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

Percentage Accurate: 93.4% → 99.7%

Time: 8.3s

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: 93.4% 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: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.6%

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

   1. associate-/l* N/A

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

   2. clear-num N/A

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

   3. un-div-inv N/A

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

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

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

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

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

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

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

   7. *-commutative N/A

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

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

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

   9. --lowering--.f64 99.8%

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

4. Applied egg-rr 99.8%

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

Alternative 2: 99.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(1 - x\right) \cdot \left(3 - x\right)\\ \mathbf{if}\;t\_0 \leq 5 \cdot 10^{+32}:\\ \;\;\;\;\frac{t\_0}{3 \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{3 \cdot y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* (- 1.0 x) (- 3.0 x))))
   (if (<= t_0 5e+32) (/ t_0 (* 3.0 y)) (/ x (/ (* 3.0 y) x)))))

C

double code(double x, double y) {
	double t_0 = (1.0 - x) * (3.0 - x);
	double tmp;
	if (t_0 <= 5e+32) {
		tmp = t_0 / (3.0 * y);
	} else {
		tmp = x / ((3.0 * y) / x);
	}
	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 = (1.0d0 - x) * (3.0d0 - x)
    if (t_0 <= 5d+32) then
        tmp = t_0 / (3.0d0 * y)
    else
        tmp = x / ((3.0d0 * y) / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (1.0 - x) * (3.0 - x);
	double tmp;
	if (t_0 <= 5e+32) {
		tmp = t_0 / (3.0 * y);
	} else {
		tmp = x / ((3.0 * y) / x);
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (1.0 - x) * (3.0 - x)
	tmp = 0
	if t_0 <= 5e+32:
		tmp = t_0 / (3.0 * y)
	else:
		tmp = x / ((3.0 * y) / x)
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(1.0 - x) * Float64(3.0 - x))
	tmp = 0.0
	if (t_0 <= 5e+32)
		tmp = Float64(t_0 / Float64(3.0 * y));
	else
		tmp = Float64(x / Float64(Float64(3.0 * y) / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (1.0 - x) * (3.0 - x);
	tmp = 0.0;
	if (t_0 <= 5e+32)
		tmp = t_0 / (3.0 * y);
	else
		tmp = x / ((3.0 * y) / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(1.0 - x), $MachinePrecision] * N[(3.0 - x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, 5e+32], N[(t$95$0 / N[(3.0 * y), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(3.0 * y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 3 binary64) x)) < 4.9999999999999997e32

   1. Initial program 99.6%

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

   if 4.9999999999999997e32 < (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 3 binary64) x))

   1. Initial program 88.2%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left({x}^{2}\right)}, \mathsf{*.f64}\left(y, 3\right)\right) \]
   4. Step-by-step derivation

      1. unpow2 N/A

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

      2. *-lowering-*.f64 88.2%

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

   5. Simplified 88.2%

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

      1. associate-/l* N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

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

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

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

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

      6. *-commutative N/A

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

      7. *-lowering-*.f64 99.8%

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

   7. Applied egg-rr 99.8%

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

4. Final simplification 99.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(1 - x\right) \cdot \left(3 - x\right) \leq 5 \cdot 10^{+32}:\\ \;\;\;\;\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{3 \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{3 \cdot y}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{y} \cdot \left(x \cdot 0.3333333333333333 + -1.3333333333333333\right)\\ \mathbf{if}\;x \leq -1.7:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.75:\\ \;\;\;\;\left(1 + x \cdot -1.3333333333333333\right) \cdot \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* (/ x y) (+ (* x 0.3333333333333333) -1.3333333333333333))))
   (if (<= x -1.7)
     t_0
     (if (<= x 1.75) (* (+ 1.0 (* x -1.3333333333333333)) (/ 1.0 y)) t_0))))

C

double code(double x, double y) {
	double t_0 = (x / y) * ((x * 0.3333333333333333) + -1.3333333333333333);
	double tmp;
	if (x <= -1.7) {
		tmp = t_0;
	} else if (x <= 1.75) {
		tmp = (1.0 + (x * -1.3333333333333333)) * (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 * 0.3333333333333333d0) + (-1.3333333333333333d0))
    if (x <= (-1.7d0)) then
        tmp = t_0
    else if (x <= 1.75d0) then
        tmp = (1.0d0 + (x * (-1.3333333333333333d0))) * (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 * 0.3333333333333333) + -1.3333333333333333);
	double tmp;
	if (x <= -1.7) {
		tmp = t_0;
	} else if (x <= 1.75) {
		tmp = (1.0 + (x * -1.3333333333333333)) * (1.0 / 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 <= -1.7:
		tmp = t_0
	elif x <= 1.75:
		tmp = (1.0 + (x * -1.3333333333333333)) * (1.0 / 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 <= -1.7)
		tmp = t_0;
	elseif (x <= 1.75)
		tmp = Float64(Float64(1.0 + Float64(x * -1.3333333333333333)) * Float64(1.0 / 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 <= -1.7)
		tmp = t_0;
	elseif (x <= 1.75)
		tmp = (1.0 + (x * -1.3333333333333333)) * (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[(N[(x * 0.3333333333333333), $MachinePrecision] + -1.3333333333333333), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.7], t$95$0, If[LessEqual[x, 1.75], N[(N[(1.0 + N[(x * -1.3333333333333333), $MachinePrecision]), $MachinePrecision] * N[(1.0 / y), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.69999999999999996 or 1.75 < x

   1. Initial program 89.0%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   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-rgt-in N/A

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

      3. associate-*l* N/A

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

      4. associate-*l/ N/A

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

      5. *-lft-identity N/A

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

      6. unpow2 N/A

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

      7. associate-/l* N/A

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

      8. associate-*r* N/A

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. distribute-neg-frac N/A

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

      12. metadata-eval N/A

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

      13. associate-*l/ N/A

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

      14. *-commutative N/A

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

      15. times-frac N/A

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

      16. unpow2 N/A

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

      17. associate-/l* N/A

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

      18. *-rgt-identity N/A

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

   5. Simplified 98.2%

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

   if -1.69999999999999996 < 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

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

      1. *-lft-identity N/A

         \[\leadsto \frac{-4}{3} \cdot \frac{1 \cdot x}{y} + \frac{1}{y} \]

      2. associate-*l/ N/A

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

      3. associate-*l* N/A

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

      4. metadata-eval N/A

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

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

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

      6. *-commutative N/A

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

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

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

      8. metadata-eval N/A

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

      9. associate-*r* N/A

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

      10. *-commutative N/A

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

      11. distribute-lft1-in N/A

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

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

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

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

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

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

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

      15. /-lowering-/.f64 98.5%

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

   5. Simplified 98.5%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.7:\\ \;\;\;\;\frac{x}{y} \cdot \left(x \cdot 0.3333333333333333 + -1.3333333333333333\right)\\ \mathbf{elif}\;x \leq 1.75:\\ \;\;\;\;\left(1 + x \cdot -1.3333333333333333\right) \cdot \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(x \cdot 0.3333333333333333 + -1.3333333333333333\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.6:\\ \;\;\;\;\frac{\frac{x}{y}}{\frac{3}{x}}\\ \mathbf{elif}\;x \leq 0.65:\\ \;\;\;\;\left(1 + x \cdot -1.3333333333333333\right) \cdot \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{3 \cdot y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -4.6)
   (/ (/ x y) (/ 3.0 x))
   (if (<= x 0.65)
     (* (+ 1.0 (* x -1.3333333333333333)) (/ 1.0 y))
     (/ x (/ (* 3.0 y) x)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -4.6) {
		tmp = (x / y) / (3.0 / x);
	} else if (x <= 0.65) {
		tmp = (1.0 + (x * -1.3333333333333333)) * (1.0 / y);
	} else {
		tmp = x / ((3.0 * y) / 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 <= (-4.6d0)) then
        tmp = (x / y) / (3.0d0 / x)
    else if (x <= 0.65d0) then
        tmp = (1.0d0 + (x * (-1.3333333333333333d0))) * (1.0d0 / y)
    else
        tmp = x / ((3.0d0 * y) / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -4.6) {
		tmp = (x / y) / (3.0 / x);
	} else if (x <= 0.65) {
		tmp = (1.0 + (x * -1.3333333333333333)) * (1.0 / y);
	} else {
		tmp = x / ((3.0 * y) / x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -4.6:
		tmp = (x / y) / (3.0 / x)
	elif x <= 0.65:
		tmp = (1.0 + (x * -1.3333333333333333)) * (1.0 / y)
	else:
		tmp = x / ((3.0 * y) / x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -4.6)
		tmp = Float64(Float64(x / y) / Float64(3.0 / x));
	elseif (x <= 0.65)
		tmp = Float64(Float64(1.0 + Float64(x * -1.3333333333333333)) * Float64(1.0 / y));
	else
		tmp = Float64(x / Float64(Float64(3.0 * y) / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -4.6)
		tmp = (x / y) / (3.0 / x);
	elseif (x <= 0.65)
		tmp = (1.0 + (x * -1.3333333333333333)) * (1.0 / y);
	else
		tmp = x / ((3.0 * y) / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -4.6], N[(N[(x / y), $MachinePrecision] / N[(3.0 / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 0.65], N[(N[(1.0 + N[(x * -1.3333333333333333), $MachinePrecision]), $MachinePrecision] * N[(1.0 / y), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(3.0 * y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.5999999999999996

   1. Initial program 86.9%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left({x}^{2}\right)}, \mathsf{*.f64}\left(y, 3\right)\right) \]
   4. Step-by-step derivation

      1. unpow2 N/A

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

      2. *-lowering-*.f64 86.4%

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

   5. Simplified 86.4%

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

      1. times-frac N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

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

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

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

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

      6. /-lowering-/.f64 99.3%

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

   7. Applied egg-rr 99.3%

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

   if -4.5999999999999996 < x < 0.650000000000000022

   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

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

      1. *-lft-identity N/A

         \[\leadsto \frac{-4}{3} \cdot \frac{1 \cdot x}{y} + \frac{1}{y} \]

      2. associate-*l/ N/A

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

      3. associate-*l* N/A

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

      4. metadata-eval N/A

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

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

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

      6. *-commutative N/A

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

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

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

      8. metadata-eval N/A

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

      9. associate-*r* N/A

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

      10. *-commutative N/A

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

      11. distribute-lft1-in N/A

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

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

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

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

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

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

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

      15. /-lowering-/.f64 98.5%

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

   5. Simplified 98.5%

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

   if 0.650000000000000022 < x

   1. Initial program 90.5%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left({x}^{2}\right)}, \mathsf{*.f64}\left(y, 3\right)\right) \]
   4. Step-by-step derivation

      1. unpow2 N/A

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

      2. *-lowering-*.f64 85.3%

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

   5. Simplified 85.3%

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

      1. associate-/l* N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

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

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

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

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

      6. *-commutative N/A

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

      7. *-lowering-*.f64 94.5%

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

   7. Applied egg-rr 94.5%

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

4. Final simplification 97.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.6:\\ \;\;\;\;\frac{\frac{x}{y}}{\frac{3}{x}}\\ \mathbf{elif}\;x \leq 0.65:\\ \;\;\;\;\left(1 + x \cdot -1.3333333333333333\right) \cdot \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{3 \cdot y}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 98.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.6:\\ \;\;\;\;\frac{\frac{x}{y}}{\frac{3}{x}}\\ \mathbf{elif}\;x \leq 0.65:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{3 \cdot y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -4.6)
   (/ (/ x y) (/ 3.0 x))
   (if (<= x 0.65)
     (/ (+ 1.0 (* x -1.3333333333333333)) y)
     (/ x (/ (* 3.0 y) x)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -4.6) {
		tmp = (x / y) / (3.0 / x);
	} else if (x <= 0.65) {
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	} else {
		tmp = x / ((3.0 * y) / 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 <= (-4.6d0)) then
        tmp = (x / y) / (3.0d0 / x)
    else if (x <= 0.65d0) then
        tmp = (1.0d0 + (x * (-1.3333333333333333d0))) / y
    else
        tmp = x / ((3.0d0 * y) / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -4.6) {
		tmp = (x / y) / (3.0 / x);
	} else if (x <= 0.65) {
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	} else {
		tmp = x / ((3.0 * y) / x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -4.6:
		tmp = (x / y) / (3.0 / x)
	elif x <= 0.65:
		tmp = (1.0 + (x * -1.3333333333333333)) / y
	else:
		tmp = x / ((3.0 * y) / x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -4.6)
		tmp = Float64(Float64(x / y) / Float64(3.0 / x));
	elseif (x <= 0.65)
		tmp = Float64(Float64(1.0 + Float64(x * -1.3333333333333333)) / y);
	else
		tmp = Float64(x / Float64(Float64(3.0 * y) / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -4.6)
		tmp = (x / y) / (3.0 / x);
	elseif (x <= 0.65)
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	else
		tmp = x / ((3.0 * y) / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -4.6], N[(N[(x / y), $MachinePrecision] / N[(3.0 / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 0.65], N[(N[(1.0 + N[(x * -1.3333333333333333), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(N[(3.0 * y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.5999999999999996

   1. Initial program 86.9%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left({x}^{2}\right)}, \mathsf{*.f64}\left(y, 3\right)\right) \]
   4. Step-by-step derivation

      1. unpow2 N/A

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

      2. *-lowering-*.f64 86.4%

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

   5. Simplified 86.4%

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

      1. times-frac N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

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

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

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

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

      6. /-lowering-/.f64 99.3%

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

   7. Applied egg-rr 99.3%

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

   if -4.5999999999999996 < x < 0.650000000000000022

   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

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

      1. *-lft-identity N/A

         \[\leadsto \frac{-4}{3} \cdot \frac{1 \cdot x}{y} + \frac{1}{y} \]

      2. associate-*l/ N/A

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

      3. associate-*l* N/A

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

      4. metadata-eval N/A

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

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

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

      6. *-commutative N/A

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

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

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

      8. metadata-eval N/A

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

      9. associate-*r* N/A

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

      10. *-commutative N/A

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

      11. distribute-lft1-in N/A

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

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

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

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

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

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

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

      15. /-lowering-/.f64 98.5%

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

   5. Simplified 98.5%

      \[\leadsto \color{blue}{\left(-1.3333333333333333 \cdot x + 1\right) \cdot \frac{1}{y}} \]
   6. Step-by-step derivation

      1. un-div-inv N/A

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

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

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

      3. +-commutative N/A

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

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

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 98.5%

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

   7. Applied egg-rr 98.5%

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

   if 0.650000000000000022 < x

   1. Initial program 90.5%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left({x}^{2}\right)}, \mathsf{*.f64}\left(y, 3\right)\right) \]
   4. Step-by-step derivation

      1. unpow2 N/A

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

      2. *-lowering-*.f64 85.3%

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

   5. Simplified 85.3%

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

      1. associate-/l* N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

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

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

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

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

      6. *-commutative N/A

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

      7. *-lowering-*.f64 94.5%

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

   7. Applied egg-rr 94.5%

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

Alternative 6: 98.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{\frac{3 \cdot y}{x}}\\ \mathbf{if}\;x \leq -4.6:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 0.65:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ x (/ (* 3.0 y) x))))
   (if (<= x -4.6)
     t_0
     (if (<= x 0.65) (/ (+ 1.0 (* x -1.3333333333333333)) y) t_0))))

C

double code(double x, double y) {
	double t_0 = x / ((3.0 * y) / x);
	double tmp;
	if (x <= -4.6) {
		tmp = t_0;
	} else if (x <= 0.65) {
		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 / ((3.0d0 * y) / x)
    if (x <= (-4.6d0)) then
        tmp = t_0
    else if (x <= 0.65d0) 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 / ((3.0 * y) / x);
	double tmp;
	if (x <= -4.6) {
		tmp = t_0;
	} else if (x <= 0.65) {
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x / ((3.0 * y) / x)
	tmp = 0
	if x <= -4.6:
		tmp = t_0
	elif x <= 0.65:
		tmp = (1.0 + (x * -1.3333333333333333)) / y
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x / Float64(Float64(3.0 * y) / x))
	tmp = 0.0
	if (x <= -4.6)
		tmp = t_0;
	elseif (x <= 0.65)
		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 / ((3.0 * y) / x);
	tmp = 0.0;
	if (x <= -4.6)
		tmp = t_0;
	elseif (x <= 0.65)
		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[(x / N[(N[(3.0 * y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.6], t$95$0, If[LessEqual[x, 0.65], 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 < -4.5999999999999996 or 0.650000000000000022 < x

   1. Initial program 89.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left({x}^{2}\right)}, \mathsf{*.f64}\left(y, 3\right)\right) \]
   4. Step-by-step derivation

      1. unpow2 N/A

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

      2. *-lowering-*.f64 85.7%

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

   5. Simplified 85.7%

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

      1. associate-/l* N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

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

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

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

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

      6. *-commutative N/A

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

      7. *-lowering-*.f64 96.5%

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

   7. Applied egg-rr 96.5%

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

   if -4.5999999999999996 < x < 0.650000000000000022

   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

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

      1. *-lft-identity N/A

         \[\leadsto \frac{-4}{3} \cdot \frac{1 \cdot x}{y} + \frac{1}{y} \]

      2. associate-*l/ N/A

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

      3. associate-*l* N/A

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

      4. metadata-eval N/A

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

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

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

      6. *-commutative N/A

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

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

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

      8. metadata-eval N/A

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

      9. associate-*r* N/A

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

      10. *-commutative N/A

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

      11. distribute-lft1-in N/A

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

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

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

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

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

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

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

      15. /-lowering-/.f64 98.5%

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

   5. Simplified 98.5%

      \[\leadsto \color{blue}{\left(-1.3333333333333333 \cdot x + 1\right) \cdot \frac{1}{y}} \]
   6. Step-by-step derivation

      1. un-div-inv N/A

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

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

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

      3. +-commutative N/A

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

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

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

      5. *-commutative N/A

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

      6. *-lowering-*.f64 98.5%

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

   7. Applied egg-rr 98.5%

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

Alternative 7: 97.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{\frac{3 \cdot y}{x}}\\ \mathbf{if}\;x \leq -3.8:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 0.7:\\ \;\;\;\;\frac{1 - x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ x (/ (* 3.0 y) x))))
   (if (<= x -3.8) t_0 (if (<= x 0.7) (/ (- 1.0 x) y) t_0))))

C

double code(double x, double y) {
	double t_0 = x / ((3.0 * y) / x);
	double tmp;
	if (x <= -3.8) {
		tmp = t_0;
	} else if (x <= 0.7) {
		tmp = (1.0 - x) / 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 / ((3.0d0 * y) / x)
    if (x <= (-3.8d0)) then
        tmp = t_0
    else if (x <= 0.7d0) then
        tmp = (1.0d0 - x) / y
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x / ((3.0 * y) / x);
	double tmp;
	if (x <= -3.8) {
		tmp = t_0;
	} else if (x <= 0.7) {
		tmp = (1.0 - x) / y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x / ((3.0 * y) / x)
	tmp = 0
	if x <= -3.8:
		tmp = t_0
	elif x <= 0.7:
		tmp = (1.0 - x) / y
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x / Float64(Float64(3.0 * y) / x))
	tmp = 0.0
	if (x <= -3.8)
		tmp = t_0;
	elseif (x <= 0.7)
		tmp = Float64(Float64(1.0 - x) / y);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x / ((3.0 * y) / x);
	tmp = 0.0;
	if (x <= -3.8)
		tmp = t_0;
	elseif (x <= 0.7)
		tmp = (1.0 - x) / y;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x / N[(N[(3.0 * y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.8], t$95$0, If[LessEqual[x, 0.7], N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.7999999999999998 or 0.69999999999999996 < x

   1. Initial program 89.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left({x}^{2}\right)}, \mathsf{*.f64}\left(y, 3\right)\right) \]
   4. Step-by-step derivation

      1. unpow2 N/A

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

      2. *-lowering-*.f64 85.7%

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

   5. Simplified 85.7%

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

      1. associate-/l* N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

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

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

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

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

      6. *-commutative N/A

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

      7. *-lowering-*.f64 96.5%

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

   7. Applied egg-rr 96.5%

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

   if -3.7999999999999998 < x < 0.69999999999999996

   1. Initial program 99.7%

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

      1. associate-/l* N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

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

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

      9. --lowering--.f64 99.7%

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(1, x\right), \color{blue}{y}\right) \]
   6. Step-by-step derivation

   7. Simplified 97.2%

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

Alternative 8: 97.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(x \cdot \frac{0.3333333333333333}{y}\right)\\ \mathbf{if}\;x \leq -3.8:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 0.7:\\ \;\;\;\;\frac{1 - x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* x (* x (/ 0.3333333333333333 y)))))
   (if (<= x -3.8) t_0 (if (<= x 0.7) (/ (- 1.0 x) y) t_0))))

C

double code(double x, double y) {
	double t_0 = x * (x * (0.3333333333333333 / y));
	double tmp;
	if (x <= -3.8) {
		tmp = t_0;
	} else if (x <= 0.7) {
		tmp = (1.0 - x) / 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 * (x * (0.3333333333333333d0 / y))
    if (x <= (-3.8d0)) then
        tmp = t_0
    else if (x <= 0.7d0) then
        tmp = (1.0d0 - x) / y
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x * (x * (0.3333333333333333 / y));
	double tmp;
	if (x <= -3.8) {
		tmp = t_0;
	} else if (x <= 0.7) {
		tmp = (1.0 - x) / y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x * (x * (0.3333333333333333 / y))
	tmp = 0
	if x <= -3.8:
		tmp = t_0
	elif x <= 0.7:
		tmp = (1.0 - x) / y
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x * Float64(x * Float64(0.3333333333333333 / y)))
	tmp = 0.0
	if (x <= -3.8)
		tmp = t_0;
	elseif (x <= 0.7)
		tmp = Float64(Float64(1.0 - x) / y);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x * (x * (0.3333333333333333 / y));
	tmp = 0.0;
	if (x <= -3.8)
		tmp = t_0;
	elseif (x <= 0.7)
		tmp = (1.0 - x) / y;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x * N[(x * N[(0.3333333333333333 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.8], t$95$0, If[LessEqual[x, 0.7], N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.7999999999999998 or 0.69999999999999996 < x

   1. Initial program 89.0%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left({x}^{2}\right)}, \mathsf{*.f64}\left(y, 3\right)\right) \]
   4. Step-by-step derivation

      1. unpow2 N/A

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

      2. *-lowering-*.f64 85.7%

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

   5. Simplified 85.7%

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

      1. clear-num N/A

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

      2. associate-/r/ N/A

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

      3. associate-*r* N/A

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

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

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

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

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

      6. *-commutative N/A

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

      7. associate-/r* N/A

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

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

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

      9. metadata-eval 96.5%

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

   7. Applied egg-rr 96.5%

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

   if -3.7999999999999998 < x < 0.69999999999999996

   1. Initial program 99.7%

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

      1. associate-/l* N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

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

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

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

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

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

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

      7. *-commutative N/A

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

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

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

      9. --lowering--.f64 99.7%

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in x around 0

      \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(1, x\right), \color{blue}{y}\right) \]
   6. Step-by-step derivation

   7. Simplified 97.2%

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

4. Final simplification 96.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.8:\\ \;\;\;\;x \cdot \left(x \cdot \frac{0.3333333333333333}{y}\right)\\ \mathbf{elif}\;x \leq 0.7:\\ \;\;\;\;\frac{1 - x}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(x \cdot \frac{0.3333333333333333}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 57.4% accurate, 1.1× 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 86.9%

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

   3. Taylor expanded in x around 0

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

      1. *-lft-identity N/A

         \[\leadsto \frac{-4}{3} \cdot \frac{1 \cdot x}{y} + \frac{1}{y} \]

      2. associate-*l/ N/A

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

      3. associate-*l* N/A

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

      4. metadata-eval N/A

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

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

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

      6. *-commutative N/A

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

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

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

      8. metadata-eval N/A

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

      9. associate-*r* N/A

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

      10. *-commutative N/A

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

      11. distribute-lft1-in N/A

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

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

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

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

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

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

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

      15. /-lowering-/.f64 26.7%

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

   5. Simplified 26.7%

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

   6. Taylor expanded in x around inf

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

      1. associate-*r/ N/A

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

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

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

      3. *-lowering-*.f64 26.7%

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

   8. Simplified 26.7%

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

   if -0.75 < x

   1. Initial program 96.5%

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

   3. Taylor expanded in x around 0

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

      1. /-lowering-/.f64 65.5%

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

   5. Simplified 65.5%

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

4. Final simplification 57.9%

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

Alternative 10: 56.5% accurate, 2.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.6%

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

   1. associate-/l* N/A

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

   2. clear-num N/A

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

   3. un-div-inv N/A

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

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

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

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

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

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

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

   7. *-commutative N/A

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

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

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

   9. --lowering--.f64 99.8%

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

4. Applied egg-rr 99.8%

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

5. Taylor expanded in x around 0

   \[\leadsto \mathsf{/.f64}\left(\mathsf{\_.f64}\left(1, x\right), \color{blue}{y}\right) \]
6. Step-by-step derivation

7. Simplified 56.7%

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

Alternative 11: 51.5% accurate, 3.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.6%

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

3. Taylor expanded in x around 0

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

   1. /-lowering-/.f64 53.6%

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

5. Simplified 53.6%

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

Developer Target 1: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024161 
(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)))