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

Percentage Accurate: 94.1% → 99.9%

Time: 20.5s

Alternatives: 15

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: 94.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.0%

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

   1. associate-/l* 99.7%

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

   2. *-commutative 99.7%

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

3. Simplified 99.7%

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

   1. associate-/l* 99.7%

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

   2. associate-/r/ 99.9%

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

5. Applied egg-rr 99.9%

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

6. Final simplification 99.9%

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

Alternative 2: 98.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.4 \lor \neg \left(x \leq 1.3\right):\\ \;\;\;\;x \cdot \left(\left(3 - x\right) \cdot \frac{-0.3333333333333333}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -2.4) (not (<= x 1.3)))
   (* x (* (- 3.0 x) (/ -0.3333333333333333 y)))
   (/ (+ 1.0 (* x -1.3333333333333333)) y)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -2.4) || !(x <= 1.3)) {
		tmp = x * ((3.0 - x) * (-0.3333333333333333 / 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 <= (-2.4d0)) .or. (.not. (x <= 1.3d0))) then
        tmp = x * ((3.0d0 - x) * ((-0.3333333333333333d0) / 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 <= -2.4) || !(x <= 1.3)) {
		tmp = x * ((3.0 - x) * (-0.3333333333333333 / y));
	} else {
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -2.4) or not (x <= 1.3):
		tmp = x * ((3.0 - x) * (-0.3333333333333333 / y))
	else:
		tmp = (1.0 + (x * -1.3333333333333333)) / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -2.4) || !(x <= 1.3))
		tmp = Float64(x * Float64(Float64(3.0 - x) * Float64(-0.3333333333333333 / 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 <= -2.4) || ~((x <= 1.3)))
		tmp = x * ((3.0 - x) * (-0.3333333333333333 / y));
	else
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -2.4], N[Not[LessEqual[x, 1.3]], $MachinePrecision]], N[(x * N[(N[(3.0 - x), $MachinePrecision] * N[(-0.3333333333333333 / 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 < -2.39999999999999991 or 1.30000000000000004 < x

   1. Initial program 91.0%

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

      1. *-commutative 91.0%

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

      2. associate-*r/ 99.7%

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

      3. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 96.2%

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

      1. associate-*r/ 96.2%

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

      2. *-commutative 96.2%

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

   6. Simplified 96.2%

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

   7. Taylor expanded in x around 0 78.6%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{y} + 0.3333333333333333 \cdot \frac{{x}^{2}}{y}} \]
   8. Step-by-step derivation

      1. *-commutative 78.6%

         \[\leadsto -1 \cdot \frac{x}{y} + \color{blue}{\frac{{x}^{2}}{y} \cdot 0.3333333333333333} \]

      2. unpow2 78.6%

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

      3. associate-*r/ 87.4%

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

      4. associate-*l* 87.4%

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

      5. metadata-eval 87.4%

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

      6. distribute-rgt-neg-in 87.4%

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

      7. *-commutative 87.4%

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

      8. distribute-rgt-neg-in 87.4%

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

      9. distribute-lft-neg-in 87.4%

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

      10. metadata-eval 87.4%

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

      11. associate-*r* 87.4%

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

      12. distribute-rgt-out 96.2%

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

      13. sub-neg 96.2%

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

      14. *-commutative 96.2%

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

      15. associate-*l/ 96.2%

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

      16. associate-*r/ 96.2%

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

      17. associate-*l* 96.2%

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

   9. Simplified 96.2%

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

   if -2.39999999999999991 < x < 1.30000000000000004

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

      2. associate-*r/ 99.4%

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

      3. *-commutative 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in x around 0 99.0%

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

   5. Taylor expanded in y around 0 99.0%

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

4. Final simplification 97.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.4 \lor \neg \left(x \leq 1.3\right):\\ \;\;\;\;x \cdot \left(\left(3 - x\right) \cdot \frac{-0.3333333333333333}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \end{array} \]

Alternative 3: 98.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.4 \lor \neg \left(x \leq 1.3\right):\\ \;\;\;\;x \cdot \frac{3 - x}{y \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -2.4) (not (<= x 1.3)))
   (* x (/ (- 3.0 x) (* y -3.0)))
   (/ (+ 1.0 (* x -1.3333333333333333)) y)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -2.4) || !(x <= 1.3)) {
		tmp = x * ((3.0 - x) / (y * -3.0));
	} 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 <= (-2.4d0)) .or. (.not. (x <= 1.3d0))) then
        tmp = x * ((3.0d0 - x) / (y * (-3.0d0)))
    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 <= -2.4) || !(x <= 1.3)) {
		tmp = x * ((3.0 - x) / (y * -3.0));
	} else {
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -2.4) or not (x <= 1.3):
		tmp = x * ((3.0 - x) / (y * -3.0))
	else:
		tmp = (1.0 + (x * -1.3333333333333333)) / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -2.4) || !(x <= 1.3))
		tmp = Float64(x * Float64(Float64(3.0 - x) / Float64(y * -3.0)));
	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 <= -2.4) || ~((x <= 1.3)))
		tmp = x * ((3.0 - x) / (y * -3.0));
	else
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -2.4], N[Not[LessEqual[x, 1.3]], $MachinePrecision]], N[(x * N[(N[(3.0 - x), $MachinePrecision] / N[(y * -3.0), $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 < -2.39999999999999991 or 1.30000000000000004 < x

   1. Initial program 91.0%

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

      1. *-commutative 91.0%

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

      2. associate-*r/ 99.7%

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

      3. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 96.2%

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

      1. associate-*r/ 96.2%

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

      2. *-commutative 96.2%

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

   6. Simplified 96.2%

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

   7. Taylor expanded in x around 0 78.6%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{y} + 0.3333333333333333 \cdot \frac{{x}^{2}}{y}} \]
   8. Step-by-step derivation

      1. *-commutative 78.6%

         \[\leadsto -1 \cdot \frac{x}{y} + \color{blue}{\frac{{x}^{2}}{y} \cdot 0.3333333333333333} \]

      2. unpow2 78.6%

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

      3. associate-*r/ 87.4%

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

      4. associate-*l* 87.4%

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

      5. metadata-eval 87.4%

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

      6. distribute-rgt-neg-in 87.4%

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

      7. *-commutative 87.4%

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

      8. distribute-rgt-neg-in 87.4%

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

      9. distribute-lft-neg-in 87.4%

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

      10. metadata-eval 87.4%

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

      11. associate-*r* 87.4%

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

      12. distribute-rgt-out 96.2%

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

      13. sub-neg 96.2%

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

      14. *-commutative 96.2%

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

      15. associate-*l/ 96.2%

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

      16. associate-*r/ 96.2%

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

      17. associate-*l* 96.2%

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

   9. Simplified 96.2%

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

       1. *-commutative 96.2%

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

       2. clear-num 96.2%

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

       3. un-div-inv 96.2%

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

       4. div-inv 96.2%

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

       5. metadata-eval 96.2%

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

   11. Applied egg-rr 96.2%

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

   if -2.39999999999999991 < x < 1.30000000000000004

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

      2. associate-*r/ 99.4%

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

      3. *-commutative 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in x around 0 99.0%

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

   5. Taylor expanded in y around 0 99.0%

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

4. Final simplification 97.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.4 \lor \neg \left(x \leq 1.3\right):\\ \;\;\;\;x \cdot \frac{3 - x}{y \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \end{array} \]

Alternative 4: 98.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.4:\\ \;\;\;\;x \cdot \left(\left(3 - x\right) \cdot \frac{-0.3333333333333333}{y}\right)\\ \mathbf{elif}\;x \leq 1.3:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-0.3333333333333333}{\frac{y}{3 - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2.4)
   (* x (* (- 3.0 x) (/ -0.3333333333333333 y)))
   (if (<= x 1.3)
     (/ (+ 1.0 (* x -1.3333333333333333)) y)
     (* x (/ -0.3333333333333333 (/ y (- 3.0 x)))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.4) {
		tmp = x * ((3.0 - x) * (-0.3333333333333333 / y));
	} else if (x <= 1.3) {
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	} else {
		tmp = x * (-0.3333333333333333 / (y / (3.0 - x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-2.4d0)) then
        tmp = x * ((3.0d0 - x) * ((-0.3333333333333333d0) / y))
    else if (x <= 1.3d0) then
        tmp = (1.0d0 + (x * (-1.3333333333333333d0))) / y
    else
        tmp = x * ((-0.3333333333333333d0) / (y / (3.0d0 - x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -2.4) {
		tmp = x * ((3.0 - x) * (-0.3333333333333333 / y));
	} else if (x <= 1.3) {
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	} else {
		tmp = x * (-0.3333333333333333 / (y / (3.0 - x)));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2.4:
		tmp = x * ((3.0 - x) * (-0.3333333333333333 / y))
	elif x <= 1.3:
		tmp = (1.0 + (x * -1.3333333333333333)) / y
	else:
		tmp = x * (-0.3333333333333333 / (y / (3.0 - x)))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2.4)
		tmp = Float64(x * Float64(Float64(3.0 - x) * Float64(-0.3333333333333333 / y)));
	elseif (x <= 1.3)
		tmp = Float64(Float64(1.0 + Float64(x * -1.3333333333333333)) / y);
	else
		tmp = Float64(x * Float64(-0.3333333333333333 / Float64(y / Float64(3.0 - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2.4)
		tmp = x * ((3.0 - x) * (-0.3333333333333333 / y));
	elseif (x <= 1.3)
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	else
		tmp = x * (-0.3333333333333333 / (y / (3.0 - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2.4], N[(x * N[(N[(3.0 - x), $MachinePrecision] * N[(-0.3333333333333333 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.3], N[(N[(1.0 + N[(x * -1.3333333333333333), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x * N[(-0.3333333333333333 / N[(y / N[(3.0 - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.39999999999999991

   1. Initial program 92.1%

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

      1. *-commutative 92.1%

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

      2. associate-*r/ 99.7%

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

      3. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 97.2%

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

      1. associate-*r/ 97.2%

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

      2. *-commutative 97.2%

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

   6. Simplified 97.2%

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

   7. Taylor expanded in x around 0 89.7%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{y} + 0.3333333333333333 \cdot \frac{{x}^{2}}{y}} \]
   8. Step-by-step derivation

      1. *-commutative 89.7%

         \[\leadsto -1 \cdot \frac{x}{y} + \color{blue}{\frac{{x}^{2}}{y} \cdot 0.3333333333333333} \]

      2. unpow2 89.7%

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

      3. associate-*r/ 97.2%

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

      4. associate-*l* 97.2%

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

      5. metadata-eval 97.2%

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

      6. distribute-rgt-neg-in 97.2%

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

      7. *-commutative 97.2%

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

      8. distribute-rgt-neg-in 97.2%

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

      9. distribute-lft-neg-in 97.2%

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

      10. metadata-eval 97.2%

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

      11. associate-*r* 97.2%

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

      12. distribute-rgt-out 97.2%

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

      13. sub-neg 97.2%

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

      14. *-commutative 97.2%

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

      15. associate-*l/ 97.2%

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

      16. associate-*r/ 97.2%

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

      17. associate-*l* 97.2%

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

   9. Simplified 97.2%

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

   if -2.39999999999999991 < x < 1.30000000000000004

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

      2. associate-*r/ 99.4%

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

      3. *-commutative 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in x around 0 99.0%

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

   5. Taylor expanded in y around 0 99.0%

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

   if 1.30000000000000004 < x

   1. Initial program 89.6%

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

      1. *-commutative 89.6%

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

      2. associate-*r/ 99.7%

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

      3. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 95.0%

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

      1. associate-*r/ 95.0%

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

      2. *-commutative 95.0%

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

   6. Simplified 95.0%

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

   7. Taylor expanded in x around 0 65.4%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{y} + 0.3333333333333333 \cdot \frac{{x}^{2}}{y}} \]
   8. Step-by-step derivation

      1. *-commutative 65.4%

         \[\leadsto -1 \cdot \frac{x}{y} + \color{blue}{\frac{{x}^{2}}{y} \cdot 0.3333333333333333} \]

      2. unpow2 65.4%

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

      3. associate-*r/ 75.6%

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

      4. associate-*l* 75.6%

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

      5. metadata-eval 75.6%

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

      6. distribute-rgt-neg-in 75.6%

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

      7. *-commutative 75.6%

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

      8. distribute-rgt-neg-in 75.6%

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

      9. distribute-lft-neg-in 75.6%

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

      10. metadata-eval 75.6%

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

      11. associate-*r* 75.6%

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

      12. distribute-rgt-out 95.0%

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

      13. sub-neg 95.0%

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

      14. *-commutative 95.0%

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

      15. associate-*l/ 95.0%

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

      16. associate-*r/ 94.9%

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

      17. associate-*l* 94.9%

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

   9. Simplified 94.9%

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

   10. Taylor expanded in y around 0 95.0%

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

       1. associate-*r/ 95.0%

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

       2. associate-/l* 95.0%

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

   12. Simplified 95.0%

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

4. Final simplification 97.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.4:\\ \;\;\;\;x \cdot \left(\left(3 - x\right) \cdot \frac{-0.3333333333333333}{y}\right)\\ \mathbf{elif}\;x \leq 1.3:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-0.3333333333333333}{\frac{y}{3 - x}}\\ \end{array} \]

Alternative 5: 97.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if x < -3.7999999999999998 or 3 < x

   1. Initial program 91.0%

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

      1. *-commutative 91.0%

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

      2. associate-*r/ 99.7%

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

      3. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 87.1%

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

      1. unpow2 87.1%

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

   6. Simplified 87.1%

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

      1. associate-/l* 95.9%

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

      2. add-sqr-sqrt 43.1%

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

      3. *-un-lft-identity 43.1%

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

      4. times-frac 43.1%

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

   8. Applied egg-rr 43.1%

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

      1. /-rgt-identity 43.1%

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

      2. associate-*r/ 43.1%

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

      3. rem-square-sqrt 95.9%

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

   10. Simplified 95.9%

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

   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. associate-/l* 99.8%

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

      2. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 97.6%

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

4. Final simplification 96.7%

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

Alternative 6: 97.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 3 regimes

2. if x < -3.7999999999999998

   1. Initial program 92.1%

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

      1. *-commutative 92.1%

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

      2. associate-*r/ 99.7%

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

      3. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 89.5%

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

      1. unpow2 89.5%

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

   6. Simplified 89.5%

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

      1. associate-/l* 97.1%

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

      2. add-sqr-sqrt 0.0%

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

      3. *-un-lft-identity 0.0%

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

      4. times-frac 0.0%

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

   8. Applied egg-rr 0.0%

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

      1. /-rgt-identity 0.0%

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

      2. associate-*r/ 0.0%

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

      3. rem-square-sqrt 97.1%

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

   10. Simplified 97.1%

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

   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. associate-/l* 99.8%

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

      2. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 97.6%

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

   if 3 < x

   1. Initial program 89.6%

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

      1. *-commutative 89.6%

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

      2. associate-*r/ 99.7%

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

      3. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 84.4%

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

      1. unpow2 84.4%

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

   6. Simplified 84.4%

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

      1. associate-*r/ 84.4%

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

      2. clear-num 84.4%

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

      3. *-commutative 84.4%

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

   8. Applied egg-rr 84.4%

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

      1. associate-/r/ 84.4%

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

      2. /-rgt-identity 84.4%

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

      3. associate-/l* 84.4%

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

      4. metadata-eval 84.4%

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

      5. associate-*r/ 84.4%

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

      6. associate-*l/ 84.4%

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

      7. *-lft-identity 84.4%

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

      8. associate-*r/ 94.7%

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

   10. Simplified 94.7%

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

       1. div-inv 94.6%

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

       2. *-commutative 94.6%

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

       3. associate-/r/ 94.6%

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

       4. metadata-eval 94.6%

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

       5. *-commutative 94.6%

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

       6. associate-*r/ 94.6%

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

       7. associate-/r/ 94.6%

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

       8. *-commutative 94.6%

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

   12. Applied egg-rr 94.6%

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

4. Final simplification 96.7%

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

Alternative 7: 97.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 3 regimes

2. if x < -3.7999999999999998

   1. Initial program 92.1%

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

      1. *-commutative 92.1%

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

      2. associate-*r/ 99.7%

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

      3. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 89.5%

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

      1. unpow2 89.5%

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

   6. Simplified 89.5%

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

      1. associate-/l* 97.1%

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

      2. add-sqr-sqrt 0.0%

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

      3. *-un-lft-identity 0.0%

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

      4. times-frac 0.0%

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

   8. Applied egg-rr 0.0%

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

      1. /-rgt-identity 0.0%

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

      2. associate-*r/ 0.0%

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

      3. rem-square-sqrt 97.1%

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

   10. Simplified 97.1%

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

   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. associate-/l* 99.8%

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

      2. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 97.6%

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

   if 3 < x

   1. Initial program 89.6%

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

      1. *-commutative 89.6%

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

      2. associate-*r/ 99.7%

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

      3. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 84.4%

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

      1. unpow2 84.4%

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

   6. Simplified 84.4%

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

      1. associate-*r/ 84.4%

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

      2. clear-num 84.4%

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

      3. *-commutative 84.4%

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

   8. Applied egg-rr 84.4%

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

      1. associate-/r/ 84.4%

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

      2. /-rgt-identity 84.4%

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

      3. associate-/l* 84.4%

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

      4. metadata-eval 84.4%

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

      5. associate-*r/ 84.4%

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

      6. associate-*l/ 84.4%

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

      7. *-lft-identity 84.4%

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

      8. associate-*r/ 94.7%

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

   10. Simplified 94.7%

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

4. Final simplification 96.7%

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

Alternative 8: 98.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.5:\\ \;\;\;\;0.3333333333333333 \cdot \frac{x}{\frac{y}{x}}\\ \mathbf{elif}\;x \leq 3:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{x}{y}}{3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -4.5)
   (* 0.3333333333333333 (/ x (/ y x)))
   (if (<= x 3.0)
     (/ (+ 1.0 (* x -1.3333333333333333)) y)
     (/ (* x (/ x y)) 3.0))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -4.5) {
		tmp = 0.3333333333333333 * (x / (y / x));
	} else if (x <= 3.0) {
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	} else {
		tmp = (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 <= (-4.5d0)) then
        tmp = 0.3333333333333333d0 * (x / (y / x))
    else if (x <= 3.0d0) then
        tmp = (1.0d0 + (x * (-1.3333333333333333d0))) / y
    else
        tmp = (x * (x / y)) / 3.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -4.5) {
		tmp = 0.3333333333333333 * (x / (y / x));
	} else if (x <= 3.0) {
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	} else {
		tmp = (x * (x / y)) / 3.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -4.5:
		tmp = 0.3333333333333333 * (x / (y / x))
	elif x <= 3.0:
		tmp = (1.0 + (x * -1.3333333333333333)) / y
	else:
		tmp = (x * (x / y)) / 3.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -4.5)
		tmp = Float64(0.3333333333333333 * Float64(x / Float64(y / x)));
	elseif (x <= 3.0)
		tmp = Float64(Float64(1.0 + Float64(x * -1.3333333333333333)) / y);
	else
		tmp = Float64(Float64(x * Float64(x / y)) / 3.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -4.5)
		tmp = 0.3333333333333333 * (x / (y / x));
	elseif (x <= 3.0)
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	else
		tmp = (x * (x / y)) / 3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -4.5], N[(0.3333333333333333 * N[(x / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.0], N[(N[(1.0 + N[(x * -1.3333333333333333), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x * N[(x / y), $MachinePrecision]), $MachinePrecision] / 3.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.5

   1. Initial program 92.1%

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

      1. *-commutative 92.1%

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

      2. associate-*r/ 99.7%

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

      3. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 89.5%

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

      1. unpow2 89.5%

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

   6. Simplified 89.5%

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

      1. associate-/l* 97.1%

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

      2. add-sqr-sqrt 0.0%

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

      3. *-un-lft-identity 0.0%

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

      4. times-frac 0.0%

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

   8. Applied egg-rr 0.0%

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

      1. /-rgt-identity 0.0%

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

      2. associate-*r/ 0.0%

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

      3. rem-square-sqrt 97.1%

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

   10. Simplified 97.1%

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

   if -4.5 < 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-*r/ 99.4%

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

      3. *-commutative 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in x around 0 99.0%

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

   5. Taylor expanded in y around 0 99.0%

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

   if 3 < x

   1. Initial program 89.6%

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

      1. *-commutative 89.6%

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

      2. associate-*r/ 99.7%

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

      3. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 84.4%

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

      1. unpow2 84.4%

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

   6. Simplified 84.4%

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

      1. associate-*r/ 84.4%

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

      2. clear-num 84.4%

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

      3. *-commutative 84.4%

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

   8. Applied egg-rr 84.4%

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

      1. associate-/r/ 84.4%

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

      2. /-rgt-identity 84.4%

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

      3. associate-/l* 84.4%

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

      4. metadata-eval 84.4%

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

      5. associate-*r/ 84.4%

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

      6. associate-*l/ 84.4%

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

      7. *-lft-identity 84.4%

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

      8. associate-*r/ 94.7%

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

   10. Simplified 94.7%

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

4. Final simplification 97.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.5:\\ \;\;\;\;0.3333333333333333 \cdot \frac{x}{\frac{y}{x}}\\ \mathbf{elif}\;x \leq 3:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{x}{y}}{3}\\ \end{array} \]

Alternative 9: 99.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.0%

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

   1. *-commutative 95.0%

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

   2. associate-*r/ 99.6%

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

   3. *-commutative 99.6%

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

3. Simplified 99.6%

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

4. Final simplification 99.6%

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

Alternative 10: 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 95.0%

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

   1. times-frac 99.8%

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

3. Simplified 99.8%

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

4. Final simplification 99.8%

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

Alternative 11: 57.6% 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 92.1%

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

      1. *-commutative 92.1%

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

      2. associate-*r/ 99.7%

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

      3. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around 0 29.2%

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

   5. Taylor expanded in x around inf 29.2%

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

   if -0.75 < x

   1. Initial program 96.2%

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

      1. *-commutative 96.2%

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

      2. associate-*r/ 99.5%

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

      3. *-commutative 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in x around 0 66.1%

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

4. Final simplification 55.4%

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

Alternative 12: 57.6% 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 92.1%

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

      1. *-commutative 92.1%

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

      2. associate-*r/ 99.7%

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

      3. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around 0 29.2%

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

   5. Taylor expanded in y around 0 30.5%

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

   6. Taylor expanded in x around inf 30.5%

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

   if -0.75 < x

   1. Initial program 96.2%

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

      1. *-commutative 96.2%

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

      2. associate-*r/ 99.5%

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

      3. *-commutative 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in x around 0 66.1%

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

4. Final simplification 55.8%

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

Alternative 13: 57.6% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if x < -1

   1. Initial program 92.1%

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

      1. *-commutative 92.1%

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

      2. associate-*r/ 99.7%

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

      3. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 97.2%

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

      1. associate-*r/ 97.2%

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

      2. *-commutative 97.2%

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

   6. Simplified 97.2%

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

   7. Taylor expanded in x around 0 29.2%

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

      1. associate-*r/ 29.2%

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

      2. neg-mul-1 29.2%

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

   9. Simplified 29.2%

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

   if -1 < x

   1. Initial program 96.2%

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

      1. *-commutative 96.2%

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

      2. associate-*r/ 99.5%

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

      3. *-commutative 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in x around 0 66.1%

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

4. Final simplification 55.4%

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

Alternative 14: 56.6% 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 95.0%

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

   1. associate-/l* 99.7%

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

   2. *-commutative 99.7%

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

3. Simplified 99.7%

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

4. Taylor expanded in x around 0 54.4%

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

5. Final simplification 54.4%

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

Alternative 15: 51.3% 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 95.0%

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

   1. *-commutative 95.0%

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

   2. associate-*r/ 99.6%

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

   3. *-commutative 99.6%

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

3. Simplified 99.6%

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

4. Taylor expanded in x around 0 48.4%

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

5. Final simplification 48.4%

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

Developer target: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023285 
(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)))