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

Percentage Accurate: 93.8% → 99.8%

Time: 9.2s

Alternatives: 15

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: 93.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.9%

   \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
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. clear-num 99.7%

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

   2. un-div-inv 99.7%

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

   3. *-commutative 99.7%

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

   4. associate-/l* 99.8%

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

6. Applied egg-rr 99.8%

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

Alternative 2: 98.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.5:\\ \;\;\;\;x \cdot \frac{\frac{x}{y}}{3}\\ \mathbf{elif}\;x \leq 1.3:\\ \;\;\;\;\frac{x}{y} \cdot -1.3333333333333333 + \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(x + -3\right) \cdot \frac{0.3333333333333333}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -4.5)
   (* x (/ (/ x y) 3.0))
   (if (<= x 1.3)
     (+ (* (/ x y) -1.3333333333333333) (/ 1.0 y))
     (* x (* (+ x -3.0) (/ 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 <= 1.3) {
		tmp = ((x / y) * -1.3333333333333333) + (1.0 / y);
	} else {
		tmp = x * ((x + -3.0) * (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 <= 1.3d0) then
        tmp = ((x / y) * (-1.3333333333333333d0)) + (1.0d0 / y)
    else
        tmp = x * ((x + (-3.0d0)) * (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 <= 1.3) {
		tmp = ((x / y) * -1.3333333333333333) + (1.0 / y);
	} else {
		tmp = x * ((x + -3.0) * (0.3333333333333333 / y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -4.5:
		tmp = x * ((x / y) / 3.0)
	elif x <= 1.3:
		tmp = ((x / y) * -1.3333333333333333) + (1.0 / y)
	else:
		tmp = x * ((x + -3.0) * (0.3333333333333333 / y))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -4.5)
		tmp = Float64(x * Float64(Float64(x / y) / 3.0));
	elseif (x <= 1.3)
		tmp = Float64(Float64(Float64(x / y) * -1.3333333333333333) + Float64(1.0 / y));
	else
		tmp = Float64(x * Float64(Float64(x + -3.0) * 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 <= 1.3)
		tmp = ((x / y) * -1.3333333333333333) + (1.0 / y);
	else
		tmp = x * ((x + -3.0) * (0.3333333333333333 / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -4.5], N[(x * N[(N[(x / y), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.3], N[(N[(N[(x / y), $MachinePrecision] * -1.3333333333333333), $MachinePrecision] + N[(1.0 / y), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(x + -3.0), $MachinePrecision] * N[(0.3333333333333333 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.5

   1. Initial program 94.3%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   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 99.8%

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

      7. *-rgt-identity 99.8%

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

      8. associate-/l* 99.8%

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

      9. metadata-eval 99.8%

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

      10. *-commutative 99.8%

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

      11. sub-neg 99.8%

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

      12. +-commutative 99.8%

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

      13. distribute-lft-in 99.8%

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

      14. neg-mul-1 99.8%

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

      15. remove-double-neg 99.8%

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

      16. metadata-eval 99.8%

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

      17. distribute-lft-neg-out 99.8%

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

      18. *-commutative 99.8%

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

      19. distribute-lft-neg-in 99.8%

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

      20. associate-/r* 99.8%

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

      21. metadata-eval 99.8%

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

      22. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 99.0%

      \[\leadsto \color{blue}{\left(-1 \cdot x\right)} \cdot \left(\left(x + -3\right) \cdot \frac{-0.3333333333333333}{y}\right) \]
   6. Step-by-step derivation

      1. neg-mul-1 99.0%

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

   7. Simplified 99.0%

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

   8. Taylor expanded in x around 0 99.0%

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

      1. sub-neg 99.0%

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

      2. associate-*r/ 99.0%

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

      3. associate-*l/ 99.0%

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

      4. metadata-eval 99.0%

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

      5. associate-/r* 99.0%

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

      6. *-commutative 99.0%

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

      7. metadata-eval 99.0%

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

      8. associate-*l/ 99.0%

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

      9. metadata-eval 99.0%

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

      10. associate-*r/ 99.0%

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

      11. distribute-rgt-neg-in 99.0%

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

      12. associate-*r/ 99.0%

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

      13. metadata-eval 99.0%

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

      14. metadata-eval 99.0%

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

      15. associate-/r* 99.0%

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

      16. *-commutative 99.0%

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

      17. metadata-eval 99.0%

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

      18. distribute-lft-in 99.0%

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

      19. *-commutative 99.0%

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

      20. associate-/r* 99.0%

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

      21. metadata-eval 99.0%

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

   10. Simplified 99.0%

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

   11. Taylor expanded in x around inf 99.0%

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

       1. *-commutative 99.0%

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

       2. clear-num 98.8%

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

       3. un-div-inv 98.9%

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

       4. add-sqr-sqrt 0.0%

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

       5. sqrt-unprod 0.5%

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

       6. sqr-neg 0.5%

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

       7. sqrt-unprod 0.5%

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

       8. add-sqr-sqrt 0.5%

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

       9. div-inv 0.5%

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

       10. metadata-eval 0.5%

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

       11. metadata-eval 0.5%

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

       12. distribute-rgt-neg-in 0.5%

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

       13. frac-2neg 0.5%

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

       14. associate-/r* 0.5%

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

       15. frac-2neg 0.5%

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

       16. distribute-frac-neg 0.5%

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

       17. add-sqr-sqrt 0.5%

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

       18. sqrt-unprod 0.5%

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

       19. sqr-neg 0.5%

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

       20. sqrt-unprod 0.0%

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

       21. add-sqr-sqrt 99.0%

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

       22. metadata-eval 99.0%

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

   13. Applied egg-rr 99.0%

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

   if -4.5 < x < 1.30000000000000004

   1. Initial program 99.5%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   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 99.4%

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

      7. *-rgt-identity 99.4%

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

      8. associate-/l* 99.4%

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

      9. metadata-eval 99.4%

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

      10. *-commutative 99.4%

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

      11. sub-neg 99.4%

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

      12. +-commutative 99.4%

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

      13. distribute-lft-in 99.4%

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

      14. neg-mul-1 99.4%

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

      15. remove-double-neg 99.4%

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

      16. metadata-eval 99.4%

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

      17. distribute-lft-neg-out 99.4%

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

      18. *-commutative 99.4%

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

      19. distribute-lft-neg-in 99.4%

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

      20. associate-/r* 99.4%

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

      21. metadata-eval 99.4%

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

      22. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x around 0 97.9%

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

   if 1.30000000000000004 < x

   1. Initial program 86.7%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   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 99.7%

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

      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 inf 95.9%

      \[\leadsto \color{blue}{\left(-1 \cdot x\right)} \cdot \left(\left(x + -3\right) \cdot \frac{-0.3333333333333333}{y}\right) \]
   6. Step-by-step derivation

      1. neg-mul-1 95.9%

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

   7. Simplified 95.9%

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

   8. Taylor expanded in x around 0 95.9%

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

      1. sub-neg 95.9%

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

      2. associate-*r/ 95.9%

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

      3. associate-*l/ 95.9%

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

      4. metadata-eval 95.9%

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

      5. associate-/r* 95.9%

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

      6. *-commutative 95.9%

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

      7. metadata-eval 95.9%

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

      8. associate-*l/ 95.9%

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

      9. metadata-eval 95.9%

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

      10. associate-*r/ 95.9%

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

      11. distribute-rgt-neg-in 95.9%

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

      12. associate-*r/ 95.9%

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

      13. metadata-eval 95.9%

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

      14. metadata-eval 95.9%

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

      15. associate-/r* 95.9%

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

      16. *-commutative 95.9%

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

      17. metadata-eval 95.9%

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

      18. distribute-lft-in 95.9%

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

      19. *-commutative 95.9%

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

      20. associate-/r* 95.9%

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

      21. metadata-eval 95.9%

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

   10. Simplified 95.9%

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

4. Final simplification 97.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.5:\\ \;\;\;\;x \cdot \frac{\frac{x}{y}}{3}\\ \mathbf{elif}\;x \leq 1.3:\\ \;\;\;\;\frac{x}{y} \cdot -1.3333333333333333 + \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(x + -3\right) \cdot \frac{0.3333333333333333}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.5:\\ \;\;\;\;x \cdot \frac{\frac{x}{y}}{3}\\ \mathbf{elif}\;x \leq 1.3:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(x + -3\right) \cdot \frac{0.3333333333333333}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -4.5)
   (* x (/ (/ x y) 3.0))
   (if (<= x 1.3)
     (/ (+ 1.0 (* x -1.3333333333333333)) y)
     (* x (* (+ x -3.0) (/ 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 <= 1.3) {
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	} else {
		tmp = x * ((x + -3.0) * (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 <= 1.3d0) then
        tmp = (1.0d0 + (x * (-1.3333333333333333d0))) / y
    else
        tmp = x * ((x + (-3.0d0)) * (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 <= 1.3) {
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	} else {
		tmp = x * ((x + -3.0) * (0.3333333333333333 / y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -4.5:
		tmp = x * ((x / y) / 3.0)
	elif x <= 1.3:
		tmp = (1.0 + (x * -1.3333333333333333)) / y
	else:
		tmp = x * ((x + -3.0) * (0.3333333333333333 / y))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -4.5)
		tmp = Float64(x * Float64(Float64(x / y) / 3.0));
	elseif (x <= 1.3)
		tmp = Float64(Float64(1.0 + Float64(x * -1.3333333333333333)) / y);
	else
		tmp = Float64(x * Float64(Float64(x + -3.0) * 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 <= 1.3)
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	else
		tmp = x * ((x + -3.0) * (0.3333333333333333 / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -4.5], N[(x * N[(N[(x / y), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.3], N[(N[(1.0 + N[(x * -1.3333333333333333), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x * N[(N[(x + -3.0), $MachinePrecision] * N[(0.3333333333333333 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.5

   1. Initial program 94.3%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   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 99.8%

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

      7. *-rgt-identity 99.8%

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

      8. associate-/l* 99.8%

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

      9. metadata-eval 99.8%

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

      10. *-commutative 99.8%

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

      11. sub-neg 99.8%

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

      12. +-commutative 99.8%

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

      13. distribute-lft-in 99.8%

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

      14. neg-mul-1 99.8%

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

      15. remove-double-neg 99.8%

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

      16. metadata-eval 99.8%

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

      17. distribute-lft-neg-out 99.8%

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

      18. *-commutative 99.8%

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

      19. distribute-lft-neg-in 99.8%

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

      20. associate-/r* 99.8%

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

      21. metadata-eval 99.8%

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

      22. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 99.0%

      \[\leadsto \color{blue}{\left(-1 \cdot x\right)} \cdot \left(\left(x + -3\right) \cdot \frac{-0.3333333333333333}{y}\right) \]
   6. Step-by-step derivation

      1. neg-mul-1 99.0%

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

   7. Simplified 99.0%

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

   8. Taylor expanded in x around 0 99.0%

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

      1. sub-neg 99.0%

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

      2. associate-*r/ 99.0%

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

      3. associate-*l/ 99.0%

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

      4. metadata-eval 99.0%

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

      5. associate-/r* 99.0%

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

      6. *-commutative 99.0%

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

      7. metadata-eval 99.0%

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

      8. associate-*l/ 99.0%

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

      9. metadata-eval 99.0%

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

      10. associate-*r/ 99.0%

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

      11. distribute-rgt-neg-in 99.0%

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

      12. associate-*r/ 99.0%

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

      13. metadata-eval 99.0%

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

      14. metadata-eval 99.0%

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

      15. associate-/r* 99.0%

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

      16. *-commutative 99.0%

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

      17. metadata-eval 99.0%

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

      18. distribute-lft-in 99.0%

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

      19. *-commutative 99.0%

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

      20. associate-/r* 99.0%

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

      21. metadata-eval 99.0%

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

   10. Simplified 99.0%

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

   11. Taylor expanded in x around inf 99.0%

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

       1. *-commutative 99.0%

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

       2. clear-num 98.8%

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

       3. un-div-inv 98.9%

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

       4. add-sqr-sqrt 0.0%

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

       5. sqrt-unprod 0.5%

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

       6. sqr-neg 0.5%

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

       7. sqrt-unprod 0.5%

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

       8. add-sqr-sqrt 0.5%

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

       9. div-inv 0.5%

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

       10. metadata-eval 0.5%

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

       11. metadata-eval 0.5%

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

       12. distribute-rgt-neg-in 0.5%

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

       13. frac-2neg 0.5%

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

       14. associate-/r* 0.5%

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

       15. frac-2neg 0.5%

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

       16. distribute-frac-neg 0.5%

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

       17. add-sqr-sqrt 0.5%

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

       18. sqrt-unprod 0.5%

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

       19. sqr-neg 0.5%

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

       20. sqrt-unprod 0.0%

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

       21. add-sqr-sqrt 99.0%

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

       22. metadata-eval 99.0%

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

   13. Applied egg-rr 99.0%

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

   if -4.5 < x < 1.30000000000000004

   1. Initial program 99.5%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   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 99.4%

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

      7. *-rgt-identity 99.4%

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

      8. associate-/l* 99.4%

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

      9. metadata-eval 99.4%

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

      10. *-commutative 99.4%

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

      11. sub-neg 99.4%

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

      12. +-commutative 99.4%

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

      13. distribute-lft-in 99.4%

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

      14. neg-mul-1 99.4%

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

      15. remove-double-neg 99.4%

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

      16. metadata-eval 99.4%

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

      17. distribute-lft-neg-out 99.4%

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

      18. *-commutative 99.4%

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

      19. distribute-lft-neg-in 99.4%

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

      20. associate-/r* 99.4%

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

      21. metadata-eval 99.4%

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

      22. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x around 0 97.9%

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

   6. Taylor expanded in y around 0 97.9%

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

      1. *-commutative 97.9%

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

   8. Simplified 97.9%

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

   if 1.30000000000000004 < x

   1. Initial program 86.7%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   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 99.7%

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

      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 inf 95.9%

      \[\leadsto \color{blue}{\left(-1 \cdot x\right)} \cdot \left(\left(x + -3\right) \cdot \frac{-0.3333333333333333}{y}\right) \]
   6. Step-by-step derivation

      1. neg-mul-1 95.9%

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

   7. Simplified 95.9%

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

   8. Taylor expanded in x around 0 95.9%

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

      1. sub-neg 95.9%

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

      2. associate-*r/ 95.9%

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

      3. associate-*l/ 95.9%

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

      4. metadata-eval 95.9%

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

      5. associate-/r* 95.9%

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

      6. *-commutative 95.9%

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

      7. metadata-eval 95.9%

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

      8. associate-*l/ 95.9%

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

      9. metadata-eval 95.9%

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

      10. associate-*r/ 95.9%

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

      11. distribute-rgt-neg-in 95.9%

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

      12. associate-*r/ 95.9%

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

      13. metadata-eval 95.9%

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

      14. metadata-eval 95.9%

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

      15. associate-/r* 95.9%

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

      16. *-commutative 95.9%

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

      17. metadata-eval 95.9%

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

      18. distribute-lft-in 95.9%

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

      19. *-commutative 95.9%

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

      20. associate-/r* 95.9%

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

      21. metadata-eval 95.9%

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

   10. Simplified 95.9%

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

4. Final simplification 97.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.5:\\ \;\;\;\;x \cdot \frac{\frac{x}{y}}{3}\\ \mathbf{elif}\;x \leq 1.3:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(x + -3\right) \cdot \frac{0.3333333333333333}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.3% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if x < -4.5 or 3 < x

   1. Initial program 91.2%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   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 99.8%

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

      7. *-rgt-identity 99.8%

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

      8. associate-/l* 99.8%

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

      9. metadata-eval 99.8%

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

      10. *-commutative 99.8%

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

      11. sub-neg 99.8%

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

      12. +-commutative 99.8%

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

      13. distribute-lft-in 99.8%

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

      14. neg-mul-1 99.8%

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

      15. remove-double-neg 99.8%

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

      16. metadata-eval 99.8%

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

      17. distribute-lft-neg-out 99.8%

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

      18. *-commutative 99.8%

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

      19. distribute-lft-neg-in 99.8%

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

      20. associate-/r* 99.8%

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

      21. metadata-eval 99.8%

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

      22. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 97.7%

      \[\leadsto \color{blue}{\left(-1 \cdot x\right)} \cdot \left(\left(x + -3\right) \cdot \frac{-0.3333333333333333}{y}\right) \]
   6. Step-by-step derivation

      1. neg-mul-1 97.7%

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

   7. Simplified 97.7%

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

   8. Taylor expanded in x around 0 97.7%

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

      1. sub-neg 97.7%

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

      2. associate-*r/ 97.7%

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

      3. associate-*l/ 97.7%

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

      4. metadata-eval 97.7%

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

      5. associate-/r* 97.7%

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

      6. *-commutative 97.7%

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

      7. metadata-eval 97.7%

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

      8. associate-*l/ 97.7%

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

      9. metadata-eval 97.7%

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

      10. associate-*r/ 97.7%

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

      11. distribute-rgt-neg-in 97.7%

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

      12. associate-*r/ 97.7%

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

      13. metadata-eval 97.7%

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

      14. metadata-eval 97.7%

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

      15. associate-/r* 97.7%

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

      16. *-commutative 97.7%

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

      17. metadata-eval 97.7%

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

      18. distribute-lft-in 97.7%

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

      19. *-commutative 97.7%

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

      20. associate-/r* 97.7%

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

      21. metadata-eval 97.7%

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

   10. Simplified 97.7%

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

   11. Taylor expanded in x around inf 97.6%

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

       1. *-commutative 97.6%

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

       2. clear-num 97.5%

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

       3. un-div-inv 97.5%

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

       4. add-sqr-sqrt 39.0%

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

       5. sqrt-unprod 34.0%

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

       6. sqr-neg 34.0%

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

       7. sqrt-unprod 0.3%

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

       8. add-sqr-sqrt 0.5%

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

       9. div-inv 0.5%

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

       10. metadata-eval 0.5%

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

       11. metadata-eval 0.5%

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

       12. distribute-rgt-neg-in 0.5%

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

       13. frac-2neg 0.5%

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

       14. associate-/r* 0.5%

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

       15. frac-2neg 0.5%

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

       16. distribute-frac-neg 0.5%

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

       17. add-sqr-sqrt 0.3%

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

       18. sqrt-unprod 34.1%

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

       19. sqr-neg 34.1%

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

       20. sqrt-unprod 39.0%

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

       21. add-sqr-sqrt 97.7%

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

       22. metadata-eval 97.7%

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

   13. Applied egg-rr 97.7%

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

   if -4.5 < x < 3

   1. Initial program 99.5%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   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 99.4%

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

      7. *-rgt-identity 99.4%

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

      8. associate-/l* 99.4%

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

      9. metadata-eval 99.4%

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

      10. *-commutative 99.4%

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

      11. sub-neg 99.4%

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

      12. +-commutative 99.4%

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

      13. distribute-lft-in 99.4%

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

      14. neg-mul-1 99.4%

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

      15. remove-double-neg 99.4%

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

      16. metadata-eval 99.4%

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

      17. distribute-lft-neg-out 99.4%

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

      18. *-commutative 99.4%

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

      19. distribute-lft-neg-in 99.4%

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

      20. associate-/r* 99.4%

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

      21. metadata-eval 99.4%

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

      22. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x around 0 97.9%

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

   6. Taylor expanded in y around 0 97.9%

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

      1. *-commutative 97.9%

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

   8. Simplified 97.9%

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

4. Final simplification 97.7%

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

Alternative 5: 97.9% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if x < -3.7999999999999998 or 3 < x

   1. Initial program 91.2%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   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 99.8%

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

      7. *-rgt-identity 99.8%

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

      8. associate-/l* 99.8%

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

      9. metadata-eval 99.8%

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

      10. *-commutative 99.8%

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

      11. sub-neg 99.8%

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

      12. +-commutative 99.8%

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

      13. distribute-lft-in 99.8%

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

      14. neg-mul-1 99.8%

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

      15. remove-double-neg 99.8%

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

      16. metadata-eval 99.8%

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

      17. distribute-lft-neg-out 99.8%

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

      18. *-commutative 99.8%

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

      19. distribute-lft-neg-in 99.8%

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

      20. associate-/r* 99.8%

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

      21. metadata-eval 99.8%

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

      22. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 97.7%

      \[\leadsto \color{blue}{\left(-1 \cdot x\right)} \cdot \left(\left(x + -3\right) \cdot \frac{-0.3333333333333333}{y}\right) \]
   6. Step-by-step derivation

      1. neg-mul-1 97.7%

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

   7. Simplified 97.7%

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

   8. Taylor expanded in x around 0 97.7%

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

      1. sub-neg 97.7%

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

      2. associate-*r/ 97.7%

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

      3. associate-*l/ 97.7%

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

      4. metadata-eval 97.7%

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

      5. associate-/r* 97.7%

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

      6. *-commutative 97.7%

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

      7. metadata-eval 97.7%

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

      8. associate-*l/ 97.7%

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

      9. metadata-eval 97.7%

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

      10. associate-*r/ 97.7%

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

      11. distribute-rgt-neg-in 97.7%

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

      12. associate-*r/ 97.7%

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

      13. metadata-eval 97.7%

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

      14. metadata-eval 97.7%

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

      15. associate-/r* 97.7%

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

      16. *-commutative 97.7%

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

      17. metadata-eval 97.7%

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

      18. distribute-lft-in 97.7%

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

      19. *-commutative 97.7%

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

      20. associate-/r* 97.7%

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

      21. metadata-eval 97.7%

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

   10. Simplified 97.7%

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

   11. Taylor expanded in x around inf 97.6%

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

       1. *-commutative 97.6%

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

       2. clear-num 97.5%

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

       3. un-div-inv 97.5%

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

       4. add-sqr-sqrt 39.0%

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

       5. sqrt-unprod 34.0%

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

       6. sqr-neg 34.0%

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

       7. sqrt-unprod 0.3%

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

       8. add-sqr-sqrt 0.5%

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

       9. div-inv 0.5%

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

       10. metadata-eval 0.5%

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

       11. metadata-eval 0.5%

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

       12. distribute-rgt-neg-in 0.5%

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

       13. frac-2neg 0.5%

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

       14. associate-/r* 0.5%

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

       15. frac-2neg 0.5%

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

       16. distribute-frac-neg 0.5%

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

       17. add-sqr-sqrt 0.3%

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

       18. sqrt-unprod 34.1%

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

       19. sqr-neg 34.1%

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

       20. sqrt-unprod 39.0%

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

       21. add-sqr-sqrt 97.7%

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

       22. metadata-eval 97.7%

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

   13. Applied egg-rr 97.7%

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

   if -3.7999999999999998 < x < 3

   1. Initial program 99.5%

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

      1. clear-num 99.7%

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

      2. un-div-inv 99.7%

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

      3. *-commutative 99.7%

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

      4. associate-/l* 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in x around 0 96.1%

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

4. Final simplification 96.9%

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

Alternative 6: 97.8% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if x < -3.7999999999999998 or 3 < x

   1. Initial program 91.2%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   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 99.8%

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

      7. *-rgt-identity 99.8%

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

      8. associate-/l* 99.8%

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

      9. metadata-eval 99.8%

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

      10. *-commutative 99.8%

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

      11. sub-neg 99.8%

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

      12. +-commutative 99.8%

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

      13. distribute-lft-in 99.8%

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

      14. neg-mul-1 99.8%

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

      15. remove-double-neg 99.8%

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

      16. metadata-eval 99.8%

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

      17. distribute-lft-neg-out 99.8%

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

      18. *-commutative 99.8%

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

      19. distribute-lft-neg-in 99.8%

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

      20. associate-/r* 99.8%

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

      21. metadata-eval 99.8%

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

      22. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 97.7%

      \[\leadsto \color{blue}{\left(-1 \cdot x\right)} \cdot \left(\left(x + -3\right) \cdot \frac{-0.3333333333333333}{y}\right) \]
   6. Step-by-step derivation

      1. neg-mul-1 97.7%

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

   7. Simplified 97.7%

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

   8. Taylor expanded in x around 0 97.7%

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

      1. sub-neg 97.7%

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

      2. associate-*r/ 97.7%

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

      3. associate-*l/ 97.7%

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

      4. metadata-eval 97.7%

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

      5. associate-/r* 97.7%

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

      6. *-commutative 97.7%

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

      7. metadata-eval 97.7%

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

      8. associate-*l/ 97.7%

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

      9. metadata-eval 97.7%

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

      10. associate-*r/ 97.7%

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

      11. distribute-rgt-neg-in 97.7%

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

      12. associate-*r/ 97.7%

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

      13. metadata-eval 97.7%

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

      14. metadata-eval 97.7%

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

      15. associate-/r* 97.7%

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

      16. *-commutative 97.7%

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

      17. metadata-eval 97.7%

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

      18. distribute-lft-in 97.7%

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

      19. *-commutative 97.7%

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

      20. associate-/r* 97.7%

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

      21. metadata-eval 97.7%

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

   10. Simplified 97.7%

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

   11. Taylor expanded in x around inf 97.6%

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

   if -3.7999999999999998 < x < 3

   1. Initial program 99.5%

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

      1. clear-num 99.7%

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

      2. un-div-inv 99.7%

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

      3. *-commutative 99.7%

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

      4. associate-/l* 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in x around 0 96.1%

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

4. Final simplification 96.9%

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

Alternative 7: 97.8% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if x < -3.7999999999999998 or 3 < x

   1. Initial program 91.2%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   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 99.8%

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

      7. *-rgt-identity 99.8%

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

      8. associate-/l* 99.8%

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

      9. metadata-eval 99.8%

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

      10. *-commutative 99.8%

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

      11. sub-neg 99.8%

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

      12. +-commutative 99.8%

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

      13. distribute-lft-in 99.8%

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

      14. neg-mul-1 99.8%

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

      15. remove-double-neg 99.8%

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

      16. metadata-eval 99.8%

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

      17. distribute-lft-neg-out 99.8%

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

      18. *-commutative 99.8%

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

      19. distribute-lft-neg-in 99.8%

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

      20. associate-/r* 99.8%

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

      21. metadata-eval 99.8%

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

      22. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 97.7%

      \[\leadsto \color{blue}{\left(-1 \cdot x\right)} \cdot \left(\left(x + -3\right) \cdot \frac{-0.3333333333333333}{y}\right) \]
   6. Step-by-step derivation

      1. neg-mul-1 97.7%

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

   7. Simplified 97.7%

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

   8. Taylor expanded in x around 0 97.7%

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

      1. sub-neg 97.7%

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

      2. associate-*r/ 97.7%

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

      3. associate-*l/ 97.7%

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

      4. metadata-eval 97.7%

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

      5. associate-/r* 97.7%

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

      6. *-commutative 97.7%

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

      7. metadata-eval 97.7%

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

      8. associate-*l/ 97.7%

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

      9. metadata-eval 97.7%

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

      10. associate-*r/ 97.7%

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

      11. distribute-rgt-neg-in 97.7%

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

      12. associate-*r/ 97.7%

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

      13. metadata-eval 97.7%

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

      14. metadata-eval 97.7%

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

      15. associate-/r* 97.7%

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

      16. *-commutative 97.7%

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

      17. metadata-eval 97.7%

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

      18. distribute-lft-in 97.7%

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

      19. *-commutative 97.7%

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

      20. associate-/r* 97.7%

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

      21. metadata-eval 97.7%

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

   10. Simplified 97.7%

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

   11. Taylor expanded in x around inf 97.6%

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

   if -3.7999999999999998 < x < 3

   1. Initial program 99.5%

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

      1. clear-num 99.7%

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

      2. un-div-inv 99.7%

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

      3. *-commutative 99.7%

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

      4. associate-/l* 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in x around 0 96.1%

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

4. Final simplification 96.9%

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

Alternative 8: 64.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.75:\\ \;\;\;\;\frac{x}{y} \cdot -1.3333333333333333\\ \mathbf{elif}\;x \leq 0.3:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1.3333333333333333}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -0.75)
   (* (/ x y) -1.3333333333333333)
   (if (<= x 0.3) (/ 1.0 y) (* x (/ 1.3333333333333333 y)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -0.75) {
		tmp = (x / y) * -1.3333333333333333;
	} else if (x <= 0.3) {
		tmp = 1.0 / y;
	} else {
		tmp = x * (1.3333333333333333 / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-0.75d0)) then
        tmp = (x / y) * (-1.3333333333333333d0)
    else if (x <= 0.3d0) then
        tmp = 1.0d0 / y
    else
        tmp = x * (1.3333333333333333d0 / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -0.75) {
		tmp = (x / y) * -1.3333333333333333;
	} else if (x <= 0.3) {
		tmp = 1.0 / y;
	} else {
		tmp = x * (1.3333333333333333 / y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -0.75:
		tmp = (x / y) * -1.3333333333333333
	elif x <= 0.3:
		tmp = 1.0 / y
	else:
		tmp = x * (1.3333333333333333 / y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -0.75)
		tmp = Float64(Float64(x / y) * -1.3333333333333333);
	elseif (x <= 0.3)
		tmp = Float64(1.0 / y);
	else
		tmp = Float64(x * Float64(1.3333333333333333 / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -0.75)
		tmp = (x / y) * -1.3333333333333333;
	elseif (x <= 0.3)
		tmp = 1.0 / y;
	else
		tmp = x * (1.3333333333333333 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -0.75], N[(N[(x / y), $MachinePrecision] * -1.3333333333333333), $MachinePrecision], If[LessEqual[x, 0.3], N[(1.0 / y), $MachinePrecision], N[(x * N[(1.3333333333333333 / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -0.75

   1. Initial program 94.3%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   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 99.8%

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

      7. *-rgt-identity 99.8%

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

      8. associate-/l* 99.8%

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

      9. metadata-eval 99.8%

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

      10. *-commutative 99.8%

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

      11. sub-neg 99.8%

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

      12. +-commutative 99.8%

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

      13. distribute-lft-in 99.8%

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

      14. neg-mul-1 99.8%

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

      15. remove-double-neg 99.8%

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

      16. metadata-eval 99.8%

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

      17. distribute-lft-neg-out 99.8%

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

      18. *-commutative 99.8%

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

      19. distribute-lft-neg-in 99.8%

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

      20. associate-/r* 99.8%

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

      21. metadata-eval 99.8%

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

      22. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0 37.8%

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

   6. Taylor expanded in x around inf 37.8%

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

   if -0.75 < x < 0.299999999999999989

   1. Initial program 99.5%

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

      1. clear-num 99.7%

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

      2. un-div-inv 99.7%

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

      3. *-commutative 99.7%

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

      4. associate-/l* 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in x around 0 96.4%

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

   if 0.299999999999999989 < x

   1. Initial program 87.0%

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

      1. associate-/l* 99.7%

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

      2. *-rgt-identity 99.7%

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

      3. remove-double-neg 99.7%

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

      4. distribute-lft-neg-out 99.7%

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

      5. neg-mul-1 99.7%

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

      6. times-frac 99.7%

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

      7. *-rgt-identity 99.7%

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

      8. associate-/l* 99.7%

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

      9. metadata-eval 99.7%

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

      10. *-commutative 99.7%

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

      11. sub-neg 99.7%

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

      12. +-commutative 99.7%

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

      13. distribute-lft-in 99.7%

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

      14. neg-mul-1 99.7%

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

      15. remove-double-neg 99.7%

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

      16. metadata-eval 99.7%

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

      17. distribute-lft-neg-out 99.7%

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

      18. *-commutative 99.7%

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

      19. distribute-lft-neg-in 99.7%

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

      20. associate-/r* 99.7%

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

      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 1.2%

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

   6. Taylor expanded in x around inf 0.8%

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

      1. *-commutative 0.8%

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

      2. associate-*l/ 0.8%

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

      3. associate-/l* 0.8%

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

   8. Simplified 0.8%

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

      1. clear-num 0.8%

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

      2. un-div-inv 0.8%

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

      3. div-inv 0.8%

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

      4. metadata-eval 0.8%

         \[\leadsto \frac{x}{y \cdot \color{blue}{-0.75}} \]

   10. Applied egg-rr 0.8%

       \[\leadsto \color{blue}{\frac{x}{y \cdot -0.75}} \]
   11. Step-by-step derivation

       1. frac-2neg 0.8%

          \[\leadsto \color{blue}{\frac{-x}{-y \cdot -0.75}} \]

       2. neg-sub0 0.8%

          \[\leadsto \frac{\color{blue}{0 - x}}{-y \cdot -0.75} \]

       3. div-sub 0.8%

          \[\leadsto \color{blue}{\frac{0}{-y \cdot -0.75} - \frac{x}{-y \cdot -0.75}} \]

       4. distribute-lft-neg-in 0.8%

          \[\leadsto \frac{0}{\color{blue}{\left(-y\right) \cdot -0.75}} - \frac{x}{-y \cdot -0.75} \]

       5. add-sqr-sqrt 0.4%

          \[\leadsto \frac{0}{\color{blue}{\left(\sqrt{-y} \cdot \sqrt{-y}\right)} \cdot -0.75} - \frac{x}{-y \cdot -0.75} \]

       6. sqrt-unprod 0.8%

          \[\leadsto \frac{0}{\color{blue}{\sqrt{\left(-y\right) \cdot \left(-y\right)}} \cdot -0.75} - \frac{x}{-y \cdot -0.75} \]

       7. sqr-neg 0.8%

          \[\leadsto \frac{0}{\sqrt{\color{blue}{y \cdot y}} \cdot -0.75} - \frac{x}{-y \cdot -0.75} \]

       8. sqrt-unprod 0.4%

          \[\leadsto \frac{0}{\color{blue}{\left(\sqrt{y} \cdot \sqrt{y}\right)} \cdot -0.75} - \frac{x}{-y \cdot -0.75} \]

       9. add-sqr-sqrt 0.8%

          \[\leadsto \frac{0}{\color{blue}{y} \cdot -0.75} - \frac{x}{-y \cdot -0.75} \]

       10. add-sqr-sqrt 0.8%

           \[\leadsto \frac{0}{y \cdot -0.75} - \frac{\color{blue}{\sqrt{x} \cdot \sqrt{x}}}{-y \cdot -0.75} \]

       11. sqrt-unprod 0.7%

           \[\leadsto \frac{0}{y \cdot -0.75} - \frac{\color{blue}{\sqrt{x \cdot x}}}{-y \cdot -0.75} \]

       12. sqr-neg 0.7%

           \[\leadsto \frac{0}{y \cdot -0.75} - \frac{\sqrt{\color{blue}{\left(-x\right) \cdot \left(-x\right)}}}{-y \cdot -0.75} \]

       13. sqrt-unprod 0.0%

           \[\leadsto \frac{0}{y \cdot -0.75} - \frac{\color{blue}{\sqrt{-x} \cdot \sqrt{-x}}}{-y \cdot -0.75} \]

       14. add-sqr-sqrt 33.8%

           \[\leadsto \frac{0}{y \cdot -0.75} - \frac{\color{blue}{-x}}{-y \cdot -0.75} \]

       15. frac-2neg 33.8%

           \[\leadsto \frac{0}{y \cdot -0.75} - \color{blue}{\frac{x}{y \cdot -0.75}} \]

       16. div-inv 33.8%

           \[\leadsto \frac{0}{y \cdot -0.75} - \color{blue}{x \cdot \frac{1}{y \cdot -0.75}} \]

       17. *-commutative 33.8%

           \[\leadsto \frac{0}{y \cdot -0.75} - x \cdot \frac{1}{\color{blue}{-0.75 \cdot y}} \]

       18. associate-/r* 33.8%

           \[\leadsto \frac{0}{y \cdot -0.75} - x \cdot \color{blue}{\frac{\frac{1}{-0.75}}{y}} \]

       19. metadata-eval 33.8%

           \[\leadsto \frac{0}{y \cdot -0.75} - x \cdot \frac{\color{blue}{-1.3333333333333333}}{y} \]

   12. Applied egg-rr 33.8%

       \[\leadsto \color{blue}{\frac{0}{y \cdot -0.75} - x \cdot \frac{-1.3333333333333333}{y}} \]
   13. Step-by-step derivation

       1. div0 33.8%

          \[\leadsto \color{blue}{0} - x \cdot \frac{-1.3333333333333333}{y} \]

       2. neg-sub0 33.8%

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

       3. distribute-rgt-neg-in 33.8%

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

       4. distribute-neg-frac 33.8%

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

       5. metadata-eval 33.8%

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

   14. Simplified 33.8%

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

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.75:\\ \;\;\;\;\frac{x}{y} \cdot -1.3333333333333333\\ \mathbf{elif}\;x \leq 0.3:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1.3333333333333333}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 64.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.75:\\ \;\;\;\;\frac{x}{y} \cdot -1.3333333333333333\\ \mathbf{elif}\;x \leq 0.34:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -0.75)
   (* (/ x y) -1.3333333333333333)
   (if (<= x 0.34) (/ 1.0 y) (/ x y))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -0.75) {
		tmp = (x / y) * -1.3333333333333333;
	} 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 = (x / y) * (-1.3333333333333333d0)
    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 = (x / y) * -1.3333333333333333;
	} 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 = (x / y) * -1.3333333333333333
	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(Float64(x / y) * -1.3333333333333333);
	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 = (x / y) * -1.3333333333333333;
	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[(N[(x / y), $MachinePrecision] * -1.3333333333333333), $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 94.3%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   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 99.8%

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

      7. *-rgt-identity 99.8%

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

      8. associate-/l* 99.8%

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

      9. metadata-eval 99.8%

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

      10. *-commutative 99.8%

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

      11. sub-neg 99.8%

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

      12. +-commutative 99.8%

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

      13. distribute-lft-in 99.8%

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

      14. neg-mul-1 99.8%

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

      15. remove-double-neg 99.8%

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

      16. metadata-eval 99.8%

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

      17. distribute-lft-neg-out 99.8%

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

      18. *-commutative 99.8%

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

      19. distribute-lft-neg-in 99.8%

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

      20. associate-/r* 99.8%

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

      21. metadata-eval 99.8%

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

      22. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0 37.8%

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

   6. Taylor expanded in x around inf 37.8%

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

   if -0.75 < x < 0.340000000000000024

   1. Initial program 99.5%

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

      1. clear-num 99.7%

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

      2. un-div-inv 99.7%

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

      3. *-commutative 99.7%

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

      4. associate-/l* 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in x around 0 96.4%

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

   if 0.340000000000000024 < x

   1. Initial program 87.0%

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

      1. associate-/l* 99.7%

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

      2. *-rgt-identity 99.7%

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

      3. remove-double-neg 99.7%

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

      4. distribute-lft-neg-out 99.7%

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

      5. neg-mul-1 99.7%

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

      6. times-frac 99.7%

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

      7. *-rgt-identity 99.7%

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

      8. associate-/l* 99.7%

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

      9. metadata-eval 99.7%

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

      10. *-commutative 99.7%

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

      11. sub-neg 99.7%

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

      12. +-commutative 99.7%

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

      13. distribute-lft-in 99.7%

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

      14. neg-mul-1 99.7%

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

      15. remove-double-neg 99.7%

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

      16. metadata-eval 99.7%

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

      17. distribute-lft-neg-out 99.7%

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

      18. *-commutative 99.7%

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

      19. distribute-lft-neg-in 99.7%

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

      20. associate-/r* 99.7%

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

      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 inf 94.3%

      \[\leadsto \color{blue}{\left(-1 \cdot x\right)} \cdot \left(\left(x + -3\right) \cdot \frac{-0.3333333333333333}{y}\right) \]
   6. Step-by-step derivation

      1. neg-mul-1 94.3%

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

   7. Simplified 94.3%

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

   8. Taylor expanded in x around 0 0.8%

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

      1. neg-mul-1 0.8%

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

      2. distribute-neg-frac2 0.8%

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

   10. Simplified 0.8%

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

       1. neg-sub0 0.8%

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

       2. sub-neg 0.8%

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

       3. add-sqr-sqrt 0.4%

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

       4. sqrt-unprod 18.3%

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

       5. sqr-neg 18.3%

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

       6. sqrt-unprod 18.3%

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

       7. add-sqr-sqrt 33.8%

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

   12. Applied egg-rr 33.8%

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

       1. +-lft-identity 33.8%

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

   14. Simplified 33.8%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.75:\\ \;\;\;\;\frac{x}{y} \cdot -1.3333333333333333\\ \mathbf{elif}\;x \leq 0.34:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 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(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 <= -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 94.3%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   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 99.8%

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

      7. *-rgt-identity 99.8%

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

      8. associate-/l* 99.8%

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

      9. metadata-eval 99.8%

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

      10. *-commutative 99.8%

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

      11. sub-neg 99.8%

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

      12. +-commutative 99.8%

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

      13. distribute-lft-in 99.8%

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

      14. neg-mul-1 99.8%

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

      15. remove-double-neg 99.8%

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

      16. metadata-eval 99.8%

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

      17. distribute-lft-neg-out 99.8%

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

      18. *-commutative 99.8%

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

      19. distribute-lft-neg-in 99.8%

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

      20. associate-/r* 99.8%

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

      21. metadata-eval 99.8%

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

      22. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 99.0%

      \[\leadsto \color{blue}{\left(-1 \cdot x\right)} \cdot \left(\left(x + -3\right) \cdot \frac{-0.3333333333333333}{y}\right) \]
   6. Step-by-step derivation

      1. neg-mul-1 99.0%

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

   7. Simplified 99.0%

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

   8. Taylor expanded in x around 0 37.8%

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

      1. neg-mul-1 37.8%

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

      2. distribute-neg-frac2 37.8%

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

   10. Simplified 37.8%

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

   if -1 < x < 0.340000000000000024

   1. Initial program 99.5%

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

      1. clear-num 99.7%

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

      2. un-div-inv 99.7%

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

      3. *-commutative 99.7%

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

      4. associate-/l* 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in x around 0 96.4%

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

   if 0.340000000000000024 < x

   1. Initial program 87.0%

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

      1. associate-/l* 99.7%

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

      2. *-rgt-identity 99.7%

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

      3. remove-double-neg 99.7%

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

      4. distribute-lft-neg-out 99.7%

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

      5. neg-mul-1 99.7%

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

      6. times-frac 99.7%

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

      7. *-rgt-identity 99.7%

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

      8. associate-/l* 99.7%

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

      9. metadata-eval 99.7%

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

      10. *-commutative 99.7%

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

      11. sub-neg 99.7%

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

      12. +-commutative 99.7%

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

      13. distribute-lft-in 99.7%

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

      14. neg-mul-1 99.7%

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

      15. remove-double-neg 99.7%

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

      16. metadata-eval 99.7%

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

      17. distribute-lft-neg-out 99.7%

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

      18. *-commutative 99.7%

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

      19. distribute-lft-neg-in 99.7%

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

      20. associate-/r* 99.7%

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

      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 inf 94.3%

      \[\leadsto \color{blue}{\left(-1 \cdot x\right)} \cdot \left(\left(x + -3\right) \cdot \frac{-0.3333333333333333}{y}\right) \]
   6. Step-by-step derivation

      1. neg-mul-1 94.3%

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

   7. Simplified 94.3%

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

   8. Taylor expanded in x around 0 0.8%

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

      1. neg-mul-1 0.8%

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

      2. distribute-neg-frac2 0.8%

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

   10. Simplified 0.8%

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

       1. neg-sub0 0.8%

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

       2. sub-neg 0.8%

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

       3. add-sqr-sqrt 0.4%

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

       4. sqrt-unprod 18.3%

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

       5. sqr-neg 18.3%

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

       6. sqrt-unprod 18.3%

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

       7. add-sqr-sqrt 33.8%

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

   12. Applied egg-rr 33.8%

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

       1. +-lft-identity 33.8%

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

   14. Simplified 33.8%

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

4. Final simplification 62.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;\frac{-x}{y}\\ \mathbf{elif}\;x \leq 0.34:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 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 94.9%

   \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
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 12: 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 94.9%

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

   1. associate-/l* 99.7%

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

   2. *-rgt-identity 99.7%

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

   3. remove-double-neg 99.7%

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

   4. distribute-lft-neg-out 99.7%

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

   5. neg-mul-1 99.7%

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

   6. times-frac 99.6%

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

   7. *-rgt-identity 99.6%

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

   8. associate-/l* 99.6%

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

   9. metadata-eval 99.6%

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

   10. *-commutative 99.6%

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

   11. sub-neg 99.6%

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

   12. +-commutative 99.6%

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

   13. distribute-lft-in 99.6%

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

   14. neg-mul-1 99.6%

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

   15. remove-double-neg 99.6%

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

   16. metadata-eval 99.6%

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

   17. distribute-lft-neg-out 99.6%

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

   18. *-commutative 99.6%

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

   19. distribute-lft-neg-in 99.6%

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

   20. associate-/r* 99.6%

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

   21. metadata-eval 99.6%

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

   22. metadata-eval 99.6%

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

3. Simplified 99.6%

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

Alternative 13: 64.1% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if x < 3

   1. Initial program 97.3%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   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. clear-num 99.7%

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

      2. un-div-inv 99.7%

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

      3. *-commutative 99.7%

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

      4. associate-/l* 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in x around 0 71.3%

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

   if 3 < x

   1. Initial program 86.7%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   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 99.7%

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

      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 0.8%

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

   6. Taylor expanded in x around inf 0.8%

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

      1. *-commutative 0.8%

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

      2. associate-*l/ 0.8%

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

      3. associate-/l* 0.8%

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

   8. Simplified 0.8%

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

      1. clear-num 0.8%

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

      2. un-div-inv 0.8%

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

      3. div-inv 0.8%

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

      4. metadata-eval 0.8%

         \[\leadsto \frac{x}{y \cdot \color{blue}{-0.75}} \]

   10. Applied egg-rr 0.8%

       \[\leadsto \color{blue}{\frac{x}{y \cdot -0.75}} \]
   11. Step-by-step derivation

       1. frac-2neg 0.8%

          \[\leadsto \color{blue}{\frac{-x}{-y \cdot -0.75}} \]

       2. neg-sub0 0.8%

          \[\leadsto \frac{\color{blue}{0 - x}}{-y \cdot -0.75} \]

       3. div-sub 0.8%

          \[\leadsto \color{blue}{\frac{0}{-y \cdot -0.75} - \frac{x}{-y \cdot -0.75}} \]

       4. distribute-lft-neg-in 0.8%

          \[\leadsto \frac{0}{\color{blue}{\left(-y\right) \cdot -0.75}} - \frac{x}{-y \cdot -0.75} \]

       5. add-sqr-sqrt 0.4%

          \[\leadsto \frac{0}{\color{blue}{\left(\sqrt{-y} \cdot \sqrt{-y}\right)} \cdot -0.75} - \frac{x}{-y \cdot -0.75} \]

       6. sqrt-unprod 0.8%

          \[\leadsto \frac{0}{\color{blue}{\sqrt{\left(-y\right) \cdot \left(-y\right)}} \cdot -0.75} - \frac{x}{-y \cdot -0.75} \]

       7. sqr-neg 0.8%

          \[\leadsto \frac{0}{\sqrt{\color{blue}{y \cdot y}} \cdot -0.75} - \frac{x}{-y \cdot -0.75} \]

       8. sqrt-unprod 0.4%

          \[\leadsto \frac{0}{\color{blue}{\left(\sqrt{y} \cdot \sqrt{y}\right)} \cdot -0.75} - \frac{x}{-y \cdot -0.75} \]

       9. add-sqr-sqrt 0.8%

          \[\leadsto \frac{0}{\color{blue}{y} \cdot -0.75} - \frac{x}{-y \cdot -0.75} \]

       10. add-sqr-sqrt 0.8%

           \[\leadsto \frac{0}{y \cdot -0.75} - \frac{\color{blue}{\sqrt{x} \cdot \sqrt{x}}}{-y \cdot -0.75} \]

       11. sqrt-unprod 0.6%

           \[\leadsto \frac{0}{y \cdot -0.75} - \frac{\color{blue}{\sqrt{x \cdot x}}}{-y \cdot -0.75} \]

       12. sqr-neg 0.6%

           \[\leadsto \frac{0}{y \cdot -0.75} - \frac{\sqrt{\color{blue}{\left(-x\right) \cdot \left(-x\right)}}}{-y \cdot -0.75} \]

       13. sqrt-unprod 0.0%

           \[\leadsto \frac{0}{y \cdot -0.75} - \frac{\color{blue}{\sqrt{-x} \cdot \sqrt{-x}}}{-y \cdot -0.75} \]

       14. add-sqr-sqrt 34.1%

           \[\leadsto \frac{0}{y \cdot -0.75} - \frac{\color{blue}{-x}}{-y \cdot -0.75} \]

       15. frac-2neg 34.1%

           \[\leadsto \frac{0}{y \cdot -0.75} - \color{blue}{\frac{x}{y \cdot -0.75}} \]

       16. div-inv 34.1%

           \[\leadsto \frac{0}{y \cdot -0.75} - \color{blue}{x \cdot \frac{1}{y \cdot -0.75}} \]

       17. *-commutative 34.1%

           \[\leadsto \frac{0}{y \cdot -0.75} - x \cdot \frac{1}{\color{blue}{-0.75 \cdot y}} \]

       18. associate-/r* 34.1%

           \[\leadsto \frac{0}{y \cdot -0.75} - x \cdot \color{blue}{\frac{\frac{1}{-0.75}}{y}} \]

       19. metadata-eval 34.1%

           \[\leadsto \frac{0}{y \cdot -0.75} - x \cdot \frac{\color{blue}{-1.3333333333333333}}{y} \]

   12. Applied egg-rr 34.1%

       \[\leadsto \color{blue}{\frac{0}{y \cdot -0.75} - x \cdot \frac{-1.3333333333333333}{y}} \]
   13. Step-by-step derivation

       1. div0 34.1%

          \[\leadsto \color{blue}{0} - x \cdot \frac{-1.3333333333333333}{y} \]

       2. neg-sub0 34.1%

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

       3. distribute-rgt-neg-in 34.1%

          \[\leadsto \color{blue}{x \cdot \left(-\frac{-1.3333333333333333}{y}\right)} \]

       4. distribute-neg-frac 34.1%

          \[\leadsto x \cdot \color{blue}{\frac{--1.3333333333333333}{y}} \]

       5. metadata-eval 34.1%

          \[\leadsto x \cdot \frac{\color{blue}{1.3333333333333333}}{y} \]

   14. Simplified 34.1%

       \[\leadsto \color{blue}{x \cdot \frac{1.3333333333333333}{y}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 14: 57.7% 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 97.3%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   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. clear-num 99.7%

         \[\leadsto \left(1 - x\right) \cdot \color{blue}{\frac{1}{\frac{3 \cdot y}{3 - x}}} \]

      2. un-div-inv 99.7%

         \[\leadsto \color{blue}{\frac{1 - x}{\frac{3 \cdot y}{3 - x}}} \]

      3. *-commutative 99.7%

         \[\leadsto \frac{1 - x}{\frac{\color{blue}{y \cdot 3}}{3 - x}} \]

      4. associate-/l* 99.9%

         \[\leadsto \frac{1 - x}{\color{blue}{y \cdot \frac{3}{3 - x}}} \]

   6. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{\frac{1 - x}{y \cdot \frac{3}{3 - x}}} \]

   7. Taylor expanded in x around 0 57.5%

      \[\leadsto \color{blue}{\frac{1}{y}} \]

   if 0.340000000000000024 < x

   1. Initial program 87.0%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   2. Step-by-step derivation

      1. associate-/l* 99.7%

         \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{3 - x}{y \cdot 3}} \]

      2. *-rgt-identity 99.7%

         \[\leadsto \left(1 - x\right) \cdot \frac{\color{blue}{\left(3 - x\right) \cdot 1}}{y \cdot 3} \]

      3. remove-double-neg 99.7%

         \[\leadsto \left(1 - x\right) \cdot \frac{\left(3 - x\right) \cdot 1}{\color{blue}{-\left(-y \cdot 3\right)}} \]

      4. distribute-lft-neg-out 99.7%

         \[\leadsto \left(1 - x\right) \cdot \frac{\left(3 - x\right) \cdot 1}{-\color{blue}{\left(-y\right) \cdot 3}} \]

      5. neg-mul-1 99.7%

         \[\leadsto \left(1 - x\right) \cdot \frac{\left(3 - x\right) \cdot 1}{\color{blue}{-1 \cdot \left(\left(-y\right) \cdot 3\right)}} \]

      6. times-frac 99.7%

         \[\leadsto \left(1 - x\right) \cdot \color{blue}{\left(\frac{3 - x}{-1} \cdot \frac{1}{\left(-y\right) \cdot 3}\right)} \]

      7. *-rgt-identity 99.7%

         \[\leadsto \left(1 - x\right) \cdot \left(\frac{\color{blue}{\left(3 - x\right) \cdot 1}}{-1} \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      8. associate-/l* 99.7%

         \[\leadsto \left(1 - x\right) \cdot \left(\color{blue}{\left(\left(3 - x\right) \cdot \frac{1}{-1}\right)} \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      9. metadata-eval 99.7%

         \[\leadsto \left(1 - x\right) \cdot \left(\left(\left(3 - x\right) \cdot \color{blue}{-1}\right) \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      10. *-commutative 99.7%

          \[\leadsto \left(1 - x\right) \cdot \left(\color{blue}{\left(-1 \cdot \left(3 - x\right)\right)} \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      11. sub-neg 99.7%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(-1 \cdot \color{blue}{\left(3 + \left(-x\right)\right)}\right) \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      12. +-commutative 99.7%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(-1 \cdot \color{blue}{\left(\left(-x\right) + 3\right)}\right) \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      13. distribute-lft-in 99.7%

          \[\leadsto \left(1 - x\right) \cdot \left(\color{blue}{\left(-1 \cdot \left(-x\right) + -1 \cdot 3\right)} \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      14. neg-mul-1 99.7%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(\color{blue}{\left(-\left(-x\right)\right)} + -1 \cdot 3\right) \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      15. remove-double-neg 99.7%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(\color{blue}{x} + -1 \cdot 3\right) \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      16. metadata-eval 99.7%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(x + \color{blue}{-3}\right) \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      17. distribute-lft-neg-out 99.7%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(x + -3\right) \cdot \frac{1}{\color{blue}{-y \cdot 3}}\right) \]

      18. *-commutative 99.7%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(x + -3\right) \cdot \frac{1}{-\color{blue}{3 \cdot y}}\right) \]

      19. distribute-lft-neg-in 99.7%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(x + -3\right) \cdot \frac{1}{\color{blue}{\left(-3\right) \cdot y}}\right) \]

      20. associate-/r* 99.7%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(x + -3\right) \cdot \color{blue}{\frac{\frac{1}{-3}}{y}}\right) \]

      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 inf 94.3%

      \[\leadsto \color{blue}{\left(-1 \cdot x\right)} \cdot \left(\left(x + -3\right) \cdot \frac{-0.3333333333333333}{y}\right) \]
   6. Step-by-step derivation

      1. neg-mul-1 94.3%

         \[\leadsto \color{blue}{\left(-x\right)} \cdot \left(\left(x + -3\right) \cdot \frac{-0.3333333333333333}{y}\right) \]

   7. Simplified 94.3%

      \[\leadsto \color{blue}{\left(-x\right)} \cdot \left(\left(x + -3\right) \cdot \frac{-0.3333333333333333}{y}\right) \]

   8. Taylor expanded in x around 0 0.8%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{y}} \]
   9. Step-by-step derivation

      1. neg-mul-1 0.8%

         \[\leadsto \color{blue}{-\frac{x}{y}} \]

      2. distribute-neg-frac2 0.8%

         \[\leadsto \color{blue}{\frac{x}{-y}} \]

   10. Simplified 0.8%

       \[\leadsto \color{blue}{\frac{x}{-y}} \]
   11. Step-by-step derivation

       1. neg-sub0 0.8%

          \[\leadsto \frac{x}{\color{blue}{0 - y}} \]

       2. sub-neg 0.8%

          \[\leadsto \frac{x}{\color{blue}{0 + \left(-y\right)}} \]

       3. add-sqr-sqrt 0.4%

          \[\leadsto \frac{x}{0 + \color{blue}{\sqrt{-y} \cdot \sqrt{-y}}} \]

       4. sqrt-unprod 18.3%

          \[\leadsto \frac{x}{0 + \color{blue}{\sqrt{\left(-y\right) \cdot \left(-y\right)}}} \]

       5. sqr-neg 18.3%

          \[\leadsto \frac{x}{0 + \sqrt{\color{blue}{y \cdot y}}} \]

       6. sqrt-unprod 18.3%

          \[\leadsto \frac{x}{0 + \color{blue}{\sqrt{y} \cdot \sqrt{y}}} \]

       7. add-sqr-sqrt 33.8%

          \[\leadsto \frac{x}{0 + \color{blue}{y}} \]

   12. Applied egg-rr 33.8%

       \[\leadsto \frac{x}{\color{blue}{0 + y}} \]
   13. Step-by-step derivation

       1. +-lft-identity 33.8%

          \[\leadsto \frac{x}{\color{blue}{y}} \]

   14. Simplified 33.8%

       \[\leadsto \frac{x}{\color{blue}{y}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 15: 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 94.9%

   \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
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. clear-num 99.7%

      \[\leadsto \left(1 - x\right) \cdot \color{blue}{\frac{1}{\frac{3 \cdot y}{3 - x}}} \]

   2. un-div-inv 99.7%

      \[\leadsto \color{blue}{\frac{1 - x}{\frac{3 \cdot y}{3 - x}}} \]

   3. *-commutative 99.7%

      \[\leadsto \frac{1 - x}{\frac{\color{blue}{y \cdot 3}}{3 - x}} \]

   4. associate-/l* 99.8%

      \[\leadsto \frac{1 - x}{\color{blue}{y \cdot \frac{3}{3 - x}}} \]

6. Applied egg-rr 99.8%

   \[\leadsto \color{blue}{\frac{1 - x}{y \cdot \frac{3}{3 - x}}} \]

7. Taylor expanded in x around 0 45.5%

   \[\leadsto \color{blue}{\frac{1}{y}} \]
8. Add Preprocessing

Developer Target 1: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{1 - x}{y} \cdot \frac{3 - x}{3} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* (/ (- 1.0 x) y) (/ (- 3.0 x) 3.0)))

C

double code(double x, double y) {
	return ((1.0 - x) / y) * ((3.0 - x) / 3.0);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = ((1.0d0 - x) / y) * ((3.0d0 - x) / 3.0d0)
end function

Java

public static double code(double x, double y) {
	return ((1.0 - x) / y) * ((3.0 - x) / 3.0);
}

Python

def code(x, y):
	return ((1.0 - x) / y) * ((3.0 - x) / 3.0)

Julia

function code(x, y)
	return Float64(Float64(Float64(1.0 - x) / y) * Float64(Float64(3.0 - x) / 3.0))
end

MATLAB

function tmp = code(x, y)
	tmp = ((1.0 - x) / y) * ((3.0 - x) / 3.0);
end

Wolfram

code[x_, y_] := N[(N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision] * N[(N[(3.0 - x), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024139 
(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)))