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

Percentage Accurate: 94.0% → 99.9%

Time: 29.5s

Alternatives: 17

Speedup: 1.0×

• 25.1% 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: 94.0% 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: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.1%

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

   1. clear-num 99.8%

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

   2. un-div-inv 99.9%

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

5. Applied egg-rr 99.9%

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

6. Final simplification 99.9%

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

Alternative 2: 98.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.75 \lor \neg \left(x \leq 1\right):\\ \;\;\;\;\frac{x}{y} \cdot \left(-1.3333333333333333 + x \cdot 0.3333333333333333\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{y + x \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -0.75) (not (<= x 1.0)))
   (* (/ x y) (+ -1.3333333333333333 (* x 0.3333333333333333)))
   (/ 1.0 (+ y (* x y)))))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -0.75) || !(x <= 1.0)) {
		tmp = (x / y) * (-1.3333333333333333 + (x * 0.3333333333333333));
	} else {
		tmp = 1.0 / (y + (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 <= (-0.75d0)) .or. (.not. (x <= 1.0d0))) then
        tmp = (x / y) * ((-1.3333333333333333d0) + (x * 0.3333333333333333d0))
    else
        tmp = 1.0d0 / (y + (x * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -0.75) || !(x <= 1.0)) {
		tmp = (x / y) * (-1.3333333333333333 + (x * 0.3333333333333333));
	} else {
		tmp = 1.0 / (y + (x * y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -0.75) or not (x <= 1.0):
		tmp = (x / y) * (-1.3333333333333333 + (x * 0.3333333333333333))
	else:
		tmp = 1.0 / (y + (x * y))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -0.75) || !(x <= 1.0))
		tmp = Float64(Float64(x / y) * Float64(-1.3333333333333333 + Float64(x * 0.3333333333333333)));
	else
		tmp = Float64(1.0 / Float64(y + Float64(x * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -0.75) || ~((x <= 1.0)))
		tmp = (x / y) * (-1.3333333333333333 + (x * 0.3333333333333333));
	else
		tmp = 1.0 / (y + (x * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -0.75], N[Not[LessEqual[x, 1.0]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] * N[(-1.3333333333333333 + N[(x * 0.3333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(y + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -0.75 or 1 < x

   1. Initial program 88.5%

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

      1. associate-/l* 99.7%

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

      2. add-sqr-sqrt 47.0%

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

      3. *-commutative 47.0%

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

      4. div-inv 47.0%

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

      5. times-frac 45.5%

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

      6. *-commutative 45.5%

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

   3. Applied egg-rr 45.5%

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

      1. associate-*r/ 47.0%

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

      2. *-commutative 47.0%

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

      3. associate-*r/ 46.9%

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

      4. rem-square-sqrt 99.6%

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

   5. Simplified 99.6%

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

   6. Taylor expanded in x around inf 71.3%

      \[\leadsto \color{blue}{-1.3333333333333333 \cdot \frac{x}{y} + 0.3333333333333333 \cdot \frac{{x}^{2}}{y}} \]
   7. Step-by-step derivation

      1. *-commutative 71.3%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot -1.3333333333333333} + 0.3333333333333333 \cdot \frac{{x}^{2}}{y} \]

      2. *-commutative 71.3%

         \[\leadsto \frac{x}{y} \cdot -1.3333333333333333 + \color{blue}{\frac{{x}^{2}}{y} \cdot 0.3333333333333333} \]

      3. unpow2 71.3%

         \[\leadsto \frac{x}{y} \cdot -1.3333333333333333 + \frac{\color{blue}{x \cdot x}}{y} \cdot 0.3333333333333333 \]

      4. metadata-eval 71.3%

         \[\leadsto \frac{x}{y} \cdot -1.3333333333333333 + \frac{x \cdot x}{y} \cdot \color{blue}{\frac{0.3333333333333333}{1}} \]

      5. times-frac 71.4%

         \[\leadsto \frac{x}{y} \cdot -1.3333333333333333 + \color{blue}{\frac{\left(x \cdot x\right) \cdot 0.3333333333333333}{y \cdot 1}} \]

      6. associate-*r* 71.4%

         \[\leadsto \frac{x}{y} \cdot -1.3333333333333333 + \frac{\color{blue}{x \cdot \left(x \cdot 0.3333333333333333\right)}}{y \cdot 1} \]

      7. times-frac 82.6%

         \[\leadsto \frac{x}{y} \cdot -1.3333333333333333 + \color{blue}{\frac{x}{y} \cdot \frac{x \cdot 0.3333333333333333}{1}} \]

      8. /-rgt-identity 82.6%

         \[\leadsto \frac{x}{y} \cdot -1.3333333333333333 + \frac{x}{y} \cdot \color{blue}{\left(x \cdot 0.3333333333333333\right)} \]

      9. distribute-lft-out 98.6%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot \left(-1.3333333333333333 + x \cdot 0.3333333333333333\right)} \]

   8. Simplified 98.6%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot \left(-1.3333333333333333 + x \cdot 0.3333333333333333\right)} \]

   if -0.75 < x < 1

   1. Initial program 99.5%

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

      1. associate-/l* 99.7%

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

      2. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around 0 98.2%

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

      1. clear-num 98.2%

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

      2. inv-pow 98.2%

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

   6. Applied egg-rr 98.2%

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

      1. unpow-1 98.2%

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

   8. Simplified 98.2%

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

   9. Taylor expanded in x around 0 98.2%

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

       1. *-commutative 98.2%

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

   11. Simplified 98.2%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.75 \lor \neg \left(x \leq 1\right):\\ \;\;\;\;\frac{x}{y} \cdot \left(-1.3333333333333333 + x \cdot 0.3333333333333333\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{y + x \cdot y}\\ \end{array} \]

Alternative 3: 98.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.75 \lor \neg \left(x \leq 1.75\right):\\ \;\;\;\;\frac{x}{y} \cdot \left(-1.3333333333333333 + x \cdot 0.3333333333333333\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{3 + x \cdot -4}{y \cdot 3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -1.75) (not (<= x 1.75)))
   (* (/ x y) (+ -1.3333333333333333 (* x 0.3333333333333333)))
   (/ (+ 3.0 (* x -4.0)) (* y 3.0))))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -1.75) || !(x <= 1.75)) {
		tmp = (x / y) * (-1.3333333333333333 + (x * 0.3333333333333333));
	} else {
		tmp = (3.0 + (x * -4.0)) / (y * 3.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-1.75d0)) .or. (.not. (x <= 1.75d0))) then
        tmp = (x / y) * ((-1.3333333333333333d0) + (x * 0.3333333333333333d0))
    else
        tmp = (3.0d0 + (x * (-4.0d0))) / (y * 3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -1.75) || !(x <= 1.75)) {
		tmp = (x / y) * (-1.3333333333333333 + (x * 0.3333333333333333));
	} else {
		tmp = (3.0 + (x * -4.0)) / (y * 3.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -1.75) or not (x <= 1.75):
		tmp = (x / y) * (-1.3333333333333333 + (x * 0.3333333333333333))
	else:
		tmp = (3.0 + (x * -4.0)) / (y * 3.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -1.75) || !(x <= 1.75))
		tmp = Float64(Float64(x / y) * Float64(-1.3333333333333333 + Float64(x * 0.3333333333333333)));
	else
		tmp = Float64(Float64(3.0 + Float64(x * -4.0)) / Float64(y * 3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -1.75) || ~((x <= 1.75)))
		tmp = (x / y) * (-1.3333333333333333 + (x * 0.3333333333333333));
	else
		tmp = (3.0 + (x * -4.0)) / (y * 3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -1.75], N[Not[LessEqual[x, 1.75]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] * N[(-1.3333333333333333 + N[(x * 0.3333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(3.0 + N[(x * -4.0), $MachinePrecision]), $MachinePrecision] / N[(y * 3.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.75 or 1.75 < x

   1. Initial program 88.5%

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

      1. associate-/l* 99.7%

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

      2. add-sqr-sqrt 47.0%

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

      3. *-commutative 47.0%

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

      4. div-inv 47.0%

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

      5. times-frac 45.5%

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

      6. *-commutative 45.5%

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

   3. Applied egg-rr 45.5%

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

      1. associate-*r/ 47.0%

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

      2. *-commutative 47.0%

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

      3. associate-*r/ 46.9%

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

      4. rem-square-sqrt 99.6%

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

   5. Simplified 99.6%

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

   6. Taylor expanded in x around inf 71.3%

      \[\leadsto \color{blue}{-1.3333333333333333 \cdot \frac{x}{y} + 0.3333333333333333 \cdot \frac{{x}^{2}}{y}} \]
   7. Step-by-step derivation

      1. *-commutative 71.3%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot -1.3333333333333333} + 0.3333333333333333 \cdot \frac{{x}^{2}}{y} \]

      2. *-commutative 71.3%

         \[\leadsto \frac{x}{y} \cdot -1.3333333333333333 + \color{blue}{\frac{{x}^{2}}{y} \cdot 0.3333333333333333} \]

      3. unpow2 71.3%

         \[\leadsto \frac{x}{y} \cdot -1.3333333333333333 + \frac{\color{blue}{x \cdot x}}{y} \cdot 0.3333333333333333 \]

      4. metadata-eval 71.3%

         \[\leadsto \frac{x}{y} \cdot -1.3333333333333333 + \frac{x \cdot x}{y} \cdot \color{blue}{\frac{0.3333333333333333}{1}} \]

      5. times-frac 71.4%

         \[\leadsto \frac{x}{y} \cdot -1.3333333333333333 + \color{blue}{\frac{\left(x \cdot x\right) \cdot 0.3333333333333333}{y \cdot 1}} \]

      6. associate-*r* 71.4%

         \[\leadsto \frac{x}{y} \cdot -1.3333333333333333 + \frac{\color{blue}{x \cdot \left(x \cdot 0.3333333333333333\right)}}{y \cdot 1} \]

      7. times-frac 82.6%

         \[\leadsto \frac{x}{y} \cdot -1.3333333333333333 + \color{blue}{\frac{x}{y} \cdot \frac{x \cdot 0.3333333333333333}{1}} \]

      8. /-rgt-identity 82.6%

         \[\leadsto \frac{x}{y} \cdot -1.3333333333333333 + \frac{x}{y} \cdot \color{blue}{\left(x \cdot 0.3333333333333333\right)} \]

      9. distribute-lft-out 98.6%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot \left(-1.3333333333333333 + x \cdot 0.3333333333333333\right)} \]

   8. Simplified 98.6%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot \left(-1.3333333333333333 + x \cdot 0.3333333333333333\right)} \]

   if -1.75 < x < 1.75

   1. Initial program 99.5%

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

   2. Taylor expanded in x around 0 99.1%

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

      1. *-commutative 99.1%

         \[\leadsto \frac{3 + \color{blue}{x \cdot -4}}{y \cdot 3} \]

   4. Simplified 99.1%

      \[\leadsto \frac{\color{blue}{3 + x \cdot -4}}{y \cdot 3} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.75 \lor \neg \left(x \leq 1.75\right):\\ \;\;\;\;\frac{x}{y} \cdot \left(-1.3333333333333333 + x \cdot 0.3333333333333333\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{3 + x \cdot -4}{y \cdot 3}\\ \end{array} \]

Alternative 4: 97.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.95:\\ \;\;\;\;x \cdot \frac{\frac{x}{y}}{3}\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;\frac{1}{y + x \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\left(3 - x\right) \cdot \left(\frac{x}{y} \cdot -0.3333333333333333\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -0.95)
   (* x (/ (/ x y) 3.0))
   (if (<= x 1.0)
     (/ 1.0 (+ y (* x y)))
     (* (- 3.0 x) (* (/ x y) -0.3333333333333333)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -0.95) {
		tmp = x * ((x / y) / 3.0);
	} else if (x <= 1.0) {
		tmp = 1.0 / (y + (x * y));
	} else {
		tmp = (3.0 - x) * ((x / y) * -0.3333333333333333);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-0.95d0)) then
        tmp = x * ((x / y) / 3.0d0)
    else if (x <= 1.0d0) then
        tmp = 1.0d0 / (y + (x * y))
    else
        tmp = (3.0d0 - x) * ((x / y) * (-0.3333333333333333d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -0.95) {
		tmp = x * ((x / y) / 3.0);
	} else if (x <= 1.0) {
		tmp = 1.0 / (y + (x * y));
	} else {
		tmp = (3.0 - x) * ((x / y) * -0.3333333333333333);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -0.95:
		tmp = x * ((x / y) / 3.0)
	elif x <= 1.0:
		tmp = 1.0 / (y + (x * y))
	else:
		tmp = (3.0 - x) * ((x / y) * -0.3333333333333333)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -0.95)
		tmp = Float64(x * Float64(Float64(x / y) / 3.0));
	elseif (x <= 1.0)
		tmp = Float64(1.0 / Float64(y + Float64(x * y)));
	else
		tmp = Float64(Float64(3.0 - x) * Float64(Float64(x / y) * -0.3333333333333333));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -0.95)
		tmp = x * ((x / y) / 3.0);
	elseif (x <= 1.0)
		tmp = 1.0 / (y + (x * y));
	else
		tmp = (3.0 - x) * ((x / y) * -0.3333333333333333);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -0.95], N[(x * N[(N[(x / y), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.0], N[(1.0 / N[(y + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(3.0 - x), $MachinePrecision] * N[(N[(x / y), $MachinePrecision] * -0.3333333333333333), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -0.94999999999999996

   1. Initial program 87.0%

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

   2. Taylor expanded in x around inf 85.0%

      \[\leadsto \frac{\color{blue}{{x}^{2}}}{y \cdot 3} \]
   3. Step-by-step derivation

      1. unpow2 85.0%

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

   4. Simplified 85.0%

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

      1. div-inv 85.0%

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

      2. associate-*l* 97.7%

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

      3. *-commutative 97.7%

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

      4. associate-/r* 97.6%

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

      5. metadata-eval 97.6%

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

   6. Applied egg-rr 97.6%

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

      1. associate-*r/ 97.7%

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

      2. associate-/l* 97.6%

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

      3. div-inv 97.7%

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

      4. metadata-eval 97.7%

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

      5. associate-/r* 97.7%

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

   8. Applied egg-rr 97.7%

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

   if -0.94999999999999996 < x < 1

   1. Initial program 99.5%

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

      1. associate-/l* 99.7%

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

      2. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around 0 98.2%

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

      1. clear-num 98.2%

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

      2. inv-pow 98.2%

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

   6. Applied egg-rr 98.2%

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

      1. unpow-1 98.2%

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

   8. Simplified 98.2%

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

   9. Taylor expanded in x around 0 98.2%

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

       1. *-commutative 98.2%

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

   11. Simplified 98.2%

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

   if 1 < x

   1. Initial program 89.8%

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

      1. *-commutative 89.8%

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

      2. associate-*r/ 99.7%

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

      3. associate-/r* 99.8%

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

      4. associate-/r* 99.7%

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

      5. div-sub 99.7%

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

      6. sub-neg 99.7%

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

      7. distribute-frac-neg 99.7%

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

      8. *-lft-identity 99.7%

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

      9. metadata-eval 99.7%

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

      10. times-frac 99.7%

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

      11. neg-mul-1 99.7%

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

      12. remove-double-neg 99.7%

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

      13. *-rgt-identity 99.7%

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

      14. times-frac 99.7%

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

      15. remove-double-neg 99.7%

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

      16. neg-mul-1 99.7%

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

      17. *-commutative 99.7%

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

      18. associate-/l* 99.7%

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

      19. metadata-eval 99.7%

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

      20. /-rgt-identity 99.7%

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

      21. distribute-rgt1-in 99.7%

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

      22. +-commutative 99.7%

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

      23. sub-neg 99.7%

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

      24. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 96.9%

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

4. Final simplification 97.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.95:\\ \;\;\;\;x \cdot \frac{\frac{x}{y}}{3}\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;\frac{1}{y + x \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\left(3 - x\right) \cdot \left(\frac{x}{y} \cdot -0.3333333333333333\right)\\ \end{array} \]

Alternative 5: 97.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.8:\\ \;\;\;\;\left(3 - x\right) \cdot \frac{x \cdot -0.3333333333333333}{y}\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;\frac{1}{y + x \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\left(3 - x\right) \cdot \left(\frac{x}{y} \cdot -0.3333333333333333\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -0.8)
   (* (- 3.0 x) (/ (* x -0.3333333333333333) y))
   (if (<= x 1.0)
     (/ 1.0 (+ y (* x y)))
     (* (- 3.0 x) (* (/ x y) -0.3333333333333333)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -0.8) {
		tmp = (3.0 - x) * ((x * -0.3333333333333333) / y);
	} else if (x <= 1.0) {
		tmp = 1.0 / (y + (x * y));
	} else {
		tmp = (3.0 - x) * ((x / y) * -0.3333333333333333);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-0.8d0)) then
        tmp = (3.0d0 - x) * ((x * (-0.3333333333333333d0)) / y)
    else if (x <= 1.0d0) then
        tmp = 1.0d0 / (y + (x * y))
    else
        tmp = (3.0d0 - x) * ((x / y) * (-0.3333333333333333d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -0.8) {
		tmp = (3.0 - x) * ((x * -0.3333333333333333) / y);
	} else if (x <= 1.0) {
		tmp = 1.0 / (y + (x * y));
	} else {
		tmp = (3.0 - x) * ((x / y) * -0.3333333333333333);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -0.8:
		tmp = (3.0 - x) * ((x * -0.3333333333333333) / y)
	elif x <= 1.0:
		tmp = 1.0 / (y + (x * y))
	else:
		tmp = (3.0 - x) * ((x / y) * -0.3333333333333333)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -0.8)
		tmp = Float64(Float64(3.0 - x) * Float64(Float64(x * -0.3333333333333333) / y));
	elseif (x <= 1.0)
		tmp = Float64(1.0 / Float64(y + Float64(x * y)));
	else
		tmp = Float64(Float64(3.0 - x) * Float64(Float64(x / y) * -0.3333333333333333));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -0.8)
		tmp = (3.0 - x) * ((x * -0.3333333333333333) / y);
	elseif (x <= 1.0)
		tmp = 1.0 / (y + (x * y));
	else
		tmp = (3.0 - x) * ((x / y) * -0.3333333333333333);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -0.8], N[(N[(3.0 - x), $MachinePrecision] * N[(N[(x * -0.3333333333333333), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.0], N[(1.0 / N[(y + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(3.0 - x), $MachinePrecision] * N[(N[(x / y), $MachinePrecision] * -0.3333333333333333), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -0.80000000000000004

   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-*r/ 99.7%

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

      3. associate-/r* 99.8%

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

      4. associate-/r* 99.7%

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

      5. div-sub 99.7%

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

      6. sub-neg 99.7%

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

      7. distribute-frac-neg 99.7%

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

      8. *-lft-identity 99.7%

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

      9. metadata-eval 99.7%

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

      10. times-frac 99.7%

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

      11. neg-mul-1 99.7%

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

      12. remove-double-neg 99.7%

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

      13. *-rgt-identity 99.7%

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

      14. times-frac 99.8%

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

      15. remove-double-neg 99.8%

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

      16. neg-mul-1 99.8%

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

      17. *-commutative 99.8%

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

      18. associate-/l* 99.8%

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

      19. metadata-eval 99.8%

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

      20. /-rgt-identity 99.8%

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

      21. distribute-rgt1-in 99.8%

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

      22. +-commutative 99.8%

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

      23. sub-neg 99.8%

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

      24. *-commutative 99.8%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 97.7%

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

      1. associate-*r/ 97.8%

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

      2. *-commutative 97.8%

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

   6. Simplified 97.8%

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

   if -0.80000000000000004 < x < 1

   1. Initial program 99.5%

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

      1. associate-/l* 99.7%

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

      2. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around 0 98.2%

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

      1. clear-num 98.2%

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

      2. inv-pow 98.2%

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

   6. Applied egg-rr 98.2%

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

      1. unpow-1 98.2%

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

   8. Simplified 98.2%

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

   9. Taylor expanded in x around 0 98.2%

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

       1. *-commutative 98.2%

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

   11. Simplified 98.2%

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

   if 1 < x

   1. Initial program 89.8%

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

      1. *-commutative 89.8%

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

      2. associate-*r/ 99.7%

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

      3. associate-/r* 99.8%

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

      4. associate-/r* 99.7%

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

      5. div-sub 99.7%

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

      6. sub-neg 99.7%

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

      7. distribute-frac-neg 99.7%

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

      8. *-lft-identity 99.7%

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

      9. metadata-eval 99.7%

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

      10. times-frac 99.7%

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

      11. neg-mul-1 99.7%

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

      12. remove-double-neg 99.7%

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

      13. *-rgt-identity 99.7%

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

      14. times-frac 99.7%

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

      15. remove-double-neg 99.7%

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

      16. neg-mul-1 99.7%

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

      17. *-commutative 99.7%

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

      18. associate-/l* 99.7%

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

      19. metadata-eval 99.7%

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

      20. /-rgt-identity 99.7%

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

      21. distribute-rgt1-in 99.7%

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

      22. +-commutative 99.7%

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

      23. sub-neg 99.7%

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

      24. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 96.9%

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

4. Final simplification 97.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.8:\\ \;\;\;\;\left(3 - x\right) \cdot \frac{x \cdot -0.3333333333333333}{y}\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;\frac{1}{y + x \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\left(3 - x\right) \cdot \left(\frac{x}{y} \cdot -0.3333333333333333\right)\\ \end{array} \]

Alternative 6: 92.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y) {
	double tmp;
	if ((x <= -3.8) || !(x <= 3.0)) {
		tmp = 0.3333333333333333 * ((x * 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 = 0.3333333333333333d0 * ((x * 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 = 0.3333333333333333 * ((x * 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 = 0.3333333333333333 * ((x * 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(0.3333333333333333 * Float64(Float64(x * 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 = 0.3333333333333333 * ((x * 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[(0.3333333333333333 * N[(N[(x * x), $MachinePrecision] / y), $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 88.4%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   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 86.4%

      \[\leadsto \color{blue}{0.3333333333333333 \cdot \frac{{x}^{2}}{y}} \]
   5. Step-by-step derivation

      1. unpow2 86.4%

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

   6. Simplified 86.4%

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

   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. associate-/l* 99.7%

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

      2. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around 0 97.6%

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

4. Final simplification 92.1%

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

Alternative 7: 97.7% 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 88.4%

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

   2. Taylor expanded in x around inf 86.4%

      \[\leadsto \frac{\color{blue}{{x}^{2}}}{y \cdot 3} \]
   3. Step-by-step derivation

      1. unpow2 86.4%

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

   4. Simplified 86.4%

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

      1. div-inv 86.5%

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

      2. associate-*l* 97.8%

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

      3. *-commutative 97.8%

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

      4. associate-/r* 97.7%

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

      5. metadata-eval 97.7%

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

   6. Applied egg-rr 97.7%

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

   7. Taylor expanded in x around 0 97.7%

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

   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. associate-/l* 99.7%

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

      2. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around 0 97.6%

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

4. Final simplification 97.6%

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

Alternative 8: 97.7% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -3.8)
   (* x (* x (/ 0.3333333333333333 y)))
   (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 * (0.3333333333333333 / y));
	} 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 * (0.3333333333333333d0 / y))
    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 * (0.3333333333333333 / y));
	} 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 * (0.3333333333333333 / y))
	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(0.3333333333333333 / y)));
	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 * (0.3333333333333333 / y));
	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[(0.3333333333333333 / y), $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. Taylor expanded in x around inf 85.0%

      \[\leadsto \frac{\color{blue}{{x}^{2}}}{y \cdot 3} \]
   3. Step-by-step derivation

      1. unpow2 85.0%

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

   4. Simplified 85.0%

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

      1. div-inv 85.0%

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

      2. associate-*l* 97.7%

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

      3. *-commutative 97.7%

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

      4. associate-/r* 97.6%

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

      5. metadata-eval 97.6%

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

   6. Applied egg-rr 97.6%

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

   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. associate-/l* 99.7%

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

      2. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around 0 97.6%

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

   if 3 < x

   1. Initial program 89.6%

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

   2. Taylor expanded in x around inf 87.8%

      \[\leadsto \frac{\color{blue}{{x}^{2}}}{y \cdot 3} \]
   3. Step-by-step derivation

      1. unpow2 87.8%

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

   4. Simplified 87.8%

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

      1. div-inv 87.8%

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

      2. associate-*l* 97.8%

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

      3. *-commutative 97.8%

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

      4. associate-/r* 97.8%

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

      5. metadata-eval 97.8%

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

   6. Applied egg-rr 97.8%

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

   7. Taylor expanded in x around 0 97.9%

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

4. Final simplification 97.7%

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

Alternative 9: 97.8% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -3.8)
   (* x (/ (/ x 3.0) y))
   (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 / 3.0) / y);
	} 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 / 3.0d0) / y)
    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 / 3.0) / y);
	} 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 / 3.0) / y)
	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(Float64(x / 3.0) / y));
	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 / 3.0) / y);
	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[(N[(x / 3.0), $MachinePrecision] / y), $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. Taylor expanded in x around inf 85.0%

      \[\leadsto \frac{\color{blue}{{x}^{2}}}{y \cdot 3} \]
   3. Step-by-step derivation

      1. unpow2 85.0%

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

   4. Simplified 85.0%

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

      1. div-inv 85.0%

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

      2. associate-*l* 97.7%

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

      3. *-commutative 97.7%

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

      4. associate-/r* 97.6%

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

      5. metadata-eval 97.6%

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

   6. Applied egg-rr 97.6%

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

      1. associate-*r/ 97.7%

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

      2. associate-/l* 97.6%

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

      3. div-inv 97.7%

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

      4. metadata-eval 97.7%

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

      5. *-commutative 97.7%

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

      6. associate-/r* 97.6%

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

   8. Applied egg-rr 97.6%

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

   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. associate-/l* 99.7%

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

      2. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around 0 97.6%

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

   if 3 < x

   1. Initial program 89.6%

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

   2. Taylor expanded in x around inf 87.8%

      \[\leadsto \frac{\color{blue}{{x}^{2}}}{y \cdot 3} \]
   3. Step-by-step derivation

      1. unpow2 87.8%

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

   4. Simplified 87.8%

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

      1. div-inv 87.8%

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

      2. associate-*l* 97.8%

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

      3. *-commutative 97.8%

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

      4. associate-/r* 97.8%

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

      5. metadata-eval 97.8%

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

   6. Applied egg-rr 97.8%

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

   7. Taylor expanded in x around 0 97.9%

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

4. Final simplification 97.7%

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

Alternative 10: 97.8% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -3.8)
   (* x (/ (/ x y) 3.0))
   (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) / 3.0);
	} 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) / 3.0d0)
    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) / 3.0);
	} 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) / 3.0)
	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(Float64(x / y) / 3.0));
	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) / 3.0);
	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[(N[(x / y), $MachinePrecision] / 3.0), $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. Taylor expanded in x around inf 85.0%

      \[\leadsto \frac{\color{blue}{{x}^{2}}}{y \cdot 3} \]
   3. Step-by-step derivation

      1. unpow2 85.0%

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

   4. Simplified 85.0%

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

      1. div-inv 85.0%

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

      2. associate-*l* 97.7%

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

      3. *-commutative 97.7%

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

      4. associate-/r* 97.6%

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

      5. metadata-eval 97.6%

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

   6. Applied egg-rr 97.6%

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

      1. associate-*r/ 97.7%

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

      2. associate-/l* 97.6%

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

      3. div-inv 97.7%

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

      4. metadata-eval 97.7%

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

      5. associate-/r* 97.7%

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

   8. Applied egg-rr 97.7%

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

   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. associate-/l* 99.7%

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

      2. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around 0 97.6%

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

   if 3 < x

   1. Initial program 89.6%

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

   2. Taylor expanded in x around inf 87.8%

      \[\leadsto \frac{\color{blue}{{x}^{2}}}{y \cdot 3} \]
   3. Step-by-step derivation

      1. unpow2 87.8%

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

   4. Simplified 87.8%

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

      1. div-inv 87.8%

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

      2. associate-*l* 97.8%

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

      3. *-commutative 97.8%

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

      4. associate-/r* 97.8%

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

      5. metadata-eval 97.8%

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

   6. Applied egg-rr 97.8%

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

   7. Taylor expanded in x around 0 97.9%

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

4. Final simplification 97.7%

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

Alternative 11: 99.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.1%

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

   1. *-commutative 94.1%

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

   2. associate-*r/ 99.5%

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

   3. associate-/r* 99.8%

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

   4. associate-/r* 99.5%

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

   5. div-sub 99.5%

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

   6. sub-neg 99.5%

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

   7. distribute-frac-neg 99.5%

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

   8. *-lft-identity 99.5%

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

   9. metadata-eval 99.5%

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

   10. times-frac 99.5%

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

   11. neg-mul-1 99.5%

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

   12. remove-double-neg 99.5%

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

   13. *-rgt-identity 99.5%

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

   14. times-frac 99.6%

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

   15. remove-double-neg 99.6%

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

   16. neg-mul-1 99.6%

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

   17. *-commutative 99.6%

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

   18. associate-/l* 99.6%

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

   19. metadata-eval 99.6%

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

   20. /-rgt-identity 99.6%

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

   21. distribute-rgt1-in 99.5%

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

   22. +-commutative 99.5%

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

   23. sub-neg 99.5%

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

   24. *-commutative 99.5%

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

3. Simplified 99.5%

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

4. Final simplification 99.5%

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

Alternative 12: 99.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.1%

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

   1. *-commutative 94.1%

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

   2. associate-*r/ 99.5%

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

   3. *-commutative 99.5%

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

3. Simplified 99.5%

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

4. Final simplification 99.5%

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

Alternative 13: 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 94.1%

   \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
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. Final simplification 99.8%

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

Alternative 14: 58.3% accurate, 1.6× speedup

Math

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

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -0.75) (* (/ x y) -1.3333333333333333) (/ 1.0 y)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -0.75) {
		tmp = (x / y) * -1.3333333333333333;
	} 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 = (x / y) * (-1.3333333333333333d0)
    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 = (x / y) * -1.3333333333333333;
	} else {
		tmp = 1.0 / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -0.75:
		tmp = (x / y) * -1.3333333333333333
	else:
		tmp = 1.0 / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -0.75)
		tmp = Float64(Float64(x / y) * -1.3333333333333333);
	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 = (x / y) * -1.3333333333333333;
	else
		tmp = 1.0 / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -0.75], N[(N[(x / y), $MachinePrecision] * -1.3333333333333333), $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. Taylor expanded in x around 0 28.9%

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

      1. *-commutative 28.9%

         \[\leadsto \frac{3 + \color{blue}{x \cdot -4}}{y \cdot 3} \]

   4. Simplified 28.9%

      \[\leadsto \frac{\color{blue}{3 + x \cdot -4}}{y \cdot 3} \]

   5. Taylor expanded in x around inf 28.9%

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

   if -0.75 < x

   1. Initial program 96.3%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   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. Taylor expanded in x around 0 66.8%

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

4. Final simplification 58.1%

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

Alternative 15: 58.3% 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-*r/ 99.7%

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

      3. associate-/r* 99.8%

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

      4. associate-/r* 99.7%

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

      5. div-sub 99.7%

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

      6. sub-neg 99.7%

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

      7. distribute-frac-neg 99.7%

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

      8. *-lft-identity 99.7%

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

      9. metadata-eval 99.7%

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

      10. times-frac 99.7%

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

      11. neg-mul-1 99.7%

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

      12. remove-double-neg 99.7%

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

      13. *-rgt-identity 99.7%

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

      14. times-frac 99.8%

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

      15. remove-double-neg 99.8%

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

      16. neg-mul-1 99.8%

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

      17. *-commutative 99.8%

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

      18. associate-/l* 99.8%

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

      19. metadata-eval 99.8%

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

      20. /-rgt-identity 99.8%

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

      21. distribute-rgt1-in 99.8%

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

      22. +-commutative 99.8%

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

      23. sub-neg 99.8%

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

      24. *-commutative 99.8%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 97.7%

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

      1. associate-*r/ 97.8%

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

      2. *-commutative 97.8%

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

   6. Simplified 97.8%

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

   7. Taylor expanded in x around 0 28.9%

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

      1. associate-*r/ 28.9%

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

      2. neg-mul-1 28.9%

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

   9. Simplified 28.9%

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

   if -1 < x

   1. Initial program 96.3%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   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. Taylor expanded in x around 0 66.8%

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

4. Final simplification 58.1%

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

Alternative 16: 57.4% 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 94.1%

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

   1. associate-/l* 99.7%

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

   2. *-commutative 99.7%

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

3. Simplified 99.7%

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

4. Taylor expanded in x around 0 57.1%

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

5. Final simplification 57.1%

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

Alternative 17: 52.1% 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 94.1%

   \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
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 0 52.6%

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

5. Final simplification 52.6%

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

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 2023271 
(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)))