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

Percentage Accurate: 94.2% → 99.8%

Time: 7.5s

Alternatives: 12

Speedup: 1.0×

• 24.5% 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: 94.2% 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 92.7%

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

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.3 \lor \neg \left(x \leq 1.3\right):\\ \;\;\;\;-0.3333333333333333 \cdot \frac{3 - x}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot -1.3333333333333333 + 1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -2.3) (not (<= x 1.3)))
   (* -0.3333333333333333 (/ (- 3.0 x) (/ y x)))
   (/ (+ (* x -1.3333333333333333) 1.0) y)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -2.3) || !(x <= 1.3)) {
		tmp = -0.3333333333333333 * ((3.0 - x) / (y / x));
	} 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 = (-0.3333333333333333d0) * ((3.0d0 - x) / (y / x))
    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 = -0.3333333333333333 * ((3.0 - x) / (y / x));
	} 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 = -0.3333333333333333 * ((3.0 - x) / (y / x))
	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(-0.3333333333333333 * Float64(Float64(3.0 - x) / Float64(y / x)));
	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 = -0.3333333333333333 * ((3.0 - x) / (y / x));
	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[(-0.3333333333333333 * N[(N[(3.0 - x), $MachinePrecision] / N[(y / x), $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 < -2.2999999999999998 or 1.30000000000000004 < x

   1. Initial program 86.0%

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

      1. times-frac 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 98.0%

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

      1. neg-mul-1 98.0%

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

      2. distribute-neg-frac 98.0%

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

   6. Simplified 98.0%

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

   7. Taylor expanded in y around 0 84.1%

      \[\leadsto \color{blue}{-0.3333333333333333 \cdot \frac{x \cdot \left(3 - x\right)}{y}} \]
   8. Step-by-step derivation

      1. *-commutative 84.1%

         \[\leadsto -0.3333333333333333 \cdot \frac{\color{blue}{\left(3 - x\right) \cdot x}}{y} \]

      2. associate-/l* 97.9%

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

   9. Simplified 97.9%

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

   if -2.2999999999999998 < x < 1.30000000000000004

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

      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. *-lft-identity 99.6%

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

      5. associate-*l/ 99.4%

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

      6. *-commutative 99.4%

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

      7. *-commutative 99.4%

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

      8. associate-/r* 99.3%

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

      9. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in x around 0 99.8%

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

   5. Taylor expanded in y around 0 99.8%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3 \lor \neg \left(x \leq 1.3\right):\\ \;\;\;\;-0.3333333333333333 \cdot \frac{3 - x}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot -1.3333333333333333 + 1}{y}\\ \end{array} \]

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 86.0%

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

      1. times-frac 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 98.0%

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

      1. neg-mul-1 98.0%

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

      2. distribute-neg-frac 98.0%

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

   6. Simplified 98.0%

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

   if -2.2999999999999998 < x < 1.30000000000000004

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

      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. *-lft-identity 99.6%

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

      5. associate-*l/ 99.4%

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

      6. *-commutative 99.4%

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

      7. *-commutative 99.4%

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

      8. associate-/r* 99.3%

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

      9. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in x around 0 99.8%

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

   5. Taylor expanded in y around 0 99.8%

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

4. Final simplification 98.9%

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

Alternative 4: 98.3% accurate, 0.9× speedup

Math

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

FPCore

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

C

double code(double x, double y) {
	double tmp;
	if ((x <= -4.6) || !(x <= 3.0)) {
		tmp = (-x / y) * (x * -0.3333333333333333);
	} 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 = (-x / y) * (x * (-0.3333333333333333d0))
    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 = (-x / y) * (x * -0.3333333333333333);
	} 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 = (-x / y) * (x * -0.3333333333333333)
	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(Float64(Float64(-x) / y) * Float64(x * -0.3333333333333333));
	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 = (-x / y) * (x * -0.3333333333333333);
	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[(N[((-x) / y), $MachinePrecision] * N[(x * -0.3333333333333333), $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 86.0%

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

      1. times-frac 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 97.8%

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

   5. Taylor expanded in x around inf 97.8%

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

      1. neg-mul-1 98.0%

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

      2. distribute-neg-frac 98.0%

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

   7. Simplified 97.8%

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

   if -4.5999999999999996 < x < 3

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

      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. *-lft-identity 99.6%

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

      5. associate-*l/ 99.4%

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

      6. *-commutative 99.4%

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

      7. *-commutative 99.4%

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

      8. associate-/r* 99.3%

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

      9. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in x around 0 99.8%

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

   5. Taylor expanded in y around 0 99.8%

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

4. Final simplification 98.8%

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

Alternative 5: 97.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.75 \lor \neg \left(x \leq 0.56\right):\\ \;\;\;\;x \cdot \left(0.3333333333333333 \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -1.75) (not (<= x 0.56)))
   (* x (* 0.3333333333333333 (/ x y)))
   (/ 1.0 y)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -1.75) || !(x <= 0.56)) {
		tmp = x * (0.3333333333333333 * (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 <= (-1.75d0)) .or. (.not. (x <= 0.56d0))) then
        tmp = x * (0.3333333333333333d0 * (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 <= -1.75) || !(x <= 0.56)) {
		tmp = x * (0.3333333333333333 * (x / y));
	} else {
		tmp = 1.0 / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -1.75) or not (x <= 0.56):
		tmp = x * (0.3333333333333333 * (x / y))
	else:
		tmp = 1.0 / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -1.75) || !(x <= 0.56))
		tmp = Float64(x * Float64(0.3333333333333333 * 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 <= -1.75) || ~((x <= 0.56)))
		tmp = x * (0.3333333333333333 * (x / y));
	else
		tmp = 1.0 / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -1.75], N[Not[LessEqual[x, 0.56]], $MachinePrecision]], N[(x * N[(0.3333333333333333 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.75 or 0.56000000000000005 < x

   1. Initial program 86.0%

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

      1. times-frac 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 98.0%

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

      1. neg-mul-1 98.0%

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

      2. distribute-neg-frac 98.0%

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

   6. Simplified 98.0%

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

      1. frac-2neg 98.0%

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

      2. frac-2neg 98.0%

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

      3. frac-times 84.1%

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

      4. remove-double-neg 84.1%

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

      5. sub-neg 84.1%

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

      6. distribute-neg-in 84.1%

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

      7. metadata-eval 84.1%

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

      8. remove-double-neg 84.1%

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

      9. metadata-eval 84.1%

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

   8. Applied egg-rr 84.1%

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

      1. *-commutative 84.1%

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

      2. *-commutative 84.1%

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

      3. distribute-rgt-neg-out 84.1%

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

      4. distribute-lft-neg-in 84.1%

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

      5. metadata-eval 84.1%

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

      6. *-commutative 84.1%

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

      7. associate-/l* 97.1%

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

      8. associate-/r/ 97.1%

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

      9. +-commutative 97.1%

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

   10. Simplified 97.1%

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

   11. Taylor expanded in x around inf 97.7%

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

   if -1.75 < x < 0.56000000000000005

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

      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. *-lft-identity 99.6%

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

      5. associate-*l/ 99.4%

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

      6. *-commutative 99.4%

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

      7. *-commutative 99.4%

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

      8. associate-/r* 99.3%

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

      9. metadata-eval 99.3%

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

   3. Simplified 99.3%

      \[\leadsto \color{blue}{\left(1 - x\right) \cdot \left(\left(3 - x\right) \cdot \frac{0.3333333333333333}{y}\right)} \]
   4. Step-by-step derivation

      1. associate-*r/ 100.0%

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

      2. metadata-eval 100.0%

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

      3. div-inv 100.0%

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

      4. associate-*r/ 100.0%

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

      5. associate-*l/ 100.0%

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

      6. clear-num 100.0%

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

      7. associate-*l/ 100.0%

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

      8. *-un-lft-identity 100.0%

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

      9. div-sub 100.0%

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

      10. metadata-eval 100.0%

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

      11. div-inv 100.0%

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

      12. metadata-eval 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in x around 0 98.9%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.75 \lor \neg \left(x \leq 0.56\right):\\ \;\;\;\;x \cdot \left(0.3333333333333333 \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{y}\\ \end{array} \]

Alternative 6: 97.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.75:\\ \;\;\;\;x \cdot \left(0.3333333333333333 \cdot \frac{x}{y}\right)\\ \mathbf{elif}\;x \leq 0.6:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(x \cdot \frac{0.3333333333333333}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.75)
   (* x (* 0.3333333333333333 (/ x y)))
   (if (<= x 0.6) (/ 1.0 y) (* x (* x (/ 0.3333333333333333 y))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.75) {
		tmp = x * (0.3333333333333333 * (x / y));
	} else if (x <= 0.6) {
		tmp = 1.0 / y;
	} else {
		tmp = x * (x * (0.3333333333333333 / 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 <= (-1.75d0)) then
        tmp = x * (0.3333333333333333d0 * (x / y))
    else if (x <= 0.6d0) then
        tmp = 1.0d0 / y
    else
        tmp = x * (x * (0.3333333333333333d0 / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -1.75) {
		tmp = x * (0.3333333333333333 * (x / y));
	} else if (x <= 0.6) {
		tmp = 1.0 / y;
	} else {
		tmp = x * (x * (0.3333333333333333 / y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.75:
		tmp = x * (0.3333333333333333 * (x / y))
	elif x <= 0.6:
		tmp = 1.0 / y
	else:
		tmp = x * (x * (0.3333333333333333 / y))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.75)
		tmp = Float64(x * Float64(0.3333333333333333 * Float64(x / y)));
	elseif (x <= 0.6)
		tmp = Float64(1.0 / y);
	else
		tmp = Float64(x * Float64(x * Float64(0.3333333333333333 / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.75)
		tmp = x * (0.3333333333333333 * (x / y));
	elseif (x <= 0.6)
		tmp = 1.0 / y;
	else
		tmp = x * (x * (0.3333333333333333 / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.75], N[(x * N[(0.3333333333333333 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 0.6], N[(1.0 / y), $MachinePrecision], N[(x * N[(x * N[(0.3333333333333333 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.75

   1. Initial program 84.4%

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

      1. times-frac 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 98.3%

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

      1. neg-mul-1 98.3%

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

      2. distribute-neg-frac 98.3%

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

   6. Simplified 98.3%

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

      1. frac-2neg 98.3%

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

      2. frac-2neg 98.3%

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

      3. frac-times 82.9%

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

      4. remove-double-neg 82.9%

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

      5. sub-neg 82.9%

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

      6. distribute-neg-in 82.9%

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

      7. metadata-eval 82.9%

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

      8. remove-double-neg 82.9%

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

      9. metadata-eval 82.9%

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

   8. Applied egg-rr 82.9%

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

      1. *-commutative 82.9%

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

      2. *-commutative 82.9%

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

      3. distribute-rgt-neg-out 82.9%

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

      4. distribute-lft-neg-in 82.9%

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

      5. metadata-eval 82.9%

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

      6. *-commutative 82.9%

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

      7. associate-/l* 96.9%

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

      8. associate-/r/ 96.8%

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

      9. +-commutative 96.8%

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

   10. Simplified 96.8%

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

   11. Taylor expanded in x around inf 98.1%

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

   if -1.75 < x < 0.599999999999999978

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

      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. *-lft-identity 99.6%

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

      5. associate-*l/ 99.4%

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

      6. *-commutative 99.4%

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

      7. *-commutative 99.4%

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

      8. associate-/r* 99.3%

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

      9. metadata-eval 99.3%

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

   3. Simplified 99.3%

      \[\leadsto \color{blue}{\left(1 - x\right) \cdot \left(\left(3 - x\right) \cdot \frac{0.3333333333333333}{y}\right)} \]
   4. Step-by-step derivation

      1. associate-*r/ 100.0%

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

      2. metadata-eval 100.0%

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

      3. div-inv 100.0%

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

      4. associate-*r/ 100.0%

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

      5. associate-*l/ 100.0%

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

      6. clear-num 100.0%

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

      7. associate-*l/ 100.0%

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

      8. *-un-lft-identity 100.0%

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

      9. div-sub 100.0%

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

      10. metadata-eval 100.0%

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

      11. div-inv 100.0%

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

      12. metadata-eval 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in x around 0 98.9%

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

   if 0.599999999999999978 < x

   1. Initial program 88.0%

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

      1. times-frac 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 97.5%

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

      1. neg-mul-1 97.5%

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

      2. distribute-neg-frac 97.5%

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

   6. Simplified 97.5%

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

      1. frac-2neg 97.5%

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

      2. frac-2neg 97.5%

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

      3. frac-times 85.8%

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

      4. remove-double-neg 85.8%

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

      5. sub-neg 85.8%

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

      6. distribute-neg-in 85.8%

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

      7. metadata-eval 85.8%

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

      8. remove-double-neg 85.8%

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

      9. metadata-eval 85.8%

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

   8. Applied egg-rr 85.8%

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

      1. *-commutative 85.8%

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

      2. *-commutative 85.8%

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

      3. distribute-rgt-neg-out 85.8%

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

      4. distribute-lft-neg-in 85.8%

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

      5. metadata-eval 85.8%

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

      6. *-commutative 85.8%

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

      7. associate-/l* 97.5%

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

      8. associate-/r/ 97.5%

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

      9. +-commutative 97.5%

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

   10. Simplified 97.5%

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

   11. Taylor expanded in x around inf 97.2%

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

       1. associate-*r/ 97.2%

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

       2. associate-*l/ 97.2%

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

       3. *-commutative 97.2%

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

   13. Simplified 97.2%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.75:\\ \;\;\;\;x \cdot \left(0.3333333333333333 \cdot \frac{x}{y}\right)\\ \mathbf{elif}\;x \leq 0.6:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(x \cdot \frac{0.3333333333333333}{y}\right)\\ \end{array} \]

Alternative 7: 97.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 3 regimes

2. if x < -3.7999999999999998

   1. Initial program 84.4%

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

      1. times-frac 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 98.3%

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

      1. neg-mul-1 98.3%

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

      2. distribute-neg-frac 98.3%

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

   6. Simplified 98.3%

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

      1. frac-2neg 98.3%

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

      2. frac-2neg 98.3%

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

      3. frac-times 82.9%

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

      4. remove-double-neg 82.9%

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

      5. sub-neg 82.9%

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

      6. distribute-neg-in 82.9%

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

      7. metadata-eval 82.9%

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

      8. remove-double-neg 82.9%

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

      9. metadata-eval 82.9%

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

   8. Applied egg-rr 82.9%

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

      1. *-commutative 82.9%

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

      2. *-commutative 82.9%

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

      3. distribute-rgt-neg-out 82.9%

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

      4. distribute-lft-neg-in 82.9%

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

      5. metadata-eval 82.9%

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

      6. *-commutative 82.9%

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

      7. associate-/l* 96.9%

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

      8. associate-/r/ 96.8%

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

      9. +-commutative 96.8%

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

   10. Simplified 96.8%

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

   11. Taylor expanded in x around inf 98.1%

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

   if -3.7999999999999998 < x < 3

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

      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. *-lft-identity 99.6%

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

      5. associate-*l/ 99.4%

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

      6. *-commutative 99.4%

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

      7. *-commutative 99.4%

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

      8. associate-/r* 99.3%

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

      9. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in x around 0 99.0%

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

   if 3 < x

   1. Initial program 88.0%

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

      1. times-frac 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 97.5%

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

      1. neg-mul-1 97.5%

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

      2. distribute-neg-frac 97.5%

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

   6. Simplified 97.5%

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

      1. frac-2neg 97.5%

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

      2. frac-2neg 97.5%

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

      3. frac-times 85.8%

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

      4. remove-double-neg 85.8%

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

      5. sub-neg 85.8%

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

      6. distribute-neg-in 85.8%

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

      7. metadata-eval 85.8%

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

      8. remove-double-neg 85.8%

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

      9. metadata-eval 85.8%

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

   8. Applied egg-rr 85.8%

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

      1. *-commutative 85.8%

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

      2. *-commutative 85.8%

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

      3. distribute-rgt-neg-out 85.8%

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

      4. distribute-lft-neg-in 85.8%

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

      5. metadata-eval 85.8%

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

      6. *-commutative 85.8%

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

      7. associate-/l* 97.5%

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

      8. associate-/r/ 97.5%

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

      9. +-commutative 97.5%

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

   10. Simplified 97.5%

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

   11. Taylor expanded in x around inf 97.2%

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

       1. associate-*r/ 97.2%

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

       2. associate-*l/ 97.2%

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

       3. *-commutative 97.2%

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

   13. Simplified 97.2%

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

4. Final simplification 98.3%

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

Alternative 8: 98.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 3 regimes

2. if x < -4.5999999999999996

   1. Initial program 84.4%

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

      1. times-frac 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 98.3%

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

      1. neg-mul-1 98.3%

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

      2. distribute-neg-frac 98.3%

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

   6. Simplified 98.3%

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

      1. frac-2neg 98.3%

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

      2. frac-2neg 98.3%

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

      3. frac-times 82.9%

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

      4. remove-double-neg 82.9%

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

      5. sub-neg 82.9%

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

      6. distribute-neg-in 82.9%

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

      7. metadata-eval 82.9%

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

      8. remove-double-neg 82.9%

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

      9. metadata-eval 82.9%

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

   8. Applied egg-rr 82.9%

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

      1. *-commutative 82.9%

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

      2. *-commutative 82.9%

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

      3. distribute-rgt-neg-out 82.9%

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

      4. distribute-lft-neg-in 82.9%

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

      5. metadata-eval 82.9%

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

      6. *-commutative 82.9%

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

      7. associate-/l* 96.9%

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

      8. associate-/r/ 96.8%

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

      9. +-commutative 96.8%

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

   10. Simplified 96.8%

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

   11. Taylor expanded in x around inf 98.1%

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

   if -4.5999999999999996 < x < 3

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

      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. *-lft-identity 99.6%

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

      5. associate-*l/ 99.4%

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

      6. *-commutative 99.4%

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

      7. *-commutative 99.4%

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

      8. associate-/r* 99.3%

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

      9. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in x around 0 99.8%

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

   5. Taylor expanded in y around 0 99.8%

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

   if 3 < x

   1. Initial program 88.0%

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

      1. times-frac 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 97.5%

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

      1. neg-mul-1 97.5%

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

      2. distribute-neg-frac 97.5%

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

   6. Simplified 97.5%

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

      1. frac-2neg 97.5%

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

      2. frac-2neg 97.5%

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

      3. frac-times 85.8%

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

      4. remove-double-neg 85.8%

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

      5. sub-neg 85.8%

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

      6. distribute-neg-in 85.8%

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

      7. metadata-eval 85.8%

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

      8. remove-double-neg 85.8%

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

      9. metadata-eval 85.8%

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

   8. Applied egg-rr 85.8%

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

      1. *-commutative 85.8%

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

      2. *-commutative 85.8%

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

      3. distribute-rgt-neg-out 85.8%

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

      4. distribute-lft-neg-in 85.8%

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

      5. metadata-eval 85.8%

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

      6. *-commutative 85.8%

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

      7. associate-/l* 97.5%

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

      8. associate-/r/ 97.5%

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

      9. +-commutative 97.5%

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

   10. Simplified 97.5%

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

   11. Taylor expanded in x around inf 97.2%

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

       1. associate-*r/ 97.2%

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

       2. associate-*l/ 97.2%

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

       3. *-commutative 97.2%

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

   13. Simplified 97.2%

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

4. Final simplification 98.7%

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

Alternative 9: 99.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(1 - x\right) \cdot \left(\left(3 - x\right) \cdot \frac{0.3333333333333333}{y}\right) \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (* (- 1.0 x) (* (- 3.0 x) (/ 0.3333333333333333 y))))

C

double code(double x, double y) {
	return (1.0 - x) * ((3.0 - x) * (0.3333333333333333 / y));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (1.0d0 - x) * ((3.0d0 - x) * (0.3333333333333333d0 / y))
end function

Java

public static double code(double x, double y) {
	return (1.0 - x) * ((3.0 - x) * (0.3333333333333333 / y));
}

Python

def code(x, y):
	return (1.0 - x) * ((3.0 - x) * (0.3333333333333333 / y))

Julia

function code(x, y)
	return Float64(Float64(1.0 - x) * Float64(Float64(3.0 - x) * Float64(0.3333333333333333 / y)))
end

MATLAB

function tmp = code(x, y)
	tmp = (1.0 - x) * ((3.0 - x) * (0.3333333333333333 / y));
end

Wolfram

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

Derivation

1. Initial program 92.7%

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

   1. *-commutative 92.7%

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

   2. associate-*l/ 99.3%

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

   3. *-commutative 99.3%

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

   4. *-lft-identity 99.3%

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

   5. associate-*l/ 99.2%

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

   6. *-commutative 99.2%

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

   7. *-commutative 99.2%

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

   8. associate-/r* 99.5%

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

   9. metadata-eval 99.5%

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

3. Simplified 99.5%

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

4. Final simplification 99.5%

   \[\leadsto \left(1 - x\right) \cdot \left(\left(3 - x\right) \cdot \frac{0.3333333333333333}{y}\right) \]

Alternative 10: 58.5% 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 84.4%

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

      1. *-commutative 84.4%

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

      2. associate-*l/ 98.3%

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

      3. *-commutative 98.3%

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

      4. *-lft-identity 98.3%

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

      5. associate-*l/ 98.3%

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

      6. *-commutative 98.3%

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

      7. *-commutative 98.3%

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

      8. associate-/r* 99.6%

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

      9. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in x around 0 34.4%

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

   5. Taylor expanded in x around inf 34.4%

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

   if -0.75 < x

   1. Initial program 96.0%

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

      1. *-commutative 96.0%

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

      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. *-lft-identity 99.6%

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

      5. associate-*l/ 99.5%

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

      6. *-commutative 99.5%

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

      7. *-commutative 99.5%

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

      8. associate-/r* 99.4%

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

      9. metadata-eval 99.4%

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

   3. Simplified 99.4%

      \[\leadsto \color{blue}{\left(1 - x\right) \cdot \left(\left(3 - x\right) \cdot \frac{0.3333333333333333}{y}\right)} \]
   4. Step-by-step derivation

      1. associate-*r/ 99.9%

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

      2. metadata-eval 99.9%

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

      3. div-inv 99.9%

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

      4. associate-*r/ 96.4%

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

      5. associate-*l/ 99.9%

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

      6. clear-num 99.9%

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

      7. associate-*l/ 99.9%

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

      8. *-un-lft-identity 99.9%

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

      9. div-sub 99.9%

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

      10. metadata-eval 99.9%

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

      11. div-inv 99.9%

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

      12. metadata-eval 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in x around 0 70.2%

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

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.75:\\ \;\;\;\;-1.3333333333333333 \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{y}\\ \end{array} \]

Alternative 11: 58.5% 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 84.4%

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

      1. times-frac 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 98.3%

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

      1. neg-mul-1 98.3%

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

      2. distribute-neg-frac 98.3%

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

   6. Simplified 98.3%

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

   7. Taylor expanded in x around 0 34.4%

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

      1. mul-1-neg 34.4%

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

      2. distribute-neg-frac 34.4%

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

   9. Simplified 34.4%

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

   if -1 < x

   1. Initial program 96.0%

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

      1. *-commutative 96.0%

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

      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. *-lft-identity 99.6%

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

      5. associate-*l/ 99.5%

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

      6. *-commutative 99.5%

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

      7. *-commutative 99.5%

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

      8. associate-/r* 99.4%

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

      9. metadata-eval 99.4%

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

   3. Simplified 99.4%

      \[\leadsto \color{blue}{\left(1 - x\right) \cdot \left(\left(3 - x\right) \cdot \frac{0.3333333333333333}{y}\right)} \]
   4. Step-by-step derivation

      1. associate-*r/ 99.9%

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

      2. metadata-eval 99.9%

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

      3. div-inv 99.9%

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

      4. associate-*r/ 96.4%

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

      5. associate-*l/ 99.9%

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

      6. clear-num 99.9%

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

      7. associate-*l/ 99.9%

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

      8. *-un-lft-identity 99.9%

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

      9. div-sub 99.9%

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

      10. metadata-eval 99.9%

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

      11. div-inv 99.9%

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

      12. metadata-eval 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in x around 0 70.2%

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

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;\frac{-x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{y}\\ \end{array} \]

Alternative 12: 52.4% 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 92.7%

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

   1. *-commutative 92.7%

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

   2. associate-*l/ 99.3%

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

   3. *-commutative 99.3%

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

   4. *-lft-identity 99.3%

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

   5. associate-*l/ 99.2%

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

   6. *-commutative 99.2%

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

   7. *-commutative 99.2%

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

   8. associate-/r* 99.5%

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

   9. metadata-eval 99.5%

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

3. Simplified 99.5%

   \[\leadsto \color{blue}{\left(1 - x\right) \cdot \left(\left(3 - x\right) \cdot \frac{0.3333333333333333}{y}\right)} \]
4. Step-by-step derivation

   1. associate-*r/ 99.8%

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

   2. metadata-eval 99.8%

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

   3. div-inv 99.9%

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

   4. associate-*r/ 93.0%

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

   5. associate-*l/ 99.9%

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

   6. clear-num 99.9%

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

   7. associate-*l/ 99.9%

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

   8. *-un-lft-identity 99.9%

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

   9. div-sub 99.9%

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

   10. metadata-eval 99.9%

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

   11. div-inv 99.9%

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

   12. metadata-eval 99.9%

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

5. Applied egg-rr 99.9%

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

6. Taylor expanded in x around 0 51.6%

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

7. Final simplification 51.6%

   \[\leadsto \frac{1}{y} \]

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 2023306 
(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)))