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

Percentage Accurate: 93.6% → 99.8%

Time: 8.1s

Alternatives: 11

Speedup: 1.0×

• 24.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 93.6% 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

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.4%

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

   1. times-frac N/A

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

   2. *-commutative N/A

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

   3. clear-num N/A

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

   4. un-div-inv N/A

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

   5. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\left(\frac{3 - x}{3}\right), \color{blue}{\left(\frac{y}{1 - x}\right)}\right) \]

   6. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(3 - x\right), 3\right), \left(\frac{\color{blue}{y}}{1 - x}\right)\right) \]

   7. --lowering--.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(3, x\right), 3\right), \left(\frac{y}{1 - x}\right)\right) \]

   8. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(3, x\right), 3\right), \mathsf{/.f64}\left(y, \color{blue}{\left(1 - x\right)}\right)\right) \]

   9. --lowering--.f64 99.8%

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(3, x\right), 3\right), \mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(1, \color{blue}{x}\right)\right)\right) \]

4. Applied egg-rr 99.8%

   \[\leadsto \color{blue}{\frac{\frac{3 - x}{3}}{\frac{y}{1 - x}}} \]
5. Add Preprocessing

Alternative 2: 98.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{y} \cdot \left(x \cdot 0.3333333333333333 + -1.3333333333333333\right)\\ \mathbf{if}\;x \leq -1.72:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.75:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* (/ x y) (+ (* x 0.3333333333333333) -1.3333333333333333))))
   (if (<= x -1.72)
     t_0
     (if (<= x 1.75) (/ (+ 1.0 (* x -1.3333333333333333)) y) t_0))))

C

double code(double x, double y) {
	double t_0 = (x / y) * ((x * 0.3333333333333333) + -1.3333333333333333);
	double tmp;
	if (x <= -1.72) {
		tmp = t_0;
	} else if (x <= 1.75) {
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x / y) * ((x * 0.3333333333333333d0) + (-1.3333333333333333d0))
    if (x <= (-1.72d0)) then
        tmp = t_0
    else if (x <= 1.75d0) then
        tmp = (1.0d0 + (x * (-1.3333333333333333d0))) / y
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (x / y) * ((x * 0.3333333333333333) + -1.3333333333333333);
	double tmp;
	if (x <= -1.72) {
		tmp = t_0;
	} else if (x <= 1.75) {
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (x / y) * ((x * 0.3333333333333333) + -1.3333333333333333)
	tmp = 0
	if x <= -1.72:
		tmp = t_0
	elif x <= 1.75:
		tmp = (1.0 + (x * -1.3333333333333333)) / y
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(x / y) * Float64(Float64(x * 0.3333333333333333) + -1.3333333333333333))
	tmp = 0.0
	if (x <= -1.72)
		tmp = t_0;
	elseif (x <= 1.75)
		tmp = Float64(Float64(1.0 + Float64(x * -1.3333333333333333)) / y);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (x / y) * ((x * 0.3333333333333333) + -1.3333333333333333);
	tmp = 0.0;
	if (x <= -1.72)
		tmp = t_0;
	elseif (x <= 1.75)
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(x / y), $MachinePrecision] * N[(N[(x * 0.3333333333333333), $MachinePrecision] + -1.3333333333333333), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.72], t$95$0, If[LessEqual[x, 1.75], N[(N[(1.0 + N[(x * -1.3333333333333333), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.71999999999999997 or 1.75 < x

   1. Initial program 87.6%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{{x}^{2} \cdot \left(\frac{1}{3} \cdot \frac{1}{y} - \frac{4}{3} \cdot \frac{1}{x \cdot y}\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto {x}^{2} \cdot \left(\frac{1}{3} \cdot \frac{1}{y} + \color{blue}{\left(\mathsf{neg}\left(\frac{4}{3} \cdot \frac{1}{x \cdot y}\right)\right)}\right) \]

      2. distribute-lft-in N/A

         \[\leadsto {x}^{2} \cdot \left(\frac{1}{3} \cdot \frac{1}{y}\right) + \color{blue}{{x}^{2} \cdot \left(\mathsf{neg}\left(\frac{4}{3} \cdot \frac{1}{x \cdot y}\right)\right)} \]

      3. *-commutative N/A

         \[\leadsto \left(\frac{1}{3} \cdot \frac{1}{y}\right) \cdot {x}^{2} + \color{blue}{{x}^{2}} \cdot \left(\mathsf{neg}\left(\frac{4}{3} \cdot \frac{1}{x \cdot y}\right)\right) \]

      4. unpow2 N/A

         \[\leadsto \left(\frac{1}{3} \cdot \frac{1}{y}\right) \cdot \left(x \cdot x\right) + {x}^{\color{blue}{2}} \cdot \left(\mathsf{neg}\left(\frac{4}{3} \cdot \frac{1}{x \cdot y}\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto \left(\left(\frac{1}{3} \cdot \frac{1}{y}\right) \cdot x\right) \cdot x + \color{blue}{{x}^{2}} \cdot \left(\mathsf{neg}\left(\frac{4}{3} \cdot \frac{1}{x \cdot y}\right)\right) \]

      6. associate-*r/ N/A

         \[\leadsto \left(\frac{\frac{1}{3} \cdot 1}{y} \cdot x\right) \cdot x + {x}^{2} \cdot \left(\mathsf{neg}\left(\frac{4}{3} \cdot \frac{1}{x \cdot y}\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \left(\frac{\frac{1}{3}}{y} \cdot x\right) \cdot x + {x}^{2} \cdot \left(\mathsf{neg}\left(\frac{4}{3} \cdot \frac{1}{x \cdot y}\right)\right) \]

      8. associate-*l/ N/A

         \[\leadsto \frac{\frac{1}{3} \cdot x}{y} \cdot x + {\color{blue}{x}}^{2} \cdot \left(\mathsf{neg}\left(\frac{4}{3} \cdot \frac{1}{x \cdot y}\right)\right) \]

      9. associate-*r/ N/A

         \[\leadsto \left(\frac{1}{3} \cdot \frac{x}{y}\right) \cdot x + {\color{blue}{x}}^{2} \cdot \left(\mathsf{neg}\left(\frac{4}{3} \cdot \frac{1}{x \cdot y}\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \left(\frac{x}{y} \cdot \frac{1}{3}\right) \cdot x + {\color{blue}{x}}^{2} \cdot \left(\mathsf{neg}\left(\frac{4}{3} \cdot \frac{1}{x \cdot y}\right)\right) \]

      11. associate-*l* N/A

          \[\leadsto \frac{x}{y} \cdot \left(\frac{1}{3} \cdot x\right) + \color{blue}{{x}^{2}} \cdot \left(\mathsf{neg}\left(\frac{4}{3} \cdot \frac{1}{x \cdot y}\right)\right) \]

      12. associate-*r/ N/A

          \[\leadsto \frac{x}{y} \cdot \left(\frac{1}{3} \cdot x\right) + {x}^{2} \cdot \left(\mathsf{neg}\left(\frac{\frac{4}{3} \cdot 1}{x \cdot y}\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \frac{x}{y} \cdot \left(\frac{1}{3} \cdot x\right) + {x}^{2} \cdot \left(\mathsf{neg}\left(\frac{\frac{4}{3}}{x \cdot y}\right)\right) \]

      14. distribute-neg-frac N/A

          \[\leadsto \frac{x}{y} \cdot \left(\frac{1}{3} \cdot x\right) + {x}^{2} \cdot \frac{\mathsf{neg}\left(\frac{4}{3}\right)}{\color{blue}{x \cdot y}} \]

      15. metadata-eval N/A

          \[\leadsto \frac{x}{y} \cdot \left(\frac{1}{3} \cdot x\right) + {x}^{2} \cdot \frac{\frac{-4}{3}}{\color{blue}{x} \cdot y} \]

      16. associate-*r/ N/A

          \[\leadsto \frac{x}{y} \cdot \left(\frac{1}{3} \cdot x\right) + \frac{{x}^{2} \cdot \frac{-4}{3}}{\color{blue}{x \cdot y}} \]

      17. times-frac N/A

          \[\leadsto \frac{x}{y} \cdot \left(\frac{1}{3} \cdot x\right) + \frac{{x}^{2}}{x} \cdot \color{blue}{\frac{\frac{-4}{3}}{y}} \]

   5. Simplified 98.9%

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

   if -1.71999999999999997 < x < 1.75

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(3 + -4 \cdot x\right)}, \mathsf{*.f64}\left(y, 3\right)\right) \]
   4. Step-by-step derivation

      1. *-rgt-identity N/A

         \[\leadsto \mathsf{/.f64}\left(\left(3 + -4 \cdot \left(x \cdot 1\right)\right), \mathsf{*.f64}\left(y, 3\right)\right) \]

      2. rgt-mult-inverse N/A

         \[\leadsto \mathsf{/.f64}\left(\left(3 + -4 \cdot \left(x \cdot \left(x \cdot \frac{1}{x}\right)\right)\right), \mathsf{*.f64}\left(y, 3\right)\right) \]

      3. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(\left(3 + -4 \cdot \left(x \cdot \frac{x \cdot 1}{x}\right)\right), \mathsf{*.f64}\left(y, 3\right)\right) \]

      4. *-rgt-identity N/A

         \[\leadsto \mathsf{/.f64}\left(\left(3 + -4 \cdot \left(x \cdot \frac{x}{x}\right)\right), \mathsf{*.f64}\left(y, 3\right)\right) \]

      5. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(3 + -4 \cdot \frac{x \cdot x}{x}\right), \mathsf{*.f64}\left(y, 3\right)\right) \]

      6. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(3 + -4 \cdot \frac{{x}^{2}}{x}\right), \mathsf{*.f64}\left(y, 3\right)\right) \]

      7. *-lft-identity N/A

         \[\leadsto \mathsf{/.f64}\left(\left(3 + -4 \cdot \frac{1 \cdot {x}^{2}}{x}\right), \mathsf{*.f64}\left(y, 3\right)\right) \]

      8. associate-*l/ N/A

         \[\leadsto \mathsf{/.f64}\left(\left(3 + -4 \cdot \left(\frac{1}{x} \cdot {x}^{2}\right)\right), \mathsf{*.f64}\left(y, 3\right)\right) \]

      9. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(3 + \left(-4 \cdot \frac{1}{x}\right) \cdot {x}^{2}\right), \mathsf{*.f64}\left(y, 3\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\left(3 + \left(\left(\mathsf{neg}\left(4\right)\right) \cdot \frac{1}{x}\right) \cdot {x}^{2}\right), \mathsf{*.f64}\left(y, 3\right)\right) \]

      11. distribute-lft-neg-in N/A

          \[\leadsto \mathsf{/.f64}\left(\left(3 + \left(\mathsf{neg}\left(4 \cdot \frac{1}{x}\right)\right) \cdot {x}^{2}\right), \mathsf{*.f64}\left(y, 3\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\left(3 + {x}^{2} \cdot \left(\mathsf{neg}\left(4 \cdot \frac{1}{x}\right)\right)\right), \mathsf{*.f64}\left(y, 3\right)\right) \]

      13. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(3, \left({x}^{2} \cdot \left(\mathsf{neg}\left(4 \cdot \frac{1}{x}\right)\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{y}, 3\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(3, \left({x}^{2} \cdot \left(\mathsf{neg}\left(\frac{1}{x} \cdot 4\right)\right)\right)\right), \mathsf{*.f64}\left(y, 3\right)\right) \]

      15. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(3, \left({x}^{2} \cdot \left(\frac{1}{x} \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \mathsf{*.f64}\left(y, 3\right)\right) \]

      16. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(3, \left({x}^{2} \cdot \left(\frac{1}{x} \cdot -4\right)\right)\right), \mathsf{*.f64}\left(y, 3\right)\right) \]

      17. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(3, \left(\left({x}^{2} \cdot \frac{1}{x}\right) \cdot -4\right)\right), \mathsf{*.f64}\left(y, 3\right)\right) \]

   5. Simplified 98.7%

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

   6. Taylor expanded in y around 0

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{3} \cdot \left(3 + -4 \cdot x\right)\right), \color{blue}{y}\right) \]

      3. distribute-lft-in N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{3} \cdot 3 + \frac{1}{3} \cdot \left(-4 \cdot x\right)\right), y\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\left(1 + \frac{1}{3} \cdot \left(-4 \cdot x\right)\right), y\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(1 + \left(\frac{1}{3} \cdot -4\right) \cdot x\right), y\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\left(1 + \frac{-4}{3} \cdot x\right), y\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(1, \left(\frac{-4}{3} \cdot x\right)\right), y\right) \]

      8. *-lowering-*.f64 99.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(1, \mathsf{*.f64}\left(\frac{-4}{3}, x\right)\right), y\right) \]

   8. Simplified 99.0%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.72:\\ \;\;\;\;\frac{x}{y} \cdot \left(x \cdot 0.3333333333333333 + -1.3333333333333333\right)\\ \mathbf{elif}\;x \leq 1.75:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(x \cdot 0.3333333333333333 + -1.3333333333333333\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.7:\\ \;\;\;\;\frac{x}{\frac{y}{\frac{x}{3}}}\\ \mathbf{elif}\;x \leq 3:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{\frac{3}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -4.7)
   (/ x (/ y (/ x 3.0)))
   (if (<= x 3.0)
     (/ (+ 1.0 (* x -1.3333333333333333)) y)
     (/ (/ x y) (/ 3.0 x)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -4.7) {
		tmp = x / (y / (x / 3.0));
	} else if (x <= 3.0) {
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	} else {
		tmp = (x / y) / (3.0 / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-4.7d0)) then
        tmp = x / (y / (x / 3.0d0))
    else if (x <= 3.0d0) then
        tmp = (1.0d0 + (x * (-1.3333333333333333d0))) / y
    else
        tmp = (x / y) / (3.0d0 / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -4.7) {
		tmp = x / (y / (x / 3.0));
	} else if (x <= 3.0) {
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	} else {
		tmp = (x / y) / (3.0 / x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -4.7:
		tmp = x / (y / (x / 3.0))
	elif x <= 3.0:
		tmp = (1.0 + (x * -1.3333333333333333)) / y
	else:
		tmp = (x / y) / (3.0 / x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -4.7)
		tmp = Float64(x / Float64(y / Float64(x / 3.0)));
	elseif (x <= 3.0)
		tmp = Float64(Float64(1.0 + Float64(x * -1.3333333333333333)) / y);
	else
		tmp = Float64(Float64(x / y) / Float64(3.0 / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -4.7)
		tmp = x / (y / (x / 3.0));
	elseif (x <= 3.0)
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	else
		tmp = (x / y) / (3.0 / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -4.7], N[(x / N[(y / N[(x / 3.0), $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[(3.0 / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.70000000000000018

   1. Initial program 86.8%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{1}{3} \cdot \frac{{x}^{2}}{y}} \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \frac{\frac{1}{3} \cdot {x}^{2}}{\color{blue}{y}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{3} \cdot {x}^{2}\right), \color{blue}{y}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{3}, \left({x}^{2}\right)\right), y\right) \]

      4. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{3}, \left(x \cdot x\right)\right), y\right) \]

      5. *-lowering-*.f64 85.2%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{3}, \mathsf{*.f64}\left(x, x\right)\right), y\right) \]

   5. Simplified 85.2%

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r/ N/A

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

      4. associate-*l* N/A

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

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{1}{3} \cdot \frac{x}{y}\right)}\right) \]

      6. clear-num N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{1}{3} \cdot \frac{1}{\color{blue}{\frac{y}{x}}}\right)\right) \]

      7. un-div-inv N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{\frac{1}{3}}{\color{blue}{\frac{y}{x}}}\right)\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\frac{1}{3}, \color{blue}{\left(\frac{y}{x}\right)}\right)\right) \]

      9. /-lowering-/.f64 98.1%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\frac{1}{3}, \mathsf{/.f64}\left(y, \color{blue}{x}\right)\right)\right) \]

   7. Applied egg-rr 98.1%

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

      1. associate-*r/ N/A

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

      2. metadata-eval N/A

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

      3. div-inv N/A

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

      4. div-inv N/A

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

      5. clear-num N/A

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

      6. clear-num N/A

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

      7. times-frac N/A

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

      8. *-lft-identity N/A

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

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(\frac{3}{x} \cdot y\right)}\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(y \cdot \color{blue}{\frac{3}{x}}\right)\right) \]

      11. clear-num N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(y \cdot \frac{1}{\color{blue}{\frac{x}{3}}}\right)\right) \]

      12. div-inv N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(\frac{y}{\color{blue}{\frac{x}{3}}}\right)\right) \]

      13. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(y, \color{blue}{\left(\frac{x}{3}\right)}\right)\right) \]

      14. /-lowering-/.f64 98.3%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{/.f64}\left(x, \color{blue}{3}\right)\right)\right) \]

   9. Applied egg-rr 98.3%

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

   if -4.70000000000000018 < x < 3

   1. Initial program 99.6%

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

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(3 + -4 \cdot x\right)}, \mathsf{*.f64}\left(y, 3\right)\right) \]
   4. Step-by-step derivation

      1. *-rgt-identity N/A

         \[\leadsto \mathsf{/.f64}\left(\left(3 + -4 \cdot \left(x \cdot 1\right)\right), \mathsf{*.f64}\left(y, 3\right)\right) \]

      2. rgt-mult-inverse N/A

         \[\leadsto \mathsf{/.f64}\left(\left(3 + -4 \cdot \left(x \cdot \left(x \cdot \frac{1}{x}\right)\right)\right), \mathsf{*.f64}\left(y, 3\right)\right) \]

      3. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(\left(3 + -4 \cdot \left(x \cdot \frac{x \cdot 1}{x}\right)\right), \mathsf{*.f64}\left(y, 3\right)\right) \]

      4. *-rgt-identity N/A

         \[\leadsto \mathsf{/.f64}\left(\left(3 + -4 \cdot \left(x \cdot \frac{x}{x}\right)\right), \mathsf{*.f64}\left(y, 3\right)\right) \]

      5. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(3 + -4 \cdot \frac{x \cdot x}{x}\right), \mathsf{*.f64}\left(y, 3\right)\right) \]

      6. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(3 + -4 \cdot \frac{{x}^{2}}{x}\right), \mathsf{*.f64}\left(y, 3\right)\right) \]

      7. *-lft-identity N/A

         \[\leadsto \mathsf{/.f64}\left(\left(3 + -4 \cdot \frac{1 \cdot {x}^{2}}{x}\right), \mathsf{*.f64}\left(y, 3\right)\right) \]

      8. associate-*l/ N/A

         \[\leadsto \mathsf{/.f64}\left(\left(3 + -4 \cdot \left(\frac{1}{x} \cdot {x}^{2}\right)\right), \mathsf{*.f64}\left(y, 3\right)\right) \]

      9. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(3 + \left(-4 \cdot \frac{1}{x}\right) \cdot {x}^{2}\right), \mathsf{*.f64}\left(y, 3\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\left(3 + \left(\left(\mathsf{neg}\left(4\right)\right) \cdot \frac{1}{x}\right) \cdot {x}^{2}\right), \mathsf{*.f64}\left(y, 3\right)\right) \]

      11. distribute-lft-neg-in N/A

          \[\leadsto \mathsf{/.f64}\left(\left(3 + \left(\mathsf{neg}\left(4 \cdot \frac{1}{x}\right)\right) \cdot {x}^{2}\right), \mathsf{*.f64}\left(y, 3\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\left(3 + {x}^{2} \cdot \left(\mathsf{neg}\left(4 \cdot \frac{1}{x}\right)\right)\right), \mathsf{*.f64}\left(y, 3\right)\right) \]

      13. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(3, \left({x}^{2} \cdot \left(\mathsf{neg}\left(4 \cdot \frac{1}{x}\right)\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{y}, 3\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(3, \left({x}^{2} \cdot \left(\mathsf{neg}\left(\frac{1}{x} \cdot 4\right)\right)\right)\right), \mathsf{*.f64}\left(y, 3\right)\right) \]

      15. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(3, \left({x}^{2} \cdot \left(\frac{1}{x} \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \mathsf{*.f64}\left(y, 3\right)\right) \]

      16. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(3, \left({x}^{2} \cdot \left(\frac{1}{x} \cdot -4\right)\right)\right), \mathsf{*.f64}\left(y, 3\right)\right) \]

      17. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(3, \left(\left({x}^{2} \cdot \frac{1}{x}\right) \cdot -4\right)\right), \mathsf{*.f64}\left(y, 3\right)\right) \]

   5. Simplified 98.0%

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

   6. Taylor expanded in y around 0

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{3} \cdot \left(3 + -4 \cdot x\right)\right), \color{blue}{y}\right) \]

      3. distribute-lft-in N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{3} \cdot 3 + \frac{1}{3} \cdot \left(-4 \cdot x\right)\right), y\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\left(1 + \frac{1}{3} \cdot \left(-4 \cdot x\right)\right), y\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(1 + \left(\frac{1}{3} \cdot -4\right) \cdot x\right), y\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\left(1 + \frac{-4}{3} \cdot x\right), y\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(1, \left(\frac{-4}{3} \cdot x\right)\right), y\right) \]

      8. *-lowering-*.f64 98.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(1, \mathsf{*.f64}\left(\frac{-4}{3}, x\right)\right), y\right) \]

   8. Simplified 98.3%

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

   if 3 < x

   1. Initial program 88.4%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{1}{3} \cdot \frac{{x}^{2}}{y}} \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \frac{\frac{1}{3} \cdot {x}^{2}}{\color{blue}{y}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{3} \cdot {x}^{2}\right), \color{blue}{y}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{3}, \left({x}^{2}\right)\right), y\right) \]

      4. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{3}, \left(x \cdot x\right)\right), y\right) \]

      5. *-lowering-*.f64 88.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{3}, \mathsf{*.f64}\left(x, x\right)\right), y\right) \]

   5. Simplified 88.0%

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

      1. *-commutative N/A

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

      2. associate-*l* N/A

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

      3. associate-*l/ N/A

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

      4. metadata-eval N/A

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

      5. div-inv N/A

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

      6. clear-num N/A

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

      7. un-div-inv N/A

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

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{x}{y}\right), \color{blue}{\left(\frac{3}{x}\right)}\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{\color{blue}{3}}{x}\right)\right) \]

      10. /-lowering-/.f64 99.4%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(3, \color{blue}{x}\right)\right) \]

   7. Applied egg-rr 99.4%

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

4. Final simplification 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.7:\\ \;\;\;\;\frac{x}{\frac{y}{\frac{x}{3}}}\\ \mathbf{elif}\;x \leq 3:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{\frac{3}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.7:\\ \;\;\;\;\frac{x}{\frac{y}{\frac{x}{3}}}\\ \mathbf{elif}\;x \leq 3:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{x}{3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -4.7)
   (/ x (/ y (/ x 3.0)))
   (if (<= x 3.0)
     (/ (+ 1.0 (* x -1.3333333333333333)) y)
     (* (/ x y) (/ x 3.0)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -4.7) {
		tmp = x / (y / (x / 3.0));
	} else if (x <= 3.0) {
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	} else {
		tmp = (x / y) * (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 <= (-4.7d0)) then
        tmp = x / (y / (x / 3.0d0))
    else if (x <= 3.0d0) then
        tmp = (1.0d0 + (x * (-1.3333333333333333d0))) / y
    else
        tmp = (x / y) * (x / 3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -4.7) {
		tmp = x / (y / (x / 3.0));
	} else if (x <= 3.0) {
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	} else {
		tmp = (x / y) * (x / 3.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -4.7:
		tmp = x / (y / (x / 3.0))
	elif x <= 3.0:
		tmp = (1.0 + (x * -1.3333333333333333)) / y
	else:
		tmp = (x / y) * (x / 3.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -4.7)
		tmp = Float64(x / Float64(y / Float64(x / 3.0)));
	elseif (x <= 3.0)
		tmp = Float64(Float64(1.0 + Float64(x * -1.3333333333333333)) / y);
	else
		tmp = Float64(Float64(x / y) * Float64(x / 3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -4.7)
		tmp = x / (y / (x / 3.0));
	elseif (x <= 3.0)
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	else
		tmp = (x / y) * (x / 3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -4.7], N[(x / N[(y / N[(x / 3.0), $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[(x / 3.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.70000000000000018

   1. Initial program 86.8%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{1}{3} \cdot \frac{{x}^{2}}{y}} \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \frac{\frac{1}{3} \cdot {x}^{2}}{\color{blue}{y}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{3} \cdot {x}^{2}\right), \color{blue}{y}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{3}, \left({x}^{2}\right)\right), y\right) \]

      4. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{3}, \left(x \cdot x\right)\right), y\right) \]

      5. *-lowering-*.f64 85.2%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{3}, \mathsf{*.f64}\left(x, x\right)\right), y\right) \]

   5. Simplified 85.2%

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r/ N/A

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

      4. associate-*l* N/A

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

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{1}{3} \cdot \frac{x}{y}\right)}\right) \]

      6. clear-num N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{1}{3} \cdot \frac{1}{\color{blue}{\frac{y}{x}}}\right)\right) \]

      7. un-div-inv N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{\frac{1}{3}}{\color{blue}{\frac{y}{x}}}\right)\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\frac{1}{3}, \color{blue}{\left(\frac{y}{x}\right)}\right)\right) \]

      9. /-lowering-/.f64 98.1%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\frac{1}{3}, \mathsf{/.f64}\left(y, \color{blue}{x}\right)\right)\right) \]

   7. Applied egg-rr 98.1%

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

      1. associate-*r/ N/A

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

      2. metadata-eval N/A

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

      3. div-inv N/A

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

      4. div-inv N/A

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

      5. clear-num N/A

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

      6. clear-num N/A

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

      7. times-frac N/A

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

      8. *-lft-identity N/A

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

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(\frac{3}{x} \cdot y\right)}\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(y \cdot \color{blue}{\frac{3}{x}}\right)\right) \]

      11. clear-num N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(y \cdot \frac{1}{\color{blue}{\frac{x}{3}}}\right)\right) \]

      12. div-inv N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(\frac{y}{\color{blue}{\frac{x}{3}}}\right)\right) \]

      13. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(y, \color{blue}{\left(\frac{x}{3}\right)}\right)\right) \]

      14. /-lowering-/.f64 98.3%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{/.f64}\left(x, \color{blue}{3}\right)\right)\right) \]

   9. Applied egg-rr 98.3%

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

   if -4.70000000000000018 < x < 3

   1. Initial program 99.6%

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

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(3 + -4 \cdot x\right)}, \mathsf{*.f64}\left(y, 3\right)\right) \]
   4. Step-by-step derivation

      1. *-rgt-identity N/A

         \[\leadsto \mathsf{/.f64}\left(\left(3 + -4 \cdot \left(x \cdot 1\right)\right), \mathsf{*.f64}\left(y, 3\right)\right) \]

      2. rgt-mult-inverse N/A

         \[\leadsto \mathsf{/.f64}\left(\left(3 + -4 \cdot \left(x \cdot \left(x \cdot \frac{1}{x}\right)\right)\right), \mathsf{*.f64}\left(y, 3\right)\right) \]

      3. associate-*r/ N/A

         \[\leadsto \mathsf{/.f64}\left(\left(3 + -4 \cdot \left(x \cdot \frac{x \cdot 1}{x}\right)\right), \mathsf{*.f64}\left(y, 3\right)\right) \]

      4. *-rgt-identity N/A

         \[\leadsto \mathsf{/.f64}\left(\left(3 + -4 \cdot \left(x \cdot \frac{x}{x}\right)\right), \mathsf{*.f64}\left(y, 3\right)\right) \]

      5. associate-/l* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(3 + -4 \cdot \frac{x \cdot x}{x}\right), \mathsf{*.f64}\left(y, 3\right)\right) \]

      6. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(3 + -4 \cdot \frac{{x}^{2}}{x}\right), \mathsf{*.f64}\left(y, 3\right)\right) \]

      7. *-lft-identity N/A

         \[\leadsto \mathsf{/.f64}\left(\left(3 + -4 \cdot \frac{1 \cdot {x}^{2}}{x}\right), \mathsf{*.f64}\left(y, 3\right)\right) \]

      8. associate-*l/ N/A

         \[\leadsto \mathsf{/.f64}\left(\left(3 + -4 \cdot \left(\frac{1}{x} \cdot {x}^{2}\right)\right), \mathsf{*.f64}\left(y, 3\right)\right) \]

      9. associate-*l* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(3 + \left(-4 \cdot \frac{1}{x}\right) \cdot {x}^{2}\right), \mathsf{*.f64}\left(y, 3\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\left(3 + \left(\left(\mathsf{neg}\left(4\right)\right) \cdot \frac{1}{x}\right) \cdot {x}^{2}\right), \mathsf{*.f64}\left(y, 3\right)\right) \]

      11. distribute-lft-neg-in N/A

          \[\leadsto \mathsf{/.f64}\left(\left(3 + \left(\mathsf{neg}\left(4 \cdot \frac{1}{x}\right)\right) \cdot {x}^{2}\right), \mathsf{*.f64}\left(y, 3\right)\right) \]

      12. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\left(3 + {x}^{2} \cdot \left(\mathsf{neg}\left(4 \cdot \frac{1}{x}\right)\right)\right), \mathsf{*.f64}\left(y, 3\right)\right) \]

      13. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(3, \left({x}^{2} \cdot \left(\mathsf{neg}\left(4 \cdot \frac{1}{x}\right)\right)\right)\right), \mathsf{*.f64}\left(\color{blue}{y}, 3\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(3, \left({x}^{2} \cdot \left(\mathsf{neg}\left(\frac{1}{x} \cdot 4\right)\right)\right)\right), \mathsf{*.f64}\left(y, 3\right)\right) \]

      15. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(3, \left({x}^{2} \cdot \left(\frac{1}{x} \cdot \left(\mathsf{neg}\left(4\right)\right)\right)\right)\right), \mathsf{*.f64}\left(y, 3\right)\right) \]

      16. metadata-eval N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(3, \left({x}^{2} \cdot \left(\frac{1}{x} \cdot -4\right)\right)\right), \mathsf{*.f64}\left(y, 3\right)\right) \]

      17. associate-*r* N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(3, \left(\left({x}^{2} \cdot \frac{1}{x}\right) \cdot -4\right)\right), \mathsf{*.f64}\left(y, 3\right)\right) \]

   5. Simplified 98.0%

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

   6. Taylor expanded in y around 0

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{3} \cdot \left(3 + -4 \cdot x\right)\right), \color{blue}{y}\right) \]

      3. distribute-lft-in N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{3} \cdot 3 + \frac{1}{3} \cdot \left(-4 \cdot x\right)\right), y\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\left(1 + \frac{1}{3} \cdot \left(-4 \cdot x\right)\right), y\right) \]

      5. associate-*r* N/A

         \[\leadsto \mathsf{/.f64}\left(\left(1 + \left(\frac{1}{3} \cdot -4\right) \cdot x\right), y\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\left(1 + \frac{-4}{3} \cdot x\right), y\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(1, \left(\frac{-4}{3} \cdot x\right)\right), y\right) \]

      8. *-lowering-*.f64 98.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(1, \mathsf{*.f64}\left(\frac{-4}{3}, x\right)\right), y\right) \]

   8. Simplified 98.3%

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

   if 3 < x

   1. Initial program 88.4%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{1}{3} \cdot \frac{{x}^{2}}{y}} \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \frac{\frac{1}{3} \cdot {x}^{2}}{\color{blue}{y}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{3} \cdot {x}^{2}\right), \color{blue}{y}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{3}, \left({x}^{2}\right)\right), y\right) \]

      4. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{3}, \left(x \cdot x\right)\right), y\right) \]

      5. *-lowering-*.f64 88.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{3}, \mathsf{*.f64}\left(x, x\right)\right), y\right) \]

   5. Simplified 88.0%

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

      1. *-commutative N/A

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

      2. associate-*l* N/A

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

      3. associate-*l/ N/A

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

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{x}{y}\right), \color{blue}{\left(x \cdot \frac{1}{3}\right)}\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\color{blue}{x} \cdot \frac{1}{3}\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(x \cdot \frac{1}{\color{blue}{3}}\right)\right) \]

      7. div-inv N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{x}{\color{blue}{3}}\right)\right) \]

      8. /-lowering-/.f64 99.3%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(x, \color{blue}{3}\right)\right) \]

   7. Applied egg-rr 99.3%

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

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.7:\\ \;\;\;\;\frac{x}{\frac{y}{\frac{x}{3}}}\\ \mathbf{elif}\;x \leq 3:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{x}{3}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 97.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.72:\\ \;\;\;\;\frac{x}{\frac{y}{\frac{x}{3}}}\\ \mathbf{elif}\;x \leq 0.56:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{x}{3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.72)
   (/ x (/ y (/ x 3.0)))
   (if (<= x 0.56) (/ 1.0 y) (* (/ x y) (/ x 3.0)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.72) {
		tmp = x / (y / (x / 3.0));
	} else if (x <= 0.56) {
		tmp = 1.0 / y;
	} else {
		tmp = (x / y) * (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 <= (-1.72d0)) then
        tmp = x / (y / (x / 3.0d0))
    else if (x <= 0.56d0) then
        tmp = 1.0d0 / y
    else
        tmp = (x / y) * (x / 3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -1.72) {
		tmp = x / (y / (x / 3.0));
	} else if (x <= 0.56) {
		tmp = 1.0 / y;
	} else {
		tmp = (x / y) * (x / 3.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.72:
		tmp = x / (y / (x / 3.0))
	elif x <= 0.56:
		tmp = 1.0 / y
	else:
		tmp = (x / y) * (x / 3.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.72)
		tmp = Float64(x / Float64(y / Float64(x / 3.0)));
	elseif (x <= 0.56)
		tmp = Float64(1.0 / y);
	else
		tmp = Float64(Float64(x / y) * Float64(x / 3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.72)
		tmp = x / (y / (x / 3.0));
	elseif (x <= 0.56)
		tmp = 1.0 / y;
	else
		tmp = (x / y) * (x / 3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.72], N[(x / N[(y / N[(x / 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 0.56], N[(1.0 / y), $MachinePrecision], N[(N[(x / y), $MachinePrecision] * N[(x / 3.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.71999999999999997

   1. Initial program 87.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{1}{3} \cdot \frac{{x}^{2}}{y}} \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \frac{\frac{1}{3} \cdot {x}^{2}}{\color{blue}{y}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{3} \cdot {x}^{2}\right), \color{blue}{y}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{3}, \left({x}^{2}\right)\right), y\right) \]

      4. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{3}, \left(x \cdot x\right)\right), y\right) \]

      5. *-lowering-*.f64 84.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{3}, \mathsf{*.f64}\left(x, x\right)\right), y\right) \]

   5. Simplified 84.3%

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r/ N/A

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

      4. associate-*l* N/A

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

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{1}{3} \cdot \frac{x}{y}\right)}\right) \]

      6. clear-num N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{1}{3} \cdot \frac{1}{\color{blue}{\frac{y}{x}}}\right)\right) \]

      7. un-div-inv N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{\frac{1}{3}}{\color{blue}{\frac{y}{x}}}\right)\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\frac{1}{3}, \color{blue}{\left(\frac{y}{x}\right)}\right)\right) \]

      9. /-lowering-/.f64 97.0%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\frac{1}{3}, \mathsf{/.f64}\left(y, \color{blue}{x}\right)\right)\right) \]

   7. Applied egg-rr 97.0%

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

      1. associate-*r/ N/A

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

      2. metadata-eval N/A

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

      3. div-inv N/A

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

      4. div-inv N/A

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

      5. clear-num N/A

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

      6. clear-num N/A

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

      7. times-frac N/A

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

      8. *-lft-identity N/A

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

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(x, \color{blue}{\left(\frac{3}{x} \cdot y\right)}\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(y \cdot \color{blue}{\frac{3}{x}}\right)\right) \]

      11. clear-num N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(y \cdot \frac{1}{\color{blue}{\frac{x}{3}}}\right)\right) \]

      12. div-inv N/A

          \[\leadsto \mathsf{/.f64}\left(x, \left(\frac{y}{\color{blue}{\frac{x}{3}}}\right)\right) \]

      13. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(y, \color{blue}{\left(\frac{x}{3}\right)}\right)\right) \]

      14. /-lowering-/.f64 97.2%

          \[\leadsto \mathsf{/.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{/.f64}\left(x, \color{blue}{3}\right)\right)\right) \]

   9. Applied egg-rr 97.2%

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

   if -1.71999999999999997 < x < 0.56000000000000005

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0

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

      1. /-lowering-/.f64 97.6%

         \[\leadsto \mathsf{/.f64}\left(1, \color{blue}{y}\right) \]

   5. Simplified 97.6%

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

   if 0.56000000000000005 < x

   1. Initial program 88.4%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{1}{3} \cdot \frac{{x}^{2}}{y}} \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \frac{\frac{1}{3} \cdot {x}^{2}}{\color{blue}{y}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{3} \cdot {x}^{2}\right), \color{blue}{y}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{3}, \left({x}^{2}\right)\right), y\right) \]

      4. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{3}, \left(x \cdot x\right)\right), y\right) \]

      5. *-lowering-*.f64 88.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{3}, \mathsf{*.f64}\left(x, x\right)\right), y\right) \]

   5. Simplified 88.0%

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

      1. *-commutative N/A

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

      2. associate-*l* N/A

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

      3. associate-*l/ N/A

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

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{x}{y}\right), \color{blue}{\left(x \cdot \frac{1}{3}\right)}\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\color{blue}{x} \cdot \frac{1}{3}\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(x \cdot \frac{1}{\color{blue}{3}}\right)\right) \]

      7. div-inv N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{x}{\color{blue}{3}}\right)\right) \]

      8. /-lowering-/.f64 99.3%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(x, \color{blue}{3}\right)\right) \]

   7. Applied egg-rr 99.3%

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

Alternative 6: 97.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{y} \cdot \frac{x}{3}\\ \mathbf{if}\;x \leq -1.72:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 0.56:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* (/ x y) (/ x 3.0))))
   (if (<= x -1.72) t_0 (if (<= x 0.56) (/ 1.0 y) t_0))))

C

double code(double x, double y) {
	double t_0 = (x / y) * (x / 3.0);
	double tmp;
	if (x <= -1.72) {
		tmp = t_0;
	} else if (x <= 0.56) {
		tmp = 1.0 / y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x / y) * (x / 3.0d0)
    if (x <= (-1.72d0)) then
        tmp = t_0
    else if (x <= 0.56d0) then
        tmp = 1.0d0 / y
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (x / y) * (x / 3.0);
	double tmp;
	if (x <= -1.72) {
		tmp = t_0;
	} else if (x <= 0.56) {
		tmp = 1.0 / y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (x / y) * (x / 3.0)
	tmp = 0
	if x <= -1.72:
		tmp = t_0
	elif x <= 0.56:
		tmp = 1.0 / y
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(x / y) * Float64(x / 3.0))
	tmp = 0.0
	if (x <= -1.72)
		tmp = t_0;
	elseif (x <= 0.56)
		tmp = Float64(1.0 / y);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (x / y) * (x / 3.0);
	tmp = 0.0;
	if (x <= -1.72)
		tmp = t_0;
	elseif (x <= 0.56)
		tmp = 1.0 / y;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(x / y), $MachinePrecision] * N[(x / 3.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.72], t$95$0, If[LessEqual[x, 0.56], N[(1.0 / y), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.71999999999999997 or 0.56000000000000005 < x

   1. Initial program 87.6%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{1}{3} \cdot \frac{{x}^{2}}{y}} \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \frac{\frac{1}{3} \cdot {x}^{2}}{\color{blue}{y}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{3} \cdot {x}^{2}\right), \color{blue}{y}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{3}, \left({x}^{2}\right)\right), y\right) \]

      4. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{3}, \left(x \cdot x\right)\right), y\right) \]

      5. *-lowering-*.f64 85.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{3}, \mathsf{*.f64}\left(x, x\right)\right), y\right) \]

   5. Simplified 85.9%

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

      1. *-commutative N/A

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

      2. associate-*l* N/A

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

      3. associate-*l/ N/A

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

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{x}{y}\right), \color{blue}{\left(x \cdot \frac{1}{3}\right)}\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\color{blue}{x} \cdot \frac{1}{3}\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(x \cdot \frac{1}{\color{blue}{3}}\right)\right) \]

      7. div-inv N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, y\right), \left(\frac{x}{\color{blue}{3}}\right)\right) \]

      8. /-lowering-/.f64 98.1%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, y\right), \mathsf{/.f64}\left(x, \color{blue}{3}\right)\right) \]

   7. Applied egg-rr 98.1%

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

   if -1.71999999999999997 < x < 0.56000000000000005

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0

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

      1. /-lowering-/.f64 97.6%

         \[\leadsto \mathsf{/.f64}\left(1, \color{blue}{y}\right) \]

   5. Simplified 97.6%

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

Alternative 7: 97.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \frac{0.3333333333333333}{\frac{y}{x}}\\ \mathbf{if}\;x \leq -1.72:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 0.56:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* x (/ 0.3333333333333333 (/ y x)))))
   (if (<= x -1.72) t_0 (if (<= x 0.56) (/ 1.0 y) t_0))))

C

double code(double x, double y) {
	double t_0 = x * (0.3333333333333333 / (y / x));
	double tmp;
	if (x <= -1.72) {
		tmp = t_0;
	} else if (x <= 0.56) {
		tmp = 1.0 / y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * (0.3333333333333333d0 / (y / x))
    if (x <= (-1.72d0)) then
        tmp = t_0
    else if (x <= 0.56d0) then
        tmp = 1.0d0 / y
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x * (0.3333333333333333 / (y / x));
	double tmp;
	if (x <= -1.72) {
		tmp = t_0;
	} else if (x <= 0.56) {
		tmp = 1.0 / y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x * (0.3333333333333333 / (y / x))
	tmp = 0
	if x <= -1.72:
		tmp = t_0
	elif x <= 0.56:
		tmp = 1.0 / y
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x * Float64(0.3333333333333333 / Float64(y / x)))
	tmp = 0.0
	if (x <= -1.72)
		tmp = t_0;
	elseif (x <= 0.56)
		tmp = Float64(1.0 / y);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x * (0.3333333333333333 / (y / x));
	tmp = 0.0;
	if (x <= -1.72)
		tmp = t_0;
	elseif (x <= 0.56)
		tmp = 1.0 / y;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x * N[(0.3333333333333333 / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.72], t$95$0, If[LessEqual[x, 0.56], N[(1.0 / y), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.71999999999999997 or 0.56000000000000005 < x

   1. Initial program 87.6%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{1}{3} \cdot \frac{{x}^{2}}{y}} \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

         \[\leadsto \frac{\frac{1}{3} \cdot {x}^{2}}{\color{blue}{y}} \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{3} \cdot {x}^{2}\right), \color{blue}{y}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{3}, \left({x}^{2}\right)\right), y\right) \]

      4. unpow2 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{3}, \left(x \cdot x\right)\right), y\right) \]

      5. *-lowering-*.f64 85.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{3}, \mathsf{*.f64}\left(x, x\right)\right), y\right) \]

   5. Simplified 85.9%

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*r/ N/A

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

      4. associate-*l* N/A

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

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{\left(\frac{1}{3} \cdot \frac{x}{y}\right)}\right) \]

      6. clear-num N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{1}{3} \cdot \frac{1}{\color{blue}{\frac{y}{x}}}\right)\right) \]

      7. un-div-inv N/A

         \[\leadsto \mathsf{*.f64}\left(x, \left(\frac{\frac{1}{3}}{\color{blue}{\frac{y}{x}}}\right)\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\frac{1}{3}, \color{blue}{\left(\frac{y}{x}\right)}\right)\right) \]

      9. /-lowering-/.f64 98.0%

         \[\leadsto \mathsf{*.f64}\left(x, \mathsf{/.f64}\left(\frac{1}{3}, \mathsf{/.f64}\left(y, \color{blue}{x}\right)\right)\right) \]

   7. Applied egg-rr 98.0%

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

   if -1.71999999999999997 < x < 0.56000000000000005

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0

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

      1. /-lowering-/.f64 97.6%

         \[\leadsto \mathsf{/.f64}\left(1, \color{blue}{y}\right) \]

   5. Simplified 97.6%

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

Alternative 8: 99.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{3 - x}{\frac{\frac{y}{0.3333333333333333}}{1 - x}} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.4%

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

   1. times-frac N/A

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

   2. *-commutative N/A

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

   3. clear-num N/A

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

   4. un-div-inv N/A

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

   5. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\left(\frac{3 - x}{3}\right), \color{blue}{\left(\frac{y}{1 - x}\right)}\right) \]

   6. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(3 - x\right), 3\right), \left(\frac{\color{blue}{y}}{1 - x}\right)\right) \]

   7. --lowering--.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(3, x\right), 3\right), \left(\frac{y}{1 - x}\right)\right) \]

   8. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(3, x\right), 3\right), \mathsf{/.f64}\left(y, \color{blue}{\left(1 - x\right)}\right)\right) \]

   9. --lowering--.f64 99.8%

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(3, x\right), 3\right), \mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(1, \color{blue}{x}\right)\right)\right) \]

4. Applied egg-rr 99.8%

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

   1. associate-/l/ N/A

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

   2. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\left(3 - x\right), \color{blue}{\left(\frac{y}{1 - x} \cdot 3\right)}\right) \]

   3. --lowering--.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(3, x\right), \left(\color{blue}{\frac{y}{1 - x}} \cdot 3\right)\right) \]

   4. associate-*l/ N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(3, x\right), \left(\frac{y \cdot 3}{\color{blue}{1 - x}}\right)\right) \]

   5. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(3, x\right), \mathsf{/.f64}\left(\left(y \cdot 3\right), \color{blue}{\left(1 - x\right)}\right)\right) \]

   6. metadata-eval N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(3, x\right), \mathsf{/.f64}\left(\left(y \cdot \frac{1}{\frac{1}{3}}\right), \left(1 - x\right)\right)\right) \]

   7. div-inv N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(3, x\right), \mathsf{/.f64}\left(\left(\frac{y}{\frac{1}{3}}\right), \left(\color{blue}{1} - x\right)\right)\right) \]

   8. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(3, x\right), \mathsf{/.f64}\left(\mathsf{/.f64}\left(y, \frac{1}{3}\right), \left(\color{blue}{1} - x\right)\right)\right) \]

   9. --lowering--.f64 99.6%

      \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(3, x\right), \mathsf{/.f64}\left(\mathsf{/.f64}\left(y, \frac{1}{3}\right), \mathsf{\_.f64}\left(1, \color{blue}{x}\right)\right)\right) \]

6. Applied egg-rr 99.6%

   \[\leadsto \color{blue}{\frac{3 - x}{\frac{\frac{y}{0.3333333333333333}}{1 - x}}} \]
7. Add Preprocessing

Alternative 9: 99.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.4%

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

   1. associate-/r* N/A

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

   2. div-inv N/A

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

   3. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\left(\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y}\right), \color{blue}{\left(\frac{1}{3}\right)}\right) \]

   4. *-commutative N/A

      \[\leadsto \mathsf{*.f64}\left(\left(\frac{\left(3 - x\right) \cdot \left(1 - x\right)}{y}\right), \left(\frac{1}{3}\right)\right) \]

   5. associate-/l* N/A

      \[\leadsto \mathsf{*.f64}\left(\left(\left(3 - x\right) \cdot \frac{1 - x}{y}\right), \left(\frac{\color{blue}{1}}{3}\right)\right) \]

   6. clear-num N/A

      \[\leadsto \mathsf{*.f64}\left(\left(\left(3 - x\right) \cdot \frac{1}{\frac{y}{1 - x}}\right), \left(\frac{1}{3}\right)\right) \]

   7. un-div-inv N/A

      \[\leadsto \mathsf{*.f64}\left(\left(\frac{3 - x}{\frac{y}{1 - x}}\right), \left(\frac{\color{blue}{1}}{3}\right)\right) \]

   8. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(3 - x\right), \left(\frac{y}{1 - x}\right)\right), \left(\frac{\color{blue}{1}}{3}\right)\right) \]

   9. --lowering--.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(3, x\right), \left(\frac{y}{1 - x}\right)\right), \left(\frac{1}{3}\right)\right) \]

   10. /-lowering-/.f64 N/A

       \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(3, x\right), \mathsf{/.f64}\left(y, \left(1 - x\right)\right)\right), \left(\frac{1}{3}\right)\right) \]

   11. --lowering--.f64 N/A

       \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(3, x\right), \mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(1, x\right)\right)\right), \left(\frac{1}{3}\right)\right) \]

   12. metadata-eval 99.6%

       \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(3, x\right), \mathsf{/.f64}\left(y, \mathsf{\_.f64}\left(1, x\right)\right)\right), \frac{1}{3}\right) \]

4. Applied egg-rr 99.6%

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

5. Final simplification 99.6%

   \[\leadsto 0.3333333333333333 \cdot \frac{3 - x}{\frac{y}{1 - x}} \]
6. Add Preprocessing

Alternative 10: 58.0% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-0.75d0)) then
        tmp = (x / y) * (-1.3333333333333333d0)
    else
        tmp = 1.0d0 / y
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if x < -0.75

   1. Initial program 87.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{{x}^{2} \cdot \left(\frac{1}{3} \cdot \frac{1}{y} - \frac{4}{3} \cdot \frac{1}{x \cdot y}\right)} \]
   4. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto {x}^{2} \cdot \left(\frac{1}{3} \cdot \frac{1}{y} + \color{blue}{\left(\mathsf{neg}\left(\frac{4}{3} \cdot \frac{1}{x \cdot y}\right)\right)}\right) \]

      2. distribute-lft-in N/A

         \[\leadsto {x}^{2} \cdot \left(\frac{1}{3} \cdot \frac{1}{y}\right) + \color{blue}{{x}^{2} \cdot \left(\mathsf{neg}\left(\frac{4}{3} \cdot \frac{1}{x \cdot y}\right)\right)} \]

      3. *-commutative N/A

         \[\leadsto \left(\frac{1}{3} \cdot \frac{1}{y}\right) \cdot {x}^{2} + \color{blue}{{x}^{2}} \cdot \left(\mathsf{neg}\left(\frac{4}{3} \cdot \frac{1}{x \cdot y}\right)\right) \]

      4. unpow2 N/A

         \[\leadsto \left(\frac{1}{3} \cdot \frac{1}{y}\right) \cdot \left(x \cdot x\right) + {x}^{\color{blue}{2}} \cdot \left(\mathsf{neg}\left(\frac{4}{3} \cdot \frac{1}{x \cdot y}\right)\right) \]

      5. associate-*r* N/A

         \[\leadsto \left(\left(\frac{1}{3} \cdot \frac{1}{y}\right) \cdot x\right) \cdot x + \color{blue}{{x}^{2}} \cdot \left(\mathsf{neg}\left(\frac{4}{3} \cdot \frac{1}{x \cdot y}\right)\right) \]

      6. associate-*r/ N/A

         \[\leadsto \left(\frac{\frac{1}{3} \cdot 1}{y} \cdot x\right) \cdot x + {x}^{2} \cdot \left(\mathsf{neg}\left(\frac{4}{3} \cdot \frac{1}{x \cdot y}\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \left(\frac{\frac{1}{3}}{y} \cdot x\right) \cdot x + {x}^{2} \cdot \left(\mathsf{neg}\left(\frac{4}{3} \cdot \frac{1}{x \cdot y}\right)\right) \]

      8. associate-*l/ N/A

         \[\leadsto \frac{\frac{1}{3} \cdot x}{y} \cdot x + {\color{blue}{x}}^{2} \cdot \left(\mathsf{neg}\left(\frac{4}{3} \cdot \frac{1}{x \cdot y}\right)\right) \]

      9. associate-*r/ N/A

         \[\leadsto \left(\frac{1}{3} \cdot \frac{x}{y}\right) \cdot x + {\color{blue}{x}}^{2} \cdot \left(\mathsf{neg}\left(\frac{4}{3} \cdot \frac{1}{x \cdot y}\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \left(\frac{x}{y} \cdot \frac{1}{3}\right) \cdot x + {\color{blue}{x}}^{2} \cdot \left(\mathsf{neg}\left(\frac{4}{3} \cdot \frac{1}{x \cdot y}\right)\right) \]

      11. associate-*l* N/A

          \[\leadsto \frac{x}{y} \cdot \left(\frac{1}{3} \cdot x\right) + \color{blue}{{x}^{2}} \cdot \left(\mathsf{neg}\left(\frac{4}{3} \cdot \frac{1}{x \cdot y}\right)\right) \]

      12. associate-*r/ N/A

          \[\leadsto \frac{x}{y} \cdot \left(\frac{1}{3} \cdot x\right) + {x}^{2} \cdot \left(\mathsf{neg}\left(\frac{\frac{4}{3} \cdot 1}{x \cdot y}\right)\right) \]

      13. metadata-eval N/A

          \[\leadsto \frac{x}{y} \cdot \left(\frac{1}{3} \cdot x\right) + {x}^{2} \cdot \left(\mathsf{neg}\left(\frac{\frac{4}{3}}{x \cdot y}\right)\right) \]

      14. distribute-neg-frac N/A

          \[\leadsto \frac{x}{y} \cdot \left(\frac{1}{3} \cdot x\right) + {x}^{2} \cdot \frac{\mathsf{neg}\left(\frac{4}{3}\right)}{\color{blue}{x \cdot y}} \]

      15. metadata-eval N/A

          \[\leadsto \frac{x}{y} \cdot \left(\frac{1}{3} \cdot x\right) + {x}^{2} \cdot \frac{\frac{-4}{3}}{\color{blue}{x} \cdot y} \]

      16. associate-*r/ N/A

          \[\leadsto \frac{x}{y} \cdot \left(\frac{1}{3} \cdot x\right) + \frac{{x}^{2} \cdot \frac{-4}{3}}{\color{blue}{x \cdot y}} \]

      17. times-frac N/A

          \[\leadsto \frac{x}{y} \cdot \left(\frac{1}{3} \cdot x\right) + \frac{{x}^{2}}{x} \cdot \color{blue}{\frac{\frac{-4}{3}}{y}} \]

   5. Simplified 98.4%

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

   6. Taylor expanded in x around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(x, y\right), \color{blue}{\frac{-4}{3}}\right) \]
   7. Step-by-step derivation

   8. Simplified 29.6%

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

   if -0.75 < x

   1. Initial program 96.0%

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

   3. Taylor expanded in x around 0

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

      1. /-lowering-/.f64 67.8%

         \[\leadsto \mathsf{/.f64}\left(1, \color{blue}{y}\right) \]

   5. Simplified 67.8%

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

Alternative 11: 52.0% 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 93.4%

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

3. Taylor expanded in x around 0

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

   1. /-lowering-/.f64 49.6%

      \[\leadsto \mathsf{/.f64}\left(1, \color{blue}{y}\right) \]

5. Simplified 49.6%

   \[\leadsto \color{blue}{\frac{1}{y}} \]
6. Add Preprocessing

Developer Target 1: 99.9% 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 2024149 
(FPCore (x y)
  :name "Diagrams.TwoD.Arc:bezierFromSweepQ1 from diagrams-lib-1.3.0.3"
  :precision binary64

  :alt
  (! :herbie-platform default (* (/ (- 1 x) y) (/ (- 3 x) 3)))

  (/ (* (- 1.0 x) (- 3.0 x)) (* y 3.0)))