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

Percentage Accurate: 93.7% → 99.7%

Time: 9.1s

Alternatives: 17

Speedup: 1.0×

• 25.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 93.7% 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: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.8%

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

   1. *-commutative 99.7%

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

   2. associate-/l* 92.8%

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

   3. times-frac 99.8%

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

   4. associate-*r/ 99.8%

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

6. Applied egg-rr 99.8%

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

7. Final simplification 99.8%

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

Alternative 2: 98.4% accurate, 0.6× speedup

Math

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

FPCore

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

C

double code(double x, double y) {
	double tmp;
	if ((x <= -2.3) || !(x <= 1.3)) {
		tmp = ((x / y) * (x - 3.0)) / 3.0;
	} else {
		tmp = (-1.3333333333333333 * (x / y)) + (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 <= (-2.3d0)) .or. (.not. (x <= 1.3d0))) then
        tmp = ((x / y) * (x - 3.0d0)) / 3.0d0
    else
        tmp = ((-1.3333333333333333d0) * (x / y)) + (1.0d0 / 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 / y) * (x - 3.0)) / 3.0;
	} else {
		tmp = (-1.3333333333333333 * (x / y)) + (1.0 / y);
	}
	return tmp;
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if x < -2.2999999999999998 or 1.30000000000000004 < x

   1. Initial program 87.1%

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

      1. *-commutative 99.6%

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

      2. associate-/l* 87.1%

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

      3. times-frac 99.7%

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

      4. associate-*r/ 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in x around inf 98.1%

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

      1. neg-mul-1 98.1%

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

   9. Simplified 98.1%

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

   if -2.2999999999999998 < x < 1.30000000000000004

   1. Initial program 99.7%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   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 99.5%

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

      7. *-rgt-identity 99.5%

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

      8. associate-/l* 99.5%

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

      9. metadata-eval 99.5%

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

      10. *-commutative 99.5%

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

      11. sub-neg 99.5%

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

      12. +-commutative 99.5%

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

      13. distribute-lft-in 99.5%

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

      14. neg-mul-1 99.5%

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

      15. remove-double-neg 99.5%

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

      16. metadata-eval 99.5%

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

      17. distribute-lft-neg-out 99.5%

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

      18. *-commutative 99.5%

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

      19. distribute-lft-neg-in 99.5%

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

      20. associate-/r* 99.3%

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

      21. metadata-eval 99.3%

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

      22. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in x around 0 99.4%

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

4. Final simplification 98.7%

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

Alternative 3: 98.4% accurate, 0.6× speedup

Math

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

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -2.3) (not (<= x 1.3)))
   (* (+ x -3.0) (* x (/ 0.3333333333333333 y)))
   (/ (+ (* x -1.3333333333333333) 1.0) 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 = ((x * -1.3333333333333333) + 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 <= (-2.3d0)) .or. (.not. (x <= 1.3d0))) then
        tmp = (x + (-3.0d0)) * (x * (0.3333333333333333d0 / y))
    else
        tmp = ((x * (-1.3333333333333333d0)) + 1.0d0) / 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 = ((x * -1.3333333333333333) + 1.0) / 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 = ((x * -1.3333333333333333) + 1.0) / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -2.3) || !(x <= 1.3))
		tmp = Float64(Float64(x + -3.0) * Float64(x * Float64(0.3333333333333333 / y)));
	else
		tmp = Float64(Float64(Float64(x * -1.3333333333333333) + 1.0) / 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 = ((x * -1.3333333333333333) + 1.0) / y;
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if x < -2.2999999999999998 or 1.30000000000000004 < x

   1. Initial program 87.1%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   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 x around inf 97.9%

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

      1. neg-mul-1 98.1%

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

   7. Simplified 97.9%

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

      1. distribute-lft-neg-out 97.9%

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

      2. neg-sub0 97.9%

         \[\leadsto \color{blue}{0 - x \cdot \frac{3 - x}{3 \cdot y}} \]

      3. clear-num 97.8%

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

      4. un-div-inv 97.9%

         \[\leadsto 0 - \color{blue}{\frac{x}{\frac{3 \cdot y}{3 - x}}} \]

      5. frac-2neg 97.9%

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

      6. *-commutative 97.9%

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

      7. distribute-rgt-neg-in 97.9%

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

      8. metadata-eval 97.9%

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

      9. sub-neg 97.9%

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

      10. distribute-neg-in 97.9%

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

      11. metadata-eval 97.9%

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

      12. add-sqr-sqrt 57.8%

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

      13. sqrt-unprod 51.6%

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

      14. sqr-neg 51.6%

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

      15. sqrt-unprod 0.3%

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

      16. add-sqr-sqrt 0.7%

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

      17. add-sqr-sqrt 0.4%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-3 + \color{blue}{\sqrt{-x} \cdot \sqrt{-x}}}} \]

      18. sqrt-unprod 34.4%

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

      19. sqr-neg 34.4%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-3 + \sqrt{\color{blue}{x \cdot x}}}} \]

      20. sqrt-unprod 39.9%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-3 + \color{blue}{\sqrt{x} \cdot \sqrt{x}}}} \]

      21. add-sqr-sqrt 97.9%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-3 + \color{blue}{x}}} \]

   9. Applied egg-rr 97.9%

      \[\leadsto \color{blue}{0 - \frac{x}{\frac{y \cdot -3}{-3 + x}}} \]
   10. Step-by-step derivation

       1. neg-sub0 97.9%

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

       2. associate-/r/ 97.9%

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

       3. *-rgt-identity 97.9%

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

       4. times-frac 97.9%

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

       5. metadata-eval 97.9%

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

       6. *-commutative 97.9%

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

       7. distribute-lft-neg-in 97.9%

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

       8. associate-*r/ 97.9%

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

       9. *-commutative 97.9%

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

       10. distribute-frac-neg 97.9%

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

       11. distribute-rgt-neg-in 97.9%

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

       12. metadata-eval 97.9%

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

       13. associate-/l* 97.9%

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

       14. +-commutative 97.9%

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

   11. Simplified 97.9%

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

   if -2.2999999999999998 < x < 1.30000000000000004

   1. Initial program 99.7%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   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 99.5%

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

      7. *-rgt-identity 99.5%

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

      8. associate-/l* 99.5%

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

      9. metadata-eval 99.5%

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

      10. *-commutative 99.5%

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

      11. sub-neg 99.5%

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

      12. +-commutative 99.5%

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

      13. distribute-lft-in 99.5%

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

      14. neg-mul-1 99.5%

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

      15. remove-double-neg 99.5%

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

      16. metadata-eval 99.5%

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

      17. distribute-lft-neg-out 99.5%

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

      18. *-commutative 99.5%

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

      19. distribute-lft-neg-in 99.5%

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

      20. associate-/r* 99.3%

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

      21. metadata-eval 99.3%

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

      22. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in x around 0 99.4%

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

   6. Taylor expanded in y around 0 99.4%

      \[\leadsto \color{blue}{\frac{1 + -1.3333333333333333 \cdot x}{y}} \]
   7. Step-by-step derivation

      1. *-commutative 99.4%

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

   8. Simplified 99.4%

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

4. Final simplification 98.6%

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

Alternative 4: 98.4% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-2.3d0)) then
        tmp = x * ((x - 3.0d0) / (y * 3.0d0))
    else if (x <= 1.3d0) then
        tmp = ((-1.3333333333333333d0) * (x / y)) + (1.0d0 / y)
    else
        tmp = (x + (-3.0d0)) * (x * (0.3333333333333333d0 / y))
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 3 regimes

2. if x < -2.2999999999999998

   1. Initial program 88.6%

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

      1. associate-/l* 99.8%

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

      2. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 97.7%

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

      1. neg-mul-1 97.7%

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

   7. Simplified 97.7%

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

   if -2.2999999999999998 < x < 1.30000000000000004

   1. Initial program 99.7%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   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 99.5%

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

      7. *-rgt-identity 99.5%

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

      8. associate-/l* 99.5%

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

      9. metadata-eval 99.5%

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

      10. *-commutative 99.5%

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

      11. sub-neg 99.5%

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

      12. +-commutative 99.5%

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

      13. distribute-lft-in 99.5%

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

      14. neg-mul-1 99.5%

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

      15. remove-double-neg 99.5%

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

      16. metadata-eval 99.5%

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

      17. distribute-lft-neg-out 99.5%

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

      18. *-commutative 99.5%

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

      19. distribute-lft-neg-in 99.5%

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

      20. associate-/r* 99.3%

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

      21. metadata-eval 99.3%

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

      22. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in x around 0 99.4%

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

   if 1.30000000000000004 < x

   1. Initial program 84.9%

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

      1. associate-/l* 99.5%

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

      2. *-commutative 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around inf 98.3%

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

      1. neg-mul-1 98.5%

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

   7. Simplified 98.3%

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

      1. distribute-lft-neg-out 98.3%

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

      2. neg-sub0 98.3%

         \[\leadsto \color{blue}{0 - x \cdot \frac{3 - x}{3 \cdot y}} \]

      3. clear-num 98.1%

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

      4. un-div-inv 98.2%

         \[\leadsto 0 - \color{blue}{\frac{x}{\frac{3 \cdot y}{3 - x}}} \]

      5. frac-2neg 98.2%

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

      6. *-commutative 98.2%

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

      7. distribute-rgt-neg-in 98.2%

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

      8. metadata-eval 98.2%

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

      9. sub-neg 98.2%

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

      10. distribute-neg-in 98.2%

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

      11. metadata-eval 98.2%

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

      12. add-sqr-sqrt 0.0%

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

      13. sqrt-unprod 0.7%

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

      14. sqr-neg 0.7%

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

      15. sqrt-unprod 0.8%

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

      16. add-sqr-sqrt 0.8%

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

      17. add-sqr-sqrt 0.0%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-3 + \color{blue}{\sqrt{-x} \cdot \sqrt{-x}}}} \]

      18. sqrt-unprod 83.5%

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

      19. sqr-neg 83.5%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-3 + \sqrt{\color{blue}{x \cdot x}}}} \]

      20. sqrt-unprod 98.1%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-3 + \color{blue}{\sqrt{x} \cdot \sqrt{x}}}} \]

      21. add-sqr-sqrt 98.2%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-3 + \color{blue}{x}}} \]

   9. Applied egg-rr 98.2%

      \[\leadsto \color{blue}{0 - \frac{x}{\frac{y \cdot -3}{-3 + x}}} \]
   10. Step-by-step derivation

       1. neg-sub0 98.2%

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

       2. associate-/r/ 98.3%

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

       3. *-rgt-identity 98.3%

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

       4. times-frac 98.4%

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

       5. metadata-eval 98.4%

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

       6. *-commutative 98.4%

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

       7. distribute-lft-neg-in 98.4%

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

       8. associate-*r/ 98.3%

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

       9. *-commutative 98.3%

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

       10. distribute-frac-neg 98.3%

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

       11. distribute-rgt-neg-in 98.3%

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

       12. metadata-eval 98.3%

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

       13. associate-/l* 98.5%

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

       14. +-commutative 98.5%

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

   11. Simplified 98.5%

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

4. Final simplification 98.6%

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

Alternative 5: 98.4% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-2.3d0)) then
        tmp = (x + (-3.0d0)) * (x / (y * 3.0d0))
    else if (x <= 1.3d0) then
        tmp = ((-1.3333333333333333d0) * (x / y)) + (1.0d0 / y)
    else
        tmp = (x + (-3.0d0)) * (x * (0.3333333333333333d0 / y))
    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 / (y * 3.0));
	} else if (x <= 1.3) {
		tmp = (-1.3333333333333333 * (x / y)) + (1.0 / y);
	} else {
		tmp = (x + -3.0) * (x * (0.3333333333333333 / y));
	}
	return tmp;
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 3 regimes

2. if x < -2.2999999999999998

   1. Initial program 88.6%

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

      1. associate-/l* 99.8%

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

      2. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 97.7%

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

      1. neg-mul-1 97.7%

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

   7. Simplified 97.7%

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

      1. distribute-lft-neg-out 97.7%

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

      2. neg-sub0 97.7%

         \[\leadsto \color{blue}{0 - x \cdot \frac{3 - x}{3 \cdot y}} \]

      3. clear-num 97.6%

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

      4. un-div-inv 97.7%

         \[\leadsto 0 - \color{blue}{\frac{x}{\frac{3 \cdot y}{3 - x}}} \]

      5. frac-2neg 97.7%

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

      6. *-commutative 97.7%

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

      7. distribute-rgt-neg-in 97.7%

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

      8. metadata-eval 97.7%

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

      9. sub-neg 97.7%

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

      10. distribute-neg-in 97.7%

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

      11. metadata-eval 97.7%

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

      12. add-sqr-sqrt 97.5%

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

      13. sqrt-unprod 86.6%

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

      14. sqr-neg 86.6%

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

      15. sqrt-unprod 0.0%

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

      16. add-sqr-sqrt 0.6%

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

      17. add-sqr-sqrt 0.6%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-3 + \color{blue}{\sqrt{-x} \cdot \sqrt{-x}}}} \]

      18. sqrt-unprod 0.6%

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

      19. sqr-neg 0.6%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-3 + \sqrt{\color{blue}{x \cdot x}}}} \]

      20. sqrt-unprod 0.0%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-3 + \color{blue}{\sqrt{x} \cdot \sqrt{x}}}} \]

      21. add-sqr-sqrt 97.7%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-3 + \color{blue}{x}}} \]

   9. Applied egg-rr 97.7%

      \[\leadsto \color{blue}{0 - \frac{x}{\frac{y \cdot -3}{-3 + x}}} \]
   10. Step-by-step derivation

       1. neg-sub0 97.7%

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

       2. associate-/r/ 97.7%

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

       3. *-rgt-identity 97.7%

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

       4. times-frac 97.6%

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

       5. metadata-eval 97.6%

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

       6. *-commutative 97.6%

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

       7. distribute-lft-neg-in 97.6%

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

       8. associate-*r/ 97.6%

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

       9. *-commutative 97.6%

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

       10. distribute-frac-neg 97.6%

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

       11. distribute-rgt-neg-in 97.6%

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

       12. metadata-eval 97.6%

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

       13. associate-/l* 97.6%

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

       14. +-commutative 97.6%

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

   11. Simplified 97.6%

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

       1. metadata-eval 97.6%

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

       2. associate-/r* 97.6%

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

       3. *-commutative 97.6%

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

       4. un-div-inv 97.7%

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

   13. Applied egg-rr 97.7%

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

   if -2.2999999999999998 < x < 1.30000000000000004

   1. Initial program 99.7%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   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 99.5%

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

      7. *-rgt-identity 99.5%

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

      8. associate-/l* 99.5%

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

      9. metadata-eval 99.5%

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

      10. *-commutative 99.5%

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

      11. sub-neg 99.5%

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

      12. +-commutative 99.5%

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

      13. distribute-lft-in 99.5%

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

      14. neg-mul-1 99.5%

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

      15. remove-double-neg 99.5%

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

      16. metadata-eval 99.5%

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

      17. distribute-lft-neg-out 99.5%

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

      18. *-commutative 99.5%

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

      19. distribute-lft-neg-in 99.5%

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

      20. associate-/r* 99.3%

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

      21. metadata-eval 99.3%

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

      22. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in x around 0 99.4%

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

   if 1.30000000000000004 < x

   1. Initial program 84.9%

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

      1. associate-/l* 99.5%

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

      2. *-commutative 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around inf 98.3%

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

      1. neg-mul-1 98.5%

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

   7. Simplified 98.3%

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

      1. distribute-lft-neg-out 98.3%

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

      2. neg-sub0 98.3%

         \[\leadsto \color{blue}{0 - x \cdot \frac{3 - x}{3 \cdot y}} \]

      3. clear-num 98.1%

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

      4. un-div-inv 98.2%

         \[\leadsto 0 - \color{blue}{\frac{x}{\frac{3 \cdot y}{3 - x}}} \]

      5. frac-2neg 98.2%

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

      6. *-commutative 98.2%

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

      7. distribute-rgt-neg-in 98.2%

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

      8. metadata-eval 98.2%

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

      9. sub-neg 98.2%

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

      10. distribute-neg-in 98.2%

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

      11. metadata-eval 98.2%

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

      12. add-sqr-sqrt 0.0%

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

      13. sqrt-unprod 0.7%

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

      14. sqr-neg 0.7%

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

      15. sqrt-unprod 0.8%

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

      16. add-sqr-sqrt 0.8%

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

      17. add-sqr-sqrt 0.0%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-3 + \color{blue}{\sqrt{-x} \cdot \sqrt{-x}}}} \]

      18. sqrt-unprod 83.5%

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

      19. sqr-neg 83.5%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-3 + \sqrt{\color{blue}{x \cdot x}}}} \]

      20. sqrt-unprod 98.1%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-3 + \color{blue}{\sqrt{x} \cdot \sqrt{x}}}} \]

      21. add-sqr-sqrt 98.2%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-3 + \color{blue}{x}}} \]

   9. Applied egg-rr 98.2%

      \[\leadsto \color{blue}{0 - \frac{x}{\frac{y \cdot -3}{-3 + x}}} \]
   10. Step-by-step derivation

       1. neg-sub0 98.2%

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

       2. associate-/r/ 98.3%

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

       3. *-rgt-identity 98.3%

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

       4. times-frac 98.4%

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

       5. metadata-eval 98.4%

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

       6. *-commutative 98.4%

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

       7. distribute-lft-neg-in 98.4%

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

       8. associate-*r/ 98.3%

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

       9. *-commutative 98.3%

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

       10. distribute-frac-neg 98.3%

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

       11. distribute-rgt-neg-in 98.3%

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

       12. metadata-eval 98.3%

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

       13. associate-/l* 98.5%

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

       14. +-commutative 98.5%

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

   11. Simplified 98.5%

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

4. Final simplification 98.6%

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

Alternative 6: 98.4% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-2.3d0)) then
        tmp = (x + (-3.0d0)) * (x / (y * 3.0d0))
    else if (x <= 1.3d0) then
        tmp = ((x * (-1.3333333333333333d0)) + 1.0d0) / y
    else
        tmp = (x + (-3.0d0)) * (x * (0.3333333333333333d0 / y))
    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 / (y * 3.0));
	} else if (x <= 1.3) {
		tmp = ((x * -1.3333333333333333) + 1.0) / y;
	} else {
		tmp = (x + -3.0) * (x * (0.3333333333333333 / y));
	}
	return tmp;
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 3 regimes

2. if x < -2.2999999999999998

   1. Initial program 88.6%

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

      1. associate-/l* 99.8%

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

      2. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 97.7%

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

      1. neg-mul-1 97.7%

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

   7. Simplified 97.7%

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

      1. distribute-lft-neg-out 97.7%

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

      2. neg-sub0 97.7%

         \[\leadsto \color{blue}{0 - x \cdot \frac{3 - x}{3 \cdot y}} \]

      3. clear-num 97.6%

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

      4. un-div-inv 97.7%

         \[\leadsto 0 - \color{blue}{\frac{x}{\frac{3 \cdot y}{3 - x}}} \]

      5. frac-2neg 97.7%

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

      6. *-commutative 97.7%

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

      7. distribute-rgt-neg-in 97.7%

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

      8. metadata-eval 97.7%

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

      9. sub-neg 97.7%

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

      10. distribute-neg-in 97.7%

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

      11. metadata-eval 97.7%

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

      12. add-sqr-sqrt 97.5%

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

      13. sqrt-unprod 86.6%

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

      14. sqr-neg 86.6%

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

      15. sqrt-unprod 0.0%

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

      16. add-sqr-sqrt 0.6%

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

      17. add-sqr-sqrt 0.6%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-3 + \color{blue}{\sqrt{-x} \cdot \sqrt{-x}}}} \]

      18. sqrt-unprod 0.6%

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

      19. sqr-neg 0.6%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-3 + \sqrt{\color{blue}{x \cdot x}}}} \]

      20. sqrt-unprod 0.0%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-3 + \color{blue}{\sqrt{x} \cdot \sqrt{x}}}} \]

      21. add-sqr-sqrt 97.7%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-3 + \color{blue}{x}}} \]

   9. Applied egg-rr 97.7%

      \[\leadsto \color{blue}{0 - \frac{x}{\frac{y \cdot -3}{-3 + x}}} \]
   10. Step-by-step derivation

       1. neg-sub0 97.7%

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

       2. associate-/r/ 97.7%

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

       3. *-rgt-identity 97.7%

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

       4. times-frac 97.6%

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

       5. metadata-eval 97.6%

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

       6. *-commutative 97.6%

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

       7. distribute-lft-neg-in 97.6%

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

       8. associate-*r/ 97.6%

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

       9. *-commutative 97.6%

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

       10. distribute-frac-neg 97.6%

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

       11. distribute-rgt-neg-in 97.6%

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

       12. metadata-eval 97.6%

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

       13. associate-/l* 97.6%

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

       14. +-commutative 97.6%

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

   11. Simplified 97.6%

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

       1. metadata-eval 97.6%

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

       2. associate-/r* 97.6%

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

       3. *-commutative 97.6%

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

       4. un-div-inv 97.7%

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

   13. Applied egg-rr 97.7%

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

   if -2.2999999999999998 < x < 1.30000000000000004

   1. Initial program 99.7%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   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 99.5%

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

      7. *-rgt-identity 99.5%

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

      8. associate-/l* 99.5%

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

      9. metadata-eval 99.5%

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

      10. *-commutative 99.5%

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

      11. sub-neg 99.5%

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

      12. +-commutative 99.5%

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

      13. distribute-lft-in 99.5%

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

      14. neg-mul-1 99.5%

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

      15. remove-double-neg 99.5%

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

      16. metadata-eval 99.5%

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

      17. distribute-lft-neg-out 99.5%

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

      18. *-commutative 99.5%

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

      19. distribute-lft-neg-in 99.5%

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

      20. associate-/r* 99.3%

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

      21. metadata-eval 99.3%

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

      22. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in x around 0 99.4%

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

   6. Taylor expanded in y around 0 99.4%

      \[\leadsto \color{blue}{\frac{1 + -1.3333333333333333 \cdot x}{y}} \]
   7. Step-by-step derivation

      1. *-commutative 99.4%

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

   8. Simplified 99.4%

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

   if 1.30000000000000004 < x

   1. Initial program 84.9%

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

      1. associate-/l* 99.5%

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

      2. *-commutative 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around inf 98.3%

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

      1. neg-mul-1 98.5%

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

   7. Simplified 98.3%

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

      1. distribute-lft-neg-out 98.3%

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

      2. neg-sub0 98.3%

         \[\leadsto \color{blue}{0 - x \cdot \frac{3 - x}{3 \cdot y}} \]

      3. clear-num 98.1%

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

      4. un-div-inv 98.2%

         \[\leadsto 0 - \color{blue}{\frac{x}{\frac{3 \cdot y}{3 - x}}} \]

      5. frac-2neg 98.2%

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

      6. *-commutative 98.2%

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

      7. distribute-rgt-neg-in 98.2%

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

      8. metadata-eval 98.2%

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

      9. sub-neg 98.2%

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

      10. distribute-neg-in 98.2%

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

      11. metadata-eval 98.2%

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

      12. add-sqr-sqrt 0.0%

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

      13. sqrt-unprod 0.7%

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

      14. sqr-neg 0.7%

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

      15. sqrt-unprod 0.8%

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

      16. add-sqr-sqrt 0.8%

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

      17. add-sqr-sqrt 0.0%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-3 + \color{blue}{\sqrt{-x} \cdot \sqrt{-x}}}} \]

      18. sqrt-unprod 83.5%

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

      19. sqr-neg 83.5%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-3 + \sqrt{\color{blue}{x \cdot x}}}} \]

      20. sqrt-unprod 98.1%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-3 + \color{blue}{\sqrt{x} \cdot \sqrt{x}}}} \]

      21. add-sqr-sqrt 98.2%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-3 + \color{blue}{x}}} \]

   9. Applied egg-rr 98.2%

      \[\leadsto \color{blue}{0 - \frac{x}{\frac{y \cdot -3}{-3 + x}}} \]
   10. Step-by-step derivation

       1. neg-sub0 98.2%

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

       2. associate-/r/ 98.3%

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

       3. *-rgt-identity 98.3%

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

       4. times-frac 98.4%

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

       5. metadata-eval 98.4%

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

       6. *-commutative 98.4%

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

       7. distribute-lft-neg-in 98.4%

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

       8. associate-*r/ 98.3%

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

       9. *-commutative 98.3%

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

       10. distribute-frac-neg 98.3%

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

       11. distribute-rgt-neg-in 98.3%

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

       12. metadata-eval 98.3%

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

       13. associate-/l* 98.5%

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

       14. +-commutative 98.5%

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

   11. Simplified 98.5%

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

4. Final simplification 98.6%

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

Alternative 7: 97.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.75 \lor \neg \left(x \leq 0.58\right):\\ \;\;\;\;x \cdot \left(x \cdot \frac{0.3333333333333333}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -1.75) (not (<= x 0.58)))
   (* x (* x (/ 0.3333333333333333 y)))
   (/ 1.0 y)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -1.75) || !(x <= 0.58)) {
		tmp = x * (x * (0.3333333333333333 / y));
	} else {
		tmp = 1.0 / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-1.75d0)) .or. (.not. (x <= 0.58d0))) then
        tmp = x * (x * (0.3333333333333333d0 / y))
    else
        tmp = 1.0d0 / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -1.75) || !(x <= 0.58)) {
		tmp = x * (x * (0.3333333333333333 / y));
	} else {
		tmp = 1.0 / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -1.75) or not (x <= 0.58):
		tmp = x * (x * (0.3333333333333333 / y))
	else:
		tmp = 1.0 / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -1.75) || !(x <= 0.58))
		tmp = Float64(x * Float64(x * Float64(0.3333333333333333 / y)));
	else
		tmp = Float64(1.0 / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -1.75) || ~((x <= 0.58)))
		tmp = x * (x * (0.3333333333333333 / y));
	else
		tmp = 1.0 / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -1.75], N[Not[LessEqual[x, 0.58]], $MachinePrecision]], N[(x * N[(x * N[(0.3333333333333333 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.75 or 0.57999999999999996 < x

   1. Initial program 87.1%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   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 x around inf 97.9%

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

      1. neg-mul-1 98.1%

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

   7. Simplified 97.9%

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

      1. distribute-lft-neg-out 97.9%

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

      2. neg-sub0 97.9%

         \[\leadsto \color{blue}{0 - x \cdot \frac{3 - x}{3 \cdot y}} \]

      3. clear-num 97.8%

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

      4. un-div-inv 97.9%

         \[\leadsto 0 - \color{blue}{\frac{x}{\frac{3 \cdot y}{3 - x}}} \]

      5. frac-2neg 97.9%

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

      6. *-commutative 97.9%

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

      7. distribute-rgt-neg-in 97.9%

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

      8. metadata-eval 97.9%

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

      9. sub-neg 97.9%

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

      10. distribute-neg-in 97.9%

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

      11. metadata-eval 97.9%

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

      12. add-sqr-sqrt 57.8%

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

      13. sqrt-unprod 51.6%

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

      14. sqr-neg 51.6%

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

      15. sqrt-unprod 0.3%

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

      16. add-sqr-sqrt 0.7%

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

      17. add-sqr-sqrt 0.4%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-3 + \color{blue}{\sqrt{-x} \cdot \sqrt{-x}}}} \]

      18. sqrt-unprod 34.4%

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

      19. sqr-neg 34.4%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-3 + \sqrt{\color{blue}{x \cdot x}}}} \]

      20. sqrt-unprod 39.9%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-3 + \color{blue}{\sqrt{x} \cdot \sqrt{x}}}} \]

      21. add-sqr-sqrt 97.9%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-3 + \color{blue}{x}}} \]

   9. Applied egg-rr 97.9%

      \[\leadsto \color{blue}{0 - \frac{x}{\frac{y \cdot -3}{-3 + x}}} \]
   10. Step-by-step derivation

       1. neg-sub0 97.9%

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

       2. associate-/r/ 97.9%

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

       3. *-rgt-identity 97.9%

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

       4. times-frac 97.9%

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

       5. metadata-eval 97.9%

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

       6. *-commutative 97.9%

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

       7. distribute-lft-neg-in 97.9%

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

       8. associate-*r/ 97.9%

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

       9. *-commutative 97.9%

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

       10. distribute-frac-neg 97.9%

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

       11. distribute-rgt-neg-in 97.9%

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

       12. metadata-eval 97.9%

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

       13. associate-/l* 97.9%

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

       14. +-commutative 97.9%

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

   11. Simplified 97.9%

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

   12. Taylor expanded in x around inf 97.7%

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

   if -1.75 < x < 0.57999999999999996

   1. Initial program 99.7%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   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 99.5%

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

      7. *-rgt-identity 99.5%

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

      8. associate-/l* 99.5%

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

      9. metadata-eval 99.5%

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

      10. *-commutative 99.5%

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

      11. sub-neg 99.5%

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

      12. +-commutative 99.5%

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

      13. distribute-lft-in 99.5%

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

      14. neg-mul-1 99.5%

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

      15. remove-double-neg 99.5%

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

      16. metadata-eval 99.5%

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

      17. distribute-lft-neg-out 99.5%

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

      18. *-commutative 99.5%

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

      19. distribute-lft-neg-in 99.5%

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

      20. associate-/r* 99.3%

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

      21. metadata-eval 99.3%

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

      22. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in x around 0 97.9%

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

4. Final simplification 97.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.75 \lor \neg \left(x \leq 0.58\right):\\ \;\;\;\;x \cdot \left(x \cdot \frac{0.3333333333333333}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 91.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.75 \lor \neg \left(x \leq 0.58\right):\\ \;\;\;\;0.3333333333333333 \cdot \frac{x \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -1.75) (not (<= x 0.58)))
   (* 0.3333333333333333 (/ (* x x) y))
   (/ 1.0 y)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -1.75) || !(x <= 0.58)) {
		tmp = 0.3333333333333333 * ((x * 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 <= (-1.75d0)) .or. (.not. (x <= 0.58d0))) then
        tmp = 0.3333333333333333d0 * ((x * 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 <= -1.75) || !(x <= 0.58)) {
		tmp = 0.3333333333333333 * ((x * x) / y);
	} else {
		tmp = 1.0 / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -1.75) or not (x <= 0.58):
		tmp = 0.3333333333333333 * ((x * x) / y)
	else:
		tmp = 1.0 / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -1.75) || !(x <= 0.58))
		tmp = Float64(0.3333333333333333 * Float64(Float64(x * x) / y));
	else
		tmp = Float64(1.0 / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -1.75) || ~((x <= 0.58)))
		tmp = 0.3333333333333333 * ((x * x) / y);
	else
		tmp = 1.0 / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -1.75], N[Not[LessEqual[x, 0.58]], $MachinePrecision]], N[(0.3333333333333333 * N[(N[(x * x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(1.0 / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.75 or 0.57999999999999996 < x

   1. Initial program 87.1%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   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 x around inf 97.9%

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

      1. neg-mul-1 98.1%

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

   7. Simplified 97.9%

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

      1. distribute-lft-neg-out 97.9%

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

      2. neg-sub0 97.9%

         \[\leadsto \color{blue}{0 - x \cdot \frac{3 - x}{3 \cdot y}} \]

      3. clear-num 97.8%

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

      4. un-div-inv 97.9%

         \[\leadsto 0 - \color{blue}{\frac{x}{\frac{3 \cdot y}{3 - x}}} \]

      5. frac-2neg 97.9%

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

      6. *-commutative 97.9%

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

      7. distribute-rgt-neg-in 97.9%

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

      8. metadata-eval 97.9%

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

      9. sub-neg 97.9%

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

      10. distribute-neg-in 97.9%

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

      11. metadata-eval 97.9%

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

      12. add-sqr-sqrt 57.8%

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

      13. sqrt-unprod 51.6%

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

      14. sqr-neg 51.6%

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

      15. sqrt-unprod 0.3%

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

      16. add-sqr-sqrt 0.7%

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

      17. add-sqr-sqrt 0.4%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-3 + \color{blue}{\sqrt{-x} \cdot \sqrt{-x}}}} \]

      18. sqrt-unprod 34.4%

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

      19. sqr-neg 34.4%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-3 + \sqrt{\color{blue}{x \cdot x}}}} \]

      20. sqrt-unprod 39.9%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-3 + \color{blue}{\sqrt{x} \cdot \sqrt{x}}}} \]

      21. add-sqr-sqrt 97.9%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-3 + \color{blue}{x}}} \]

   9. Applied egg-rr 97.9%

      \[\leadsto \color{blue}{0 - \frac{x}{\frac{y \cdot -3}{-3 + x}}} \]
   10. Step-by-step derivation

       1. neg-sub0 97.9%

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

       2. associate-/r/ 97.9%

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

       3. *-rgt-identity 97.9%

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

       4. times-frac 97.9%

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

       5. metadata-eval 97.9%

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

       6. *-commutative 97.9%

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

       7. distribute-lft-neg-in 97.9%

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

       8. associate-*r/ 97.9%

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

       9. *-commutative 97.9%

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

       10. distribute-frac-neg 97.9%

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

       11. distribute-rgt-neg-in 97.9%

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

       12. metadata-eval 97.9%

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

       13. associate-/l* 97.9%

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

       14. +-commutative 97.9%

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

   11. Simplified 97.9%

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

   12. Taylor expanded in y around 0 85.3%

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

   13. Taylor expanded in x around inf 85.1%

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

   if -1.75 < x < 0.57999999999999996

   1. Initial program 99.7%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   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 99.5%

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

      7. *-rgt-identity 99.5%

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

      8. associate-/l* 99.5%

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

      9. metadata-eval 99.5%

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

      10. *-commutative 99.5%

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

      11. sub-neg 99.5%

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

      12. +-commutative 99.5%

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

      13. distribute-lft-in 99.5%

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

      14. neg-mul-1 99.5%

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

      15. remove-double-neg 99.5%

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

      16. metadata-eval 99.5%

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

      17. distribute-lft-neg-out 99.5%

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

      18. *-commutative 99.5%

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

      19. distribute-lft-neg-in 99.5%

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

      20. associate-/r* 99.3%

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

      21. metadata-eval 99.3%

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

      22. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in x around 0 97.9%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.75 \lor \neg \left(x \leq 0.58\right):\\ \;\;\;\;0.3333333333333333 \cdot \frac{x \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 98.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.5:\\ \;\;\;\;x \cdot \frac{x}{y \cdot 3}\\ \mathbf{elif}\;x \leq 0.65:\\ \;\;\;\;\frac{x \cdot -1.3333333333333333 + 1}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(x \cdot \frac{0.3333333333333333}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -4.5)
   (* x (/ x (* y 3.0)))
   (if (<= x 0.65)
     (/ (+ (* x -1.3333333333333333) 1.0) y)
     (* x (* x (/ 0.3333333333333333 y))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -4.5) {
		tmp = x * (x / (y * 3.0));
	} else if (x <= 0.65) {
		tmp = ((x * -1.3333333333333333) + 1.0) / y;
	} else {
		tmp = x * (x * (0.3333333333333333 / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-4.5d0)) then
        tmp = x * (x / (y * 3.0d0))
    else if (x <= 0.65d0) then
        tmp = ((x * (-1.3333333333333333d0)) + 1.0d0) / y
    else
        tmp = x * (x * (0.3333333333333333d0 / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -4.5) {
		tmp = x * (x / (y * 3.0));
	} else if (x <= 0.65) {
		tmp = ((x * -1.3333333333333333) + 1.0) / y;
	} else {
		tmp = x * (x * (0.3333333333333333 / y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -4.5:
		tmp = x * (x / (y * 3.0))
	elif x <= 0.65:
		tmp = ((x * -1.3333333333333333) + 1.0) / y
	else:
		tmp = x * (x * (0.3333333333333333 / y))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -4.5)
		tmp = Float64(x * Float64(x / Float64(y * 3.0)));
	elseif (x <= 0.65)
		tmp = Float64(Float64(Float64(x * -1.3333333333333333) + 1.0) / y);
	else
		tmp = Float64(x * Float64(x * Float64(0.3333333333333333 / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -4.5)
		tmp = x * (x / (y * 3.0));
	elseif (x <= 0.65)
		tmp = ((x * -1.3333333333333333) + 1.0) / y;
	else
		tmp = x * (x * (0.3333333333333333 / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -4.5], N[(x * N[(x / N[(y * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 0.65], N[(N[(N[(x * -1.3333333333333333), $MachinePrecision] + 1.0), $MachinePrecision] / y), $MachinePrecision], N[(x * N[(x * N[(0.3333333333333333 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.5

   1. Initial program 88.6%

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

      1. associate-/l* 99.8%

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

      2. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 97.7%

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

      1. neg-mul-1 97.7%

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

   7. Simplified 97.7%

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

      1. distribute-lft-neg-out 97.7%

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

      2. neg-sub0 97.7%

         \[\leadsto \color{blue}{0 - x \cdot \frac{3 - x}{3 \cdot y}} \]

      3. clear-num 97.6%

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

      4. un-div-inv 97.7%

         \[\leadsto 0 - \color{blue}{\frac{x}{\frac{3 \cdot y}{3 - x}}} \]

      5. frac-2neg 97.7%

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

      6. *-commutative 97.7%

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

      7. distribute-rgt-neg-in 97.7%

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

      8. metadata-eval 97.7%

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

      9. sub-neg 97.7%

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

      10. distribute-neg-in 97.7%

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

      11. metadata-eval 97.7%

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

      12. add-sqr-sqrt 97.5%

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

      13. sqrt-unprod 86.6%

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

      14. sqr-neg 86.6%

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

      15. sqrt-unprod 0.0%

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

      16. add-sqr-sqrt 0.6%

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

      17. add-sqr-sqrt 0.6%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-3 + \color{blue}{\sqrt{-x} \cdot \sqrt{-x}}}} \]

      18. sqrt-unprod 0.6%

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

      19. sqr-neg 0.6%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-3 + \sqrt{\color{blue}{x \cdot x}}}} \]

      20. sqrt-unprod 0.0%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-3 + \color{blue}{\sqrt{x} \cdot \sqrt{x}}}} \]

      21. add-sqr-sqrt 97.7%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-3 + \color{blue}{x}}} \]

   9. Applied egg-rr 97.7%

      \[\leadsto \color{blue}{0 - \frac{x}{\frac{y \cdot -3}{-3 + x}}} \]
   10. Step-by-step derivation

       1. neg-sub0 97.7%

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

       2. associate-/r/ 97.7%

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

       3. *-rgt-identity 97.7%

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

       4. times-frac 97.6%

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

       5. metadata-eval 97.6%

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

       6. *-commutative 97.6%

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

       7. distribute-lft-neg-in 97.6%

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

       8. associate-*r/ 97.6%

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

       9. *-commutative 97.6%

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

       10. distribute-frac-neg 97.6%

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

       11. distribute-rgt-neg-in 97.6%

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

       12. metadata-eval 97.6%

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

       13. associate-/l* 97.6%

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

       14. +-commutative 97.6%

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

   11. Simplified 97.6%

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

   12. Taylor expanded in x around inf 97.4%

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

       1. metadata-eval 97.6%

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

       2. associate-/r* 97.6%

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

       3. *-commutative 97.6%

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

       4. un-div-inv 97.7%

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

   14. Applied egg-rr 97.4%

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

   if -4.5 < x < 0.650000000000000022

   1. Initial program 99.7%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   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 99.5%

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

      7. *-rgt-identity 99.5%

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

      8. associate-/l* 99.5%

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

      9. metadata-eval 99.5%

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

      10. *-commutative 99.5%

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

      11. sub-neg 99.5%

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

      12. +-commutative 99.5%

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

      13. distribute-lft-in 99.5%

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

      14. neg-mul-1 99.5%

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

      15. remove-double-neg 99.5%

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

      16. metadata-eval 99.5%

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

      17. distribute-lft-neg-out 99.5%

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

      18. *-commutative 99.5%

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

      19. distribute-lft-neg-in 99.5%

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

      20. associate-/r* 99.3%

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

      21. metadata-eval 99.3%

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

      22. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in x around 0 99.4%

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

   6. Taylor expanded in y around 0 99.4%

      \[\leadsto \color{blue}{\frac{1 + -1.3333333333333333 \cdot x}{y}} \]
   7. Step-by-step derivation

      1. *-commutative 99.4%

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

   8. Simplified 99.4%

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

   if 0.650000000000000022 < x

   1. Initial program 84.9%

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

      1. associate-/l* 99.5%

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

      2. *-commutative 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around inf 98.3%

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

      1. neg-mul-1 98.5%

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

   7. Simplified 98.3%

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

      1. distribute-lft-neg-out 98.3%

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

      2. neg-sub0 98.3%

         \[\leadsto \color{blue}{0 - x \cdot \frac{3 - x}{3 \cdot y}} \]

      3. clear-num 98.1%

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

      4. un-div-inv 98.2%

         \[\leadsto 0 - \color{blue}{\frac{x}{\frac{3 \cdot y}{3 - x}}} \]

      5. frac-2neg 98.2%

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

      6. *-commutative 98.2%

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

      7. distribute-rgt-neg-in 98.2%

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

      8. metadata-eval 98.2%

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

      9. sub-neg 98.2%

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

      10. distribute-neg-in 98.2%

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

      11. metadata-eval 98.2%

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

      12. add-sqr-sqrt 0.0%

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

      13. sqrt-unprod 0.7%

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

      14. sqr-neg 0.7%

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

      15. sqrt-unprod 0.8%

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

      16. add-sqr-sqrt 0.8%

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

      17. add-sqr-sqrt 0.0%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-3 + \color{blue}{\sqrt{-x} \cdot \sqrt{-x}}}} \]

      18. sqrt-unprod 83.5%

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

      19. sqr-neg 83.5%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-3 + \sqrt{\color{blue}{x \cdot x}}}} \]

      20. sqrt-unprod 98.1%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-3 + \color{blue}{\sqrt{x} \cdot \sqrt{x}}}} \]

      21. add-sqr-sqrt 98.2%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-3 + \color{blue}{x}}} \]

   9. Applied egg-rr 98.2%

      \[\leadsto \color{blue}{0 - \frac{x}{\frac{y \cdot -3}{-3 + x}}} \]
   10. Step-by-step derivation

       1. neg-sub0 98.2%

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

       2. associate-/r/ 98.3%

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

       3. *-rgt-identity 98.3%

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

       4. times-frac 98.4%

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

       5. metadata-eval 98.4%

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

       6. *-commutative 98.4%

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

       7. distribute-lft-neg-in 98.4%

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

       8. associate-*r/ 98.3%

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

       9. *-commutative 98.3%

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

       10. distribute-frac-neg 98.3%

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

       11. distribute-rgt-neg-in 98.3%

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

       12. metadata-eval 98.3%

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

       13. associate-/l* 98.5%

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

       14. +-commutative 98.5%

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

   11. Simplified 98.5%

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

   12. Taylor expanded in x around inf 98.3%

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

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.5:\\ \;\;\;\;x \cdot \frac{x}{y \cdot 3}\\ \mathbf{elif}\;x \leq 0.65:\\ \;\;\;\;\frac{x \cdot -1.3333333333333333 + 1}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(x \cdot \frac{0.3333333333333333}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 97.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.75:\\ \;\;\;\;x \cdot \frac{x}{y \cdot 3}\\ \mathbf{elif}\;x \leq 0.58:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(x \cdot \frac{0.3333333333333333}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.75)
   (* x (/ x (* y 3.0)))
   (if (<= x 0.58) (/ 1.0 y) (* x (* x (/ 0.3333333333333333 y))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.75) {
		tmp = x * (x / (y * 3.0));
	} else if (x <= 0.58) {
		tmp = 1.0 / y;
	} else {
		tmp = x * (x * (0.3333333333333333 / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-1.75d0)) then
        tmp = x * (x / (y * 3.0d0))
    else if (x <= 0.58d0) then
        tmp = 1.0d0 / y
    else
        tmp = x * (x * (0.3333333333333333d0 / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -1.75) {
		tmp = x * (x / (y * 3.0));
	} else if (x <= 0.58) {
		tmp = 1.0 / y;
	} else {
		tmp = x * (x * (0.3333333333333333 / y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.75:
		tmp = x * (x / (y * 3.0))
	elif x <= 0.58:
		tmp = 1.0 / y
	else:
		tmp = x * (x * (0.3333333333333333 / y))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.75)
		tmp = Float64(x * Float64(x / Float64(y * 3.0)));
	elseif (x <= 0.58)
		tmp = Float64(1.0 / y);
	else
		tmp = Float64(x * Float64(x * Float64(0.3333333333333333 / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.75)
		tmp = x * (x / (y * 3.0));
	elseif (x <= 0.58)
		tmp = 1.0 / y;
	else
		tmp = x * (x * (0.3333333333333333 / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.75], N[(x * N[(x / N[(y * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 0.58], N[(1.0 / y), $MachinePrecision], N[(x * N[(x * N[(0.3333333333333333 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.75

   1. Initial program 88.6%

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

      1. associate-/l* 99.8%

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

      2. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 97.7%

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

      1. neg-mul-1 97.7%

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

   7. Simplified 97.7%

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

      1. distribute-lft-neg-out 97.7%

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

      2. neg-sub0 97.7%

         \[\leadsto \color{blue}{0 - x \cdot \frac{3 - x}{3 \cdot y}} \]

      3. clear-num 97.6%

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

      4. un-div-inv 97.7%

         \[\leadsto 0 - \color{blue}{\frac{x}{\frac{3 \cdot y}{3 - x}}} \]

      5. frac-2neg 97.7%

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

      6. *-commutative 97.7%

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

      7. distribute-rgt-neg-in 97.7%

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

      8. metadata-eval 97.7%

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

      9. sub-neg 97.7%

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

      10. distribute-neg-in 97.7%

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

      11. metadata-eval 97.7%

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

      12. add-sqr-sqrt 97.5%

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

      13. sqrt-unprod 86.6%

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

      14. sqr-neg 86.6%

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

      15. sqrt-unprod 0.0%

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

      16. add-sqr-sqrt 0.6%

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

      17. add-sqr-sqrt 0.6%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-3 + \color{blue}{\sqrt{-x} \cdot \sqrt{-x}}}} \]

      18. sqrt-unprod 0.6%

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

      19. sqr-neg 0.6%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-3 + \sqrt{\color{blue}{x \cdot x}}}} \]

      20. sqrt-unprod 0.0%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-3 + \color{blue}{\sqrt{x} \cdot \sqrt{x}}}} \]

      21. add-sqr-sqrt 97.7%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-3 + \color{blue}{x}}} \]

   9. Applied egg-rr 97.7%

      \[\leadsto \color{blue}{0 - \frac{x}{\frac{y \cdot -3}{-3 + x}}} \]
   10. Step-by-step derivation

       1. neg-sub0 97.7%

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

       2. associate-/r/ 97.7%

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

       3. *-rgt-identity 97.7%

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

       4. times-frac 97.6%

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

       5. metadata-eval 97.6%

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

       6. *-commutative 97.6%

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

       7. distribute-lft-neg-in 97.6%

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

       8. associate-*r/ 97.6%

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

       9. *-commutative 97.6%

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

       10. distribute-frac-neg 97.6%

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

       11. distribute-rgt-neg-in 97.6%

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

       12. metadata-eval 97.6%

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

       13. associate-/l* 97.6%

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

       14. +-commutative 97.6%

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

   11. Simplified 97.6%

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

   12. Taylor expanded in x around inf 97.4%

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

       1. metadata-eval 97.6%

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

       2. associate-/r* 97.6%

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

       3. *-commutative 97.6%

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

       4. un-div-inv 97.7%

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

   14. Applied egg-rr 97.4%

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

   if -1.75 < x < 0.57999999999999996

   1. Initial program 99.7%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   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 99.5%

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

      7. *-rgt-identity 99.5%

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

      8. associate-/l* 99.5%

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

      9. metadata-eval 99.5%

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

      10. *-commutative 99.5%

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

      11. sub-neg 99.5%

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

      12. +-commutative 99.5%

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

      13. distribute-lft-in 99.5%

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

      14. neg-mul-1 99.5%

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

      15. remove-double-neg 99.5%

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

      16. metadata-eval 99.5%

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

      17. distribute-lft-neg-out 99.5%

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

      18. *-commutative 99.5%

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

      19. distribute-lft-neg-in 99.5%

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

      20. associate-/r* 99.3%

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

      21. metadata-eval 99.3%

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

      22. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in x around 0 97.9%

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

   if 0.57999999999999996 < x

   1. Initial program 84.9%

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

      1. associate-/l* 99.5%

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

      2. *-commutative 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around inf 98.3%

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

      1. neg-mul-1 98.5%

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

   7. Simplified 98.3%

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

      1. distribute-lft-neg-out 98.3%

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

      2. neg-sub0 98.3%

         \[\leadsto \color{blue}{0 - x \cdot \frac{3 - x}{3 \cdot y}} \]

      3. clear-num 98.1%

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

      4. un-div-inv 98.2%

         \[\leadsto 0 - \color{blue}{\frac{x}{\frac{3 \cdot y}{3 - x}}} \]

      5. frac-2neg 98.2%

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

      6. *-commutative 98.2%

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

      7. distribute-rgt-neg-in 98.2%

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

      8. metadata-eval 98.2%

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

      9. sub-neg 98.2%

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

      10. distribute-neg-in 98.2%

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

      11. metadata-eval 98.2%

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

      12. add-sqr-sqrt 0.0%

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

      13. sqrt-unprod 0.7%

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

      14. sqr-neg 0.7%

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

      15. sqrt-unprod 0.8%

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

      16. add-sqr-sqrt 0.8%

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

      17. add-sqr-sqrt 0.0%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-3 + \color{blue}{\sqrt{-x} \cdot \sqrt{-x}}}} \]

      18. sqrt-unprod 83.5%

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

      19. sqr-neg 83.5%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-3 + \sqrt{\color{blue}{x \cdot x}}}} \]

      20. sqrt-unprod 98.1%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-3 + \color{blue}{\sqrt{x} \cdot \sqrt{x}}}} \]

      21. add-sqr-sqrt 98.2%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-3 + \color{blue}{x}}} \]

   9. Applied egg-rr 98.2%

      \[\leadsto \color{blue}{0 - \frac{x}{\frac{y \cdot -3}{-3 + x}}} \]
   10. Step-by-step derivation

       1. neg-sub0 98.2%

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

       2. associate-/r/ 98.3%

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

       3. *-rgt-identity 98.3%

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

       4. times-frac 98.4%

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

       5. metadata-eval 98.4%

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

       6. *-commutative 98.4%

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

       7. distribute-lft-neg-in 98.4%

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

       8. associate-*r/ 98.3%

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

       9. *-commutative 98.3%

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

       10. distribute-frac-neg 98.3%

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

       11. distribute-rgt-neg-in 98.3%

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

       12. metadata-eval 98.3%

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

       13. associate-/l* 98.5%

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

       14. +-commutative 98.5%

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

   11. Simplified 98.5%

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

   12. Taylor expanded in x around inf 98.3%

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

4. Final simplification 97.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.75:\\ \;\;\;\;x \cdot \frac{x}{y \cdot 3}\\ \mathbf{elif}\;x \leq 0.58:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(x \cdot \frac{0.3333333333333333}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 64.1% accurate, 0.7× speedup

Math

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

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -0.75)
   (* -1.3333333333333333 (/ x y))
   (if (<= x 5.0) (/ 1.0 y) (* (/ x y) 1.3333333333333333))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -0.75) {
		tmp = -1.3333333333333333 * (x / y);
	} else if (x <= 5.0) {
		tmp = 1.0 / y;
	} else {
		tmp = (x / y) * 1.3333333333333333;
	}
	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 if (x <= 5.0d0) then
        tmp = 1.0d0 / y
    else
        tmp = (x / y) * 1.3333333333333333d0
    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 if (x <= 5.0) {
		tmp = 1.0 / y;
	} else {
		tmp = (x / y) * 1.3333333333333333;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -0.75:
		tmp = -1.3333333333333333 * (x / y)
	elif x <= 5.0:
		tmp = 1.0 / y
	else:
		tmp = (x / y) * 1.3333333333333333
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -0.75)
		tmp = Float64(-1.3333333333333333 * Float64(x / y));
	elseif (x <= 5.0)
		tmp = Float64(1.0 / y);
	else
		tmp = Float64(Float64(x / y) * 1.3333333333333333);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -0.75)
		tmp = -1.3333333333333333 * (x / y);
	elseif (x <= 5.0)
		tmp = 1.0 / y;
	else
		tmp = (x / y) * 1.3333333333333333;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -0.75], N[(-1.3333333333333333 * N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.0], N[(1.0 / y), $MachinePrecision], N[(N[(x / y), $MachinePrecision] * 1.3333333333333333), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -0.75

   1. Initial program 88.6%

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

      1. associate-/l* 99.8%

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

      2. *-rgt-identity 99.8%

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

      3. remove-double-neg 99.8%

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

      4. distribute-lft-neg-out 99.8%

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

      5. neg-mul-1 99.8%

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

      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* 99.7%

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

      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 33.7%

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

   6. Taylor expanded in x around inf 33.7%

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

   if -0.75 < x < 5

   1. Initial program 99.7%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   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 99.5%

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

      7. *-rgt-identity 99.5%

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

      8. associate-/l* 99.5%

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

      9. metadata-eval 99.5%

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

      10. *-commutative 99.5%

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

      11. sub-neg 99.5%

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

      12. +-commutative 99.5%

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

      13. distribute-lft-in 99.5%

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

      14. neg-mul-1 99.5%

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

      15. remove-double-neg 99.5%

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

      16. metadata-eval 99.5%

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

      17. distribute-lft-neg-out 99.5%

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

      18. *-commutative 99.5%

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

      19. distribute-lft-neg-in 99.5%

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

      20. associate-/r* 99.3%

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

      21. metadata-eval 99.3%

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

      22. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in x around 0 97.9%

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

   if 5 < x

   1. Initial program 84.9%

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

      1. associate-/l* 99.5%

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

      2. *-rgt-identity 99.5%

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

      3. remove-double-neg 99.5%

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

      4. distribute-lft-neg-out 99.5%

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

      5. neg-mul-1 99.5%

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

      6. times-frac 99.5%

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

      7. *-rgt-identity 99.5%

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

      8. associate-/l* 99.5%

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

      9. metadata-eval 99.5%

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

      10. *-commutative 99.5%

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

      11. sub-neg 99.5%

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

      12. +-commutative 99.5%

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

      13. distribute-lft-in 99.5%

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

      14. neg-mul-1 99.5%

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

      15. remove-double-neg 99.5%

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

      16. metadata-eval 99.5%

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

      17. distribute-lft-neg-out 99.5%

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

      18. *-commutative 99.5%

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

      19. distribute-lft-neg-in 99.5%

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

      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 1.0%

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

   6. Taylor expanded in x around inf 1.0%

      \[\leadsto \color{blue}{-1.3333333333333333 \cdot \frac{x}{y}} \]
   7. Step-by-step derivation

      1. frac-2neg 1.0%

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

      2. associate-*r/ 1.0%

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

      3. add-sqr-sqrt 0.0%

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

      4. sqrt-unprod 34.8%

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

      5. sqr-neg 34.8%

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

      6. sqrt-unprod 27.8%

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

      7. add-sqr-sqrt 27.8%

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

      8. *-commutative 27.8%

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

   8. Applied egg-rr 27.8%

      \[\leadsto \color{blue}{\frac{x \cdot -1.3333333333333333}{-y}} \]
   9. Step-by-step derivation

      1. distribute-frac-neg2 27.8%

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

      2. distribute-frac-neg 27.8%

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

      3. distribute-rgt-neg-in 27.8%

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

      4. metadata-eval 27.8%

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

      5. associate-/l* 27.8%

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

   10. Simplified 27.8%

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

   11. Taylor expanded in x around 0 27.8%

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

4. Final simplification 61.5%

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

Alternative 12: 64.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.75:\\ \;\;\;\;-1.3333333333333333 \cdot \frac{x}{y}\\ \mathbf{elif}\;x \leq 0.34:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -0.75)
   (* -1.3333333333333333 (/ x y))
   (if (<= x 0.34) (/ 1.0 y) (/ x y))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -0.75) {
		tmp = -1.3333333333333333 * (x / y);
	} else if (x <= 0.34) {
		tmp = 1.0 / y;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-0.75d0)) then
        tmp = (-1.3333333333333333d0) * (x / y)
    else if (x <= 0.34d0) then
        tmp = 1.0d0 / y
    else
        tmp = x / 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 if (x <= 0.34) {
		tmp = 1.0 / y;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -0.75:
		tmp = -1.3333333333333333 * (x / y)
	elif x <= 0.34:
		tmp = 1.0 / y
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -0.75)
		tmp = Float64(-1.3333333333333333 * Float64(x / y));
	elseif (x <= 0.34)
		tmp = Float64(1.0 / y);
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -0.75)
		tmp = -1.3333333333333333 * (x / y);
	elseif (x <= 0.34)
		tmp = 1.0 / y;
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -0.75], N[(-1.3333333333333333 * N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 0.34], N[(1.0 / y), $MachinePrecision], N[(x / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -0.75

   1. Initial program 88.6%

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

      1. associate-/l* 99.8%

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

      2. *-rgt-identity 99.8%

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

      3. remove-double-neg 99.8%

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

      4. distribute-lft-neg-out 99.8%

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

      5. neg-mul-1 99.8%

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

      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* 99.7%

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

      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 33.7%

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

   6. Taylor expanded in x around inf 33.7%

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

   if -0.75 < x < 0.340000000000000024

   1. Initial program 99.7%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   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 99.5%

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

      7. *-rgt-identity 99.5%

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

      8. associate-/l* 99.5%

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

      9. metadata-eval 99.5%

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

      10. *-commutative 99.5%

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

      11. sub-neg 99.5%

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

      12. +-commutative 99.5%

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

      13. distribute-lft-in 99.5%

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

      14. neg-mul-1 99.5%

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

      15. remove-double-neg 99.5%

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

      16. metadata-eval 99.5%

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

      17. distribute-lft-neg-out 99.5%

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

      18. *-commutative 99.5%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(x + -3\right) \cdot \frac{1}{-\color{blue}{3 \cdot y}}\right) \]

      19. distribute-lft-neg-in 99.5%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(x + -3\right) \cdot \frac{1}{\color{blue}{\left(-3\right) \cdot y}}\right) \]

      20. associate-/r* 99.3%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(x + -3\right) \cdot \color{blue}{\frac{\frac{1}{-3}}{y}}\right) \]

      21. metadata-eval 99.3%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(x + -3\right) \cdot \frac{\frac{1}{\color{blue}{-3}}}{y}\right) \]

      22. metadata-eval 99.3%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(x + -3\right) \cdot \frac{\color{blue}{-0.3333333333333333}}{y}\right) \]

   3. Simplified 99.3%

      \[\leadsto \color{blue}{\left(1 - x\right) \cdot \left(\left(x + -3\right) \cdot \frac{-0.3333333333333333}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 97.9%

      \[\leadsto \color{blue}{\frac{1}{y}} \]

   if 0.340000000000000024 < x

   1. Initial program 84.9%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   2. Step-by-step derivation

      1. associate-/l* 99.5%

         \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{3 - x}{y \cdot 3}} \]

      2. *-commutative 99.5%

         \[\leadsto \left(1 - x\right) \cdot \frac{3 - x}{\color{blue}{3 \cdot y}} \]

   3. Simplified 99.5%

      \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{3 - x}{3 \cdot y}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 98.3%

      \[\leadsto \color{blue}{\left(-1 \cdot x\right)} \cdot \frac{3 - x}{3 \cdot y} \]
   6. Step-by-step derivation

      1. neg-mul-1 98.5%

         \[\leadsto \frac{\frac{\color{blue}{-x}}{y} \cdot \left(3 - x\right)}{3} \]

   7. Simplified 98.3%

      \[\leadsto \color{blue}{\left(-x\right)} \cdot \frac{3 - x}{3 \cdot y} \]
   8. Step-by-step derivation

      1. distribute-lft-neg-out 98.3%

         \[\leadsto \color{blue}{-x \cdot \frac{3 - x}{3 \cdot y}} \]

      2. neg-sub0 98.3%

         \[\leadsto \color{blue}{0 - x \cdot \frac{3 - x}{3 \cdot y}} \]

      3. clear-num 98.1%

         \[\leadsto 0 - x \cdot \color{blue}{\frac{1}{\frac{3 \cdot y}{3 - x}}} \]

      4. un-div-inv 98.2%

         \[\leadsto 0 - \color{blue}{\frac{x}{\frac{3 \cdot y}{3 - x}}} \]

      5. frac-2neg 98.2%

         \[\leadsto 0 - \frac{x}{\color{blue}{\frac{-3 \cdot y}{-\left(3 - x\right)}}} \]

      6. *-commutative 98.2%

         \[\leadsto 0 - \frac{x}{\frac{-\color{blue}{y \cdot 3}}{-\left(3 - x\right)}} \]

      7. distribute-rgt-neg-in 98.2%

         \[\leadsto 0 - \frac{x}{\frac{\color{blue}{y \cdot \left(-3\right)}}{-\left(3 - x\right)}} \]

      8. metadata-eval 98.2%

         \[\leadsto 0 - \frac{x}{\frac{y \cdot \color{blue}{-3}}{-\left(3 - x\right)}} \]

      9. sub-neg 98.2%

         \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-\color{blue}{\left(3 + \left(-x\right)\right)}}} \]

      10. distribute-neg-in 98.2%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{\color{blue}{\left(-3\right) + \left(-\left(-x\right)\right)}}} \]

      11. metadata-eval 98.2%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{\color{blue}{-3} + \left(-\left(-x\right)\right)}} \]

      12. add-sqr-sqrt 0.0%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-3 + \left(-\color{blue}{\sqrt{-x} \cdot \sqrt{-x}}\right)}} \]

      13. sqrt-unprod 0.7%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-3 + \left(-\color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}}\right)}} \]

      14. sqr-neg 0.7%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-3 + \left(-\sqrt{\color{blue}{x \cdot x}}\right)}} \]

      15. sqrt-unprod 0.8%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-3 + \left(-\color{blue}{\sqrt{x} \cdot \sqrt{x}}\right)}} \]

      16. add-sqr-sqrt 0.8%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-3 + \left(-\color{blue}{x}\right)}} \]

      17. add-sqr-sqrt 0.0%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-3 + \color{blue}{\sqrt{-x} \cdot \sqrt{-x}}}} \]

      18. sqrt-unprod 83.5%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-3 + \color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}}}} \]

      19. sqr-neg 83.5%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-3 + \sqrt{\color{blue}{x \cdot x}}}} \]

      20. sqrt-unprod 98.1%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-3 + \color{blue}{\sqrt{x} \cdot \sqrt{x}}}} \]

      21. add-sqr-sqrt 98.2%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-3 + \color{blue}{x}}} \]

   9. Applied egg-rr 98.2%

      \[\leadsto \color{blue}{0 - \frac{x}{\frac{y \cdot -3}{-3 + x}}} \]
   10. Step-by-step derivation

       1. neg-sub0 98.2%

          \[\leadsto \color{blue}{-\frac{x}{\frac{y \cdot -3}{-3 + x}}} \]

       2. associate-/r/ 98.3%

          \[\leadsto -\color{blue}{\frac{x}{y \cdot -3} \cdot \left(-3 + x\right)} \]

       3. *-rgt-identity 98.3%

          \[\leadsto -\frac{\color{blue}{x \cdot 1}}{y \cdot -3} \cdot \left(-3 + x\right) \]

       4. times-frac 98.4%

          \[\leadsto -\color{blue}{\left(\frac{x}{y} \cdot \frac{1}{-3}\right)} \cdot \left(-3 + x\right) \]

       5. metadata-eval 98.4%

          \[\leadsto -\left(\frac{x}{y} \cdot \color{blue}{-0.3333333333333333}\right) \cdot \left(-3 + x\right) \]

       6. *-commutative 98.4%

          \[\leadsto -\color{blue}{\left(-0.3333333333333333 \cdot \frac{x}{y}\right)} \cdot \left(-3 + x\right) \]

       7. distribute-lft-neg-in 98.4%

          \[\leadsto \color{blue}{\left(--0.3333333333333333 \cdot \frac{x}{y}\right) \cdot \left(-3 + x\right)} \]

       8. associate-*r/ 98.3%

          \[\leadsto \left(-\color{blue}{\frac{-0.3333333333333333 \cdot x}{y}}\right) \cdot \left(-3 + x\right) \]

       9. *-commutative 98.3%

          \[\leadsto \left(-\frac{\color{blue}{x \cdot -0.3333333333333333}}{y}\right) \cdot \left(-3 + x\right) \]

       10. distribute-frac-neg 98.3%

           \[\leadsto \color{blue}{\frac{-x \cdot -0.3333333333333333}{y}} \cdot \left(-3 + x\right) \]

       11. distribute-rgt-neg-in 98.3%

           \[\leadsto \frac{\color{blue}{x \cdot \left(--0.3333333333333333\right)}}{y} \cdot \left(-3 + x\right) \]

       12. metadata-eval 98.3%

           \[\leadsto \frac{x \cdot \color{blue}{0.3333333333333333}}{y} \cdot \left(-3 + x\right) \]

       13. associate-/l* 98.5%

           \[\leadsto \color{blue}{\left(x \cdot \frac{0.3333333333333333}{y}\right)} \cdot \left(-3 + x\right) \]

       14. +-commutative 98.5%

           \[\leadsto \left(x \cdot \frac{0.3333333333333333}{y}\right) \cdot \color{blue}{\left(x + -3\right)} \]

   11. Simplified 98.5%

       \[\leadsto \color{blue}{\left(x \cdot \frac{0.3333333333333333}{y}\right) \cdot \left(x + -3\right)} \]

   12. Taylor expanded in x around 0 1.0%

       \[\leadsto \color{blue}{-1 \cdot \frac{x}{y}} \]
   13. Step-by-step derivation

       1. mul-1-neg 1.0%

          \[\leadsto \color{blue}{-\frac{x}{y}} \]

       2. distribute-frac-neg2 1.0%

          \[\leadsto \color{blue}{\frac{x}{-y}} \]

   14. Simplified 1.0%

       \[\leadsto \color{blue}{\frac{x}{-y}} \]
   15. Step-by-step derivation

       1. add-sqr-sqrt 0.4%

          \[\leadsto \frac{x}{\color{blue}{\sqrt{-y} \cdot \sqrt{-y}}} \]

       2. sqrt-unprod 25.5%

          \[\leadsto \frac{x}{\color{blue}{\sqrt{\left(-y\right) \cdot \left(-y\right)}}} \]

       3. sqr-neg 25.5%

          \[\leadsto \frac{x}{\sqrt{\color{blue}{y \cdot y}}} \]

       4. sqrt-unprod 20.6%

          \[\leadsto \frac{x}{\color{blue}{\sqrt{y} \cdot \sqrt{y}}} \]

       5. add-sqr-sqrt 27.8%

          \[\leadsto \frac{x}{\color{blue}{y}} \]

       6. div-inv 27.8%

          \[\leadsto \color{blue}{x \cdot \frac{1}{y}} \]

   16. Applied egg-rr 27.8%

       \[\leadsto \color{blue}{x \cdot \frac{1}{y}} \]
   17. Step-by-step derivation

       1. associate-*r/ 27.8%

          \[\leadsto \color{blue}{\frac{x \cdot 1}{y}} \]

       2. *-rgt-identity 27.8%

          \[\leadsto \frac{\color{blue}{x}}{y} \]

   18. Simplified 27.8%

       \[\leadsto \color{blue}{\frac{x}{y}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 13: 64.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;\frac{x}{-y}\\ \mathbf{elif}\;x \leq 0.34:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.0) (/ x (- y)) (if (<= x 0.34) (/ 1.0 y) (/ x y))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.0) {
		tmp = x / -y;
	} else if (x <= 0.34) {
		tmp = 1.0 / y;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-1.0d0)) then
        tmp = x / -y
    else if (x <= 0.34d0) then
        tmp = 1.0d0 / y
    else
        tmp = x / 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 if (x <= 0.34) {
		tmp = 1.0 / y;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.0:
		tmp = x / -y
	elif x <= 0.34:
		tmp = 1.0 / y
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.0)
		tmp = Float64(x / Float64(-y));
	elseif (x <= 0.34)
		tmp = Float64(1.0 / y);
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.0)
		tmp = x / -y;
	elseif (x <= 0.34)
		tmp = 1.0 / y;
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.0], N[(x / (-y)), $MachinePrecision], If[LessEqual[x, 0.34], N[(1.0 / y), $MachinePrecision], N[(x / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1

   1. Initial program 88.6%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   2. Step-by-step derivation

      1. associate-/l* 99.8%

         \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{3 - x}{y \cdot 3}} \]

      2. *-commutative 99.8%

         \[\leadsto \left(1 - x\right) \cdot \frac{3 - x}{\color{blue}{3 \cdot y}} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{3 - x}{3 \cdot y}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 97.7%

      \[\leadsto \color{blue}{\left(-1 \cdot x\right)} \cdot \frac{3 - x}{3 \cdot y} \]
   6. Step-by-step derivation

      1. neg-mul-1 97.7%

         \[\leadsto \frac{\frac{\color{blue}{-x}}{y} \cdot \left(3 - x\right)}{3} \]

   7. Simplified 97.7%

      \[\leadsto \color{blue}{\left(-x\right)} \cdot \frac{3 - x}{3 \cdot y} \]
   8. Step-by-step derivation

      1. distribute-lft-neg-out 97.7%

         \[\leadsto \color{blue}{-x \cdot \frac{3 - x}{3 \cdot y}} \]

      2. neg-sub0 97.7%

         \[\leadsto \color{blue}{0 - x \cdot \frac{3 - x}{3 \cdot y}} \]

      3. clear-num 97.6%

         \[\leadsto 0 - x \cdot \color{blue}{\frac{1}{\frac{3 \cdot y}{3 - x}}} \]

      4. un-div-inv 97.7%

         \[\leadsto 0 - \color{blue}{\frac{x}{\frac{3 \cdot y}{3 - x}}} \]

      5. frac-2neg 97.7%

         \[\leadsto 0 - \frac{x}{\color{blue}{\frac{-3 \cdot y}{-\left(3 - x\right)}}} \]

      6. *-commutative 97.7%

         \[\leadsto 0 - \frac{x}{\frac{-\color{blue}{y \cdot 3}}{-\left(3 - x\right)}} \]

      7. distribute-rgt-neg-in 97.7%

         \[\leadsto 0 - \frac{x}{\frac{\color{blue}{y \cdot \left(-3\right)}}{-\left(3 - x\right)}} \]

      8. metadata-eval 97.7%

         \[\leadsto 0 - \frac{x}{\frac{y \cdot \color{blue}{-3}}{-\left(3 - x\right)}} \]

      9. sub-neg 97.7%

         \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-\color{blue}{\left(3 + \left(-x\right)\right)}}} \]

      10. distribute-neg-in 97.7%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{\color{blue}{\left(-3\right) + \left(-\left(-x\right)\right)}}} \]

      11. metadata-eval 97.7%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{\color{blue}{-3} + \left(-\left(-x\right)\right)}} \]

      12. add-sqr-sqrt 97.5%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-3 + \left(-\color{blue}{\sqrt{-x} \cdot \sqrt{-x}}\right)}} \]

      13. sqrt-unprod 86.6%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-3 + \left(-\color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}}\right)}} \]

      14. sqr-neg 86.6%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-3 + \left(-\sqrt{\color{blue}{x \cdot x}}\right)}} \]

      15. sqrt-unprod 0.0%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-3 + \left(-\color{blue}{\sqrt{x} \cdot \sqrt{x}}\right)}} \]

      16. add-sqr-sqrt 0.6%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-3 + \left(-\color{blue}{x}\right)}} \]

      17. add-sqr-sqrt 0.6%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-3 + \color{blue}{\sqrt{-x} \cdot \sqrt{-x}}}} \]

      18. sqrt-unprod 0.6%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-3 + \color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}}}} \]

      19. sqr-neg 0.6%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-3 + \sqrt{\color{blue}{x \cdot x}}}} \]

      20. sqrt-unprod 0.0%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-3 + \color{blue}{\sqrt{x} \cdot \sqrt{x}}}} \]

      21. add-sqr-sqrt 97.7%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-3 + \color{blue}{x}}} \]

   9. Applied egg-rr 97.7%

      \[\leadsto \color{blue}{0 - \frac{x}{\frac{y \cdot -3}{-3 + x}}} \]
   10. Step-by-step derivation

       1. neg-sub0 97.7%

          \[\leadsto \color{blue}{-\frac{x}{\frac{y \cdot -3}{-3 + x}}} \]

       2. associate-/r/ 97.7%

          \[\leadsto -\color{blue}{\frac{x}{y \cdot -3} \cdot \left(-3 + x\right)} \]

       3. *-rgt-identity 97.7%

          \[\leadsto -\frac{\color{blue}{x \cdot 1}}{y \cdot -3} \cdot \left(-3 + x\right) \]

       4. times-frac 97.6%

          \[\leadsto -\color{blue}{\left(\frac{x}{y} \cdot \frac{1}{-3}\right)} \cdot \left(-3 + x\right) \]

       5. metadata-eval 97.6%

          \[\leadsto -\left(\frac{x}{y} \cdot \color{blue}{-0.3333333333333333}\right) \cdot \left(-3 + x\right) \]

       6. *-commutative 97.6%

          \[\leadsto -\color{blue}{\left(-0.3333333333333333 \cdot \frac{x}{y}\right)} \cdot \left(-3 + x\right) \]

       7. distribute-lft-neg-in 97.6%

          \[\leadsto \color{blue}{\left(--0.3333333333333333 \cdot \frac{x}{y}\right) \cdot \left(-3 + x\right)} \]

       8. associate-*r/ 97.6%

          \[\leadsto \left(-\color{blue}{\frac{-0.3333333333333333 \cdot x}{y}}\right) \cdot \left(-3 + x\right) \]

       9. *-commutative 97.6%

          \[\leadsto \left(-\frac{\color{blue}{x \cdot -0.3333333333333333}}{y}\right) \cdot \left(-3 + x\right) \]

       10. distribute-frac-neg 97.6%

           \[\leadsto \color{blue}{\frac{-x \cdot -0.3333333333333333}{y}} \cdot \left(-3 + x\right) \]

       11. distribute-rgt-neg-in 97.6%

           \[\leadsto \frac{\color{blue}{x \cdot \left(--0.3333333333333333\right)}}{y} \cdot \left(-3 + x\right) \]

       12. metadata-eval 97.6%

           \[\leadsto \frac{x \cdot \color{blue}{0.3333333333333333}}{y} \cdot \left(-3 + x\right) \]

       13. associate-/l* 97.6%

           \[\leadsto \color{blue}{\left(x \cdot \frac{0.3333333333333333}{y}\right)} \cdot \left(-3 + x\right) \]

       14. +-commutative 97.6%

           \[\leadsto \left(x \cdot \frac{0.3333333333333333}{y}\right) \cdot \color{blue}{\left(x + -3\right)} \]

   11. Simplified 97.6%

       \[\leadsto \color{blue}{\left(x \cdot \frac{0.3333333333333333}{y}\right) \cdot \left(x + -3\right)} \]

   12. Taylor expanded in x around 0 33.7%

       \[\leadsto \color{blue}{-1 \cdot \frac{x}{y}} \]
   13. Step-by-step derivation

       1. mul-1-neg 33.7%

          \[\leadsto \color{blue}{-\frac{x}{y}} \]

       2. distribute-frac-neg2 33.7%

          \[\leadsto \color{blue}{\frac{x}{-y}} \]

   14. Simplified 33.7%

       \[\leadsto \color{blue}{\frac{x}{-y}} \]

   if -1 < x < 0.340000000000000024

   1. Initial program 99.7%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   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 99.5%

         \[\leadsto \left(1 - x\right) \cdot \color{blue}{\left(\frac{3 - x}{-1} \cdot \frac{1}{\left(-y\right) \cdot 3}\right)} \]

      7. *-rgt-identity 99.5%

         \[\leadsto \left(1 - x\right) \cdot \left(\frac{\color{blue}{\left(3 - x\right) \cdot 1}}{-1} \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      8. associate-/l* 99.5%

         \[\leadsto \left(1 - x\right) \cdot \left(\color{blue}{\left(\left(3 - x\right) \cdot \frac{1}{-1}\right)} \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      9. metadata-eval 99.5%

         \[\leadsto \left(1 - x\right) \cdot \left(\left(\left(3 - x\right) \cdot \color{blue}{-1}\right) \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      10. *-commutative 99.5%

          \[\leadsto \left(1 - x\right) \cdot \left(\color{blue}{\left(-1 \cdot \left(3 - x\right)\right)} \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      11. sub-neg 99.5%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(-1 \cdot \color{blue}{\left(3 + \left(-x\right)\right)}\right) \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      12. +-commutative 99.5%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(-1 \cdot \color{blue}{\left(\left(-x\right) + 3\right)}\right) \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      13. distribute-lft-in 99.5%

          \[\leadsto \left(1 - x\right) \cdot \left(\color{blue}{\left(-1 \cdot \left(-x\right) + -1 \cdot 3\right)} \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      14. neg-mul-1 99.5%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(\color{blue}{\left(-\left(-x\right)\right)} + -1 \cdot 3\right) \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      15. remove-double-neg 99.5%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(\color{blue}{x} + -1 \cdot 3\right) \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      16. metadata-eval 99.5%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(x + \color{blue}{-3}\right) \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      17. distribute-lft-neg-out 99.5%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(x + -3\right) \cdot \frac{1}{\color{blue}{-y \cdot 3}}\right) \]

      18. *-commutative 99.5%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(x + -3\right) \cdot \frac{1}{-\color{blue}{3 \cdot y}}\right) \]

      19. distribute-lft-neg-in 99.5%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(x + -3\right) \cdot \frac{1}{\color{blue}{\left(-3\right) \cdot y}}\right) \]

      20. associate-/r* 99.3%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(x + -3\right) \cdot \color{blue}{\frac{\frac{1}{-3}}{y}}\right) \]

      21. metadata-eval 99.3%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(x + -3\right) \cdot \frac{\frac{1}{\color{blue}{-3}}}{y}\right) \]

      22. metadata-eval 99.3%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(x + -3\right) \cdot \frac{\color{blue}{-0.3333333333333333}}{y}\right) \]

   3. Simplified 99.3%

      \[\leadsto \color{blue}{\left(1 - x\right) \cdot \left(\left(x + -3\right) \cdot \frac{-0.3333333333333333}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 97.9%

      \[\leadsto \color{blue}{\frac{1}{y}} \]

   if 0.340000000000000024 < x

   1. Initial program 84.9%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   2. Step-by-step derivation

      1. associate-/l* 99.5%

         \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{3 - x}{y \cdot 3}} \]

      2. *-commutative 99.5%

         \[\leadsto \left(1 - x\right) \cdot \frac{3 - x}{\color{blue}{3 \cdot y}} \]

   3. Simplified 99.5%

      \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{3 - x}{3 \cdot y}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 98.3%

      \[\leadsto \color{blue}{\left(-1 \cdot x\right)} \cdot \frac{3 - x}{3 \cdot y} \]
   6. Step-by-step derivation

      1. neg-mul-1 98.5%

         \[\leadsto \frac{\frac{\color{blue}{-x}}{y} \cdot \left(3 - x\right)}{3} \]

   7. Simplified 98.3%

      \[\leadsto \color{blue}{\left(-x\right)} \cdot \frac{3 - x}{3 \cdot y} \]
   8. Step-by-step derivation

      1. distribute-lft-neg-out 98.3%

         \[\leadsto \color{blue}{-x \cdot \frac{3 - x}{3 \cdot y}} \]

      2. neg-sub0 98.3%

         \[\leadsto \color{blue}{0 - x \cdot \frac{3 - x}{3 \cdot y}} \]

      3. clear-num 98.1%

         \[\leadsto 0 - x \cdot \color{blue}{\frac{1}{\frac{3 \cdot y}{3 - x}}} \]

      4. un-div-inv 98.2%

         \[\leadsto 0 - \color{blue}{\frac{x}{\frac{3 \cdot y}{3 - x}}} \]

      5. frac-2neg 98.2%

         \[\leadsto 0 - \frac{x}{\color{blue}{\frac{-3 \cdot y}{-\left(3 - x\right)}}} \]

      6. *-commutative 98.2%

         \[\leadsto 0 - \frac{x}{\frac{-\color{blue}{y \cdot 3}}{-\left(3 - x\right)}} \]

      7. distribute-rgt-neg-in 98.2%

         \[\leadsto 0 - \frac{x}{\frac{\color{blue}{y \cdot \left(-3\right)}}{-\left(3 - x\right)}} \]

      8. metadata-eval 98.2%

         \[\leadsto 0 - \frac{x}{\frac{y \cdot \color{blue}{-3}}{-\left(3 - x\right)}} \]

      9. sub-neg 98.2%

         \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-\color{blue}{\left(3 + \left(-x\right)\right)}}} \]

      10. distribute-neg-in 98.2%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{\color{blue}{\left(-3\right) + \left(-\left(-x\right)\right)}}} \]

      11. metadata-eval 98.2%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{\color{blue}{-3} + \left(-\left(-x\right)\right)}} \]

      12. add-sqr-sqrt 0.0%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-3 + \left(-\color{blue}{\sqrt{-x} \cdot \sqrt{-x}}\right)}} \]

      13. sqrt-unprod 0.7%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-3 + \left(-\color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}}\right)}} \]

      14. sqr-neg 0.7%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-3 + \left(-\sqrt{\color{blue}{x \cdot x}}\right)}} \]

      15. sqrt-unprod 0.8%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-3 + \left(-\color{blue}{\sqrt{x} \cdot \sqrt{x}}\right)}} \]

      16. add-sqr-sqrt 0.8%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-3 + \left(-\color{blue}{x}\right)}} \]

      17. add-sqr-sqrt 0.0%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-3 + \color{blue}{\sqrt{-x} \cdot \sqrt{-x}}}} \]

      18. sqrt-unprod 83.5%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-3 + \color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}}}} \]

      19. sqr-neg 83.5%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-3 + \sqrt{\color{blue}{x \cdot x}}}} \]

      20. sqrt-unprod 98.1%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-3 + \color{blue}{\sqrt{x} \cdot \sqrt{x}}}} \]

      21. add-sqr-sqrt 98.2%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-3 + \color{blue}{x}}} \]

   9. Applied egg-rr 98.2%

      \[\leadsto \color{blue}{0 - \frac{x}{\frac{y \cdot -3}{-3 + x}}} \]
   10. Step-by-step derivation

       1. neg-sub0 98.2%

          \[\leadsto \color{blue}{-\frac{x}{\frac{y \cdot -3}{-3 + x}}} \]

       2. associate-/r/ 98.3%

          \[\leadsto -\color{blue}{\frac{x}{y \cdot -3} \cdot \left(-3 + x\right)} \]

       3. *-rgt-identity 98.3%

          \[\leadsto -\frac{\color{blue}{x \cdot 1}}{y \cdot -3} \cdot \left(-3 + x\right) \]

       4. times-frac 98.4%

          \[\leadsto -\color{blue}{\left(\frac{x}{y} \cdot \frac{1}{-3}\right)} \cdot \left(-3 + x\right) \]

       5. metadata-eval 98.4%

          \[\leadsto -\left(\frac{x}{y} \cdot \color{blue}{-0.3333333333333333}\right) \cdot \left(-3 + x\right) \]

       6. *-commutative 98.4%

          \[\leadsto -\color{blue}{\left(-0.3333333333333333 \cdot \frac{x}{y}\right)} \cdot \left(-3 + x\right) \]

       7. distribute-lft-neg-in 98.4%

          \[\leadsto \color{blue}{\left(--0.3333333333333333 \cdot \frac{x}{y}\right) \cdot \left(-3 + x\right)} \]

       8. associate-*r/ 98.3%

          \[\leadsto \left(-\color{blue}{\frac{-0.3333333333333333 \cdot x}{y}}\right) \cdot \left(-3 + x\right) \]

       9. *-commutative 98.3%

          \[\leadsto \left(-\frac{\color{blue}{x \cdot -0.3333333333333333}}{y}\right) \cdot \left(-3 + x\right) \]

       10. distribute-frac-neg 98.3%

           \[\leadsto \color{blue}{\frac{-x \cdot -0.3333333333333333}{y}} \cdot \left(-3 + x\right) \]

       11. distribute-rgt-neg-in 98.3%

           \[\leadsto \frac{\color{blue}{x \cdot \left(--0.3333333333333333\right)}}{y} \cdot \left(-3 + x\right) \]

       12. metadata-eval 98.3%

           \[\leadsto \frac{x \cdot \color{blue}{0.3333333333333333}}{y} \cdot \left(-3 + x\right) \]

       13. associate-/l* 98.5%

           \[\leadsto \color{blue}{\left(x \cdot \frac{0.3333333333333333}{y}\right)} \cdot \left(-3 + x\right) \]

       14. +-commutative 98.5%

           \[\leadsto \left(x \cdot \frac{0.3333333333333333}{y}\right) \cdot \color{blue}{\left(x + -3\right)} \]

   11. Simplified 98.5%

       \[\leadsto \color{blue}{\left(x \cdot \frac{0.3333333333333333}{y}\right) \cdot \left(x + -3\right)} \]

   12. Taylor expanded in x around 0 1.0%

       \[\leadsto \color{blue}{-1 \cdot \frac{x}{y}} \]
   13. Step-by-step derivation

       1. mul-1-neg 1.0%

          \[\leadsto \color{blue}{-\frac{x}{y}} \]

       2. distribute-frac-neg2 1.0%

          \[\leadsto \color{blue}{\frac{x}{-y}} \]

   14. Simplified 1.0%

       \[\leadsto \color{blue}{\frac{x}{-y}} \]
   15. Step-by-step derivation

       1. add-sqr-sqrt 0.4%

          \[\leadsto \frac{x}{\color{blue}{\sqrt{-y} \cdot \sqrt{-y}}} \]

       2. sqrt-unprod 25.5%

          \[\leadsto \frac{x}{\color{blue}{\sqrt{\left(-y\right) \cdot \left(-y\right)}}} \]

       3. sqr-neg 25.5%

          \[\leadsto \frac{x}{\sqrt{\color{blue}{y \cdot y}}} \]

       4. sqrt-unprod 20.6%

          \[\leadsto \frac{x}{\color{blue}{\sqrt{y} \cdot \sqrt{y}}} \]

       5. add-sqr-sqrt 27.8%

          \[\leadsto \frac{x}{\color{blue}{y}} \]

       6. div-inv 27.8%

          \[\leadsto \color{blue}{x \cdot \frac{1}{y}} \]

   16. Applied egg-rr 27.8%

       \[\leadsto \color{blue}{x \cdot \frac{1}{y}} \]
   17. Step-by-step derivation

       1. associate-*r/ 27.8%

          \[\leadsto \color{blue}{\frac{x \cdot 1}{y}} \]

       2. *-rgt-identity 27.8%

          \[\leadsto \frac{\color{blue}{x}}{y} \]

   18. Simplified 27.8%

       \[\leadsto \color{blue}{\frac{x}{y}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 14: 99.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(1 - x\right) \cdot \frac{3 - x}{y \cdot 3} \end{array} \]

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(1.0 - x) * Float64(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[(1.0 - x), $MachinePrecision] * N[(N[(3.0 - x), $MachinePrecision] / N[(y * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 92.8%

   \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
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%

   \[\leadsto \left(1 - x\right) \cdot \frac{3 - x}{y \cdot 3} \]
6. Add Preprocessing

Alternative 15: 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 92.8%

   \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
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* 99.5%

       \[\leadsto \left(1 - x\right) \cdot \left(\left(x + -3\right) \cdot \color{blue}{\frac{\frac{1}{-3}}{y}}\right) \]

   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. Add Preprocessing

Alternative 16: 57.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 0.34:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= x 0.34) (/ 1.0 y) (/ x y)))

C

double code(double x, double y) {
	double tmp;
	if (x <= 0.34) {
		tmp = 1.0 / y;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= 0.34d0) then
        tmp = 1.0d0 / y
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 0.34) {
		tmp = 1.0 / y;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 0.34:
		tmp = 1.0 / y
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 0.34)
		tmp = Float64(1.0 / y);
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 0.34)
		tmp = 1.0 / y;
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 0.34], N[(1.0 / y), $MachinePrecision], N[(x / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 0.340000000000000024

   1. Initial program 95.1%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   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* 99.5%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(x + -3\right) \cdot \color{blue}{\frac{\frac{1}{-3}}{y}}\right) \]

      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 59.1%

      \[\leadsto \color{blue}{\frac{1}{y}} \]

   if 0.340000000000000024 < x

   1. Initial program 84.9%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   2. Step-by-step derivation

      1. associate-/l* 99.5%

         \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{3 - x}{y \cdot 3}} \]

      2. *-commutative 99.5%

         \[\leadsto \left(1 - x\right) \cdot \frac{3 - x}{\color{blue}{3 \cdot y}} \]

   3. Simplified 99.5%

      \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{3 - x}{3 \cdot y}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 98.3%

      \[\leadsto \color{blue}{\left(-1 \cdot x\right)} \cdot \frac{3 - x}{3 \cdot y} \]
   6. Step-by-step derivation

      1. neg-mul-1 98.5%

         \[\leadsto \frac{\frac{\color{blue}{-x}}{y} \cdot \left(3 - x\right)}{3} \]

   7. Simplified 98.3%

      \[\leadsto \color{blue}{\left(-x\right)} \cdot \frac{3 - x}{3 \cdot y} \]
   8. Step-by-step derivation

      1. distribute-lft-neg-out 98.3%

         \[\leadsto \color{blue}{-x \cdot \frac{3 - x}{3 \cdot y}} \]

      2. neg-sub0 98.3%

         \[\leadsto \color{blue}{0 - x \cdot \frac{3 - x}{3 \cdot y}} \]

      3. clear-num 98.1%

         \[\leadsto 0 - x \cdot \color{blue}{\frac{1}{\frac{3 \cdot y}{3 - x}}} \]

      4. un-div-inv 98.2%

         \[\leadsto 0 - \color{blue}{\frac{x}{\frac{3 \cdot y}{3 - x}}} \]

      5. frac-2neg 98.2%

         \[\leadsto 0 - \frac{x}{\color{blue}{\frac{-3 \cdot y}{-\left(3 - x\right)}}} \]

      6. *-commutative 98.2%

         \[\leadsto 0 - \frac{x}{\frac{-\color{blue}{y \cdot 3}}{-\left(3 - x\right)}} \]

      7. distribute-rgt-neg-in 98.2%

         \[\leadsto 0 - \frac{x}{\frac{\color{blue}{y \cdot \left(-3\right)}}{-\left(3 - x\right)}} \]

      8. metadata-eval 98.2%

         \[\leadsto 0 - \frac{x}{\frac{y \cdot \color{blue}{-3}}{-\left(3 - x\right)}} \]

      9. sub-neg 98.2%

         \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-\color{blue}{\left(3 + \left(-x\right)\right)}}} \]

      10. distribute-neg-in 98.2%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{\color{blue}{\left(-3\right) + \left(-\left(-x\right)\right)}}} \]

      11. metadata-eval 98.2%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{\color{blue}{-3} + \left(-\left(-x\right)\right)}} \]

      12. add-sqr-sqrt 0.0%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-3 + \left(-\color{blue}{\sqrt{-x} \cdot \sqrt{-x}}\right)}} \]

      13. sqrt-unprod 0.7%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-3 + \left(-\color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}}\right)}} \]

      14. sqr-neg 0.7%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-3 + \left(-\sqrt{\color{blue}{x \cdot x}}\right)}} \]

      15. sqrt-unprod 0.8%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-3 + \left(-\color{blue}{\sqrt{x} \cdot \sqrt{x}}\right)}} \]

      16. add-sqr-sqrt 0.8%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-3 + \left(-\color{blue}{x}\right)}} \]

      17. add-sqr-sqrt 0.0%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-3 + \color{blue}{\sqrt{-x} \cdot \sqrt{-x}}}} \]

      18. sqrt-unprod 83.5%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-3 + \color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}}}} \]

      19. sqr-neg 83.5%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-3 + \sqrt{\color{blue}{x \cdot x}}}} \]

      20. sqrt-unprod 98.1%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-3 + \color{blue}{\sqrt{x} \cdot \sqrt{x}}}} \]

      21. add-sqr-sqrt 98.2%

          \[\leadsto 0 - \frac{x}{\frac{y \cdot -3}{-3 + \color{blue}{x}}} \]

   9. Applied egg-rr 98.2%

      \[\leadsto \color{blue}{0 - \frac{x}{\frac{y \cdot -3}{-3 + x}}} \]
   10. Step-by-step derivation

       1. neg-sub0 98.2%

          \[\leadsto \color{blue}{-\frac{x}{\frac{y \cdot -3}{-3 + x}}} \]

       2. associate-/r/ 98.3%

          \[\leadsto -\color{blue}{\frac{x}{y \cdot -3} \cdot \left(-3 + x\right)} \]

       3. *-rgt-identity 98.3%

          \[\leadsto -\frac{\color{blue}{x \cdot 1}}{y \cdot -3} \cdot \left(-3 + x\right) \]

       4. times-frac 98.4%

          \[\leadsto -\color{blue}{\left(\frac{x}{y} \cdot \frac{1}{-3}\right)} \cdot \left(-3 + x\right) \]

       5. metadata-eval 98.4%

          \[\leadsto -\left(\frac{x}{y} \cdot \color{blue}{-0.3333333333333333}\right) \cdot \left(-3 + x\right) \]

       6. *-commutative 98.4%

          \[\leadsto -\color{blue}{\left(-0.3333333333333333 \cdot \frac{x}{y}\right)} \cdot \left(-3 + x\right) \]

       7. distribute-lft-neg-in 98.4%

          \[\leadsto \color{blue}{\left(--0.3333333333333333 \cdot \frac{x}{y}\right) \cdot \left(-3 + x\right)} \]

       8. associate-*r/ 98.3%

          \[\leadsto \left(-\color{blue}{\frac{-0.3333333333333333 \cdot x}{y}}\right) \cdot \left(-3 + x\right) \]

       9. *-commutative 98.3%

          \[\leadsto \left(-\frac{\color{blue}{x \cdot -0.3333333333333333}}{y}\right) \cdot \left(-3 + x\right) \]

       10. distribute-frac-neg 98.3%

           \[\leadsto \color{blue}{\frac{-x \cdot -0.3333333333333333}{y}} \cdot \left(-3 + x\right) \]

       11. distribute-rgt-neg-in 98.3%

           \[\leadsto \frac{\color{blue}{x \cdot \left(--0.3333333333333333\right)}}{y} \cdot \left(-3 + x\right) \]

       12. metadata-eval 98.3%

           \[\leadsto \frac{x \cdot \color{blue}{0.3333333333333333}}{y} \cdot \left(-3 + x\right) \]

       13. associate-/l* 98.5%

           \[\leadsto \color{blue}{\left(x \cdot \frac{0.3333333333333333}{y}\right)} \cdot \left(-3 + x\right) \]

       14. +-commutative 98.5%

           \[\leadsto \left(x \cdot \frac{0.3333333333333333}{y}\right) \cdot \color{blue}{\left(x + -3\right)} \]

   11. Simplified 98.5%

       \[\leadsto \color{blue}{\left(x \cdot \frac{0.3333333333333333}{y}\right) \cdot \left(x + -3\right)} \]

   12. Taylor expanded in x around 0 1.0%

       \[\leadsto \color{blue}{-1 \cdot \frac{x}{y}} \]
   13. Step-by-step derivation

       1. mul-1-neg 1.0%

          \[\leadsto \color{blue}{-\frac{x}{y}} \]

       2. distribute-frac-neg2 1.0%

          \[\leadsto \color{blue}{\frac{x}{-y}} \]

   14. Simplified 1.0%

       \[\leadsto \color{blue}{\frac{x}{-y}} \]
   15. Step-by-step derivation

       1. add-sqr-sqrt 0.4%

          \[\leadsto \frac{x}{\color{blue}{\sqrt{-y} \cdot \sqrt{-y}}} \]

       2. sqrt-unprod 25.5%

          \[\leadsto \frac{x}{\color{blue}{\sqrt{\left(-y\right) \cdot \left(-y\right)}}} \]

       3. sqr-neg 25.5%

          \[\leadsto \frac{x}{\sqrt{\color{blue}{y \cdot y}}} \]

       4. sqrt-unprod 20.6%

          \[\leadsto \frac{x}{\color{blue}{\sqrt{y} \cdot \sqrt{y}}} \]

       5. add-sqr-sqrt 27.8%

          \[\leadsto \frac{x}{\color{blue}{y}} \]

       6. div-inv 27.8%

          \[\leadsto \color{blue}{x \cdot \frac{1}{y}} \]

   16. Applied egg-rr 27.8%

       \[\leadsto \color{blue}{x \cdot \frac{1}{y}} \]
   17. Step-by-step derivation

       1. associate-*r/ 27.8%

          \[\leadsto \color{blue}{\frac{x \cdot 1}{y}} \]

       2. *-rgt-identity 27.8%

          \[\leadsto \frac{\color{blue}{x}}{y} \]

   18. Simplified 27.8%

       \[\leadsto \color{blue}{\frac{x}{y}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 17: 50.9% 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 92.8%

   \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
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* 99.5%

       \[\leadsto \left(1 - x\right) \cdot \left(\left(x + -3\right) \cdot \color{blue}{\frac{\frac{1}{-3}}{y}}\right) \]

   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 47.2%

   \[\leadsto \color{blue}{\frac{1}{y}} \]
6. Add Preprocessing

Developer Target 1: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{1 - x}{y} \cdot \frac{3 - x}{3} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* (/ (- 1.0 x) y) (/ (- 3.0 x) 3.0)))

C

double code(double x, double y) {
	return ((1.0 - x) / y) * ((3.0 - x) / 3.0);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = ((1.0d0 - x) / y) * ((3.0d0 - x) / 3.0d0)
end function

Java

public static double code(double x, double y) {
	return ((1.0 - x) / y) * ((3.0 - x) / 3.0);
}

Python

def code(x, y):
	return ((1.0 - x) / y) * ((3.0 - x) / 3.0)

Julia

function code(x, y)
	return Float64(Float64(Float64(1.0 - x) / y) * Float64(Float64(3.0 - x) / 3.0))
end

MATLAB

function tmp = code(x, y)
	tmp = ((1.0 - x) / y) * ((3.0 - x) / 3.0);
end

Wolfram

code[x_, y_] := N[(N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision] * N[(N[(3.0 - x), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024180 
(FPCore (x y)
  :name "Diagrams.TwoD.Arc:bezierFromSweepQ1 from diagrams-lib-1.3.0.3"
  :precision binary64

  :alt
  (! :herbie-platform default (* (/ (- 1 x) y) (/ (- 3 x) 3)))

  (/ (* (- 1.0 x) (- 3.0 x)) (* y 3.0)))