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

Percentage Accurate: 93.8% → 99.8%

Time: 6.8s

Alternatives: 16

Speedup: 1.0×

• 25.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 93.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.5%

   \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
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 2: 92.5% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

def code(x, y):
	tmp = 0
	if (x <= -3.8) or not (x <= 3.0):
		tmp = -0.3333333333333333 * ((x * (1.0 - x)) / y)
	else:
		tmp = (1.0 + (x * -1.3333333333333333)) / 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 * Float64(1.0 - x)) / y));
	else
		tmp = Float64(Float64(1.0 + Float64(x * -1.3333333333333333)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -3.8) || ~((x <= 3.0)))
		tmp = -0.3333333333333333 * ((x * (1.0 - x)) / y);
	else
		tmp = (1.0 + (x * -1.3333333333333333)) / 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 * N[(1.0 - x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 + N[(x * -1.3333333333333333), $MachinePrecision]), $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. *-commutative 88.4%

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

      2. associate-*l/ 99.7%

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

      3. *-commutative 99.7%

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

      4. *-lft-identity 99.7%

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

      5. associate-*l/ 99.7%

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

      6. *-commutative 99.7%

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

      7. *-commutative 99.7%

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

      8. associate-/r* 99.7%

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

      9. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 99.4%

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

   5. Taylor expanded in y around 0 88.1%

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

   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/ 99.3%

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

      6. *-commutative 99.3%

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

      7. *-commutative 99.3%

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

      8. associate-/r* 99.5%

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

      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. Taylor expanded in x around 0 99.3%

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

   5. Taylor expanded in y around 0 99.3%

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

4. Final simplification 93.2%

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

Alternative 3: 98.3% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -3.8], N[Not[LessEqual[x, 3.0]], $MachinePrecision]], N[(N[(1.0 - x), $MachinePrecision] * N[(-0.3333333333333333 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 + N[(x * -1.3333333333333333), $MachinePrecision]), $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. *-commutative 88.4%

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

      2. associate-*l/ 99.7%

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

      3. *-commutative 99.7%

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

      4. *-lft-identity 99.7%

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

      5. associate-*l/ 99.7%

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

      6. *-commutative 99.7%

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

      7. *-commutative 99.7%

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

      8. associate-/r* 99.7%

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

      9. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 99.4%

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

   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/ 99.3%

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

      6. *-commutative 99.3%

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

      7. *-commutative 99.3%

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

      8. associate-/r* 99.5%

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

      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. Taylor expanded in x around 0 99.3%

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

   5. Taylor expanded in y around 0 99.3%

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

4. Final simplification 99.4%

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

Alternative 4: 98.3% accurate, 0.8× speedup

Math

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

FPCore

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

C

double code(double x, double y) {
	double tmp;
	if (x <= -3.8) {
		tmp = (1.0 - x) * (-0.3333333333333333 * (x / y));
	} else if (x <= 3.0) {
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	} else {
		tmp = (1.0 - 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 = (1.0d0 - x) * ((-0.3333333333333333d0) * (x / y))
    else if (x <= 3.0d0) then
        tmp = (1.0d0 + (x * (-1.3333333333333333d0))) / y
    else
        tmp = (1.0d0 - 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 = (1.0 - x) * (-0.3333333333333333 * (x / y));
	} else if (x <= 3.0) {
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	} else {
		tmp = (1.0 - x) * (x * (-0.3333333333333333 / y));
	}
	return tmp;
}

Python

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

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -3.8)
		tmp = Float64(Float64(1.0 - x) * Float64(-0.3333333333333333 * Float64(x / y)));
	elseif (x <= 3.0)
		tmp = Float64(Float64(1.0 + Float64(x * -1.3333333333333333)) / y);
	else
		tmp = Float64(Float64(1.0 - 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 = (1.0 - x) * (-0.3333333333333333 * (x / y));
	elseif (x <= 3.0)
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	else
		tmp = (1.0 - x) * (x * (-0.3333333333333333 / y));
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 3 regimes

2. if x < -3.7999999999999998

   1. Initial program 90.3%

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

      1. *-commutative 90.3%

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

      2. associate-*l/ 99.7%

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

      3. *-commutative 99.7%

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

      4. *-lft-identity 99.7%

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

      5. associate-*l/ 99.7%

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

      6. *-commutative 99.7%

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

      7. *-commutative 99.7%

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

      8. associate-/r* 99.8%

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

      9. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 99.4%

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

   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/ 99.3%

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

      6. *-commutative 99.3%

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

      7. *-commutative 99.3%

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

      8. associate-/r* 99.5%

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

      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. Taylor expanded in x around 0 99.3%

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

   5. Taylor expanded in y around 0 99.3%

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

   if 3 < x

   1. Initial program 85.8%

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

      1. *-commutative 85.8%

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

      2. associate-*l/ 99.7%

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

      3. *-commutative 99.7%

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

      4. *-lft-identity 99.7%

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

      5. associate-*l/ 99.7%

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

      6. *-commutative 99.7%

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

      7. *-commutative 99.7%

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

      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 inf 99.5%

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

      1. associate-*r/ 99.6%

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

      2. *-commutative 99.6%

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

      3. associate-*r/ 99.6%

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

   6. Simplified 99.6%

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

4. Final simplification 99.4%

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

Alternative 5: 98.2% accurate, 0.8× speedup

Math

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

FPCore

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

C

double code(double x, double y) {
	double tmp;
	if (x <= -3.8) {
		tmp = (1.0 - x) * (-0.3333333333333333 * (x / y));
	} else if (x <= 3.0) {
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	} else {
		tmp = (1.0 - x) * (x / (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 <= (-3.8d0)) then
        tmp = (1.0d0 - x) * ((-0.3333333333333333d0) * (x / y))
    else if (x <= 3.0d0) then
        tmp = (1.0d0 + (x * (-1.3333333333333333d0))) / y
    else
        tmp = (1.0d0 - x) * (x / (y * (-3.0d0)))
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 3 regimes

2. if x < -3.7999999999999998

   1. Initial program 90.3%

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

      1. *-commutative 90.3%

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

      2. associate-*l/ 99.7%

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

      3. *-commutative 99.7%

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

      4. *-lft-identity 99.7%

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

      5. associate-*l/ 99.7%

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

      6. *-commutative 99.7%

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

      7. *-commutative 99.7%

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

      8. associate-/r* 99.8%

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

      9. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 99.4%

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

   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/ 99.3%

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

      6. *-commutative 99.3%

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

      7. *-commutative 99.3%

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

      8. associate-/r* 99.5%

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

      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. Taylor expanded in x around 0 99.3%

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

   5. Taylor expanded in y around 0 99.3%

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

   if 3 < x

   1. Initial program 85.8%

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

      1. *-commutative 85.8%

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

      2. associate-*l/ 99.7%

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

      3. *-commutative 99.7%

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

      4. *-lft-identity 99.7%

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

      5. associate-*l/ 99.7%

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

      6. *-commutative 99.7%

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

      7. *-commutative 99.7%

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

      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 inf 99.5%

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

      1. associate-*r/ 99.6%

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

      2. *-commutative 99.6%

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

      3. associate-/l* 99.5%

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

      4. div-inv 99.7%

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

      5. metadata-eval 99.7%

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

      6. *-commutative 99.7%

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

   6. Applied egg-rr 99.7%

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

4. Final simplification 99.4%

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

Alternative 6: 98.3% accurate, 0.8× speedup

Math

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

FPCore

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

C

double code(double x, double y) {
	double tmp;
	if (x <= -3.8) {
		tmp = (1.0 - x) * (-0.3333333333333333 * (x / y));
	} else if (x <= 3.0) {
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	} else {
		tmp = (x / y) * (-0.3333333333333333 - (x / -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 <= (-3.8d0)) then
        tmp = (1.0d0 - x) * ((-0.3333333333333333d0) * (x / y))
    else if (x <= 3.0d0) then
        tmp = (1.0d0 + (x * (-1.3333333333333333d0))) / y
    else
        tmp = (x / y) * ((-0.3333333333333333d0) - (x / (-3.0d0)))
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 3 regimes

2. if x < -3.7999999999999998

   1. Initial program 90.3%

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

      1. *-commutative 90.3%

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

      2. associate-*l/ 99.7%

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

      3. *-commutative 99.7%

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

      4. *-lft-identity 99.7%

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

      5. associate-*l/ 99.7%

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

      6. *-commutative 99.7%

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

      7. *-commutative 99.7%

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

      8. associate-/r* 99.8%

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

      9. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 99.4%

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

   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/ 99.3%

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

      6. *-commutative 99.3%

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

      7. *-commutative 99.3%

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

      8. associate-/r* 99.5%

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

      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. Taylor expanded in x around 0 99.3%

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

   5. Taylor expanded in y around 0 99.3%

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

   if 3 < x

   1. Initial program 85.8%

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

      1. *-commutative 85.8%

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

      2. associate-*l/ 99.7%

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

      3. *-commutative 99.7%

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

      4. *-lft-identity 99.7%

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

      5. associate-*l/ 99.7%

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

      6. *-commutative 99.7%

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

      7. *-commutative 99.7%

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

      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 inf 99.5%

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

      1. associate-*r/ 99.6%

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

      2. *-commutative 99.6%

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

      3. associate-/l* 99.5%

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

      4. div-inv 99.7%

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

      5. metadata-eval 99.7%

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

      6. *-commutative 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in y around 0 85.7%

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

      1. metadata-eval 85.7%

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

      2. times-frac 85.8%

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

      3. *-commutative 85.8%

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

      4. neg-mul-1 85.8%

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

      5. distribute-lft-neg-in 85.8%

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

      6. *-commutative 85.8%

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

      7. associate-/l* 99.7%

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

      8. *-commutative 99.7%

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

      9. neg-mul-1 99.7%

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

      10. times-frac 99.7%

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

      11. metadata-eval 99.7%

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

      12. associate-*r/ 99.7%

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

      13. *-commutative 99.7%

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

      14. associate-/l* 85.8%

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

      15. *-commutative 85.8%

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

      16. times-frac 99.8%

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

      17. div-sub 99.8%

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

      18. metadata-eval 99.8%

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

   9. Simplified 99.8%

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

4. Final simplification 99.4%

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

Alternative 7: 98.3% accurate, 0.8× speedup

Math

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

FPCore

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

C

double code(double x, double y) {
	double tmp;
	if (x <= -3.8) {
		tmp = ((1.0 - x) * -0.3333333333333333) / (y / x);
	} else if (x <= 3.0) {
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	} else {
		tmp = (x / y) * (-0.3333333333333333 - (x / -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 <= (-3.8d0)) then
        tmp = ((1.0d0 - x) * (-0.3333333333333333d0)) / (y / x)
    else if (x <= 3.0d0) then
        tmp = (1.0d0 + (x * (-1.3333333333333333d0))) / y
    else
        tmp = (x / y) * ((-0.3333333333333333d0) - (x / (-3.0d0)))
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 3 regimes

2. if x < -3.7999999999999998

   1. Initial program 90.3%

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

      1. *-commutative 90.3%

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

      2. associate-*l/ 99.7%

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

      3. *-commutative 99.7%

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

      4. *-lft-identity 99.7%

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

      5. associate-*l/ 99.7%

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

      6. *-commutative 99.7%

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

      7. *-commutative 99.7%

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

      8. associate-/r* 99.8%

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

      9. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 99.4%

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

      1. associate-*r* 99.3%

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

      2. clear-num 99.2%

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

      3. un-div-inv 99.4%

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

   6. Applied egg-rr 99.4%

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

   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/ 99.3%

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

      6. *-commutative 99.3%

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

      7. *-commutative 99.3%

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

      8. associate-/r* 99.5%

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

      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. Taylor expanded in x around 0 99.3%

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

   5. Taylor expanded in y around 0 99.3%

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

   if 3 < x

   1. Initial program 85.8%

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

      1. *-commutative 85.8%

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

      2. associate-*l/ 99.7%

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

      3. *-commutative 99.7%

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

      4. *-lft-identity 99.7%

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

      5. associate-*l/ 99.7%

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

      6. *-commutative 99.7%

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

      7. *-commutative 99.7%

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

      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 inf 99.5%

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

      1. associate-*r/ 99.6%

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

      2. *-commutative 99.6%

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

      3. associate-/l* 99.5%

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

      4. div-inv 99.7%

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

      5. metadata-eval 99.7%

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

      6. *-commutative 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in y around 0 85.7%

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

      1. metadata-eval 85.7%

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

      2. times-frac 85.8%

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

      3. *-commutative 85.8%

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

      4. neg-mul-1 85.8%

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

      5. distribute-lft-neg-in 85.8%

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

      6. *-commutative 85.8%

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

      7. associate-/l* 99.7%

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

      8. *-commutative 99.7%

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

      9. neg-mul-1 99.7%

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

      10. times-frac 99.7%

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

      11. metadata-eval 99.7%

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

      12. associate-*r/ 99.7%

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

      13. *-commutative 99.7%

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

      14. associate-/l* 85.8%

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

      15. *-commutative 85.8%

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

      16. times-frac 99.8%

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

      17. div-sub 99.8%

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

      18. metadata-eval 99.8%

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

   9. Simplified 99.8%

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

4. Final simplification 99.4%

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

Alternative 8: 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 93.5%

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

   1. *-commutative 93.5%

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

   2. associate-*l/ 99.7%

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

   3. *-commutative 99.7%

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

   4. *-lft-identity 99.7%

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

   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* 99.6%

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

   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. Final simplification 99.6%

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

Alternative 9: 99.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.5%

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

   1. *-commutative 93.5%

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

   2. associate-*l/ 99.7%

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

   3. *-commutative 99.7%

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

   4. sub-neg 99.7%

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

   5. +-commutative 99.7%

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

   6. neg-sub0 99.7%

      \[\leadsto \left(1 - x\right) \cdot \frac{\color{blue}{\left(0 - x\right)} + 3}{y \cdot 3} \]

   7. associate-+l- 99.7%

      \[\leadsto \left(1 - x\right) \cdot \frac{\color{blue}{0 - \left(x - 3\right)}}{y \cdot 3} \]

   8. sub0-neg 99.7%

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

   9. distribute-frac-neg 99.7%

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

   10. sub-neg 99.7%

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

   11. remove-double-neg 99.7%

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

   12. distribute-neg-in 99.7%

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

   13. +-commutative 99.7%

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

   14. sub-neg 99.7%

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

   15. distribute-frac-neg 99.7%

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

   16. mul-1-neg 99.7%

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

   17. metadata-eval 99.7%

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

   18. times-frac 99.7%

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

   19. *-lft-identity 99.7%

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

   20. neg-mul-1 99.7%

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

   21. distribute-lft-neg-out 99.7%

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

   22. distribute-frac-neg 99.7%

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

3. Simplified 99.7%

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

4. Final simplification 99.7%

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

Alternative 10: 57.2% 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 90.3%

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

      1. *-commutative 90.3%

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

      2. associate-*l/ 99.7%

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

      3. *-commutative 99.7%

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

      4. *-lft-identity 99.7%

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

      5. associate-*l/ 99.7%

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

      6. *-commutative 99.7%

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

      7. *-commutative 99.7%

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

      8. associate-/r* 99.8%

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

      9. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 39.3%

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

   5. Taylor expanded in x around inf 39.3%

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

   if -0.75 < x

   1. Initial program 94.9%

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

      1. *-commutative 94.9%

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

      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* 99.5%

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

      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. clear-num 99.3%

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

      2. un-div-inv 99.4%

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

      3. associate-*r/ 94.8%

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

      4. associate-/l* 99.6%

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

      5. div-inv 99.8%

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

      6. metadata-eval 99.8%

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

      7. metadata-eval 99.8%

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

      8. distribute-rgt-neg-in 99.8%

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

      9. sub-neg 99.8%

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

      10. metadata-eval 99.8%

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

      11. distribute-neg-in 99.8%

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

      12. +-commutative 99.8%

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

      13. frac-2neg 99.8%

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

      14. associate-/l* 94.9%

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

      15. associate-/r* 94.5%

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

   5. Applied egg-rr 94.5%

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

   6. Taylor expanded in x around 0 67.0%

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

4. Final simplification 58.5%

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

Alternative 11: 57.2% accurate, 1.6× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

Wolfram

code[x_, y_] := If[LessEqual[x, -0.75], N[(N[(x * -1.3333333333333333), $MachinePrecision] / y), $MachinePrecision], N[(1.0 / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -0.75

   1. Initial program 90.3%

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

      1. *-commutative 90.3%

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

      2. associate-*l/ 99.7%

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

      3. *-commutative 99.7%

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

      4. *-lft-identity 99.7%

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

      5. associate-*l/ 99.7%

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

      6. *-commutative 99.7%

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

      7. *-commutative 99.7%

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

      8. associate-/r* 99.8%

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

      9. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 39.3%

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

   5. Taylor expanded in y around 0 40.5%

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

   6. Taylor expanded in x around inf 40.5%

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

   if -0.75 < x

   1. Initial program 94.9%

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

      1. *-commutative 94.9%

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

      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* 99.5%

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

      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. clear-num 99.3%

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

      2. un-div-inv 99.4%

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

      3. associate-*r/ 94.8%

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

      4. associate-/l* 99.6%

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

      5. div-inv 99.8%

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

      6. metadata-eval 99.8%

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

      7. metadata-eval 99.8%

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

      8. distribute-rgt-neg-in 99.8%

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

      9. sub-neg 99.8%

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

      10. metadata-eval 99.8%

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

      11. distribute-neg-in 99.8%

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

      12. +-commutative 99.8%

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

      13. frac-2neg 99.8%

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

      14. associate-/l* 94.9%

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

      15. associate-/r* 94.5%

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

   5. Applied egg-rr 94.5%

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

   6. Taylor expanded in x around 0 67.0%

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

4. Final simplification 58.8%

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

Alternative 12: 56.2% accurate, 1.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.5%

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

   1. *-commutative 93.5%

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

   2. associate-*l/ 99.7%

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

   3. *-commutative 99.7%

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

   4. *-lft-identity 99.7%

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

   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* 99.6%

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

   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 57.7%

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

   1. un-div-inv 57.7%

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

   2. clear-num 57.7%

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

6. Applied egg-rr 57.7%

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

7. Final simplification 57.7%

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

Alternative 13: 56.7% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \frac{1 + x \cdot -1.3333333333333333}{y} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (+ 1.0 (* x -1.3333333333333333)) y))

C

double code(double x, double y) {
	return (1.0 + (x * -1.3333333333333333)) / y;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (1.0d0 + (x * (-1.3333333333333333d0))) / y
end function

Java

public static double code(double x, double y) {
	return (1.0 + (x * -1.3333333333333333)) / y;
}

Python

def code(x, y):
	return (1.0 + (x * -1.3333333333333333)) / y

Julia

function code(x, y)
	return Float64(Float64(1.0 + Float64(x * -1.3333333333333333)) / y)
end

MATLAB

function tmp = code(x, y)
	tmp = (1.0 + (x * -1.3333333333333333)) / y;
end

Wolfram

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

Derivation

1. Initial program 93.5%

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

   1. *-commutative 93.5%

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

   2. associate-*l/ 99.7%

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

   3. *-commutative 99.7%

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

   4. *-lft-identity 99.7%

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

   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* 99.6%

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

   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 57.7%

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

5. Taylor expanded in y around 0 58.1%

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

6. Final simplification 58.1%

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

Alternative 14: 57.2% 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(x / Float64(-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 90.3%

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

      1. *-commutative 90.3%

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

      2. associate-*l/ 99.7%

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

      3. *-commutative 99.7%

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

      4. *-lft-identity 99.7%

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

      5. associate-*l/ 99.7%

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

      6. *-commutative 99.7%

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

      7. *-commutative 99.7%

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

      8. associate-/r* 99.8%

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

      9. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 39.3%

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

   5. Taylor expanded in x around inf 39.3%

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

      1. associate-*r/ 39.3%

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

      2. neg-mul-1 39.3%

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

      3. *-lft-identity 39.3%

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

      4. associate-*l/ 39.3%

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

      5. metadata-eval 39.3%

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

      6. associate-/r* 39.3%

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

      7. neg-mul-1 39.3%

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

      8. associate-*l/ 39.3%

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

      9. neg-mul-1 39.3%

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

      10. remove-double-neg 39.3%

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

   7. Simplified 39.3%

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

   if -1 < x

   1. Initial program 94.9%

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

      1. *-commutative 94.9%

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

      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* 99.5%

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

      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. clear-num 99.3%

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

      2. un-div-inv 99.4%

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

      3. associate-*r/ 94.8%

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

      4. associate-/l* 99.6%

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

      5. div-inv 99.8%

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

      6. metadata-eval 99.8%

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

      7. metadata-eval 99.8%

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

      8. distribute-rgt-neg-in 99.8%

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

      9. sub-neg 99.8%

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

      10. metadata-eval 99.8%

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

      11. distribute-neg-in 99.8%

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

      12. +-commutative 99.8%

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

      13. frac-2neg 99.8%

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

      14. associate-/l* 94.9%

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

      15. associate-/r* 94.5%

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

   5. Applied egg-rr 94.5%

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

   6. Taylor expanded in x around 0 67.0%

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

4. Final simplification 58.5%

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

Alternative 15: 56.2% accurate, 2.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.5%

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

   1. *-commutative 93.5%

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

   2. associate-*l/ 99.7%

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

   3. *-commutative 99.7%

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

   4. *-lft-identity 99.7%

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

   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* 99.6%

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

   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 57.7%

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

5. Taylor expanded in x around 0 57.7%

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

   1. neg-mul-1 57.7%

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

   2. +-commutative 57.7%

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

   3. sub-neg 57.7%

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

   4. div-sub 57.7%

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

7. Simplified 57.7%

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

8. Final simplification 57.7%

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

Alternative 16: 50.8% accurate, 3.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.5%

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

   1. *-commutative 93.5%

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

   2. associate-*l/ 99.7%

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

   3. *-commutative 99.7%

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

   4. *-lft-identity 99.7%

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

   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* 99.6%

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

   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. Step-by-step derivation

   1. clear-num 99.5%

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

   2. un-div-inv 99.5%

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

   3. associate-*r/ 93.4%

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

   4. associate-/l* 99.6%

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

   5. div-inv 99.8%

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

   6. metadata-eval 99.8%

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

   7. metadata-eval 99.8%

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

   8. distribute-rgt-neg-in 99.8%

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

   9. sub-neg 99.8%

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

   10. metadata-eval 99.8%

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

   11. distribute-neg-in 99.8%

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

   12. +-commutative 99.8%

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

   13. frac-2neg 99.8%

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

   14. associate-/l* 93.5%

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

   15. associate-/r* 93.2%

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

5. Applied egg-rr 93.2%

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

6. Taylor expanded in x around 0 47.8%

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

7. Final simplification 47.8%

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

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 2023305 
(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)))