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

Percentage Accurate: 93.7% → 99.6%

Time: 8.3s

Alternatives: 15

Speedup: 1.0×

• 24.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 93.7% 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: 99.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.8%

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

   1. associate-/l* 99.7%

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

   2. *-commutative 99.7%

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

3. Simplified 99.7%

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

5. Final simplification 99.7%

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

Alternative 2: 99.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(1 - x\right) \cdot \left(3 - x\right)\\ \mathbf{if}\;t\_0 \leq 10^{+149}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t\_0}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{x + -1}{3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* (- 1.0 x) (- 3.0 x))))
   (if (<= t_0 1e+149)
     (* 0.3333333333333333 (/ t_0 y))
     (* (/ x y) (/ (+ x -1.0) 3.0)))))

C

double code(double x, double y) {
	double t_0 = (1.0 - x) * (3.0 - x);
	double tmp;
	if (t_0 <= 1e+149) {
		tmp = 0.3333333333333333 * (t_0 / y);
	} else {
		tmp = (x / y) * ((x + -1.0) / 3.0);
	}
	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 = (1.0d0 - x) * (3.0d0 - x)
    if (t_0 <= 1d+149) then
        tmp = 0.3333333333333333d0 * (t_0 / y)
    else
        tmp = (x / y) * ((x + (-1.0d0)) / 3.0d0)
    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 <= 1e+149) {
		tmp = 0.3333333333333333 * (t_0 / y);
	} else {
		tmp = (x / y) * ((x + -1.0) / 3.0);
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (1.0 - x) * (3.0 - x)
	tmp = 0
	if t_0 <= 1e+149:
		tmp = 0.3333333333333333 * (t_0 / y)
	else:
		tmp = (x / y) * ((x + -1.0) / 3.0)
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(1.0 - x) * Float64(3.0 - x))
	tmp = 0.0
	if (t_0 <= 1e+149)
		tmp = Float64(0.3333333333333333 * Float64(t_0 / y));
	else
		tmp = Float64(Float64(x / y) * Float64(Float64(x + -1.0) / 3.0));
	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 <= 1e+149)
		tmp = 0.3333333333333333 * (t_0 / y);
	else
		tmp = (x / y) * ((x + -1.0) / 3.0);
	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, 1e+149], N[(0.3333333333333333 * N[(t$95$0 / y), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] * N[(N[(x + -1.0), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 3 binary64) x)) < 1.00000000000000005e149

   1. Initial program 99.6%

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

      1. associate-/l* 99.6%

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

      2. *-commutative 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in y around 0 99.0%

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

   if 1.00000000000000005e149 < (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 3 binary64) x))

   1. Initial program 92.0%

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

      1. *-commutative 92.0%

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

      2. times-frac 99.9%

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

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in x around inf 99.9%

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

      1. neg-mul-1 99.9%

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

      2. distribute-neg-frac2 99.9%

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

   7. Simplified 99.9%

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

4. Final simplification 99.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(1 - x\right) \cdot \left(3 - x\right) \leq 10^{+149}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{x + -1}{3}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.3 \lor \neg \left(x \leq 1.3\right):\\ \;\;\;\;x \cdot \left(\left(3 - x\right) \cdot \frac{-0.3333333333333333}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -2.3) (not (<= x 1.3)))
   (* x (* (- 3.0 x) (/ -0.3333333333333333 y)))
   (/ (+ 1.0 (* x -1.3333333333333333)) y)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -2.3) || !(x <= 1.3)) {
		tmp = x * ((3.0 - x) * (-0.3333333333333333 / y));
	} else {
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-2.3d0)) .or. (.not. (x <= 1.3d0))) then
        tmp = x * ((3.0d0 - x) * ((-0.3333333333333333d0) / y))
    else
        tmp = (1.0d0 + (x * (-1.3333333333333333d0))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -2.3) || !(x <= 1.3)) {
		tmp = x * ((3.0 - x) * (-0.3333333333333333 / y));
	} else {
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -2.3) or not (x <= 1.3):
		tmp = x * ((3.0 - x) * (-0.3333333333333333 / y))
	else:
		tmp = (1.0 + (x * -1.3333333333333333)) / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -2.3) || !(x <= 1.3))
		tmp = Float64(x * Float64(Float64(3.0 - x) * Float64(-0.3333333333333333 / y)));
	else
		tmp = Float64(Float64(1.0 + Float64(x * -1.3333333333333333)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -2.3) || ~((x <= 1.3)))
		tmp = x * ((3.0 - x) * (-0.3333333333333333 / y));
	else
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -2.3], N[Not[LessEqual[x, 1.3]], $MachinePrecision]], N[(x * N[(N[(3.0 - x), $MachinePrecision] * N[(-0.3333333333333333 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 + N[(x * -1.3333333333333333), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.2999999999999998 or 1.30000000000000004 < x

   1. Initial program 93.8%

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

      1. *-commutative 93.8%

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

      2. times-frac 99.7%

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in x around inf 98.4%

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

      1. *-commutative 98.4%

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

   7. Simplified 98.4%

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

   8. Taylor expanded in y around 0 92.5%

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

      1. associate-*r/ 92.5%

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

      2. associate-*r* 92.5%

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

      3. *-commutative 92.5%

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

      4. associate-*l/ 98.4%

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

      5. associate-/r/ 98.4%

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

      6. associate-/l* 98.5%

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

      7. associate-/r/ 98.4%

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

   10. Simplified 98.4%

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

   if -2.2999999999999998 < x < 1.30000000000000004

   1. Initial program 99.6%

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

      1. associate-/l* 99.6%

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

      2. *-rgt-identity 99.6%

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

      3. remove-double-neg 99.6%

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

      4. distribute-lft-neg-out 99.6%

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

      5. neg-mul-1 99.6%

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

      6. times-frac 99.4%

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

      7. *-rgt-identity 99.4%

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

      8. associate-/l* 99.4%

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

      9. metadata-eval 99.4%

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

      10. *-commutative 99.4%

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

      11. sub-neg 99.4%

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

      12. +-commutative 99.4%

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

      13. distribute-lft-in 99.4%

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

      14. neg-mul-1 99.4%

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

      15. remove-double-neg 99.4%

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

      16. metadata-eval 99.4%

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

      17. distribute-lft-neg-out 99.4%

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

      18. *-commutative 99.4%

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

      19. distribute-lft-neg-in 99.4%

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

      20. associate-/r* 99.5%

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

      21. metadata-eval 99.5%

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

      22. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around 0 97.7%

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

   6. Taylor expanded in y around 0 97.6%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3 \lor \neg \left(x \leq 1.3\right):\\ \;\;\;\;x \cdot \left(\left(3 - x\right) \cdot \frac{-0.3333333333333333}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.3:\\ \;\;\;\;x \cdot \left(\left(3 - x\right) \cdot \frac{-0.3333333333333333}{y}\right)\\ \mathbf{elif}\;x \leq 1.3:\\ \;\;\;\;-1.3333333333333333 \cdot \frac{x}{y} + \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{3 - x}{y}}{\frac{-3}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2.3)
   (* x (* (- 3.0 x) (/ -0.3333333333333333 y)))
   (if (<= x 1.3)
     (+ (* -1.3333333333333333 (/ x y)) (/ 1.0 y))
     (/ (/ (- 3.0 x) y) (/ -3.0 x)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.3) {
		tmp = x * ((3.0 - x) * (-0.3333333333333333 / y));
	} else if (x <= 1.3) {
		tmp = (-1.3333333333333333 * (x / y)) + (1.0 / y);
	} else {
		tmp = ((3.0 - 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 <= (-2.3d0)) then
        tmp = x * ((3.0d0 - x) * ((-0.3333333333333333d0) / y))
    else if (x <= 1.3d0) then
        tmp = ((-1.3333333333333333d0) * (x / y)) + (1.0d0 / y)
    else
        tmp = ((3.0d0 - x) / y) / ((-3.0d0) / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -2.3) {
		tmp = x * ((3.0 - x) * (-0.3333333333333333 / y));
	} else if (x <= 1.3) {
		tmp = (-1.3333333333333333 * (x / y)) + (1.0 / y);
	} else {
		tmp = ((3.0 - x) / y) / (-3.0 / x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2.3:
		tmp = x * ((3.0 - x) * (-0.3333333333333333 / y))
	elif x <= 1.3:
		tmp = (-1.3333333333333333 * (x / y)) + (1.0 / y)
	else:
		tmp = ((3.0 - x) / y) / (-3.0 / x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2.3)
		tmp = Float64(x * Float64(Float64(3.0 - x) * Float64(-0.3333333333333333 / y)));
	elseif (x <= 1.3)
		tmp = Float64(Float64(-1.3333333333333333 * Float64(x / y)) + Float64(1.0 / y));
	else
		tmp = Float64(Float64(Float64(3.0 - x) / y) / Float64(-3.0 / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2.3)
		tmp = x * ((3.0 - x) * (-0.3333333333333333 / y));
	elseif (x <= 1.3)
		tmp = (-1.3333333333333333 * (x / y)) + (1.0 / y);
	else
		tmp = ((3.0 - x) / y) / (-3.0 / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2.3], N[(x * N[(N[(3.0 - x), $MachinePrecision] * N[(-0.3333333333333333 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.3], N[(N[(-1.3333333333333333 * N[(x / y), $MachinePrecision]), $MachinePrecision] + N[(1.0 / y), $MachinePrecision]), $MachinePrecision], N[(N[(N[(3.0 - x), $MachinePrecision] / y), $MachinePrecision] / N[(-3.0 / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.2999999999999998

   1. Initial program 91.7%

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

      1. *-commutative 91.7%

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

      2. times-frac 99.7%

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in x around inf 98.7%

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

      1. *-commutative 98.7%

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

   7. Simplified 98.7%

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

   8. Taylor expanded in y around 0 90.9%

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

      1. associate-*r/ 90.8%

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

      2. associate-*r* 90.8%

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

      3. *-commutative 90.8%

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

      4. associate-*l/ 98.7%

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

      5. associate-/r/ 98.7%

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

      6. associate-/l* 98.8%

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

      7. associate-/r/ 98.8%

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

   10. Simplified 98.8%

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

   if -2.2999999999999998 < x < 1.30000000000000004

   1. Initial program 99.6%

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

      1. associate-/l* 99.6%

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

      2. *-rgt-identity 99.6%

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

      3. remove-double-neg 99.6%

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

      4. distribute-lft-neg-out 99.6%

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

      5. neg-mul-1 99.6%

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

      6. times-frac 99.4%

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

      7. *-rgt-identity 99.4%

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

      8. associate-/l* 99.4%

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

      9. metadata-eval 99.4%

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

      10. *-commutative 99.4%

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

      11. sub-neg 99.4%

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

      12. +-commutative 99.4%

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

      13. distribute-lft-in 99.4%

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

      14. neg-mul-1 99.4%

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

      15. remove-double-neg 99.4%

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

      16. metadata-eval 99.4%

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

      17. distribute-lft-neg-out 99.4%

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

      18. *-commutative 99.4%

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

      19. distribute-lft-neg-in 99.4%

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

      20. associate-/r* 99.5%

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

      21. metadata-eval 99.5%

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

      22. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around 0 97.7%

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

   if 1.30000000000000004 < x

   1. Initial program 95.6%

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

      1. *-commutative 95.6%

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

      2. times-frac 99.8%

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

   4. Applied egg-rr 99.8%

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

      1. clear-num 99.7%

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

      2. un-div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in x around inf 98.3%

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

4. Final simplification 98.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3:\\ \;\;\;\;x \cdot \left(\left(3 - x\right) \cdot \frac{-0.3333333333333333}{y}\right)\\ \mathbf{elif}\;x \leq 1.3:\\ \;\;\;\;-1.3333333333333333 \cdot \frac{x}{y} + \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{3 - x}{y}}{\frac{-3}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 98.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.3:\\ \;\;\;\;x \cdot \left(\left(3 - x\right) \cdot \frac{-0.3333333333333333}{y}\right)\\ \mathbf{elif}\;x \leq 3:\\ \;\;\;\;-1.3333333333333333 \cdot \frac{x}{y} + \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(1 - x\right) \cdot \frac{-0.3333333333333333}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2.3)
   (* x (* (- 3.0 x) (/ -0.3333333333333333 y)))
   (if (<= x 3.0)
     (+ (* -1.3333333333333333 (/ x y)) (/ 1.0 y))
     (* (- 1.0 x) (/ -0.3333333333333333 (/ y x))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.3) {
		tmp = x * ((3.0 - x) * (-0.3333333333333333 / y));
	} else if (x <= 3.0) {
		tmp = (-1.3333333333333333 * (x / y)) + (1.0 / y);
	} else {
		tmp = (1.0 - x) * (-0.3333333333333333 / (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 <= (-2.3d0)) then
        tmp = x * ((3.0d0 - x) * ((-0.3333333333333333d0) / y))
    else if (x <= 3.0d0) then
        tmp = ((-1.3333333333333333d0) * (x / y)) + (1.0d0 / y)
    else
        tmp = (1.0d0 - x) * ((-0.3333333333333333d0) / (y / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -2.3) {
		tmp = x * ((3.0 - x) * (-0.3333333333333333 / y));
	} else if (x <= 3.0) {
		tmp = (-1.3333333333333333 * (x / y)) + (1.0 / y);
	} else {
		tmp = (1.0 - x) * (-0.3333333333333333 / (y / x));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2.3:
		tmp = x * ((3.0 - x) * (-0.3333333333333333 / y))
	elif x <= 3.0:
		tmp = (-1.3333333333333333 * (x / y)) + (1.0 / y)
	else:
		tmp = (1.0 - x) * (-0.3333333333333333 / (y / x))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2.3)
		tmp = Float64(x * Float64(Float64(3.0 - x) * Float64(-0.3333333333333333 / y)));
	elseif (x <= 3.0)
		tmp = Float64(Float64(-1.3333333333333333 * Float64(x / y)) + Float64(1.0 / y));
	else
		tmp = Float64(Float64(1.0 - x) * Float64(-0.3333333333333333 / Float64(y / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2.3)
		tmp = x * ((3.0 - x) * (-0.3333333333333333 / y));
	elseif (x <= 3.0)
		tmp = (-1.3333333333333333 * (x / y)) + (1.0 / y);
	else
		tmp = (1.0 - x) * (-0.3333333333333333 / (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2.3], N[(x * N[(N[(3.0 - x), $MachinePrecision] * N[(-0.3333333333333333 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.0], N[(N[(-1.3333333333333333 * N[(x / y), $MachinePrecision]), $MachinePrecision] + N[(1.0 / y), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 - x), $MachinePrecision] * N[(-0.3333333333333333 / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.2999999999999998

   1. Initial program 91.7%

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

      1. *-commutative 91.7%

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

      2. times-frac 99.7%

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in x around inf 98.7%

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

      1. *-commutative 98.7%

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

   7. Simplified 98.7%

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

   8. Taylor expanded in y around 0 90.9%

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

      1. associate-*r/ 90.8%

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

      2. associate-*r* 90.8%

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

      3. *-commutative 90.8%

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

      4. associate-*l/ 98.7%

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

      5. associate-/r/ 98.7%

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

      6. associate-/l* 98.8%

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

      7. associate-/r/ 98.8%

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

   10. Simplified 98.8%

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

   if -2.2999999999999998 < x < 3

   1. Initial program 99.6%

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

      1. associate-/l* 99.6%

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

      2. *-rgt-identity 99.6%

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

      3. remove-double-neg 99.6%

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

      4. distribute-lft-neg-out 99.6%

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

      5. neg-mul-1 99.6%

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

      6. times-frac 99.4%

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

      7. *-rgt-identity 99.4%

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

      8. associate-/l* 99.4%

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

      9. metadata-eval 99.4%

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

      10. *-commutative 99.4%

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

      11. sub-neg 99.4%

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

      12. +-commutative 99.4%

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

      13. distribute-lft-in 99.4%

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

      14. neg-mul-1 99.4%

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

      15. remove-double-neg 99.4%

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

      16. metadata-eval 99.4%

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

      17. distribute-lft-neg-out 99.4%

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

      18. *-commutative 99.4%

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

      19. distribute-lft-neg-in 99.4%

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

      20. associate-/r* 99.5%

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

      21. metadata-eval 99.5%

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

      22. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around 0 97.7%

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

   if 3 < x

   1. Initial program 95.6%

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

      1. associate-/l* 99.7%

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

      2. *-rgt-identity 99.7%

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

      3. remove-double-neg 99.7%

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

      4. distribute-lft-neg-out 99.7%

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

      5. neg-mul-1 99.7%

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

      6. times-frac 99.7%

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

      7. *-rgt-identity 99.7%

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

      8. associate-/l* 99.7%

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

      9. metadata-eval 99.7%

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

      10. *-commutative 99.7%

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

      11. sub-neg 99.7%

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

      12. +-commutative 99.7%

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

      13. distribute-lft-in 99.7%

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

      14. neg-mul-1 99.7%

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

      15. remove-double-neg 99.7%

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

      16. metadata-eval 99.7%

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

      17. distribute-lft-neg-out 99.7%

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

      18. *-commutative 99.7%

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

      19. distribute-lft-neg-in 99.7%

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

      20. associate-/r* 99.6%

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

      21. metadata-eval 99.6%

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

      22. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around inf 98.0%

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

      1. clear-num 97.9%

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

      2. un-div-inv 98.1%

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

   7. Applied egg-rr 98.1%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3:\\ \;\;\;\;x \cdot \left(\left(3 - x\right) \cdot \frac{-0.3333333333333333}{y}\right)\\ \mathbf{elif}\;x \leq 3:\\ \;\;\;\;-1.3333333333333333 \cdot \frac{x}{y} + \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(1 - x\right) \cdot \frac{-0.3333333333333333}{\frac{y}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 98.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.3:\\ \;\;\;\;x \cdot \left(\left(3 - x\right) \cdot \frac{-0.3333333333333333}{y}\right)\\ \mathbf{elif}\;x \leq 3:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(1 - x\right) \cdot \frac{-0.3333333333333333}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2.3)
   (* x (* (- 3.0 x) (/ -0.3333333333333333 y)))
   (if (<= x 3.0)
     (/ (+ 1.0 (* x -1.3333333333333333)) y)
     (* (- 1.0 x) (/ -0.3333333333333333 (/ y x))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.3) {
		tmp = x * ((3.0 - x) * (-0.3333333333333333 / y));
	} else if (x <= 3.0) {
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	} else {
		tmp = (1.0 - x) * (-0.3333333333333333 / (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 <= (-2.3d0)) then
        tmp = x * ((3.0d0 - x) * ((-0.3333333333333333d0) / y))
    else if (x <= 3.0d0) then
        tmp = (1.0d0 + (x * (-1.3333333333333333d0))) / y
    else
        tmp = (1.0d0 - x) * ((-0.3333333333333333d0) / (y / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -2.3) {
		tmp = x * ((3.0 - x) * (-0.3333333333333333 / y));
	} else if (x <= 3.0) {
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	} else {
		tmp = (1.0 - x) * (-0.3333333333333333 / (y / x));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2.3:
		tmp = x * ((3.0 - x) * (-0.3333333333333333 / y))
	elif x <= 3.0:
		tmp = (1.0 + (x * -1.3333333333333333)) / y
	else:
		tmp = (1.0 - x) * (-0.3333333333333333 / (y / x))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2.3)
		tmp = Float64(x * Float64(Float64(3.0 - x) * Float64(-0.3333333333333333 / y)));
	elseif (x <= 3.0)
		tmp = Float64(Float64(1.0 + Float64(x * -1.3333333333333333)) / y);
	else
		tmp = Float64(Float64(1.0 - x) * Float64(-0.3333333333333333 / Float64(y / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2.3)
		tmp = x * ((3.0 - x) * (-0.3333333333333333 / y));
	elseif (x <= 3.0)
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	else
		tmp = (1.0 - x) * (-0.3333333333333333 / (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2.3], N[(x * N[(N[(3.0 - x), $MachinePrecision] * N[(-0.3333333333333333 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.0], N[(N[(1.0 + N[(x * -1.3333333333333333), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(1.0 - x), $MachinePrecision] * N[(-0.3333333333333333 / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.2999999999999998

   1. Initial program 91.7%

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

      1. *-commutative 91.7%

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

      2. times-frac 99.7%

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in x around inf 98.7%

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

      1. *-commutative 98.7%

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

   7. Simplified 98.7%

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

   8. Taylor expanded in y around 0 90.9%

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

      1. associate-*r/ 90.8%

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

      2. associate-*r* 90.8%

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

      3. *-commutative 90.8%

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

      4. associate-*l/ 98.7%

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

      5. associate-/r/ 98.7%

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

      6. associate-/l* 98.8%

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

      7. associate-/r/ 98.8%

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

   10. Simplified 98.8%

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

   if -2.2999999999999998 < x < 3

   1. Initial program 99.6%

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

      1. associate-/l* 99.6%

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

      2. *-rgt-identity 99.6%

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

      3. remove-double-neg 99.6%

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

      4. distribute-lft-neg-out 99.6%

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

      5. neg-mul-1 99.6%

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

      6. times-frac 99.4%

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

      7. *-rgt-identity 99.4%

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

      8. associate-/l* 99.4%

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

      9. metadata-eval 99.4%

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

      10. *-commutative 99.4%

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

      11. sub-neg 99.4%

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

      12. +-commutative 99.4%

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

      13. distribute-lft-in 99.4%

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

      14. neg-mul-1 99.4%

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

      15. remove-double-neg 99.4%

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

      16. metadata-eval 99.4%

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

      17. distribute-lft-neg-out 99.4%

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

      18. *-commutative 99.4%

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

      19. distribute-lft-neg-in 99.4%

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

      20. associate-/r* 99.5%

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

      21. metadata-eval 99.5%

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

      22. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around 0 97.7%

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

   6. Taylor expanded in y around 0 97.6%

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

   if 3 < x

   1. Initial program 95.6%

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

      1. associate-/l* 99.7%

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

      2. *-rgt-identity 99.7%

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

      3. remove-double-neg 99.7%

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

      4. distribute-lft-neg-out 99.7%

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

      5. neg-mul-1 99.7%

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

      6. times-frac 99.7%

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

      7. *-rgt-identity 99.7%

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

      8. associate-/l* 99.7%

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

      9. metadata-eval 99.7%

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

      10. *-commutative 99.7%

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

      11. sub-neg 99.7%

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

      12. +-commutative 99.7%

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

      13. distribute-lft-in 99.7%

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

      14. neg-mul-1 99.7%

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

      15. remove-double-neg 99.7%

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

      16. metadata-eval 99.7%

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

      17. distribute-lft-neg-out 99.7%

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

      18. *-commutative 99.7%

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

      19. distribute-lft-neg-in 99.7%

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

      20. associate-/r* 99.6%

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

      21. metadata-eval 99.6%

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

      22. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around inf 98.0%

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

      1. clear-num 97.9%

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

      2. un-div-inv 98.1%

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

   7. Applied egg-rr 98.1%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3:\\ \;\;\;\;x \cdot \left(\left(3 - x\right) \cdot \frac{-0.3333333333333333}{y}\right)\\ \mathbf{elif}\;x \leq 3:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(1 - x\right) \cdot \frac{-0.3333333333333333}{\frac{y}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 98.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.5 \lor \neg \left(x \leq 3\right):\\ \;\;\;\;\frac{x \cdot 0.3333333333333333}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -4.5) (not (<= x 3.0)))
   (/ (* x 0.3333333333333333) (/ y x))
   (/ (+ 1.0 (* x -1.3333333333333333)) y)))

C

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

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-4.5d0)) .or. (.not. (x <= 3.0d0))) then
        tmp = (x * 0.3333333333333333d0) / (y / x)
    else
        tmp = (1.0d0 + (x * (-1.3333333333333333d0))) / y
    end if
    code = tmp
end function

Java

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

Python

def code(x, y):
	tmp = 0
	if (x <= -4.5) or not (x <= 3.0):
		tmp = (x * 0.3333333333333333) / (y / x)
	else:
		tmp = (1.0 + (x * -1.3333333333333333)) / y
	return tmp

Julia

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

MATLAB

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

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -4.5], N[Not[LessEqual[x, 3.0]], $MachinePrecision]], N[(N[(x * 0.3333333333333333), $MachinePrecision] / N[(y / x), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 + N[(x * -1.3333333333333333), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.5 or 3 < x

   1. Initial program 93.8%

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

      1. *-commutative 93.8%

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

      2. times-frac 99.7%

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in x around inf 98.4%

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

      1. *-commutative 98.4%

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

   7. Simplified 98.4%

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

   8. Taylor expanded in x around inf 98.2%

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

      1. neg-mul-1 98.3%

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

      2. distribute-neg-frac2 98.3%

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

   10. Simplified 98.2%

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

       1. clear-num 98.2%

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

       2. associate-*l/ 98.2%

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

       3. *-un-lft-identity 98.2%

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

       4. add-sqr-sqrt 52.0%

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

       5. sqrt-unprod 50.1%

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

       6. sqr-neg 50.1%

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

       7. sqrt-unprod 0.2%

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

       8. add-sqr-sqrt 0.5%

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

       9. distribute-lft-neg-in 0.5%

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

       10. distribute-rgt-neg-in 0.5%

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

       11. metadata-eval 0.5%

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

       12. add-sqr-sqrt 0.3%

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

       13. sqrt-unprod 36.0%

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

       14. sqr-neg 36.0%

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

       15. sqrt-unprod 46.7%

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

       16. add-sqr-sqrt 98.2%

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

   12. Applied egg-rr 98.2%

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

   if -4.5 < x < 3

   1. Initial program 99.6%

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

      1. associate-/l* 99.6%

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

      2. *-rgt-identity 99.6%

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

      3. remove-double-neg 99.6%

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

      4. distribute-lft-neg-out 99.6%

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

      5. neg-mul-1 99.6%

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

      6. times-frac 99.4%

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

      7. *-rgt-identity 99.4%

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

      8. associate-/l* 99.4%

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

      9. metadata-eval 99.4%

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

      10. *-commutative 99.4%

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

      11. sub-neg 99.4%

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

      12. +-commutative 99.4%

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

      13. distribute-lft-in 99.4%

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

      14. neg-mul-1 99.4%

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

      15. remove-double-neg 99.4%

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

      16. metadata-eval 99.4%

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

      17. distribute-lft-neg-out 99.4%

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

      18. *-commutative 99.4%

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

      19. distribute-lft-neg-in 99.4%

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

      20. associate-/r* 99.5%

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

      21. metadata-eval 99.5%

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

      22. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around 0 97.7%

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

   6. Taylor expanded in y around 0 97.6%

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

4. Final simplification 97.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.5 \lor \neg \left(x \leq 3\right):\\ \;\;\;\;\frac{x \cdot 0.3333333333333333}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 97.9% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if x < -3.7999999999999998 or 3 < x

   1. Initial program 93.8%

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

      1. *-commutative 93.8%

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

      2. times-frac 99.7%

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in x around inf 98.4%

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

      1. *-commutative 98.4%

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

   7. Simplified 98.4%

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

   8. Taylor expanded in x around inf 98.2%

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

      1. neg-mul-1 98.3%

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

      2. distribute-neg-frac2 98.3%

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

   10. Simplified 98.2%

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

       1. clear-num 98.2%

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

       2. associate-*l/ 98.2%

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

       3. *-un-lft-identity 98.2%

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

       4. add-sqr-sqrt 52.0%

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

       5. sqrt-unprod 50.1%

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

       6. sqr-neg 50.1%

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

       7. sqrt-unprod 0.2%

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

       8. add-sqr-sqrt 0.5%

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

       9. distribute-lft-neg-in 0.5%

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

       10. distribute-rgt-neg-in 0.5%

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

       11. metadata-eval 0.5%

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

       12. add-sqr-sqrt 0.3%

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

       13. sqrt-unprod 36.0%

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

       14. sqr-neg 36.0%

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

       15. sqrt-unprod 46.7%

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

       16. add-sqr-sqrt 98.2%

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

   12. Applied egg-rr 98.2%

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

   if -3.7999999999999998 < x < 3

   1. Initial program 99.6%

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

      1. associate-/l* 99.6%

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

      2. *-rgt-identity 99.6%

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

      3. remove-double-neg 99.6%

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

      4. distribute-lft-neg-out 99.6%

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

      5. neg-mul-1 99.6%

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

      6. times-frac 99.4%

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

      7. *-rgt-identity 99.4%

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

      8. associate-/l* 99.4%

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

      9. metadata-eval 99.4%

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

      10. *-commutative 99.4%

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

      11. sub-neg 99.4%

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

      12. +-commutative 99.4%

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

      13. distribute-lft-in 99.4%

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

      14. neg-mul-1 99.4%

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

      15. remove-double-neg 99.4%

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

      16. metadata-eval 99.4%

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

      17. distribute-lft-neg-out 99.4%

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

      18. *-commutative 99.4%

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

      19. distribute-lft-neg-in 99.4%

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

      20. associate-/r* 99.5%

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

      21. metadata-eval 99.5%

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

      22. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around 0 96.4%

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

4. Final simplification 97.3%

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

Alternative 9: 98.4% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 3 regimes

2. if x < -4.5

   1. Initial program 91.7%

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

      1. *-commutative 91.7%

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

      2. times-frac 99.7%

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in x around inf 98.7%

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

      1. *-commutative 98.7%

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

   7. Simplified 98.7%

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

   8. Taylor expanded in x around inf 98.6%

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

      1. neg-mul-1 98.6%

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

      2. distribute-neg-frac2 98.6%

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

   10. Simplified 98.6%

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

   if -4.5 < x < 3

   1. Initial program 99.6%

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

      1. associate-/l* 99.6%

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

      2. *-rgt-identity 99.6%

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

      3. remove-double-neg 99.6%

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

      4. distribute-lft-neg-out 99.6%

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

      5. neg-mul-1 99.6%

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

      6. times-frac 99.4%

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

      7. *-rgt-identity 99.4%

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

      8. associate-/l* 99.4%

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

      9. metadata-eval 99.4%

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

      10. *-commutative 99.4%

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

      11. sub-neg 99.4%

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

      12. +-commutative 99.4%

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

      13. distribute-lft-in 99.4%

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

      14. neg-mul-1 99.4%

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

      15. remove-double-neg 99.4%

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

      16. metadata-eval 99.4%

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

      17. distribute-lft-neg-out 99.4%

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

      18. *-commutative 99.4%

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

      19. distribute-lft-neg-in 99.4%

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

      20. associate-/r* 99.5%

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

      21. metadata-eval 99.5%

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

      22. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around 0 97.7%

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

   6. Taylor expanded in y around 0 97.6%

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

   if 3 < x

   1. Initial program 95.6%

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

      1. *-commutative 95.6%

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

      2. times-frac 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in x around inf 98.0%

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

      1. *-commutative 98.0%

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

   7. Simplified 98.0%

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

   8. Taylor expanded in x around inf 97.9%

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

      1. neg-mul-1 98.1%

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

      2. distribute-neg-frac2 98.1%

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

   10. Simplified 97.9%

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

       1. clear-num 97.8%

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

       2. associate-*l/ 97.9%

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

       3. *-un-lft-identity 97.9%

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

       4. add-sqr-sqrt 97.8%

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

       5. sqrt-unprod 93.8%

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

       6. sqr-neg 93.8%

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

       7. sqrt-unprod 0.0%

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

       8. add-sqr-sqrt 0.6%

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

       9. distribute-lft-neg-in 0.6%

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

       10. distribute-rgt-neg-in 0.6%

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

       11. metadata-eval 0.6%

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

       12. add-sqr-sqrt 0.3%

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

       13. sqrt-unprod 37.7%

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

       14. sqr-neg 37.7%

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

       15. sqrt-unprod 49.7%

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

       16. add-sqr-sqrt 97.9%

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

   12. Applied egg-rr 97.9%

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

4. Final simplification 97.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.5:\\ \;\;\;\;\frac{x}{y} \cdot \left(x \cdot \left(--0.3333333333333333\right)\right)\\ \mathbf{elif}\;x \leq 3:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot 0.3333333333333333}{\frac{y}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 99.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.8%

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

   1. associate-/l* 99.7%

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

   2. *-rgt-identity 99.7%

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

   3. remove-double-neg 99.7%

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

   4. distribute-lft-neg-out 99.7%

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

   5. neg-mul-1 99.7%

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

   6. times-frac 99.6%

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

   7. *-rgt-identity 99.6%

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

   8. associate-/l* 99.6%

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

   9. metadata-eval 99.6%

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

   10. *-commutative 99.6%

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

   11. sub-neg 99.6%

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

   12. +-commutative 99.6%

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

   13. distribute-lft-in 99.6%

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

   14. neg-mul-1 99.6%

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

   15. remove-double-neg 99.6%

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

   16. metadata-eval 99.6%

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

   17. distribute-lft-neg-out 99.6%

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

   18. *-commutative 99.6%

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

   19. distribute-lft-neg-in 99.6%

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

   20. associate-/r* 99.6%

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

   21. metadata-eval 99.6%

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

   22. metadata-eval 99.6%

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

3. Simplified 99.6%

   \[\leadsto \color{blue}{\left(1 - x\right) \cdot \left(\left(x + -3\right) \cdot \frac{-0.3333333333333333}{y}\right)} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 11: 58.0% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if x < -0.75

   1. Initial program 91.8%

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

      1. associate-/l* 99.7%

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

      2. *-rgt-identity 99.7%

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

      3. remove-double-neg 99.7%

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

      4. distribute-lft-neg-out 99.7%

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

      5. neg-mul-1 99.7%

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

      6. times-frac 99.8%

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

      7. *-rgt-identity 99.8%

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

      8. associate-/l* 99.8%

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

      9. metadata-eval 99.8%

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

      10. *-commutative 99.8%

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

      11. sub-neg 99.8%

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

      12. +-commutative 99.8%

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

      13. distribute-lft-in 99.8%

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

      14. neg-mul-1 99.8%

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

      15. remove-double-neg 99.8%

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

      16. metadata-eval 99.8%

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

      17. distribute-lft-neg-out 99.8%

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

      18. *-commutative 99.8%

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

      19. distribute-lft-neg-in 99.8%

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

      20. associate-/r* 99.7%

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

      21. metadata-eval 99.7%

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

      22. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0 22.5%

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

   6. Taylor expanded in x around inf 22.5%

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

   if -0.75 < x

   1. Initial program 98.3%

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

      1. *-commutative 98.3%

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

      2. times-frac 99.1%

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

   4. Applied egg-rr 99.1%

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

   5. Taylor expanded in x around 0 65.4%

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

Alternative 12: 58.0% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if x < -1

   1. Initial program 91.8%

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

      1. *-commutative 91.8%

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

      2. times-frac 99.6%

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

   4. Applied egg-rr 99.6%

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

   5. Taylor expanded in x around inf 97.4%

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

      1. *-commutative 97.4%

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

   7. Simplified 97.4%

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

   8. Taylor expanded in x around 0 22.5%

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

      1. associate-*r/ 22.5%

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

      2. neg-mul-1 22.5%

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

   10. Simplified 22.5%

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

   if -1 < x

   1. Initial program 98.3%

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

      1. *-commutative 98.3%

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

      2. times-frac 99.1%

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

   4. Applied egg-rr 99.1%

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

   5. Taylor expanded in x around 0 65.4%

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

4. Final simplification 55.3%

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

Alternative 13: 57.0% accurate, 1.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.8%

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

   1. associate-/l* 99.7%

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

   2. *-rgt-identity 99.7%

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

   3. remove-double-neg 99.7%

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

   4. distribute-lft-neg-out 99.7%

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

   5. neg-mul-1 99.7%

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

   6. times-frac 99.6%

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

   7. *-rgt-identity 99.6%

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

   8. associate-/l* 99.6%

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

   9. metadata-eval 99.6%

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

   10. *-commutative 99.6%

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

   11. sub-neg 99.6%

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

   12. +-commutative 99.6%

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

   13. distribute-lft-in 99.6%

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

   14. neg-mul-1 99.6%

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

   15. remove-double-neg 99.6%

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

   16. metadata-eval 99.6%

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

   17. distribute-lft-neg-out 99.6%

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

   18. *-commutative 99.6%

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

   19. distribute-lft-neg-in 99.6%

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

   20. associate-/r* 99.6%

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

   21. metadata-eval 99.6%

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

   22. metadata-eval 99.6%

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

3. Simplified 99.6%

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

5. Taylor expanded in x around 0 54.4%

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

Alternative 14: 51.7% 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 96.8%

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

   1. *-commutative 96.8%

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

   2. times-frac 99.2%

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

4. Applied egg-rr 99.2%

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

5. Taylor expanded in x around 0 51.3%

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

Alternative 15: 1.7% 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 96.8%

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

3. Taylor expanded in x around 0 51.1%

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

   1. associate-/r* 50.8%

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

   2. div-inv 50.7%

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

   3. metadata-eval 50.7%

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

5. Applied egg-rr 50.7%

   \[\leadsto \color{blue}{\frac{3}{y} \cdot 0.3333333333333333} \]
6. Step-by-step derivation

   1. frac-2neg 50.7%

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

   2. associate-*l/ 51.3%

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

   3. metadata-eval 51.3%

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

   4. metadata-eval 51.3%

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

   5. add-sqr-sqrt 23.9%

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

   6. sqrt-unprod 18.3%

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

   7. sqr-neg 18.3%

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

   8. sqrt-unprod 0.8%

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

   9. add-sqr-sqrt 1.8%

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

7. Applied egg-rr 1.8%

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

Developer target: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024097 
(FPCore (x y)
  :name "Diagrams.TwoD.Arc:bezierFromSweepQ1 from diagrams-lib-1.3.0.3"
  :precision binary64

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

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