color{blue}{\frac{3 - x}{y \cdot 3} \cdot \left(1 - x\right)} \]

      3. *-commutative 99.7%

         \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{3 - x}{y \cdot 3}} \]

      4. associate-/l/ 99.7%

         \[\leadsto \left(1 - x\right) \cdot \color{blue}{\frac{\frac{3 - x}{3}}{y}} \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{\frac{x + -3}{-3}}{y}} \]

   4. Taylor expanded in x around inf 98.9%

      \[\leadsto \left(1 - x\right) \cdot \color{blue}{\left(-0.3333333333333333 \cdot \frac{x}{y}\right)} \]
   5. Step-by-step derivation

      1. associate-*r/ 98.8%

         \[\leadsto \left(1 - x\right) \cdot \color{blue}{\frac{-0.3333333333333333 \cdot x}{y}} \]

      2. clear-num 98.8%

         \[\leadsto \left(1 - x\right) \cdot \color{blue}{\frac{1}{\frac{y}{-0.3333333333333333 \cdot x}}} \]

      3. un-div-inv 98.9%

         \[\leadsto \color{blue}{\frac{1 - x}{\frac{y}{-0.3333333333333333 \cdot x}}} \]

      4. *-un-lft-identity 98.9%

         \[\leadsto \frac{1 - x}{\frac{\color{blue}{1 \cdot y}}{-0.3333333333333333 \cdot x}} \]

      5. times-frac 99.0%

         \[\leadsto \frac{1 - x}{\color{blue}{\frac{1}{-0.3333333333333333} \cdot \frac{y}{x}}} \]

      6. metadata-eval 99.0%

         \[\leadsto \frac{1 - x}{\color{blue}{-3} \cdot \frac{y}{x}} \]

   6. Applied egg-rr 99.0%

      \[\leadsto \color{blue}{\frac{1 - x}{-3 \cdot \frac{y}{x}}} \]
   7. Step-by-step derivation

      1. associate-/r* 98.9%

         \[\leadsto \color{blue}{\frac{\frac{1 - x}{-3}}{\frac{y}{x}}} \]

      2. div-sub 98.9%

         \[\leadsto \frac{\color{blue}{\frac{1}{-3} - \frac{x}{-3}}}{\frac{y}{x}} \]

      3. metadata-eval 98.9%

         \[\leadsto \frac{\color{blue}{-0.3333333333333333} - \frac{x}{-3}}{\frac{y}{x}} \]

      4. metadata-eval 98.9%

         \[\leadsto \frac{-0.3333333333333333 - \frac{x}{\color{blue}{\frac{1}{-0.3333333333333333}}}}{\frac{y}{x}} \]

      5. associate-/l* 98.9%

         \[\leadsto \frac{-0.3333333333333333 - \color{blue}{\frac{x \cdot -0.3333333333333333}{1}}}{\frac{y}{x}} \]

      6. /-rgt-identity 98.9%

         \[\leadsto \frac{-0.3333333333333333 - \color{blue}{x \cdot -0.3333333333333333}}{\frac{y}{x}} \]

      7. cancel-sign-sub-inv 98.9%

         \[\leadsto \frac{\color{blue}{-0.3333333333333333 + \left(-x\right) \cdot -0.3333333333333333}}{\frac{y}{x}} \]

      8. metadata-eval 98.9%

         \[\leadsto \frac{\color{blue}{1 \cdot -0.3333333333333333} + \left(-x\right) \cdot -0.3333333333333333}{\frac{y}{x}} \]

      9. distribute-rgt-in 98.9%

         \[\leadsto \frac{\color{blue}{-0.3333333333333333 \cdot \left(1 + \left(-x\right)\right)}}{\frac{y}{x}} \]

      10. sub-neg 98.9%

          \[\leadsto \frac{-0.3333333333333333 \cdot \color{blue}{\left(1 - x\right)}}{\frac{y}{x}} \]

      11. *-commutative 98.9%

          \[\leadsto \frac{\color{blue}{\left(1 - x\right) \cdot -0.3333333333333333}}{\frac{y}{x}} \]

      12. associate-/r/ 98.8%

          \[\leadsto \color{blue}{\frac{\left(1 - x\right) \cdot -0.3333333333333333}{y} \cdot x} \]

      13. *-commutative 98.8%

          \[\leadsto \frac{\color{blue}{-0.3333333333333333 \cdot \left(1 - x\right)}}{y} \cdot x \]

      14. sub-neg 98.8%

          \[\leadsto \frac{-0.3333333333333333 \cdot \color{blue}{\left(1 + \left(-x\right)\right)}}{y} \cdot x \]

      15. distribute-rgt-in 98.8%

          \[\leadsto \frac{\color{blue}{1 \cdot -0.3333333333333333 + \left(-x\right) \cdot -0.3333333333333333}}{y} \cdot x \]

      16. metadata-eval 98.8%

          \[\leadsto \frac{\color{blue}{-0.3333333333333333} + \left(-x\right) \cdot -0.3333333333333333}{y} \cdot x \]

      17. cancel-sign-sub-inv 98.8%

          \[\leadsto \frac{\color{blue}{-0.3333333333333333 - x \cdot -0.3333333333333333}}{y} \cdot x \]

      18. metadata-eval 98.8%

          \[\leadsto \frac{\color{blue}{\frac{1}{-3}} - x \cdot -0.3333333333333333}{y} \cdot x \]

      19. /-rgt-identity 98.8%

          \[\leadsto \frac{\frac{1}{-3} - \color{blue}{\frac{x \cdot -0.3333333333333333}{1}}}{y} \cdot x \]

      20. associate-/l* 98.9%

          \[\leadsto \frac{\frac{1}{-3} - \color{blue}{\frac{x}{\frac{1}{-0.3333333333333333}}}}{y} \cdot x \]

      21. metadata-eval 98.9%

          \[\leadsto \frac{\frac{1}{-3} - \frac{x}{\color{blue}{-3}}}{y} \cdot x \]

      22. div-sub 98.9%

          \[\leadsto \frac{\color{blue}{\frac{1 - x}{-3}}}{y} \cdot x \]

      23. associate-/r* 98.9%

          \[\leadsto \color{blue}{\frac{1 - x}{-3 \cdot y}} \cdot x \]

      24. *-commutative 98.9%

          \[\leadsto \color{blue}{x \cdot \frac{1 - x}{-3 \cdot y}} \]

   8. Simplified 98.9%

      \[\leadsto \color{blue}{x \cdot \frac{1 - x}{y \cdot -3}} \]

   9. Taylor expanded in x around inf 98.8%

      \[\leadsto x \cdot \color{blue}{\left(0.3333333333333333 \cdot \frac{x}{y}\right)} \]
   10. Step-by-step derivation

       1. *-commutative 98.8%

          \[\leadsto x \cdot \color{blue}{\left(\frac{x}{y} \cdot 0.3333333333333333\right)} \]

   11. Simplified 98.8%

       \[\leadsto x \cdot \color{blue}{\left(\frac{x}{y} \cdot 0.3333333333333333\right)} \]

   if -3.7999999999999998 < x < 3

   1. Initial program 99.5%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   2. Step-by-step derivation

      1. *-commutative 99.5%

         \[\leadsto \frac{\color{blue}{\left(3 - x\right) \cdot \left(1 - x\right)}}{y \cdot 3} \]

      2. associate-*l/ 99.6%

         \[\leadsto \color{blue}{\frac{3 - x}{y \cdot 3} \cdot \left(1 - x\right)} \]

      3. *-commutative 99.6%

         \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{3 - x}{y \cdot 3}} \]

      4. associate-/l/ 100.0%

         \[\leadsto \left(1 - x\right) \cdot \color{blue}{\frac{\frac{3 - x}{3}}{y}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{\frac{x + -3}{-3}}{y}} \]

   4. Taylor expanded in x around 0 97.8%

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

   5. Taylor expanded in x around 0 97.8%

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

      1. neg-mul-1 97.8%

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

      2. +-commutative 97.8%

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

      3. sub-neg 97.8%

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

      4. div-sub 97.8%

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

   7. Simplified 97.8%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.8 \lor \neg \left(x \leq 3\right):\\ \;\;\;\;x \cdot \left(0.3333333333333333 \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1 - x}{y}\\ \end{array} \]

Alternative 9: 97.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.8:\\ \;\;\;\;x \cdot \frac{x}{\frac{y}{0.3333333333333333}}\\ \mathbf{elif}\;x \leq 3:\\ \;\;\;\;\frac{1 - x}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(0.3333333333333333 \cdot \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -3.8)
   (* x (/ x (/ y 0.3333333333333333)))
   (if (<= x 3.0) (/ (- 1.0 x) y) (* x (* 0.3333333333333333 (/ x y))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -3.8) {
		tmp = x * (x / (y / 0.3333333333333333));
	} else if (x <= 3.0) {
		tmp = (1.0 - x) / y;
	} else {
		tmp = x * (0.3333333333333333 * (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 <= (-3.8d0)) then
        tmp = x * (x / (y / 0.3333333333333333d0))
    else if (x <= 3.0d0) then
        tmp = (1.0d0 - x) / y
    else
        tmp = x * (0.3333333333333333d0 * (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -3.8) {
		tmp = x * (x / (y / 0.3333333333333333));
	} else if (x <= 3.0) {
		tmp = (1.0 - x) / y;
	} else {
		tmp = x * (0.3333333333333333 * (x / y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -3.8:
		tmp = x * (x / (y / 0.3333333333333333))
	elif x <= 3.0:
		tmp = (1.0 - x) / y
	else:
		tmp = x * (0.3333333333333333 * (x / y))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -3.8)
		tmp = Float64(x * Float64(x / Float64(y / 0.3333333333333333)));
	elseif (x <= 3.0)
		tmp = Float64(Float64(1.0 - x) / y);
	else
		tmp = Float64(x * Float64(0.3333333333333333 * Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -3.8)
		tmp = x * (x / (y / 0.3333333333333333));
	elseif (x <= 3.0)
		tmp = (1.0 - x) / y;
	else
		tmp = x * (0.3333333333333333 * (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -3.8], N[(x * N[(x / N[(y / 0.3333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.0], N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision], N[(x * N[(0.3333333333333333 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.7999999999999998

   1. Initial program 87.0%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   2. Step-by-step derivation

      1. *-commutative 87.0%

         \[\leadsto \frac{\color{blue}{\left(3 - x\right) \cdot \left(1 - x\right)}}{y \cdot 3} \]

      2. associate-*l/ 99.8%

         \[\leadsto \color{blue}{\frac{3 - x}{y \cdot 3} \cdot \left(1 - x\right)} \]

      3. *-commutative 99.8%

         \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{3 - x}{y \cdot 3}} \]

      4. associate-/l/ 99.7%

         \[\leadsto \left(1 - x\right) \cdot \color{blue}{\frac{\frac{3 - x}{3}}{y}} \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{\frac{x + -3}{-3}}{y}} \]

   4. Taylor expanded in x around inf 98.6%

      \[\leadsto \left(1 - x\right) \cdot \color{blue}{\left(-0.3333333333333333 \cdot \frac{x}{y}\right)} \]
   5. Step-by-step derivation

      1. associate-*r/ 98.6%

         \[\leadsto \left(1 - x\right) \cdot \color{blue}{\frac{-0.3333333333333333 \cdot x}{y}} \]

      2. clear-num 98.7%

         \[\leadsto \left(1 - x\right) \cdot \color{blue}{\frac{1}{\frac{y}{-0.3333333333333333 \cdot x}}} \]

      3. un-div-inv 98.8%

         \[\leadsto \color{blue}{\frac{1 - x}{\frac{y}{-0.3333333333333333 \cdot x}}} \]

      4. *-un-lft-identity 98.8%

         \[\leadsto \frac{1 - x}{\frac{\color{blue}{1 \cdot y}}{-0.3333333333333333 \cdot x}} \]

      5. times-frac 98.9%

         \[\leadsto \frac{1 - x}{\color{blue}{\frac{1}{-0.3333333333333333} \cdot \frac{y}{x}}} \]

      6. metadata-eval 98.9%

         \[\leadsto \frac{1 - x}{\color{blue}{-3} \cdot \frac{y}{x}} \]

   6. Applied egg-rr 98.9%

      \[\leadsto \color{blue}{\frac{1 - x}{-3 \cdot \frac{y}{x}}} \]
   7. Step-by-step derivation

      1. associate-/r* 98.8%

         \[\leadsto \color{blue}{\frac{\frac{1 - x}{-3}}{\frac{y}{x}}} \]

      2. div-sub 98.8%

         \[\leadsto \frac{\color{blue}{\frac{1}{-3} - \frac{x}{-3}}}{\frac{y}{x}} \]

      3. metadata-eval 98.8%

         \[\leadsto \frac{\color{blue}{-0.3333333333333333} - \frac{x}{-3}}{\frac{y}{x}} \]

      4. metadata-eval 98.8%

         \[\leadsto \frac{-0.3333333333333333 - \frac{x}{\color{blue}{\frac{1}{-0.3333333333333333}}}}{\frac{y}{x}} \]

      5. associate-/l* 98.7%

         \[\leadsto \frac{-0.3333333333333333 - \color{blue}{\frac{x \cdot -0.3333333333333333}{1}}}{\frac{y}{x}} \]

      6. /-rgt-identity 98.7%

         \[\leadsto \frac{-0.3333333333333333 - \color{blue}{x \cdot -0.3333333333333333}}{\frac{y}{x}} \]

      7. cancel-sign-sub-inv 98.7%

         \[\leadsto \frac{\color{blue}{-0.3333333333333333 + \left(-x\right) \cdot -0.3333333333333333}}{\frac{y}{x}} \]

      8. metadata-eval 98.7%

         \[\leadsto \frac{\color{blue}{1 \cdot -0.3333333333333333} + \left(-x\right) \cdot -0.3333333333333333}{\frac{y}{x}} \]

      9. distribute-rgt-in 98.7%

         \[\leadsto \frac{\color{blue}{-0.3333333333333333 \cdot \left(1 + \left(-x\right)\right)}}{\frac{y}{x}} \]

      10. sub-neg 98.7%

          \[\leadsto \frac{-0.3333333333333333 \cdot \color{blue}{\left(1 - x\right)}}{\frac{y}{x}} \]

      11. *-commutative 98.7%

          \[\leadsto \frac{\color{blue}{\left(1 - x\right) \cdot -0.3333333333333333}}{\frac{y}{x}} \]

      12. associate-/r/ 98.6%

          \[\leadsto \color{blue}{\frac{\left(1 - x\right) \cdot -0.3333333333333333}{y} \cdot x} \]

      13. *-commutative 98.6%

          \[\leadsto \frac{\color{blue}{-0.3333333333333333 \cdot \left(1 - x\right)}}{y} \cdot x \]

      14. sub-neg 98.6%

          \[\leadsto \frac{-0.3333333333333333 \cdot \color{blue}{\left(1 + \left(-x\right)\right)}}{y} \cdot x \]

      15. distribute-rgt-in 98.6%

          \[\leadsto \frac{\color{blue}{1 \cdot -0.3333333333333333 + \left(-x\right) \cdot -0.3333333333333333}}{y} \cdot x \]

      16. metadata-eval 98.6%

          \[\leadsto \frac{\color{blue}{-0.3333333333333333} + \left(-x\right) \cdot -0.3333333333333333}{y} \cdot x \]

      17. cancel-sign-sub-inv 98.6%

          \[\leadsto \frac{\color{blue}{-0.3333333333333333 - x \cdot -0.3333333333333333}}{y} \cdot x \]

      18. metadata-eval 98.6%

          \[\leadsto \frac{\color{blue}{\frac{1}{-3}} - x \cdot -0.3333333333333333}{y} \cdot x \]

      19. /-rgt-identity 98.6%

          \[\leadsto \frac{\frac{1}{-3} - \color{blue}{\frac{x \cdot -0.3333333333333333}{1}}}{y} \cdot x \]

      20. associate-/l* 98.8%

          \[\leadsto \frac{\frac{1}{-3} - \color{blue}{\frac{x}{\frac{1}{-0.3333333333333333}}}}{y} \cdot x \]

      21. metadata-eval 98.8%

          \[\leadsto \frac{\frac{1}{-3} - \frac{x}{\color{blue}{-3}}}{y} \cdot x \]

      22. div-sub 98.8%

          \[\leadsto \frac{\color{blue}{\frac{1 - x}{-3}}}{y} \cdot x \]

      23. associate-/r* 98.9%

          \[\leadsto \color{blue}{\frac{1 - x}{-3 \cdot y}} \cdot x \]

      24. *-commutative 98.9%

          \[\leadsto \color{blue}{x \cdot \frac{1 - x}{-3 \cdot y}} \]

   8. Simplified 98.9%

      \[\leadsto \color{blue}{x \cdot \frac{1 - x}{y \cdot -3}} \]

   9. Taylor expanded in x around inf 98.6%

      \[\leadsto x \cdot \color{blue}{\left(0.3333333333333333 \cdot \frac{x}{y}\right)} \]
   10. Step-by-step derivation

       1. *-commutative 98.6%

          \[\leadsto x \cdot \color{blue}{\left(\frac{x}{y} \cdot 0.3333333333333333\right)} \]

   11. Simplified 98.6%

       \[\leadsto x \cdot \color{blue}{\left(\frac{x}{y} \cdot 0.3333333333333333\right)} \]
   12. Step-by-step derivation

       1. associate-*l/ 98.6%

          \[\leadsto x \cdot \color{blue}{\frac{x \cdot 0.3333333333333333}{y}} \]

       2. associate-/l* 98.6%

          \[\leadsto x \cdot \color{blue}{\frac{x}{\frac{y}{0.3333333333333333}}} \]

   13. Applied egg-rr 98.6%

       \[\leadsto x \cdot \color{blue}{\frac{x}{\frac{y}{0.3333333333333333}}} \]

   if -3.7999999999999998 < x < 3

   1. Initial program 99.5%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   2. Step-by-step derivation

      1. *-commutative 99.5%

         \[\leadsto \frac{\color{blue}{\left(3 - x\right) \cdot \left(1 - x\right)}}{y \cdot 3} \]

      2. associate-*l/ 99.6%

         \[\leadsto \color{blue}{\frac{3 - x}{y \cdot 3} \cdot \left(1 - x\right)} \]

      3. *-commutative 99.6%

         \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{3 - x}{y \cdot 3}} \]

      4. associate-/l/ 100.0%

         \[\leadsto \left(1 - x\right) \cdot \color{blue}{\frac{\frac{3 - x}{3}}{y}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{\frac{x + -3}{-3}}{y}} \]

   4. Taylor expanded in x around 0 97.8%

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

   5. Taylor expanded in x around 0 97.8%

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

      1. neg-mul-1 97.8%

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

      2. +-commutative 97.8%

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

      3. sub-neg 97.8%

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

      4. div-sub 97.8%

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

   7. Simplified 97.8%

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

   if 3 < x

   1. Initial program 87.5%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   2. Step-by-step derivation

      1. *-commutative 87.5%

         \[\leadsto \frac{\color{blue}{\left(3 - x\right) \cdot \left(1 - x\right)}}{y \cdot 3} \]

      2. associate-*l/ 99.6%

         \[\leadsto \color{blue}{\frac{3 - x}{y \cdot 3} \cdot \left(1 - x\right)} \]

      3. *-commutative 99.6%

         \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{3 - x}{y \cdot 3}} \]

      4. associate-/l/ 99.7%

         \[\leadsto \left(1 - x\right) \cdot \color{blue}{\frac{\frac{3 - x}{3}}{y}} \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{\frac{x + -3}{-3}}{y}} \]

   4. Taylor expanded in x around inf 99.1%

      \[\leadsto \left(1 - x\right) \cdot \color{blue}{\left(-0.3333333333333333 \cdot \frac{x}{y}\right)} \]
   5. Step-by-step derivation

      1. associate-*r/ 99.0%

         \[\leadsto \left(1 - x\right) \cdot \color{blue}{\frac{-0.3333333333333333 \cdot x}{y}} \]

      2. clear-num 99.0%

         \[\leadsto \left(1 - x\right) \cdot \color{blue}{\frac{1}{\frac{y}{-0.3333333333333333 \cdot x}}} \]

      3. un-div-inv 99.0%

         \[\leadsto \color{blue}{\frac{1 - x}{\frac{y}{-0.3333333333333333 \cdot x}}} \]

      4. *-un-lft-identity 99.0%

         \[\leadsto \frac{1 - x}{\frac{\color{blue}{1 \cdot y}}{-0.3333333333333333 \cdot x}} \]

      5. times-frac 99.1%

         \[\leadsto \frac{1 - x}{\color{blue}{\frac{1}{-0.3333333333333333} \cdot \frac{y}{x}}} \]

      6. metadata-eval 99.1%

         \[\leadsto \frac{1 - x}{\color{blue}{-3} \cdot \frac{y}{x}} \]

   6. Applied egg-rr 99.1%

      \[\leadsto \color{blue}{\frac{1 - x}{-3 \cdot \frac{y}{x}}} \]
   7. Step-by-step derivation

      1. associate-/r* 99.1%

         \[\leadsto \color{blue}{\frac{\frac{1 - x}{-3}}{\frac{y}{x}}} \]

      2. div-sub 99.1%

         \[\leadsto \frac{\color{blue}{\frac{1}{-3} - \frac{x}{-3}}}{\frac{y}{x}} \]

      3. metadata-eval 99.1%

         \[\leadsto \frac{\color{blue}{-0.3333333333333333} - \frac{x}{-3}}{\frac{y}{x}} \]

      4. metadata-eval 99.1%

         \[\leadsto \frac{-0.3333333333333333 - \frac{x}{\color{blue}{\frac{1}{-0.3333333333333333}}}}{\frac{y}{x}} \]

      5. associate-/l* 99.0%

         \[\leadsto \frac{-0.3333333333333333 - \color{blue}{\frac{x \cdot -0.3333333333333333}{1}}}{\frac{y}{x}} \]

      6. /-rgt-identity 99.0%

         \[\leadsto \frac{-0.3333333333333333 - \color{blue}{x \cdot -0.3333333333333333}}{\frac{y}{x}} \]

      7. cancel-sign-sub-inv 99.0%

         \[\leadsto \frac{\color{blue}{-0.3333333333333333 + \left(-x\right) \cdot -0.3333333333333333}}{\frac{y}{x}} \]

      8. metadata-eval 99.0%

         \[\leadsto \frac{\color{blue}{1 \cdot -0.3333333333333333} + \left(-x\right) \cdot -0.3333333333333333}{\frac{y}{x}} \]

      9. distribute-rgt-in 99.0%

         \[\leadsto \frac{\color{blue}{-0.3333333333333333 \cdot \left(1 + \left(-x\right)\right)}}{\frac{y}{x}} \]

      10. sub-neg 99.0%

          \[\leadsto \frac{-0.3333333333333333 \cdot \color{blue}{\left(1 - x\right)}}{\frac{y}{x}} \]

      11. *-commutative 99.0%

          \[\leadsto \frac{\color{blue}{\left(1 - x\right) \cdot -0.3333333333333333}}{\frac{y}{x}} \]

      12. associate-/r/ 99.0%

          \[\leadsto \color{blue}{\frac{\left(1 - x\right) \cdot -0.3333333333333333}{y} \cdot x} \]

      13. *-commutative 99.0%

          \[\leadsto \frac{\color{blue}{-0.3333333333333333 \cdot \left(1 - x\right)}}{y} \cdot x \]

      14. sub-neg 99.0%

          \[\leadsto \frac{-0.3333333333333333 \cdot \color{blue}{\left(1 + \left(-x\right)\right)}}{y} \cdot x \]

      15. distribute-rgt-in 99.0%

          \[\leadsto \frac{\color{blue}{1 \cdot -0.3333333333333333 + \left(-x\right) \cdot -0.3333333333333333}}{y} \cdot x \]

      16. metadata-eval 99.0%

          \[\leadsto \frac{\color{blue}{-0.3333333333333333} + \left(-x\right) \cdot -0.3333333333333333}{y} \cdot x \]

      17. cancel-sign-sub-inv 99.0%

          \[\leadsto \frac{\color{blue}{-0.3333333333333333 - x \cdot -0.3333333333333333}}{y} \cdot x \]

      18. metadata-eval 99.0%

          \[\leadsto \frac{\color{blue}{\frac{1}{-3}} - x \cdot -0.3333333333333333}{y} \cdot x \]

      19. /-rgt-identity 99.0%

          \[\leadsto \frac{\frac{1}{-3} - \color{blue}{\frac{x \cdot -0.3333333333333333}{1}}}{y} \cdot x \]

      20. associate-/l* 99.1%

          \[\leadsto \frac{\frac{1}{-3} - \color{blue}{\frac{x}{\frac{1}{-0.3333333333333333}}}}{y} \cdot x \]

      21. metadata-eval 99.1%

          \[\leadsto \frac{\frac{1}{-3} - \frac{x}{\color{blue}{-3}}}{y} \cdot x \]

      22. div-sub 99.1%

          \[\leadsto \frac{\color{blue}{\frac{1 - x}{-3}}}{y} \cdot x \]

      23. associate-/r* 99.0%

          \[\leadsto \color{blue}{\frac{1 - x}{-3 \cdot y}} \cdot x \]

      24. *-commutative 99.0%

          \[\leadsto \color{blue}{x \cdot \frac{1 - x}{-3 \cdot y}} \]

   8. Simplified 99.0%

      \[\leadsto \color{blue}{x \cdot \frac{1 - x}{y \cdot -3}} \]

   9. Taylor expanded in x around inf 99.1%

      \[\leadsto x \cdot \color{blue}{\left(0.3333333333333333 \cdot \frac{x}{y}\right)} \]
   10. Step-by-step derivation

       1. *-commutative 99.1%

          \[\leadsto x \cdot \color{blue}{\left(\frac{x}{y} \cdot 0.3333333333333333\right)} \]

   11. Simplified 99.1%

       \[\leadsto x \cdot \color{blue}{\left(\frac{x}{y} \cdot 0.3333333333333333\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.8:\\ \;\;\;\;x \cdot \frac{x}{\frac{y}{0.3333333333333333}}\\ \mathbf{elif}\;x \leq 3:\\ \;\;\;\;\frac{1 - x}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(0.3333333333333333 \cdot \frac{x}{y}\right)\\ \end{array} \]

Alternative 10: 97.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.8:\\ \;\;\;\;x \cdot \frac{x}{\frac{y}{0.3333333333333333}}\\ \mathbf{elif}\;x \leq 3:\\ \;\;\;\;\left(1 - x\right) \cdot \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(0.3333333333333333 \cdot \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -3.8)
   (* x (/ x (/ y 0.3333333333333333)))
   (if (<= x 3.0)
     (* (- 1.0 x) (/ 1.0 y))
     (* x (* 0.3333333333333333 (/ x y))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -3.8) {
		tmp = x * (x / (y / 0.3333333333333333));
	} else if (x <= 3.0) {
		tmp = (1.0 - x) * (1.0 / y);
	} else {
		tmp = x * (0.3333333333333333 * (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 <= (-3.8d0)) then
        tmp = x * (x / (y / 0.3333333333333333d0))
    else if (x <= 3.0d0) then
        tmp = (1.0d0 - x) * (1.0d0 / y)
    else
        tmp = x * (0.3333333333333333d0 * (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -3.8) {
		tmp = x * (x / (y / 0.3333333333333333));
	} else if (x <= 3.0) {
		tmp = (1.0 - x) * (1.0 / y);
	} else {
		tmp = x * (0.3333333333333333 * (x / y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -3.8:
		tmp = x * (x / (y / 0.3333333333333333))
	elif x <= 3.0:
		tmp = (1.0 - x) * (1.0 / y)
	else:
		tmp = x * (0.3333333333333333 * (x / y))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -3.8)
		tmp = Float64(x * Float64(x / Float64(y / 0.3333333333333333)));
	elseif (x <= 3.0)
		tmp = Float64(Float64(1.0 - x) * Float64(1.0 / y));
	else
		tmp = Float64(x * Float64(0.3333333333333333 * Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -3.8)
		tmp = x * (x / (y / 0.3333333333333333));
	elseif (x <= 3.0)
		tmp = (1.0 - x) * (1.0 / y);
	else
		tmp = x * (0.3333333333333333 * (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -3.8], N[(x * N[(x / N[(y / 0.3333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.0], N[(N[(1.0 - x), $MachinePrecision] * N[(1.0 / y), $MachinePrecision]), $MachinePrecision], N[(x * N[(0.3333333333333333 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.7999999999999998

   1. Initial program 87.0%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   2. Step-by-step derivation

      1. *-commutative 87.0%

         \[\leadsto \frac{\color{blue}{\left(3 - x\right) \cdot \left(1 - x\right)}}{y \cdot 3} \]

      2. associate-*l/ 99.8%

         \[\leadsto \color{blue}{\frac{3 - x}{y \cdot 3} \cdot \left(1 - x\right)} \]

      3. *-commutative 99.8%

         \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{3 - x}{y \cdot 3}} \]

      4. associate-/l/ 99.7%

         \[\leadsto \left(1 - x\right) \cdot \color{blue}{\frac{\frac{3 - x}{3}}{y}} \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{\frac{x + -3}{-3}}{y}} \]

   4. Taylor expanded in x around inf 98.6%

      \[\leadsto \left(1 - x\right) \cdot \color{blue}{\left(-0.3333333333333333 \cdot \frac{x}{y}\right)} \]
   5. Step-by-step derivation

      1. associate-*r/ 98.6%

         \[\leadsto \left(1 - x\right) \cdot \color{blue}{\frac{-0.3333333333333333 \cdot x}{y}} \]

      2. clear-num 98.7%

         \[\leadsto \left(1 - x\right) \cdot \color{blue}{\frac{1}{\frac{y}{-0.3333333333333333 \cdot x}}} \]

      3. un-div-inv 98.8%

         \[\leadsto \color{blue}{\frac{1 - x}{\frac{y}{-0.3333333333333333 \cdot x}}} \]

      4. *-un-lft-identity 98.8%

         \[\leadsto \frac{1 - x}{\frac{\color{blue}{1 \cdot y}}{-0.3333333333333333 \cdot x}} \]

      5. times-frac 98.9%

         \[\leadsto \frac{1 - x}{\color{blue}{\frac{1}{-0.3333333333333333} \cdot \frac{y}{x}}} \]

      6. metadata-eval 98.9%

         \[\leadsto \frac{1 - x}{\color{blue}{-3} \cdot \frac{y}{x}} \]

   6. Applied egg-rr 98.9%

      \[\leadsto \color{blue}{\frac{1 - x}{-3 \cdot \frac{y}{x}}} \]
   7. Step-by-step derivation

      1. associate-/r* 98.8%

         \[\leadsto \color{blue}{\frac{\frac{1 - x}{-3}}{\frac{y}{x}}} \]

      2. div-sub 98.8%

         \[\leadsto \frac{\color{blue}{\frac{1}{-3} - \frac{x}{-3}}}{\frac{y}{x}} \]

      3. metadata-eval 98.8%

         \[\leadsto \frac{\color{blue}{-0.3333333333333333} - \frac{x}{-3}}{\frac{y}{x}} \]

      4. metadata-eval 98.8%

         \[\leadsto \frac{-0.3333333333333333 - \frac{x}{\color{blue}{\frac{1}{-0.3333333333333333}}}}{\frac{y}{x}} \]

      5. associate-/l* 98.7%

         \[\leadsto \frac{-0.3333333333333333 - \color{blue}{\frac{x \cdot -0.3333333333333333}{1}}}{\frac{y}{x}} \]

      6. /-rgt-identity 98.7%

         \[\leadsto \frac{-0.3333333333333333 - \color{blue}{x \cdot -0.3333333333333333}}{\frac{y}{x}} \]

      7. cancel-sign-sub-inv 98.7%

         \[\leadsto \frac{\color{blue}{-0.3333333333333333 + \left(-x\right) \cdot -0.3333333333333333}}{\frac{y}{x}} \]

      8. metadata-eval 98.7%

         \[\leadsto \frac{\color{blue}{1 \cdot -0.3333333333333333} + \left(-x\right) \cdot -0.3333333333333333}{\frac{y}{x}} \]

      9. distribute-rgt-in 98.7%

         \[\leadsto \frac{\color{blue}{-0.3333333333333333 \cdot \left(1 + \left(-x\right)\right)}}{\frac{y}{x}} \]

      10. sub-neg 98.7%

          \[\leadsto \frac{-0.3333333333333333 \cdot \color{blue}{\left(1 - x\right)}}{\frac{y}{x}} \]

      11. *-commutative 98.7%

          \[\leadsto \frac{\color{blue}{\left(1 - x\right) \cdot -0.3333333333333333}}{\frac{y}{x}} \]

      12. associate-/r/ 98.6%

          \[\leadsto \color{blue}{\frac{\left(1 - x\right) \cdot -0.3333333333333333}{y} \cdot x} \]

      13. *-commutative 98.6%

          \[\leadsto \frac{\color{blue}{-0.3333333333333333 \cdot \left(1 - x\right)}}{y} \cdot x \]

      14. sub-neg 98.6%

          \[\leadsto \frac{-0.3333333333333333 \cdot \color{blue}{\left(1 + \left(-x\right)\right)}}{y} \cdot x \]

      15. distribute-rgt-in 98.6%

          \[\leadsto \frac{\color{blue}{1 \cdot -0.3333333333333333 + \left(-x\right) \cdot -0.3333333333333333}}{y} \cdot x \]

      16. metadata-eval 98.6%

          \[\leadsto \frac{\color{blue}{-0.3333333333333333} + \left(-x\right) \cdot -0.3333333333333333}{y} \cdot x \]

      17. cancel-sign-sub-inv 98.6%

          \[\leadsto \frac{\color{blue}{-0.3333333333333333 - x \cdot -0.3333333333333333}}{y} \cdot x \]

      18. metadata-eval 98.6%

          \[\leadsto \frac{\color{blue}{\frac{1}{-3}} - x \cdot -0.3333333333333333}{y} \cdot x \]

      19. /-rgt-identity 98.6%

          \[\leadsto \frac{\frac{1}{-3} - \color{blue}{\frac{x \cdot -0.3333333333333333}{1}}}{y} \cdot x \]

      20. associate-/l* 98.8%

          \[\leadsto \frac{\frac{1}{-3} - \color{blue}{\frac{x}{\frac{1}{-0.3333333333333333}}}}{y} \cdot x \]

      21. metadata-eval 98.8%

          \[\leadsto \frac{\frac{1}{-3} - \frac{x}{\color{blue}{-3}}}{y} \cdot x \]

      22. div-sub 98.8%

          \[\leadsto \frac{\color{blue}{\frac{1 - x}{-3}}}{y} \cdot x \]

      23. associate-/r* 98.9%

          \[\leadsto \color{blue}{\frac{1 - x}{-3 \cdot y}} \cdot x \]

      24. *-commutative 98.9%

          \[\leadsto \color{blue}{x \cdot \frac{1 - x}{-3 \cdot y}} \]

   8. Simplified 98.9%

      \[\leadsto \color{blue}{x \cdot \frac{1 - x}{y \cdot -3}} \]

   9. Taylor expanded in x around inf 98.6%

      \[\leadsto x \cdot \color{blue}{\left(0.3333333333333333 \cdot \frac{x}{y}\right)} \]
   10. Step-by-step derivation

       1. *-commutative 98.6%

          \[\leadsto x \cdot \color{blue}{\left(\frac{x}{y} \cdot 0.3333333333333333\right)} \]

   11. Simplified 98.6%

       \[\leadsto x \cdot \color{blue}{\left(\frac{x}{y} \cdot 0.3333333333333333\right)} \]
   12. Step-by-step derivation

       1. associate-*l/ 98.6%

          \[\leadsto x \cdot \color{blue}{\frac{x \cdot 0.3333333333333333}{y}} \]

       2. associate-/l* 98.6%

          \[\leadsto x \cdot \color{blue}{\frac{x}{\frac{y}{0.3333333333333333}}} \]

   13. Applied egg-rr 98.6%

       \[\leadsto x \cdot \color{blue}{\frac{x}{\frac{y}{0.3333333333333333}}} \]

   if -3.7999999999999998 < x < 3

   1. Initial program 99.5%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   2. Step-by-step derivation

      1. *-commutative 99.5%

         \[\leadsto \frac{\color{blue}{\left(3 - x\right) \cdot \left(1 - x\right)}}{y \cdot 3} \]

      2. associate-*l/ 99.6%

         \[\leadsto \color{blue}{\frac{3 - x}{y \cdot 3} \cdot \left(1 - x\right)} \]

      3. *-commutative 99.6%

         \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{3 - x}{y \cdot 3}} \]

      4. associate-/l/ 100.0%

         \[\leadsto \left(1 - x\right) \cdot \color{blue}{\frac{\frac{3 - x}{3}}{y}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{\frac{x + -3}{-3}}{y}} \]

   4. Taylor expanded in x around 0 97.8%

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

   if 3 < x

   1. Initial program 87.5%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   2. Step-by-step derivation

      1. *-commutative 87.5%

         \[\leadsto \frac{\color{blue}{\left(3 - x\right) \cdot \left(1 - x\right)}}{y \cdot 3} \]

      2. associate-*l/ 99.6%

         \[\leadsto \color{blue}{\frac{3 - x}{y \cdot 3} \cdot \left(1 - x\right)} \]

      3. *-commutative 99.6%

         \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{3 - x}{y \cdot 3}} \]

      4. associate-/l/ 99.7%

         \[\leadsto \left(1 - x\right) \cdot \color{blue}{\frac{\frac{3 - x}{3}}{y}} \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{\frac{x + -3}{-3}}{y}} \]

   4. Taylor expanded in x around inf 99.1%

      \[\leadsto \left(1 - x\right) \cdot \color{blue}{\left(-0.3333333333333333 \cdot \frac{x}{y}\right)} \]
   5. Step-by-step derivation

      1. associate-*r/ 99.0%

         \[\leadsto \left(1 - x\right) \cdot \color{blue}{\frac{-0.3333333333333333 \cdot x}{y}} \]

      2. clear-num 99.0%

         \[\leadsto \left(1 - x\right) \cdot \color{blue}{\frac{1}{\frac{y}{-0.3333333333333333 \cdot x}}} \]

      3. un-div-inv 99.0%

         \[\leadsto \color{blue}{\frac{1 - x}{\frac{y}{-0.3333333333333333 \cdot x}}} \]

      4. *-un-lft-identity 99.0%

         \[\leadsto \frac{1 - x}{\frac{\color{blue}{1 \cdot y}}{-0.3333333333333333 \cdot x}} \]

      5. times-frac 99.1%

         \[\leadsto \frac{1 - x}{\color{blue}{\frac{1}{-0.3333333333333333} \cdot \frac{y}{x}}} \]

      6. metadata-eval 99.1%

         \[\leadsto \frac{1 - x}{\color{blue}{-3} \cdot \frac{y}{x}} \]

   6. Applied egg-rr 99.1%

      \[\leadsto \color{blue}{\frac{1 - x}{-3 \cdot \frac{y}{x}}} \]
   7. Step-by-step derivation

      1. associate-/r* 99.1%

         \[\leadsto \color{blue}{\frac{\frac{1 - x}{-3}}{\frac{y}{x}}} \]

      2. div-sub 99.1%

         \[\leadsto \frac{\color{blue}{\frac{1}{-3} - \frac{x}{-3}}}{\frac{y}{x}} \]

      3. metadata-eval 99.1%

         \[\leadsto \frac{\color{blue}{-0.3333333333333333} - \frac{x}{-3}}{\frac{y}{x}} \]

      4. metadata-eval 99.1%

         \[\leadsto \frac{-0.3333333333333333 - \frac{x}{\color{blue}{\frac{1}{-0.3333333333333333}}}}{\frac{y}{x}} \]

      5. associate-/l* 99.0%

         \[\leadsto \frac{-0.3333333333333333 - \color{blue}{\frac{x \cdot -0.3333333333333333}{1}}}{\frac{y}{x}} \]

      6. /-rgt-identity 99.0%

         \[\leadsto \frac{-0.3333333333333333 - \color{blue}{x \cdot -0.3333333333333333}}{\frac{y}{x}} \]

      7. cancel-sign-sub-inv 99.0%

         \[\leadsto \frac{\color{blue}{-0.3333333333333333 + \left(-x\right) \cdot -0.3333333333333333}}{\frac{y}{x}} \]

      8. metadata-eval 99.0%

         \[\leadsto \frac{\color{blue}{1 \cdot -0.3333333333333333} + \left(-x\right) \cdot -0.3333333333333333}{\frac{y}{x}} \]

      9. distribute-rgt-in 99.0%

         \[\leadsto \frac{\color{blue}{-0.3333333333333333 \cdot \left(1 + \left(-x\right)\right)}}{\frac{y}{x}} \]

      10. sub-neg 99.0%

          \[\leadsto \frac{-0.3333333333333333 \cdot \color{blue}{\left(1 - x\right)}}{\frac{y}{x}} \]

      11. *-commutative 99.0%

          \[\leadsto \frac{\color{blue}{\left(1 - x\right) \cdot -0.3333333333333333}}{\frac{y}{x}} \]

      12. associate-/r/ 99.0%

          \[\leadsto \color{blue}{\frac{\left(1 - x\right) \cdot -0.3333333333333333}{y} \cdot x} \]

      13. *-commutative 99.0%

          \[\leadsto \frac{\color{blue}{-0.3333333333333333 \cdot \left(1 - x\right)}}{y} \cdot x \]

      14. sub-neg 99.0%

          \[\leadsto \frac{-0.3333333333333333 \cdot \color{blue}{\left(1 + \left(-x\right)\right)}}{y} \cdot x \]

      15. distribute-rgt-in 99.0%

          \[\leadsto \frac{\color{blue}{1 \cdot -0.3333333333333333 + \left(-x\right) \cdot -0.3333333333333333}}{y} \cdot x \]

      16. metadata-eval 99.0%

          \[\leadsto \frac{\color{blue}{-0.3333333333333333} + \left(-x\right) \cdot -0.3333333333333333}{y} \cdot x \]

      17. cancel-sign-sub-inv 99.0%

          \[\leadsto \frac{\color{blue}{-0.3333333333333333 - x \cdot -0.3333333333333333}}{y} \cdot x \]

      18. metadata-eval 99.0%

          \[\leadsto \frac{\color{blue}{\frac{1}{-3}} - x \cdot -0.3333333333333333}{y} \cdot x \]

      19. /-rgt-identity 99.0%

          \[\leadsto \frac{\frac{1}{-3} - \color{blue}{\frac{x \cdot -0.3333333333333333}{1}}}{y} \cdot x \]

      20. associate-/l* 99.1%

          \[\leadsto \frac{\frac{1}{-3} - \color{blue}{\frac{x}{\frac{1}{-0.3333333333333333}}}}{y} \cdot x \]

      21. metadata-eval 99.1%

          \[\leadsto \frac{\frac{1}{-3} - \frac{x}{\color{blue}{-3}}}{y} \cdot x \]

      22. div-sub 99.1%

          \[\leadsto \frac{\color{blue}{\frac{1 - x}{-3}}}{y} \cdot x \]

      23. associate-/r* 99.0%

          \[\leadsto \color{blue}{\frac{1 - x}{-3 \cdot y}} \cdot x \]

      24. *-commutative 99.0%

          \[\leadsto \color{blue}{x \cdot \frac{1 - x}{-3 \cdot y}} \]

   8. Simplified 99.0%

      \[\leadsto \color{blue}{x \cdot \frac{1 - x}{y \cdot -3}} \]

   9. Taylor expanded in x around inf 99.1%

      \[\leadsto x \cdot \color{blue}{\left(0.3333333333333333 \cdot \frac{x}{y}\right)} \]
   10. Step-by-step derivation

       1. *-commutative 99.1%

          \[\leadsto x \cdot \color{blue}{\left(\frac{x}{y} \cdot 0.3333333333333333\right)} \]

   11. Simplified 99.1%

       \[\leadsto x \cdot \color{blue}{\left(\frac{x}{y} \cdot 0.3333333333333333\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.8:\\ \;\;\;\;x \cdot \frac{x}{\frac{y}{0.3333333333333333}}\\ \mathbf{elif}\;x \leq 3:\\ \;\;\;\;\left(1 - x\right) \cdot \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(0.3333333333333333 \cdot \frac{x}{y}\right)\\ \end{array} \]

Alternative 11: 98.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.6:\\ \;\;\;\;x \cdot \frac{x}{\frac{y}{0.3333333333333333}}\\ \mathbf{elif}\;x \leq 3:\\ \;\;\;\;\frac{x \cdot -1.3333333333333333 + 1}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(0.3333333333333333 \cdot \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -4.6)
   (* x (/ x (/ y 0.3333333333333333)))
   (if (<= x 3.0)
     (/ (+ (* x -1.3333333333333333) 1.0) y)
     (* x (* 0.3333333333333333 (/ x y))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -4.6) {
		tmp = x * (x / (y / 0.3333333333333333));
	} else if (x <= 3.0) {
		tmp = ((x * -1.3333333333333333) + 1.0) / y;
	} else {
		tmp = x * (0.3333333333333333 * (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 <= (-4.6d0)) then
        tmp = x * (x / (y / 0.3333333333333333d0))
    else if (x <= 3.0d0) then
        tmp = ((x * (-1.3333333333333333d0)) + 1.0d0) / y
    else
        tmp = x * (0.3333333333333333d0 * (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -4.6) {
		tmp = x * (x / (y / 0.3333333333333333));
	} else if (x <= 3.0) {
		tmp = ((x * -1.3333333333333333) + 1.0) / y;
	} else {
		tmp = x * (0.3333333333333333 * (x / y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -4.6:
		tmp = x * (x / (y / 0.3333333333333333))
	elif x <= 3.0:
		tmp = ((x * -1.3333333333333333) + 1.0) / y
	else:
		tmp = x * (0.3333333333333333 * (x / y))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -4.6)
		tmp = Float64(x * Float64(x / Float64(y / 0.3333333333333333)));
	elseif (x <= 3.0)
		tmp = Float64(Float64(Float64(x * -1.3333333333333333) + 1.0) / y);
	else
		tmp = Float64(x * Float64(0.3333333333333333 * Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -4.6)
		tmp = x * (x / (y / 0.3333333333333333));
	elseif (x <= 3.0)
		tmp = ((x * -1.3333333333333333) + 1.0) / y;
	else
		tmp = x * (0.3333333333333333 * (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -4.6], N[(x * N[(x / N[(y / 0.3333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.0], N[(N[(N[(x * -1.3333333333333333), $MachinePrecision] + 1.0), $MachinePrecision] / y), $MachinePrecision], N[(x * N[(0.3333333333333333 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.5999999999999996

   1. Initial program 87.0%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   2. Step-by-step derivation

      1. *-commutative 87.0%

         \[\leadsto \frac{\color{blue}{\left(3 - x\right) \cdot \left(1 - x\right)}}{y \cdot 3} \]

      2. associate-*l/ 99.8%

         \[\leadsto \color{blue}{\frac{3 - x}{y \cdot 3} \cdot \left(1 - x\right)} \]

      3. *-commutative 99.8%

         \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{3 - x}{y \cdot 3}} \]

      4. associate-/l/ 99.7%

         \[\leadsto \left(1 - x\right) \cdot \color{blue}{\frac{\frac{3 - x}{3}}{y}} \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{\frac{x + -3}{-3}}{y}} \]

   4. Taylor expanded in x around inf 98.6%

      \[\leadsto \left(1 - x\right) \cdot \color{blue}{\left(-0.3333333333333333 \cdot \frac{x}{y}\right)} \]
   5. Step-by-step derivation

      1. associate-*r/ 98.6%

         \[\leadsto \left(1 - x\right) \cdot \color{blue}{\frac{-0.3333333333333333 \cdot x}{y}} \]

      2. clear-num 98.7%

         \[\leadsto \left(1 - x\right) \cdot \color{blue}{\frac{1}{\frac{y}{-0.3333333333333333 \cdot x}}} \]

      3. un-div-inv 98.8%

         \[\leadsto \color{blue}{\frac{1 - x}{\frac{y}{-0.3333333333333333 \cdot x}}} \]

      4. *-un-lft-identity 98.8%

         \[\leadsto \frac{1 - x}{\frac{\color{blue}{1 \cdot y}}{-0.3333333333333333 \cdot x}} \]

      5. times-frac 98.9%

         \[\leadsto \frac{1 - x}{\color{blue}{\frac{1}{-0.3333333333333333} \cdot \frac{y}{x}}} \]

      6. metadata-eval 98.9%

         \[\leadsto \frac{1 - x}{\color{blue}{-3} \cdot \frac{y}{x}} \]

   6. Applied egg-rr 98.9%

      \[\leadsto \color{blue}{\frac{1 - x}{-3 \cdot \frac{y}{x}}} \]
   7. Step-by-step derivation

      1. associate-/r* 98.8%

         \[\leadsto \color{blue}{\frac{\frac{1 - x}{-3}}{\frac{y}{x}}} \]

      2. div-sub 98.8%

         \[\leadsto \frac{\color{blue}{\frac{1}{-3} - \frac{x}{-3}}}{\frac{y}{x}} \]

      3. metadata-eval 98.8%

         \[\leadsto \frac{\color{blue}{-0.3333333333333333} - \frac{x}{-3}}{\frac{y}{x}} \]

      4. metadata-eval 98.8%

         \[\leadsto \frac{-0.3333333333333333 - \frac{x}{\color{blue}{\frac{1}{-0.3333333333333333}}}}{\frac{y}{x}} \]

      5. associate-/l* 98.7%

         \[\leadsto \frac{-0.3333333333333333 - \color{blue}{\frac{x \cdot -0.3333333333333333}{1}}}{\frac{y}{x}} \]

      6. /-rgt-identity 98.7%

         \[\leadsto \frac{-0.3333333333333333 - \color{blue}{x \cdot -0.3333333333333333}}{\frac{y}{x}} \]

      7. cancel-sign-sub-inv 98.7%

         \[\leadsto \frac{\color{blue}{-0.3333333333333333 + \left(-x\right) \cdot -0.3333333333333333}}{\frac{y}{x}} \]

      8. metadata-eval 98.7%

         \[\leadsto \frac{\color{blue}{1 \cdot -0.3333333333333333} + \left(-x\right) \cdot -0.3333333333333333}{\frac{y}{x}} \]

      9. distribute-rgt-in 98.7%

         \[\leadsto \frac{\color{blue}{-0.3333333333333333 \cdot \left(1 + \left(-x\right)\right)}}{\frac{y}{x}} \]

      10. sub-neg 98.7%

          \[\leadsto \frac{-0.3333333333333333 \cdot \color{blue}{\left(1 - x\right)}}{\frac{y}{x}} \]

      11. *-commutative 98.7%

          \[\leadsto \frac{\color{blue}{\left(1 - x\right) \cdot -0.3333333333333333}}{\frac{y}{x}} \]

      12. associate-/r/ 98.6%

          \[\leadsto \color{blue}{\frac{\left(1 - x\right) \cdot -0.3333333333333333}{y} \cdot x} \]

      13. *-commutative 98.6%

          \[\leadsto \frac{\color{blue}{-0.3333333333333333 \cdot \left(1 - x\right)}}{y} \cdot x \]

      14. sub-neg 98.6%

          \[\leadsto \frac{-0.3333333333333333 \cdot \color{blue}{\left(1 + \left(-x\right)\right)}}{y} \cdot x \]

      15. distribute-rgt-in 98.6%

          \[\leadsto \frac{\color{blue}{1 \cdot -0.3333333333333333 + \left(-x\right) \cdot -0.3333333333333333}}{y} \cdot x \]

      16. metadata-eval 98.6%

          \[\leadsto \frac{\color{blue}{-0.3333333333333333} + \left(-x\right) \cdot -0.3333333333333333}{y} \cdot x \]

      17. cancel-sign-sub-inv 98.6%

          \[\leadsto \frac{\color{blue}{-0.3333333333333333 - x \cdot -0.3333333333333333}}{y} \cdot x \]

      18. metadata-eval 98.6%

          \[\leadsto \frac{\color{blue}{\frac{1}{-3}} - x \cdot -0.3333333333333333}{y} \cdot x \]

      19. /-rgt-identity 98.6%

          \[\leadsto \frac{\frac{1}{-3} - \color{blue}{\frac{x \cdot -0.3333333333333333}{1}}}{y} \cdot x \]

      20. associate-/l* 98.8%

          \[\leadsto \frac{\frac{1}{-3} - \color{blue}{\frac{x}{\frac{1}{-0.3333333333333333}}}}{y} \cdot x \]

      21. metadata-eval 98.8%

          \[\leadsto \frac{\frac{1}{-3} - \frac{x}{\color{blue}{-3}}}{y} \cdot x \]

      22. div-sub 98.8%

          \[\leadsto \frac{\color{blue}{\frac{1 - x}{-3}}}{y} \cdot x \]

      23. associate-/r* 98.9%

          \[\leadsto \color{blue}{\frac{1 - x}{-3 \cdot y}} \cdot x \]

      24. *-commutative 98.9%

          \[\leadsto \color{blue}{x \cdot \frac{1 - x}{-3 \cdot y}} \]

   8. Simplified 98.9%

      \[\leadsto \color{blue}{x \cdot \frac{1 - x}{y \cdot -3}} \]

   9. Taylor expanded in x around inf 98.6%

      \[\leadsto x \cdot \color{blue}{\left(0.3333333333333333 \cdot \frac{x}{y}\right)} \]
   10. Step-by-step derivation

       1. *-commutative 98.6%

          \[\leadsto x \cdot \color{blue}{\left(\frac{x}{y} \cdot 0.3333333333333333\right)} \]

   11. Simplified 98.6%

       \[\leadsto x \cdot \color{blue}{\left(\frac{x}{y} \cdot 0.3333333333333333\right)} \]
   12. Step-by-step derivation

       1. associate-*l/ 98.6%

          \[\leadsto x \cdot \color{blue}{\frac{x \cdot 0.3333333333333333}{y}} \]

       2. associate-/l* 98.6%

          \[\leadsto x \cdot \color{blue}{\frac{x}{\frac{y}{0.3333333333333333}}} \]

   13. Applied egg-rr 98.6%

       \[\leadsto x \cdot \color{blue}{\frac{x}{\frac{y}{0.3333333333333333}}} \]

   if -4.5999999999999996 < x < 3

   1. Initial program 99.5%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   2. Step-by-step derivation

      1. *-commutative 99.5%

         \[\leadsto \frac{\color{blue}{\left(3 - x\right) \cdot \left(1 - x\right)}}{y \cdot 3} \]

      2. associate-*l/ 99.6%

         \[\leadsto \color{blue}{\frac{3 - x}{y \cdot 3} \cdot \left(1 - x\right)} \]

      3. *-commutative 99.6%

         \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{3 - x}{y \cdot 3}} \]

      4. associate-/l/ 100.0%

         \[\leadsto \left(1 - x\right) \cdot \color{blue}{\frac{\frac{3 - x}{3}}{y}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{\frac{x + -3}{-3}}{y}} \]

   4. Taylor expanded in x around 0 98.4%

      \[\leadsto \color{blue}{-1.3333333333333333 \cdot \frac{x}{y} + \frac{1}{y}} \]

   5. Taylor expanded in y around 0 98.4%

      \[\leadsto \color{blue}{\frac{1 + -1.3333333333333333 \cdot x}{y}} \]

   if 3 < x

   1. Initial program 87.5%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   2. Step-by-step derivation

      1. *-commutative 87.5%

         \[\leadsto \frac{\color{blue}{\left(3 - x\right) \cdot \left(1 - x\right)}}{y \cdot 3} \]

      2. associate-*l/ 99.6%

         \[\leadsto \color{blue}{\frac{3 - x}{y \cdot 3} \cdot \left(1 - x\right)} \]

      3. *-commutative 99.6%

         \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{3 - x}{y \cdot 3}} \]

      4. associate-/l/ 99.7%

         \[\leadsto \left(1 - x\right) \cdot \color{blue}{\frac{\frac{3 - x}{3}}{y}} \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{\frac{x + -3}{-3}}{y}} \]

   4. Taylor expanded in x around inf 99.1%

      \[\leadsto \left(1 - x\right) \cdot \color{blue}{\left(-0.3333333333333333 \cdot \frac{x}{y}\right)} \]
   5. Step-by-step derivation

      1. associate-*r/ 99.0%

         \[\leadsto \left(1 - x\right) \cdot \color{blue}{\frac{-0.3333333333333333 \cdot x}{y}} \]

      2. clear-num 99.0%

         \[\leadsto \left(1 - x\right) \cdot \color{blue}{\frac{1}{\frac{y}{-0.3333333333333333 \cdot x}}} \]

      3. un-div-inv 99.0%

         \[\leadsto \color{blue}{\frac{1 - x}{\frac{y}{-0.3333333333333333 \cdot x}}} \]

      4. *-un-lft-identity 99.0%

         \[\leadsto \frac{1 - x}{\frac{\color{blue}{1 \cdot y}}{-0.3333333333333333 \cdot x}} \]

      5. times-frac 99.1%

         \[\leadsto \frac{1 - x}{\color{blue}{\frac{1}{-0.3333333333333333} \cdot \frac{y}{x}}} \]

      6. metadata-eval 99.1%

         \[\leadsto \frac{1 - x}{\color{blue}{-3} \cdot \frac{y}{x}} \]

   6. Applied egg-rr 99.1%

      \[\leadsto \color{blue}{\frac{1 - x}{-3 \cdot \frac{y}{x}}} \]
   7. Step-by-step derivation

      1. associate-/r* 99.1%

         \[\leadsto \color{blue}{\frac{\frac{1 - x}{-3}}{\frac{y}{x}}} \]

      2. div-sub 99.1%

         \[\leadsto \frac{\color{blue}{\frac{1}{-3} - \frac{x}{-3}}}{\frac{y}{x}} \]

      3. metadata-eval 99.1%

         \[\leadsto \frac{\color{blue}{-0.3333333333333333} - \frac{x}{-3}}{\frac{y}{x}} \]

      4. metadata-eval 99.1%

         \[\leadsto \frac{-0.3333333333333333 - \frac{x}{\color{blue}{\frac{1}{-0.3333333333333333}}}}{\frac{y}{x}} \]

      5. associate-/l* 99.0%

         \[\leadsto \frac{-0.3333333333333333 - \color{blue}{\frac{x \cdot -0.3333333333333333}{1}}}{\frac{y}{x}} \]

      6. /-rgt-identity 99.0%

         \[\leadsto \frac{-0.3333333333333333 - \color{blue}{x \cdot -0.3333333333333333}}{\frac{y}{x}} \]

      7. cancel-sign-sub-inv 99.0%

         \[\leadsto \frac{\color{blue}{-0.3333333333333333 + \left(-x\right) \cdot -0.3333333333333333}}{\frac{y}{x}} \]

      8. metadata-eval 99.0%

         \[\leadsto \frac{\color{blue}{1 \cdot -0.3333333333333333} + \left(-x\right) \cdot -0.3333333333333333}{\frac{y}{x}} \]

      9. distribute-rgt-in 99.0%

         \[\leadsto \frac{\color{blue}{-0.3333333333333333 \cdot \left(1 + \left(-x\right)\right)}}{\frac{y}{x}} \]

      10. sub-neg 99.0%

          \[\leadsto \frac{-0.3333333333333333 \cdot \color{blue}{\left(1 - x\right)}}{\frac{y}{x}} \]

      11. *-commutative 99.0%

          \[\leadsto \frac{\color{blue}{\left(1 - x\right) \cdot -0.3333333333333333}}{\frac{y}{x}} \]

      12. associate-/r/ 99.0%

          \[\leadsto \color{blue}{\frac{\left(1 - x\right) \cdot -0.3333333333333333}{y} \cdot x} \]

      13. *-commutative 99.0%

          \[\leadsto \frac{\color{blue}{-0.3333333333333333 \cdot \left(1 - x\right)}}{y} \cdot x \]

      14. sub-neg 99.0%

          \[\leadsto \frac{-0.3333333333333333 \cdot \color{blue}{\left(1 + \left(-x\right)\right)}}{y} \cdot x \]

      15. distribute-rgt-in 99.0%

          \[\leadsto \frac{\color{blue}{1 \cdot -0.3333333333333333 + \left(-x\right) \cdot -0.3333333333333333}}{y} \cdot x \]

      16. metadata-eval 99.0%

          \[\leadsto \frac{\color{blue}{-0.3333333333333333} + \left(-x\right) \cdot -0.3333333333333333}{y} \cdot x \]

      17. cancel-sign-sub-inv 99.0%

          \[\leadsto \frac{\color{blue}{-0.3333333333333333 - x \cdot -0.3333333333333333}}{y} \cdot x \]

      18. metadata-eval 99.0%

          \[\leadsto \frac{\color{blue}{\frac{1}{-3}} - x \cdot -0.3333333333333333}{y} \cdot x \]

      19. /-rgt-identity 99.0%

          \[\leadsto \frac{\frac{1}{-3} - \color{blue}{\frac{x \cdot -0.3333333333333333}{1}}}{y} \cdot x \]

      20. associate-/l* 99.1%

          \[\leadsto \frac{\frac{1}{-3} - \color{blue}{\frac{x}{\frac{1}{-0.3333333333333333}}}}{y} \cdot x \]

      21. metadata-eval 99.1%

          \[\leadsto \frac{\frac{1}{-3} - \frac{x}{\color{blue}{-3}}}{y} \cdot x \]

      22. div-sub 99.1%

          \[\leadsto \frac{\color{blue}{\frac{1 - x}{-3}}}{y} \cdot x \]

      23. associate-/r* 99.0%

          \[\leadsto \color{blue}{\frac{1 - x}{-3 \cdot y}} \cdot x \]

      24. *-commutative 99.0%

          \[\leadsto \color{blue}{x \cdot \frac{1 - x}{-3 \cdot y}} \]

   8. Simplified 99.0%

      \[\leadsto \color{blue}{x \cdot \frac{1 - x}{y \cdot -3}} \]

   9. Taylor expanded in x around inf 99.1%

      \[\leadsto x \cdot \color{blue}{\left(0.3333333333333333 \cdot \frac{x}{y}\right)} \]
   10. Step-by-step derivation

       1. *-commutative 99.1%

          \[\leadsto x \cdot \color{blue}{\left(\frac{x}{y} \cdot 0.3333333333333333\right)} \]

   11. Simplified 99.1%

       \[\leadsto x \cdot \color{blue}{\left(\frac{x}{y} \cdot 0.3333333333333333\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.6:\\ \;\;\;\;x \cdot \frac{x}{\frac{y}{0.3333333333333333}}\\ \mathbf{elif}\;x \leq 3:\\ \;\;\;\;\frac{x \cdot -1.3333333333333333 + 1}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(0.3333333333333333 \cdot \frac{x}{y}\right)\\ \end{array} \]

Alternative 12: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(1 - x\right) \cdot \frac{\frac{x + -3}{-3}}{y} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* (- 1.0 x) (/ (/ (+ x -3.0) -3.0) y)))

C

double code(double x, double y) {
	return (1.0 - x) * (((x + -3.0) / -3.0) / y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (1.0d0 - x) * (((x + (-3.0d0)) / (-3.0d0)) / y)
end function

Java

public static double code(double x, double y) {
	return (1.0 - x) * (((x + -3.0) / -3.0) / y);
}

Python

def code(x, y):
	return (1.0 - x) * (((x + -3.0) / -3.0) / y)

Julia

function code(x, y)
	return Float64(Float64(1.0 - x) * Float64(Float64(Float64(x + -3.0) / -3.0) / y))
end

MATLAB

function tmp = code(x, y)
	tmp = (1.0 - x) * (((x + -3.0) / -3.0) / y);
end

Wolfram

code[x_, y_] := N[(N[(1.0 - x), $MachinePrecision] * N[(N[(N[(x + -3.0), $MachinePrecision] / -3.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 93.8%

   \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
2. Step-by-step derivation

   1. *-commutative 93.8%

      \[\leadsto \frac{\color{blue}{\left(3 - x\right) \cdot \left(1 - x\right)}}{y \cdot 3} \]

   2. associate-*l/ 99.6%

      \[\leadsto \color{blue}{\frac{3 - x}{y \cdot 3} \cdot \left(1 - x\right)} \]

   3. *-commutative 99.6%

      \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{3 - x}{y \cdot 3}} \]

   4. associate-/l/ 99.8%

      \[\leadsto \left(1 - x\right) \cdot \color{blue}{\frac{\frac{3 - x}{3}}{y}} \]

3. Simplified 99.8%

   \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{\frac{x + -3}{-3}}{y}} \]

4. Final simplification 99.8%

   \[\leadsto \left(1 - x\right) \cdot \frac{\frac{x + -3}{-3}}{y} \]

Alternative 13: 57.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.75:\\ \;\;\;\;-1.3333333333333333 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -0.75) (* -1.3333333333333333 (/ x y)) (/ 1.0 y)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -0.75) {
		tmp = -1.3333333333333333 * (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 <= (-0.75d0)) then
        tmp = (-1.3333333333333333d0) * (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 <= -0.75) {
		tmp = -1.3333333333333333 * (x / y);
	} else {
		tmp = 1.0 / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -0.75:
		tmp = -1.3333333333333333 * (x / y)
	else:
		tmp = 1.0 / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -0.75)
		tmp = Float64(-1.3333333333333333 * 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 <= -0.75)
		tmp = -1.3333333333333333 * (x / y);
	else
		tmp = 1.0 / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -0.75], N[(-1.3333333333333333 * N[(x / y), $MachinePrecision]), $MachinePrecision], N[(1.0 / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -0.75

   1. Initial program 87.0%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   2. Step-by-step derivation

      1. *-commutative 87.0%

         \[\leadsto \frac{\color{blue}{\left(3 - x\right) \cdot \left(1 - x\right)}}{y \cdot 3} \]

      2. associate-*l/ 99.8%

         \[\leadsto \color{blue}{\frac{3 - x}{y \cdot 3} \cdot \left(1 - x\right)} \]

      3. *-commutative 99.8%

         \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{3 - x}{y \cdot 3}} \]

      4. associate-/l/ 99.7%

         \[\leadsto \left(1 - x\right) \cdot \color{blue}{\frac{\frac{3 - x}{3}}{y}} \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{\frac{x + -3}{-3}}{y}} \]

   4. Taylor expanded in x around 0 30.5%

      \[\leadsto \color{blue}{-1.3333333333333333 \cdot \frac{x}{y} + \frac{1}{y}} \]

   5. Taylor expanded in x around inf 30.5%

      \[\leadsto \color{blue}{-1.3333333333333333 \cdot \frac{x}{y}} \]

   if -0.75 < x

   1. Initial program 95.8%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   2. Step-by-step derivation

      1. *-commutative 95.8%

         \[\leadsto \frac{\color{blue}{\left(3 - x\right) \cdot \left(1 - x\right)}}{y \cdot 3} \]

      2. associate-*l/ 99.6%

         \[\leadsto \color{blue}{\frac{3 - x}{y \cdot 3} \cdot \left(1 - x\right)} \]

      3. *-commutative 99.6%

         \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{3 - x}{y \cdot 3}} \]

      4. associate-/l/ 99.9%

         \[\leadsto \left(1 - x\right) \cdot \color{blue}{\frac{\frac{3 - x}{3}}{y}} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{\frac{x + -3}{-3}}{y}} \]
   4. Step-by-step derivation

      1. associate-*r/ 96.1%

         \[\leadsto \color{blue}{\frac{\left(1 - x\right) \cdot \frac{x + -3}{-3}}{y}} \]

      2. *-commutative 96.1%

         \[\leadsto \frac{\color{blue}{\frac{x + -3}{-3} \cdot \left(1 - x\right)}}{y} \]

      3. frac-2neg 96.1%

         \[\leadsto \frac{\color{blue}{\frac{-\left(x + -3\right)}{--3}} \cdot \left(1 - x\right)}{y} \]

      4. +-commutative 96.1%

         \[\leadsto \frac{\frac{-\color{blue}{\left(-3 + x\right)}}{--3} \cdot \left(1 - x\right)}{y} \]

      5. distribute-neg-in 96.1%

         \[\leadsto \frac{\frac{\color{blue}{\left(--3\right) + \left(-x\right)}}{--3} \cdot \left(1 - x\right)}{y} \]

      6. metadata-eval 96.1%

         \[\leadsto \frac{\frac{\color{blue}{3} + \left(-x\right)}{--3} \cdot \left(1 - x\right)}{y} \]

      7. sub-neg 96.1%

         \[\leadsto \frac{\frac{\color{blue}{3 - x}}{--3} \cdot \left(1 - x\right)}{y} \]

      8. metadata-eval 96.1%

         \[\leadsto \frac{\frac{3 - x}{\color{blue}{3}} \cdot \left(1 - x\right)}{y} \]

      9. associate-*r/ 99.9%

         \[\leadsto \color{blue}{\frac{3 - x}{3} \cdot \frac{1 - x}{y}} \]

      10. clear-num 99.9%

          \[\leadsto \color{blue}{\frac{1}{\frac{3}{3 - x}}} \cdot \frac{1 - x}{y} \]

      11. associate-*l/ 99.9%

          \[\leadsto \color{blue}{\frac{1 \cdot \frac{1 - x}{y}}{\frac{3}{3 - x}}} \]

      12. *-un-lft-identity 99.9%

          \[\leadsto \frac{\color{blue}{\frac{1 - x}{y}}}{\frac{3}{3 - x}} \]

      13. metadata-eval 99.9%

          \[\leadsto \frac{\frac{1 - x}{y}}{\frac{\color{blue}{--3}}{3 - x}} \]

      14. sub-neg 99.9%

          \[\leadsto \frac{\frac{1 - x}{y}}{\frac{--3}{\color{blue}{3 + \left(-x\right)}}} \]

      15. metadata-eval 99.9%

          \[\leadsto \frac{\frac{1 - x}{y}}{\frac{--3}{\color{blue}{\left(--3\right)} + \left(-x\right)}} \]

      16. distribute-neg-in 99.9%

          \[\leadsto \frac{\frac{1 - x}{y}}{\frac{--3}{\color{blue}{-\left(-3 + x\right)}}} \]

      17. +-commutative 99.9%

          \[\leadsto \frac{\frac{1 - x}{y}}{\frac{--3}{-\color{blue}{\left(x + -3\right)}}} \]

      18. frac-2neg 99.9%

          \[\leadsto \frac{\frac{1 - x}{y}}{\color{blue}{\frac{-3}{x + -3}}} \]

   5. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{\frac{\frac{1 - x}{y}}{\frac{-3}{x + -3}}} \]

   6. Taylor expanded in x around 0 68.9%

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

4. Final simplification 60.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.75:\\ \;\;\;\;-1.3333333333333333 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{y}\\ \end{array} \]

Alternative 14: 57.3% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Python

def code(x, y):
	tmp = 0
	if x <= -1.0:
		tmp = -x / y
	else:
		tmp = 1.0 / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.0)
		tmp = Float64(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)
		tmp = -x / y;
	else
		tmp = 1.0 / y;
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if x < -1

   1. Initial program 87.0%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   2. Step-by-step derivation

      1. *-commutative 87.0%

         \[\leadsto \frac{\color{blue}{\left(3 - x\right) \cdot \left(1 - x\right)}}{y \cdot 3} \]

      2. associate-*l/ 99.8%

         \[\leadsto \color{blue}{\frac{3 - x}{y \cdot 3} \cdot \left(1 - x\right)} \]

      3. *-commutative 99.8%

         \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{3 - x}{y \cdot 3}} \]

      4. associate-/l/ 99.7%

         \[\leadsto \left(1 - x\right) \cdot \color{blue}{\frac{\frac{3 - x}{3}}{y}} \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{\frac{x + -3}{-3}}{y}} \]

   4. Taylor expanded in x around 0 30.4%

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

   5. Taylor expanded in x around inf 30.4%

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

      1. neg-mul-1 30.4%

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

      2. distribute-neg-frac 30.4%

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

   7. Simplified 30.4%

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

   if -1 < x

   1. Initial program 95.8%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   2. Step-by-step derivation

      1. *-commutative 95.8%

         \[\leadsto \frac{\color{blue}{\left(3 - x\right) \cdot \left(1 - x\right)}}{y \cdot 3} \]

      2. associate-*l/ 99.6%

         \[\leadsto \color{blue}{\frac{3 - x}{y \cdot 3} \cdot \left(1 - x\right)} \]

      3. *-commutative 99.6%

         \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{3 - x}{y \cdot 3}} \]

      4. associate-/l/ 99.9%

         \[\leadsto \left(1 - x\right) \cdot \color{blue}{\frac{\frac{3 - x}{3}}{y}} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{\frac{x + -3}{-3}}{y}} \]
   4. Step-by-step derivation

      1. associate-*r/ 96.1%

         \[\leadsto \color{blue}{\frac{\left(1 - x\right) \cdot \frac{x + -3}{-3}}{y}} \]

      2. *-commutative 96.1%

         \[\leadsto \frac{\color{blue}{\frac{x + -3}{-3} \cdot \left(1 - x\right)}}{y} \]

      3. frac-2neg 96.1%

         \[\leadsto \frac{\color{blue}{\frac{-\left(x + -3\right)}{--3}} \cdot \left(1 - x\right)}{y} \]

      4. +-commutative 96.1%

         \[\leadsto \frac{\frac{-\color{blue}{\left(-3 + x\right)}}{--3} \cdot \left(1 - x\right)}{y} \]

      5. distribute-neg-in 96.1%

         \[\leadsto \frac{\frac{\color{blue}{\left(--3\right) + \left(-x\right)}}{--3} \cdot \left(1 - x\right)}{y} \]

      6. metadata-eval 96.1%

         \[\leadsto \frac{\frac{\color{blue}{3} + \left(-x\right)}{--3} \cdot \left(1 - x\right)}{y} \]

      7. sub-neg 96.1%

         \[\leadsto \frac{\frac{\color{blue}{3 - x}}{--3} \cdot \left(1 - x\right)}{y} \]

      8. metadata-eval 96.1%

         \[\leadsto \frac{\frac{3 - x}{\color{blue}{3}} \cdot \left(1 - x\right)}{y} \]

      9. associate-*r/ 99.9%

         \[\leadsto \color{blue}{\frac{3 - x}{3} \cdot \frac{1 - x}{y}} \]

      10. clear-num 99.9%

          \[\leadsto \color{blue}{\frac{1}{\frac{3}{3 - x}}} \cdot \frac{1 - x}{y} \]

      11. associate-*l/ 99.9%

          \[\leadsto \color{blue}{\frac{1 \cdot \frac{1 - x}{y}}{\frac{3}{3 - x}}} \]

      12. *-un-lft-identity 99.9%

          \[\leadsto \frac{\color{blue}{\frac{1 - x}{y}}}{\frac{3}{3 - x}} \]

      13. metadata-eval 99.9%

          \[\leadsto \frac{\frac{1 - x}{y}}{\frac{\color{blue}{--3}}{3 - x}} \]

      14. sub-neg 99.9%

          \[\leadsto \frac{\frac{1 - x}{y}}{\frac{--3}{\color{blue}{3 + \left(-x\right)}}} \]

      15. metadata-eval 99.9%

          \[\leadsto \frac{\frac{1 - x}{y}}{\frac{--3}{\color{blue}{\left(--3\right)} + \left(-x\right)}} \]

      16. distribute-neg-in 99.9%

          \[\leadsto \frac{\frac{1 - x}{y}}{\frac{--3}{\color{blue}{-\left(-3 + x\right)}}} \]

      17. +-commutative 99.9%

          \[\leadsto \frac{\frac{1 - x}{y}}{\frac{--3}{-\color{blue}{\left(x + -3\right)}}} \]

      18. frac-2neg 99.9%

          \[\leadsto \frac{\frac{1 - x}{y}}{\color{blue}{\frac{-3}{x + -3}}} \]

   5. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{\frac{\frac{1 - x}{y}}{\frac{-3}{x + -3}}} \]

   6. Taylor expanded in x around 0 68.9%

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

4. Final simplification 60.2%

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

Alternative 15: 56.3% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \frac{1 - x}{y} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.8%

   \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
2. Step-by-step derivation

   1. *-commutative 93.8%

      \[\leadsto \frac{\color{blue}{\left(3 - x\right) \cdot \left(1 - x\right)}}{y \cdot 3} \]

   2. associate-*l/ 99.6%

      \[\leadsto \color{blue}{\frac{3 - x}{y \cdot 3} \cdot \left(1 - x\right)} \]

   3. *-commutative 99.6%

      \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{3 - x}{y \cdot 3}} \]

   4. associate-/l/ 99.8%

      \[\leadsto \left(1 - x\right) \cdot \color{blue}{\frac{\frac{3 - x}{3}}{y}} \]

3. Simplified 99.8%

   \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{\frac{x + -3}{-3}}{y}} \]

4. Taylor expanded in x around 0 59.4%

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

5. Taylor expanded in x around 0 59.4%

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

   1. neg-mul-1 59.4%

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

   2. +-commutative 59.4%

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

   3. sub-neg 59.4%

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

   4. div-sub 59.4%

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

7. Simplified 59.4%

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

8. Final simplification 59.4%

   \[\leadsto \frac{1 - x}{y} \]

Alternative 16: 51.1% accurate, 3.7× speedup

Math

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

FPCore

(FPCore (x y) :precision binary64 (/ 1.0 y))

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return 1.0 / y

Julia

function code(x, y)
	return Float64(1.0 / y)
end

MATLAB

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

Wolfram

code[x_, y_] := N[(1.0 / y), $MachinePrecision]

Derivation

1. Initial program 93.8%

   \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
2. Step-by-step derivation

   1. *-commutative 93.8%

      \[\leadsto \frac{\color{blue}{\left(3 - x\right) \cdot \left(1 - x\right)}}{y \cdot 3} \]

   2. associate-*l/ 99.6%

      \[\leadsto \color{blue}{\frac{3 - x}{y \cdot 3} \cdot \left(1 - x\right)} \]

   3. *-commutative 99.6%

      \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{3 - x}{y \cdot 3}} \]

   4. associate-/l/ 99.8%

      \[\leadsto \left(1 - x\right) \cdot \color{blue}{\frac{\frac{3 - x}{3}}{y}} \]

3. Simplified 99.8%

   \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{\frac{x + -3}{-3}}{y}} \]
4. Step-by-step derivation

   1. associate-*r/ 94.1%

      \[\leadsto \color{blue}{\frac{\left(1 - x\right) \cdot \frac{x + -3}{-3}}{y}} \]

   2. *-commutative 94.1%

      \[\leadsto \frac{\color{blue}{\frac{x + -3}{-3} \cdot \left(1 - x\right)}}{y} \]

   3. frac-2neg 94.1%

      \[\leadsto \frac{\color{blue}{\frac{-\left(x + -3\right)}{--3}} \cdot \left(1 - x\right)}{y} \]

   4. +-commutative 94.1%

      \[\leadsto \frac{\frac{-\color{blue}{\left(-3 + x\right)}}{--3} \cdot \left(1 - x\right)}{y} \]

   5. distribute-neg-in 94.1%

      \[\leadsto \frac{\frac{\color{blue}{\left(--3\right) + \left(-x\right)}}{--3} \cdot \left(1 - x\right)}{y} \]

   6. metadata-eval 94.1%

      \[\leadsto \frac{\frac{\color{blue}{3} + \left(-x\right)}{--3} \cdot \left(1 - x\right)}{y} \]

   7. sub-neg 94.1%

      \[\leadsto \frac{\frac{\color{blue}{3 - x}}{--3} \cdot \left(1 - x\right)}{y} \]

   8. metadata-eval 94.1%

      \[\leadsto \frac{\frac{3 - x}{\color{blue}{3}} \cdot \left(1 - x\right)}{y} \]

   9. associate-*r/ 99.9%

      \[\leadsto \color{blue}{\frac{3 - x}{3} \cdot \frac{1 - x}{y}} \]

   10. clear-num 99.8%

       \[\leadsto \color{blue}{\frac{1}{\frac{3}{3 - x}}} \cdot \frac{1 - x}{y} \]

   11. associate-*l/ 99.8%

       \[\leadsto \color{blue}{\frac{1 \cdot \frac{1 - x}{y}}{\frac{3}{3 - x}}} \]

   12. *-un-lft-identity 99.8%

       \[\leadsto \frac{\color{blue}{\frac{1 - x}{y}}}{\frac{3}{3 - x}} \]

   13. metadata-eval 99.8%

       \[\leadsto \frac{\frac{1 - x}{y}}{\frac{\color{blue}{--3}}{3 - x}} \]

   14. sub-neg 99.8%

       \[\leadsto \frac{\frac{1 - x}{y}}{\frac{--3}{\color{blue}{3 + \left(-x\right)}}} \]

   15. metadata-eval 99.8%

       \[\leadsto \frac{\frac{1 - x}{y}}{\frac{--3}{\color{blue}{\left(--3\right)} + \left(-x\right)}} \]

   16. distribute-neg-in 99.8%

       \[\leadsto \frac{\frac{1 - x}{y}}{\frac{--3}{\color{blue}{-\left(-3 + x\right)}}} \]

   17. +-commutative 99.8%

       \[\leadsto \frac{\frac{1 - x}{y}}{\frac{--3}{-\color{blue}{\left(x + -3\right)}}} \]

   18. frac-2neg 99.8%

       \[\leadsto \frac{\frac{1 - x}{y}}{\color{blue}{\frac{-3}{x + -3}}} \]

5. Applied egg-rr 99.8%

   \[\leadsto \color{blue}{\frac{\frac{1 - x}{y}}{\frac{-3}{x + -3}}} \]

6. Taylor expanded in x around 0 54.4%

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

7. Final simplification 54.4%

   \[\leadsto \frac{1}{y} \]

Developer target: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{1 - x}{y} \cdot \frac{3 - x}{3} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* (/ (- 1.0 x) y) (/ (- 3.0 x) 3.0)))

C

double code(double x, double y) {
	return ((1.0 - x) / y) * ((3.0 - x) / 3.0);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = ((1.0d0 - x) / y) * ((3.0d0 - x) / 3.0d0)
end function

Java

public static double code(double x, double y) {
	return ((1.0 - x) / y) * ((3.0 - x) / 3.0);
}

Python

def code(x, y):
	return ((1.0 - x) / y) * ((3.0 - x) / 3.0)

Julia

function code(x, y)
	return Float64(Float64(Float64(1.0 - x) / y) * Float64(Float64(3.0 - x) / 3.0))
end

MATLAB

function tmp = code(x, y)
	tmp = ((1.0 - x) / y) * ((3.0 - x) / 3.0);
end

Wolfram

code[x_, y_] := N[(N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision] * N[(N[(3.0 - x), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2023325 
(FPCore (x y)
  :name "Diagrams.TwoD.Arc:bezierFromSweepQ1 from diagrams-lib-1.3.0.3"
  :precision binary64

  :herbie-target
  (* (/ (- 1.0 x) y) (/ (- 3.0 x) 3.0))

  (/ (* (- 1.0 x) (- 3.0 x)) (* y 3.0)))