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

Percentage Accurate: 94.0% → 99.8%

Time: 10.5s

Alternatives: 20

Speedup: 1.0×

• 25.3% 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: 94.0% 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

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

FPCore

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

C

double code(double x, double y) {
	return ((1.0 - x) / y) * (1.0 - (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) * (1.0d0 - (x / 3.0d0))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.4%

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

   1. times-frac 99.8%

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

   2. div-sub 99.9%

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

   3. metadata-eval 99.9%

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

4. Applied egg-rr 99.9%

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

Alternative 2: 98.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.3 \lor \neg \left(x \leq 1.3\right):\\ \;\;\;\;\frac{x}{y} \cdot \frac{3 - x}{-3}\\ \mathbf{else}:\\ \;\;\;\;\frac{3 + x \cdot -4}{y \cdot 3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -2.3) (not (<= x 1.3)))
   (* (/ x y) (/ (- 3.0 x) -3.0))
   (/ (+ 3.0 (* x -4.0)) (* y 3.0))))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -2.3) || !(x <= 1.3)) {
		tmp = (x / y) * ((3.0 - x) / -3.0);
	} else {
		tmp = (3.0 + (x * -4.0)) / (y * 3.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-2.3d0)) .or. (.not. (x <= 1.3d0))) then
        tmp = (x / y) * ((3.0d0 - x) / (-3.0d0))
    else
        tmp = (3.0d0 + (x * (-4.0d0))) / (y * 3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -2.3) || !(x <= 1.3)) {
		tmp = (x / y) * ((3.0 - x) / -3.0);
	} else {
		tmp = (3.0 + (x * -4.0)) / (y * 3.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -2.3) or not (x <= 1.3):
		tmp = (x / y) * ((3.0 - x) / -3.0)
	else:
		tmp = (3.0 + (x * -4.0)) / (y * 3.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -2.3) || !(x <= 1.3))
		tmp = Float64(Float64(x / y) * Float64(Float64(3.0 - x) / -3.0));
	else
		tmp = Float64(Float64(3.0 + Float64(x * -4.0)) / Float64(y * 3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -2.3) || ~((x <= 1.3)))
		tmp = (x / y) * ((3.0 - x) / -3.0);
	else
		tmp = (3.0 + (x * -4.0)) / (y * 3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -2.3], N[Not[LessEqual[x, 1.3]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] * N[(N[(3.0 - x), $MachinePrecision] / -3.0), $MachinePrecision]), $MachinePrecision], N[(N[(3.0 + N[(x * -4.0), $MachinePrecision]), $MachinePrecision] / N[(y * 3.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.2999999999999998 or 1.30000000000000004 < x

   1. Initial program 92.6%

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

      1. associate-/l* 99.6%

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

      2. *-rgt-identity 99.6%

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

      3. remove-double-neg 99.6%

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

      4. distribute-lft-neg-out 99.6%

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

      5. neg-mul-1 99.6%

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

      6. times-frac 99.6%

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

      7. *-rgt-identity 99.6%

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

      8. associate-/l* 99.6%

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

      9. metadata-eval 99.6%

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

      10. *-commutative 99.6%

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

      11. sub-neg 99.6%

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

      12. +-commutative 99.6%

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

      13. distribute-lft-in 99.6%

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

      14. neg-mul-1 99.6%

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

      15. remove-double-neg 99.6%

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

      16. metadata-eval 99.6%

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

      17. distribute-lft-neg-out 99.6%

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

      18. *-commutative 99.6%

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

      19. distribute-lft-neg-in 99.6%

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

      20. associate-/r* 99.5%

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

      21. metadata-eval 99.5%

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

      22. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around inf 95.8%

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

      1. neg-mul-1 95.8%

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

   7. Simplified 95.8%

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

   8. Taylor expanded in y around 0 88.9%

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

      1. associate-*r/ 89.0%

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

      2. clear-num 88.9%

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

      3. *-commutative 88.9%

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

      4. add-sqr-sqrt 41.9%

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

      5. sqrt-unprod 42.4%

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

      6. sqr-neg 42.4%

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

      7. sqrt-unprod 0.3%

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

      8. add-sqr-sqrt 0.6%

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

      9. distribute-lft-neg-in 0.6%

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

      10. distribute-lft-neg-in 0.6%

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

      11. add-sqr-sqrt 0.3%

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

      12. sqrt-unprod 42.4%

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

      13. sqr-neg 42.4%

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

      14. sqrt-unprod 41.9%

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

      15. add-sqr-sqrt 88.9%

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

      16. *-un-lft-identity 88.9%

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

      17. *-un-lft-identity 88.9%

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

      18. sub-neg 88.9%

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

      19. metadata-eval 88.9%

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

   10. Applied egg-rr 88.9%

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

       1. associate-/r/ 89.0%

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

       2. associate-*r* 89.0%

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

       3. *-commutative 89.0%

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

       4. associate-*r* 89.0%

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

       5. *-commutative 89.0%

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

       6. associate-*r/ 89.0%

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

       7. metadata-eval 89.0%

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

       8. associate-/l* 89.0%

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

       9. remove-double-neg 89.0%

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

       10. distribute-frac-neg2 89.0%

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

       11. associate-/l* 89.0%

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

       12. distribute-lft-neg-in 89.0%

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

       13. distribute-rgt-neg-in 89.0%

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

       14. +-commutative 89.0%

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

       15. distribute-neg-in 89.0%

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

       16. metadata-eval 89.0%

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

       17. sub-neg 89.0%

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

       18. distribute-frac-neg2 89.0%

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

       19. distribute-neg-frac 89.0%

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

       20. metadata-eval 89.0%

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

   12. Simplified 89.0%

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

       1. clear-num 89.0%

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

       2. un-div-inv 88.9%

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

       3. div-inv 89.0%

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

       4. metadata-eval 89.0%

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

   14. Applied egg-rr 89.0%

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

       1. times-frac 96.0%

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

   16. Simplified 96.0%

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

   if -2.2999999999999998 < x < 1.30000000000000004

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0 99.2%

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

      1. *-commutative 99.2%

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

   5. Simplified 99.2%

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

4. Final simplification 97.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3 \lor \neg \left(x \leq 1.3\right):\\ \;\;\;\;\frac{x}{y} \cdot \frac{3 - x}{-3}\\ \mathbf{else}:\\ \;\;\;\;\frac{3 + x \cdot -4}{y \cdot 3}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.3 \lor \neg \left(x \leq 1.3\right):\\ \;\;\;\;\frac{x}{y} \cdot \frac{3 - x}{-3}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{3 + x \cdot -4}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -2.3) (not (<= x 1.3)))
   (* (/ x y) (/ (- 3.0 x) -3.0))
   (* 0.3333333333333333 (/ (+ 3.0 (* x -4.0)) y))))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -2.3) || !(x <= 1.3)) {
		tmp = (x / y) * ((3.0 - x) / -3.0);
	} else {
		tmp = 0.3333333333333333 * ((3.0 + (x * -4.0)) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-2.3d0)) .or. (.not. (x <= 1.3d0))) then
        tmp = (x / y) * ((3.0d0 - x) / (-3.0d0))
    else
        tmp = 0.3333333333333333d0 * ((3.0d0 + (x * (-4.0d0))) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -2.3) || !(x <= 1.3)) {
		tmp = (x / y) * ((3.0 - x) / -3.0);
	} else {
		tmp = 0.3333333333333333 * ((3.0 + (x * -4.0)) / y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -2.3) or not (x <= 1.3):
		tmp = (x / y) * ((3.0 - x) / -3.0)
	else:
		tmp = 0.3333333333333333 * ((3.0 + (x * -4.0)) / y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -2.3) || !(x <= 1.3))
		tmp = Float64(Float64(x / y) * Float64(Float64(3.0 - x) / -3.0));
	else
		tmp = Float64(0.3333333333333333 * Float64(Float64(3.0 + Float64(x * -4.0)) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -2.3) || ~((x <= 1.3)))
		tmp = (x / y) * ((3.0 - x) / -3.0);
	else
		tmp = 0.3333333333333333 * ((3.0 + (x * -4.0)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -2.3], N[Not[LessEqual[x, 1.3]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] * N[(N[(3.0 - x), $MachinePrecision] / -3.0), $MachinePrecision]), $MachinePrecision], N[(0.3333333333333333 * N[(N[(3.0 + N[(x * -4.0), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.2999999999999998 or 1.30000000000000004 < x

   1. Initial program 92.6%

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

      1. associate-/l* 99.6%

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

      2. *-rgt-identity 99.6%

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

      3. remove-double-neg 99.6%

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

      4. distribute-lft-neg-out 99.6%

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

      5. neg-mul-1 99.6%

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

      6. times-frac 99.6%

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

      7. *-rgt-identity 99.6%

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

      8. associate-/l* 99.6%

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

      9. metadata-eval 99.6%

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

      10. *-commutative 99.6%

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

      11. sub-neg 99.6%

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

      12. +-commutative 99.6%

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

      13. distribute-lft-in 99.6%

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

      14. neg-mul-1 99.6%

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

      15. remove-double-neg 99.6%

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

      16. metadata-eval 99.6%

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

      17. distribute-lft-neg-out 99.6%

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

      18. *-commutative 99.6%

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

      19. distribute-lft-neg-in 99.6%

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

      20. associate-/r* 99.5%

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

      21. metadata-eval 99.5%

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

      22. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around inf 95.8%

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

      1. neg-mul-1 95.8%

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

   7. Simplified 95.8%

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

   8. Taylor expanded in y around 0 88.9%

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

      1. associate-*r/ 89.0%

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

      2. clear-num 88.9%

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

      3. *-commutative 88.9%

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

      4. add-sqr-sqrt 41.9%

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

      5. sqrt-unprod 42.4%

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

      6. sqr-neg 42.4%

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

      7. sqrt-unprod 0.3%

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

      8. add-sqr-sqrt 0.6%

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

      9. distribute-lft-neg-in 0.6%

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

      10. distribute-lft-neg-in 0.6%

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

      11. add-sqr-sqrt 0.3%

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

      12. sqrt-unprod 42.4%

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

      13. sqr-neg 42.4%

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

      14. sqrt-unprod 41.9%

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

      15. add-sqr-sqrt 88.9%

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

      16. *-un-lft-identity 88.9%

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

      17. *-un-lft-identity 88.9%

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

      18. sub-neg 88.9%

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

      19. metadata-eval 88.9%

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

   10. Applied egg-rr 88.9%

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

       1. associate-/r/ 89.0%

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

       2. associate-*r* 89.0%

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

       3. *-commutative 89.0%

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

       4. associate-*r* 89.0%

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

       5. *-commutative 89.0%

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

       6. associate-*r/ 89.0%

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

       7. metadata-eval 89.0%

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

       8. associate-/l* 89.0%

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

       9. remove-double-neg 89.0%

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

       10. distribute-frac-neg2 89.0%

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

       11. associate-/l* 89.0%

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

       12. distribute-lft-neg-in 89.0%

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

       13. distribute-rgt-neg-in 89.0%

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

       14. +-commutative 89.0%

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

       15. distribute-neg-in 89.0%

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

       16. metadata-eval 89.0%

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

       17. sub-neg 89.0%

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

       18. distribute-frac-neg2 89.0%

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

       19. distribute-neg-frac 89.0%

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

       20. metadata-eval 89.0%

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

   12. Simplified 89.0%

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

       1. clear-num 89.0%

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

       2. un-div-inv 88.9%

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

       3. div-inv 89.0%

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

       4. metadata-eval 89.0%

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

   14. Applied egg-rr 89.0%

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

       1. times-frac 96.0%

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

   16. Simplified 96.0%

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

   if -2.2999999999999998 < x < 1.30000000000000004

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0 99.2%

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

      1. *-commutative 99.2%

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

   5. Simplified 99.2%

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

   6. Taylor expanded in y around 0 99.0%

      \[\leadsto \color{blue}{0.3333333333333333 \cdot \frac{3 + -4 \cdot x}{y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 97.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3 \lor \neg \left(x \leq 1.3\right):\\ \;\;\;\;\frac{x}{y} \cdot \frac{3 - x}{-3}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{3 + x \cdot -4}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 97.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.75 \lor \neg \left(x \leq 1.7\right):\\ \;\;\;\;0.3333333333333333 \cdot \left(x \cdot \frac{x + -3}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(2 - x\right) + -1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -1.75) (not (<= x 1.7)))
   (* 0.3333333333333333 (* x (/ (+ x -3.0) y)))
   (/ (+ (- 2.0 x) -1.0) y)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -1.75) || !(x <= 1.7)) {
		tmp = 0.3333333333333333 * (x * ((x + -3.0) / y));
	} else {
		tmp = ((2.0 - x) + -1.0) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-1.75d0)) .or. (.not. (x <= 1.7d0))) then
        tmp = 0.3333333333333333d0 * (x * ((x + (-3.0d0)) / y))
    else
        tmp = ((2.0d0 - x) + (-1.0d0)) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -1.75) || !(x <= 1.7)) {
		tmp = 0.3333333333333333 * (x * ((x + -3.0) / y));
	} else {
		tmp = ((2.0 - x) + -1.0) / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -1.75) or not (x <= 1.7):
		tmp = 0.3333333333333333 * (x * ((x + -3.0) / y))
	else:
		tmp = ((2.0 - x) + -1.0) / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -1.75) || !(x <= 1.7))
		tmp = Float64(0.3333333333333333 * Float64(x * Float64(Float64(x + -3.0) / y)));
	else
		tmp = Float64(Float64(Float64(2.0 - x) + -1.0) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -1.75) || ~((x <= 1.7)))
		tmp = 0.3333333333333333 * (x * ((x + -3.0) / y));
	else
		tmp = ((2.0 - x) + -1.0) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -1.75], N[Not[LessEqual[x, 1.7]], $MachinePrecision]], N[(0.3333333333333333 * N[(x * N[(N[(x + -3.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(2.0 - x), $MachinePrecision] + -1.0), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.75 or 1.69999999999999996 < x

   1. Initial program 92.6%

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

      1. associate-/l* 99.6%

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

      2. *-rgt-identity 99.6%

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

      3. remove-double-neg 99.6%

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

      4. distribute-lft-neg-out 99.6%

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

      5. neg-mul-1 99.6%

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

      6. times-frac 99.6%

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

      7. *-rgt-identity 99.6%

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

      8. associate-/l* 99.6%

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

      9. metadata-eval 99.6%

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

      10. *-commutative 99.6%

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

      11. sub-neg 99.6%

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

      12. +-commutative 99.6%

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

      13. distribute-lft-in 99.6%

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

      14. neg-mul-1 99.6%

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

      15. remove-double-neg 99.6%

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

      16. metadata-eval 99.6%

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

      17. distribute-lft-neg-out 99.6%

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

      18. *-commutative 99.6%

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

      19. distribute-lft-neg-in 99.6%

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

      20. associate-/r* 99.5%

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

      21. metadata-eval 99.5%

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

      22. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around inf 95.8%

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

      1. neg-mul-1 95.8%

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

   7. Simplified 95.8%

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

   8. Taylor expanded in y around 0 88.9%

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

      1. sub-neg 88.9%

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

      2. metadata-eval 88.9%

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

      3. associate-/l* 95.9%

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

   10. Simplified 95.9%

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

   if -1.75 < x < 1.69999999999999996

   1. Initial program 99.7%

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

      1. associate-/l* 99.7%

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

      2. *-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 99.8%

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

      2. un-div-inv 99.8%

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

      3. *-commutative 99.8%

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

      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 98.5%

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

      1. expm1-log1p-u 98.5%

         \[\leadsto \frac{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(1 - x\right)\right)}}{y} \]

   9. Applied egg-rr 98.5%

      \[\leadsto \frac{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(1 - x\right)\right)}}{y} \]
   10. Step-by-step derivation

       1. expm1-undefine 98.5%

          \[\leadsto \frac{\color{blue}{e^{\mathsf{log1p}\left(1 - x\right)} - 1}}{y} \]

       2. sub-neg 98.5%

          \[\leadsto \frac{\color{blue}{e^{\mathsf{log1p}\left(1 - x\right)} + \left(-1\right)}}{y} \]

       3. log1p-undefine 98.5%

          \[\leadsto \frac{e^{\color{blue}{\log \left(1 + \left(1 - x\right)\right)}} + \left(-1\right)}{y} \]

       4. rem-exp-log 98.5%

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

       5. associate-+r- 98.5%

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

       6. metadata-eval 98.5%

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

       7. metadata-eval 98.5%

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

   11. Simplified 98.5%

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

4. Final simplification 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.75 \lor \neg \left(x \leq 1.7\right):\\ \;\;\;\;0.3333333333333333 \cdot \left(x \cdot \frac{x + -3}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(2 - x\right) + -1}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 98.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.3:\\ \;\;\;\;\frac{x}{y} \cdot \frac{3 - x}{-3}\\ \mathbf{elif}\;x \leq 1.3:\\ \;\;\;\;\frac{3 + x \cdot -4}{y \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y} \cdot \left(x - 3\right)}{3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2.3)
   (* (/ x y) (/ (- 3.0 x) -3.0))
   (if (<= x 1.3)
     (/ (+ 3.0 (* x -4.0)) (* y 3.0))
     (/ (* (/ x y) (- x 3.0)) 3.0))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.3) {
		tmp = (x / y) * ((3.0 - x) / -3.0);
	} else if (x <= 1.3) {
		tmp = (3.0 + (x * -4.0)) / (y * 3.0);
	} else {
		tmp = ((x / y) * (x - 3.0)) / 3.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-2.3d0)) then
        tmp = (x / y) * ((3.0d0 - x) / (-3.0d0))
    else if (x <= 1.3d0) then
        tmp = (3.0d0 + (x * (-4.0d0))) / (y * 3.0d0)
    else
        tmp = ((x / y) * (x - 3.0d0)) / 3.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -2.3) {
		tmp = (x / y) * ((3.0 - x) / -3.0);
	} else if (x <= 1.3) {
		tmp = (3.0 + (x * -4.0)) / (y * 3.0);
	} else {
		tmp = ((x / y) * (x - 3.0)) / 3.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2.3:
		tmp = (x / y) * ((3.0 - x) / -3.0)
	elif x <= 1.3:
		tmp = (3.0 + (x * -4.0)) / (y * 3.0)
	else:
		tmp = ((x / y) * (x - 3.0)) / 3.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2.3)
		tmp = Float64(Float64(x / y) * Float64(Float64(3.0 - x) / -3.0));
	elseif (x <= 1.3)
		tmp = Float64(Float64(3.0 + Float64(x * -4.0)) / Float64(y * 3.0));
	else
		tmp = Float64(Float64(Float64(x / y) * Float64(x - 3.0)) / 3.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2.3)
		tmp = (x / y) * ((3.0 - x) / -3.0);
	elseif (x <= 1.3)
		tmp = (3.0 + (x * -4.0)) / (y * 3.0);
	else
		tmp = ((x / y) * (x - 3.0)) / 3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2.3], N[(N[(x / y), $MachinePrecision] * N[(N[(3.0 - x), $MachinePrecision] / -3.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.3], N[(N[(3.0 + N[(x * -4.0), $MachinePrecision]), $MachinePrecision] / N[(y * 3.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x / y), $MachinePrecision] * N[(x - 3.0), $MachinePrecision]), $MachinePrecision] / 3.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.2999999999999998

   1. Initial program 93.6%

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

      1. associate-/l* 99.6%

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

      2. *-rgt-identity 99.6%

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

      3. remove-double-neg 99.6%

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

      4. distribute-lft-neg-out 99.6%

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

      5. neg-mul-1 99.6%

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

      6. times-frac 99.6%

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

      7. *-rgt-identity 99.6%

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

      8. associate-/l* 99.6%

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

      9. metadata-eval 99.6%

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

      10. *-commutative 99.6%

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

      11. sub-neg 99.6%

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

      12. +-commutative 99.6%

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

      13. distribute-lft-in 99.6%

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

      14. neg-mul-1 99.6%

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

      15. remove-double-neg 99.6%

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

      16. metadata-eval 99.6%

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

      17. distribute-lft-neg-out 99.6%

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

      18. *-commutative 99.6%

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

      19. distribute-lft-neg-in 99.6%

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

      20. associate-/r* 99.5%

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

      21. metadata-eval 99.5%

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

      22. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around inf 96.0%

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

      1. neg-mul-1 96.0%

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

   7. Simplified 96.0%

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

   8. Taylor expanded in y around 0 90.0%

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

      1. associate-*r/ 90.1%

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

      2. clear-num 89.9%

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

      3. *-commutative 89.9%

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

      4. add-sqr-sqrt 0.0%

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

      5. sqrt-unprod 0.7%

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

      6. sqr-neg 0.7%

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

      7. sqrt-unprod 0.7%

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

      8. add-sqr-sqrt 0.7%

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

      9. distribute-lft-neg-in 0.7%

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

      10. distribute-lft-neg-in 0.7%

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

      11. add-sqr-sqrt 0.7%

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

      12. sqrt-unprod 0.7%

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

      13. sqr-neg 0.7%

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

      14. sqrt-unprod 0.0%

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

      15. add-sqr-sqrt 89.9%

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

      16. *-un-lft-identity 89.9%

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

      17. *-un-lft-identity 89.9%

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

      18. sub-neg 89.9%

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

      19. metadata-eval 89.9%

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

   10. Applied egg-rr 89.9%

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

       1. associate-/r/ 90.0%

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

       2. associate-*r* 90.0%

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

       3. *-commutative 90.0%

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

       4. associate-*r* 90.0%

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

       5. *-commutative 90.0%

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

       6. associate-*r/ 90.1%

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

       7. metadata-eval 90.1%

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

       8. associate-/l* 90.1%

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

       9. remove-double-neg 90.1%

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

       10. distribute-frac-neg2 90.1%

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

       11. associate-/l* 90.1%

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

       12. distribute-lft-neg-in 90.1%

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

       13. distribute-rgt-neg-in 90.1%

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

       14. +-commutative 90.1%

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

       15. distribute-neg-in 90.1%

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

       16. metadata-eval 90.1%

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

       17. sub-neg 90.1%

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

       18. distribute-frac-neg2 90.1%

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

       19. distribute-neg-frac 90.1%

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

       20. metadata-eval 90.1%

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

   12. Simplified 90.1%

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

       1. clear-num 90.0%

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

       2. un-div-inv 90.0%

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

       3. div-inv 90.0%

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

       4. metadata-eval 90.0%

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

   14. Applied egg-rr 90.0%

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

       1. times-frac 96.2%

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

   16. Simplified 96.2%

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

   if -2.2999999999999998 < x < 1.30000000000000004

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0 99.2%

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

      1. *-commutative 99.2%

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

   5. Simplified 99.2%

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

   if 1.30000000000000004 < x

   1. Initial program 91.6%

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

      1. associate-/l* 99.6%

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

      2. *-commutative 99.6%

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

   3. Simplified 99.6%

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

      1. *-commutative 99.6%

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

      2. associate-/l* 91.6%

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

      3. times-frac 99.7%

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

      4. associate-*r/ 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in x around inf 95.9%

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

      1. neg-mul-1 95.9%

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

      2. distribute-neg-frac 95.9%

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

   9. Simplified 95.9%

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

4. Final simplification 97.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3:\\ \;\;\;\;\frac{x}{y} \cdot \frac{3 - x}{-3}\\ \mathbf{elif}\;x \leq 1.3:\\ \;\;\;\;\frac{3 + x \cdot -4}{y \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y} \cdot \left(x - 3\right)}{3}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 98.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.3:\\ \;\;\;\;0.3333333333333333 \cdot \left(x \cdot \frac{x + -3}{y}\right)\\ \mathbf{elif}\;x \leq 1.3:\\ \;\;\;\;0.3333333333333333 \cdot \frac{3 + x \cdot -4}{y}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \left(\left(x + -3\right) \cdot \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2.3)
   (* 0.3333333333333333 (* x (/ (+ x -3.0) y)))
   (if (<= x 1.3)
     (* 0.3333333333333333 (/ (+ 3.0 (* x -4.0)) y))
     (* 0.3333333333333333 (* (+ x -3.0) (/ x y))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.3) {
		tmp = 0.3333333333333333 * (x * ((x + -3.0) / y));
	} else if (x <= 1.3) {
		tmp = 0.3333333333333333 * ((3.0 + (x * -4.0)) / y);
	} else {
		tmp = 0.3333333333333333 * ((x + -3.0) * (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 <= (-2.3d0)) then
        tmp = 0.3333333333333333d0 * (x * ((x + (-3.0d0)) / y))
    else if (x <= 1.3d0) then
        tmp = 0.3333333333333333d0 * ((3.0d0 + (x * (-4.0d0))) / y)
    else
        tmp = 0.3333333333333333d0 * ((x + (-3.0d0)) * (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -2.3) {
		tmp = 0.3333333333333333 * (x * ((x + -3.0) / y));
	} else if (x <= 1.3) {
		tmp = 0.3333333333333333 * ((3.0 + (x * -4.0)) / y);
	} else {
		tmp = 0.3333333333333333 * ((x + -3.0) * (x / y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2.3:
		tmp = 0.3333333333333333 * (x * ((x + -3.0) / y))
	elif x <= 1.3:
		tmp = 0.3333333333333333 * ((3.0 + (x * -4.0)) / y)
	else:
		tmp = 0.3333333333333333 * ((x + -3.0) * (x / y))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2.3)
		tmp = Float64(0.3333333333333333 * Float64(x * Float64(Float64(x + -3.0) / y)));
	elseif (x <= 1.3)
		tmp = Float64(0.3333333333333333 * Float64(Float64(3.0 + Float64(x * -4.0)) / y));
	else
		tmp = Float64(0.3333333333333333 * Float64(Float64(x + -3.0) * Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2.3)
		tmp = 0.3333333333333333 * (x * ((x + -3.0) / y));
	elseif (x <= 1.3)
		tmp = 0.3333333333333333 * ((3.0 + (x * -4.0)) / y);
	else
		tmp = 0.3333333333333333 * ((x + -3.0) * (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2.3], N[(0.3333333333333333 * N[(x * N[(N[(x + -3.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.3], N[(0.3333333333333333 * N[(N[(3.0 + N[(x * -4.0), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(0.3333333333333333 * N[(N[(x + -3.0), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.2999999999999998

   1. Initial program 93.6%

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

      1. associate-/l* 99.6%

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

      2. *-rgt-identity 99.6%

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

      3. remove-double-neg 99.6%

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

      4. distribute-lft-neg-out 99.6%

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

      5. neg-mul-1 99.6%

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

      6. times-frac 99.6%

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

      7. *-rgt-identity 99.6%

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

      8. associate-/l* 99.6%

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

      9. metadata-eval 99.6%

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

      10. *-commutative 99.6%

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

      11. sub-neg 99.6%

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

      12. +-commutative 99.6%

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

      13. distribute-lft-in 99.6%

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

      14. neg-mul-1 99.6%

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

      15. remove-double-neg 99.6%

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

      16. metadata-eval 99.6%

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

      17. distribute-lft-neg-out 99.6%

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

      18. *-commutative 99.6%

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

      19. distribute-lft-neg-in 99.6%

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

      20. associate-/r* 99.5%

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

      21. metadata-eval 99.5%

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

      22. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around inf 96.0%

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

      1. neg-mul-1 96.0%

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

   7. Simplified 96.0%

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

   8. Taylor expanded in y around 0 90.0%

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

      1. sub-neg 90.0%

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

      2. metadata-eval 90.0%

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

      3. associate-/l* 96.1%

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

   10. Simplified 96.1%

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

   if -2.2999999999999998 < x < 1.30000000000000004

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0 99.2%

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

      1. *-commutative 99.2%

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

   5. Simplified 99.2%

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

   6. Taylor expanded in y around 0 99.0%

      \[\leadsto \color{blue}{0.3333333333333333 \cdot \frac{3 + -4 \cdot x}{y}} \]

   if 1.30000000000000004 < x

   1. Initial program 91.6%

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

      1. associate-/l* 99.6%

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

      2. *-rgt-identity 99.6%

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

      3. remove-double-neg 99.6%

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

      4. distribute-lft-neg-out 99.6%

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

      5. neg-mul-1 99.6%

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

      6. times-frac 99.5%

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

      7. *-rgt-identity 99.5%

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

      8. associate-/l* 99.5%

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

      9. metadata-eval 99.5%

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

      10. *-commutative 99.5%

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

      11. sub-neg 99.5%

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

      12. +-commutative 99.5%

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

      13. distribute-lft-in 99.5%

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

      14. neg-mul-1 99.5%

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

      15. remove-double-neg 99.5%

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

      16. metadata-eval 99.5%

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

      17. distribute-lft-neg-out 99.5%

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

      18. *-commutative 99.5%

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

      19. distribute-lft-neg-in 99.5%

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

      20. associate-/r* 99.4%

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

      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 inf 95.7%

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

      1. neg-mul-1 95.7%

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

   7. Simplified 95.7%

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

   8. Taylor expanded in y around 0 87.8%

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

   9. Taylor expanded in x around 0 95.8%

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

       1. sub-neg 95.8%

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

       2. distribute-rgt-in 69.5%

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

       3. distribute-lft-neg-in 69.5%

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

       4. metadata-eval 69.5%

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

       5. associate-*r* 69.5%

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

       6. associate-*l/ 69.5%

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

       7. *-lft-identity 69.5%

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

       8. *-commutative 69.5%

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

       9. distribute-lft-in 95.8%

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

   11. Simplified 95.8%

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

4. Final simplification 97.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3:\\ \;\;\;\;0.3333333333333333 \cdot \left(x \cdot \frac{x + -3}{y}\right)\\ \mathbf{elif}\;x \leq 1.3:\\ \;\;\;\;0.3333333333333333 \cdot \frac{3 + x \cdot -4}{y}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \left(\left(x + -3\right) \cdot \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 97.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.75:\\ \;\;\;\;0.3333333333333333 \cdot \left(x \cdot \frac{x + -3}{y}\right)\\ \mathbf{elif}\;x \leq 1.7:\\ \;\;\;\;\frac{\left(2 - x\right) + -1}{y}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \left(\left(x + -3\right) \cdot \frac{x}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.75)
   (* 0.3333333333333333 (* x (/ (+ x -3.0) y)))
   (if (<= x 1.7)
     (/ (+ (- 2.0 x) -1.0) y)
     (* 0.3333333333333333 (* (+ x -3.0) (/ x y))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.75) {
		tmp = 0.3333333333333333 * (x * ((x + -3.0) / y));
	} else if (x <= 1.7) {
		tmp = ((2.0 - x) + -1.0) / y;
	} else {
		tmp = 0.3333333333333333 * ((x + -3.0) * (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 <= (-1.75d0)) then
        tmp = 0.3333333333333333d0 * (x * ((x + (-3.0d0)) / y))
    else if (x <= 1.7d0) then
        tmp = ((2.0d0 - x) + (-1.0d0)) / y
    else
        tmp = 0.3333333333333333d0 * ((x + (-3.0d0)) * (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -1.75) {
		tmp = 0.3333333333333333 * (x * ((x + -3.0) / y));
	} else if (x <= 1.7) {
		tmp = ((2.0 - x) + -1.0) / y;
	} else {
		tmp = 0.3333333333333333 * ((x + -3.0) * (x / y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.75:
		tmp = 0.3333333333333333 * (x * ((x + -3.0) / y))
	elif x <= 1.7:
		tmp = ((2.0 - x) + -1.0) / y
	else:
		tmp = 0.3333333333333333 * ((x + -3.0) * (x / y))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.75)
		tmp = Float64(0.3333333333333333 * Float64(x * Float64(Float64(x + -3.0) / y)));
	elseif (x <= 1.7)
		tmp = Float64(Float64(Float64(2.0 - x) + -1.0) / y);
	else
		tmp = Float64(0.3333333333333333 * Float64(Float64(x + -3.0) * Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.75)
		tmp = 0.3333333333333333 * (x * ((x + -3.0) / y));
	elseif (x <= 1.7)
		tmp = ((2.0 - x) + -1.0) / y;
	else
		tmp = 0.3333333333333333 * ((x + -3.0) * (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.75], N[(0.3333333333333333 * N[(x * N[(N[(x + -3.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.7], N[(N[(N[(2.0 - x), $MachinePrecision] + -1.0), $MachinePrecision] / y), $MachinePrecision], N[(0.3333333333333333 * N[(N[(x + -3.0), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.75

   1. Initial program 93.6%

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

      1. associate-/l* 99.6%

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

      2. *-rgt-identity 99.6%

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

      3. remove-double-neg 99.6%

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

      4. distribute-lft-neg-out 99.6%

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

      5. neg-mul-1 99.6%

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

      6. times-frac 99.6%

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

      7. *-rgt-identity 99.6%

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

      8. associate-/l* 99.6%

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

      9. metadata-eval 99.6%

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

      10. *-commutative 99.6%

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

      11. sub-neg 99.6%

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

      12. +-commutative 99.6%

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

      13. distribute-lft-in 99.6%

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

      14. neg-mul-1 99.6%

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

      15. remove-double-neg 99.6%

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

      16. metadata-eval 99.6%

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

      17. distribute-lft-neg-out 99.6%

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

      18. *-commutative 99.6%

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

      19. distribute-lft-neg-in 99.6%

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

      20. associate-/r* 99.5%

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

      21. metadata-eval 99.5%

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

      22. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around inf 96.0%

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

      1. neg-mul-1 96.0%

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

   7. Simplified 96.0%

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

   8. Taylor expanded in y around 0 90.0%

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

      1. sub-neg 90.0%

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

      2. metadata-eval 90.0%

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

      3. associate-/l* 96.1%

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

   10. Simplified 96.1%

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

   if -1.75 < x < 1.69999999999999996

   1. Initial program 99.7%

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

      1. associate-/l* 99.7%

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

      2. *-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 99.8%

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

      2. un-div-inv 99.8%

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

      3. *-commutative 99.8%

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

      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 98.5%

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

      1. expm1-log1p-u 98.5%

         \[\leadsto \frac{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(1 - x\right)\right)}}{y} \]

   9. Applied egg-rr 98.5%

      \[\leadsto \frac{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(1 - x\right)\right)}}{y} \]
   10. Step-by-step derivation

       1. expm1-undefine 98.5%

          \[\leadsto \frac{\color{blue}{e^{\mathsf{log1p}\left(1 - x\right)} - 1}}{y} \]

       2. sub-neg 98.5%

          \[\leadsto \frac{\color{blue}{e^{\mathsf{log1p}\left(1 - x\right)} + \left(-1\right)}}{y} \]

       3. log1p-undefine 98.5%

          \[\leadsto \frac{e^{\color{blue}{\log \left(1 + \left(1 - x\right)\right)}} + \left(-1\right)}{y} \]

       4. rem-exp-log 98.5%

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

       5. associate-+r- 98.5%

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

       6. metadata-eval 98.5%

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

       7. metadata-eval 98.5%

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

   11. Simplified 98.5%

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

   if 1.69999999999999996 < x

   1. Initial program 91.6%

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

      1. associate-/l* 99.6%

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

      2. *-rgt-identity 99.6%

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

      3. remove-double-neg 99.6%

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

      4. distribute-lft-neg-out 99.6%

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

      5. neg-mul-1 99.6%

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

      6. times-frac 99.5%

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

      7. *-rgt-identity 99.5%

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

      8. associate-/l* 99.5%

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

      9. metadata-eval 99.5%

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

      10. *-commutative 99.5%

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

      11. sub-neg 99.5%

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

      12. +-commutative 99.5%

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

      13. distribute-lft-in 99.5%

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

      14. neg-mul-1 99.5%

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

      15. remove-double-neg 99.5%

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

      16. metadata-eval 99.5%

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

      17. distribute-lft-neg-out 99.5%

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

      18. *-commutative 99.5%

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

      19. distribute-lft-neg-in 99.5%

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

      20. associate-/r* 99.4%

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

      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 inf 95.7%

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

      1. neg-mul-1 95.7%

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

   7. Simplified 95.7%

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

   8. Taylor expanded in y around 0 87.8%

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

   9. Taylor expanded in x around 0 95.8%

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

       1. sub-neg 95.8%

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

       2. distribute-rgt-in 69.5%

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

       3. distribute-lft-neg-in 69.5%

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

       4. metadata-eval 69.5%

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

       5. associate-*r* 69.5%

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

       6. associate-*l/ 69.5%

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

       7. *-lft-identity 69.5%

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

       8. *-commutative 69.5%

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

       9. distribute-lft-in 95.8%

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

   11. Simplified 95.8%

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

4. Final simplification 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.75:\\ \;\;\;\;0.3333333333333333 \cdot \left(x \cdot \frac{x + -3}{y}\right)\\ \mathbf{elif}\;x \leq 1.7:\\ \;\;\;\;\frac{\left(2 - x\right) + -1}{y}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \left(\left(x + -3\right) \cdot \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 97.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.8:\\ \;\;\;\;\frac{x \cdot 0.3333333333333333}{\frac{y}{x}}\\ \mathbf{elif}\;x \leq 3:\\ \;\;\;\;\frac{\left(2 - x\right) + -1}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(-x\right) \cdot \frac{x \cdot -0.3333333333333333}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -3.8)
   (/ (* x 0.3333333333333333) (/ y x))
   (if (<= x 3.0)
     (/ (+ (- 2.0 x) -1.0) y)
     (* (- x) (/ (* x -0.3333333333333333) y)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -3.8) {
		tmp = (x * 0.3333333333333333) / (y / x);
	} else if (x <= 3.0) {
		tmp = ((2.0 - x) + -1.0) / y;
	} else {
		tmp = -x * ((x * -0.3333333333333333) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-3.8d0)) then
        tmp = (x * 0.3333333333333333d0) / (y / x)
    else if (x <= 3.0d0) then
        tmp = ((2.0d0 - x) + (-1.0d0)) / y
    else
        tmp = -x * ((x * (-0.3333333333333333d0)) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -3.8) {
		tmp = (x * 0.3333333333333333) / (y / x);
	} else if (x <= 3.0) {
		tmp = ((2.0 - x) + -1.0) / y;
	} else {
		tmp = -x * ((x * -0.3333333333333333) / y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -3.8:
		tmp = (x * 0.3333333333333333) / (y / x)
	elif x <= 3.0:
		tmp = ((2.0 - x) + -1.0) / y
	else:
		tmp = -x * ((x * -0.3333333333333333) / y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -3.8)
		tmp = Float64(Float64(x * 0.3333333333333333) / Float64(y / x));
	elseif (x <= 3.0)
		tmp = Float64(Float64(Float64(2.0 - x) + -1.0) / y);
	else
		tmp = Float64(Float64(-x) * Float64(Float64(x * -0.3333333333333333) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -3.8)
		tmp = (x * 0.3333333333333333) / (y / x);
	elseif (x <= 3.0)
		tmp = ((2.0 - x) + -1.0) / y;
	else
		tmp = -x * ((x * -0.3333333333333333) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -3.8], N[(N[(x * 0.3333333333333333), $MachinePrecision] / N[(y / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.0], N[(N[(N[(2.0 - x), $MachinePrecision] + -1.0), $MachinePrecision] / y), $MachinePrecision], N[((-x) * N[(N[(x * -0.3333333333333333), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.7999999999999998

   1. Initial program 93.6%

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

      1. associate-/l* 99.6%

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

      2. *-rgt-identity 99.6%

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

      3. remove-double-neg 99.6%

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

      4. distribute-lft-neg-out 99.6%

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

      5. neg-mul-1 99.6%

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

      6. times-frac 99.6%

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

      7. *-rgt-identity 99.6%

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

      8. associate-/l* 99.6%

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

      9. metadata-eval 99.6%

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

      10. *-commutative 99.6%

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

      11. sub-neg 99.6%

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

      12. +-commutative 99.6%

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

      13. distribute-lft-in 99.6%

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

      14. neg-mul-1 99.6%

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

      15. remove-double-neg 99.6%

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

      16. metadata-eval 99.6%

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

      17. distribute-lft-neg-out 99.6%

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

      18. *-commutative 99.6%

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

      19. distribute-lft-neg-in 99.6%

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

      20. associate-/r* 99.5%

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

      21. metadata-eval 99.5%

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

      22. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around inf 96.0%

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

      1. neg-mul-1 96.0%

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

   7. Simplified 96.0%

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

   8. Taylor expanded in x around inf 95.6%

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

      1. distribute-lft-neg-out 95.6%

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

      2. *-commutative 95.6%

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

      3. *-commutative 95.6%

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

      4. add-sqr-sqrt 0.0%

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

      5. sqrt-unprod 0.7%

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

      6. sqr-neg 0.7%

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

      7. sqrt-unprod 0.7%

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

      8. add-sqr-sqrt 0.7%

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

      9. associate-*l* 0.7%

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

      10. add-sqr-sqrt 0.7%

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

      11. sqrt-unprod 0.7%

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

      12. sqr-neg 0.7%

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

      13. sqrt-unprod 0.0%

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

      14. add-sqr-sqrt 95.7%

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

      15. *-commutative 95.7%

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

   10. Applied egg-rr 95.7%

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

       1. distribute-rgt-neg-in 95.7%

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

       2. clear-num 95.7%

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

       3. associate-*l/ 95.7%

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

       4. *-un-lft-identity 95.7%

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

       5. distribute-rgt-neg-in 95.7%

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

       6. metadata-eval 95.7%

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

   12. Applied egg-rr 95.7%

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

   if -3.7999999999999998 < x < 3

   1. Initial program 99.7%

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

      1. associate-/l* 99.7%

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

      2. *-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 99.8%

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

      2. un-div-inv 99.8%

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

      3. *-commutative 99.8%

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

      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 98.5%

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

      1. expm1-log1p-u 98.5%

         \[\leadsto \frac{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(1 - x\right)\right)}}{y} \]

   9. Applied egg-rr 98.5%

      \[\leadsto \frac{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(1 - x\right)\right)}}{y} \]
   10. Step-by-step derivation

       1. expm1-undefine 98.5%

          \[\leadsto \frac{\color{blue}{e^{\mathsf{log1p}\left(1 - x\right)} - 1}}{y} \]

       2. sub-neg 98.5%

          \[\leadsto \frac{\color{blue}{e^{\mathsf{log1p}\left(1 - x\right)} + \left(-1\right)}}{y} \]

       3. log1p-undefine 98.5%

          \[\leadsto \frac{e^{\color{blue}{\log \left(1 + \left(1 - x\right)\right)}} + \left(-1\right)}{y} \]

       4. rem-exp-log 98.5%

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

       5. associate-+r- 98.5%

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

       6. metadata-eval 98.5%

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

       7. metadata-eval 98.5%

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

   11. Simplified 98.5%

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

   if 3 < x

   1. Initial program 91.6%

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

      1. associate-/l* 99.6%

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

      2. *-rgt-identity 99.6%

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

      3. remove-double-neg 99.6%

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

      4. distribute-lft-neg-out 99.6%

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

      5. neg-mul-1 99.6%

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

      6. times-frac 99.5%

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

      7. *-rgt-identity 99.5%

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

      8. associate-/l* 99.5%

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

      9. metadata-eval 99.5%

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

      10. *-commutative 99.5%

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

      11. sub-neg 99.5%

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

      12. +-commutative 99.5%

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

      13. distribute-lft-in 99.5%

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

      14. neg-mul-1 99.5%

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

      15. remove-double-neg 99.5%

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

      16. metadata-eval 99.5%

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

      17. distribute-lft-neg-out 99.5%

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

      18. *-commutative 99.5%

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

      19. distribute-lft-neg-in 99.5%

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

      20. associate-/r* 99.4%

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

      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 inf 95.7%

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

      1. neg-mul-1 95.7%

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

   7. Simplified 95.7%

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

   8. Taylor expanded in x around inf 95.4%

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

      1. associate-*r/ 95.6%

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

      2. associate-*l/ 95.4%

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

      3. *-commutative 95.4%

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

      4. associate-*r/ 95.6%

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

   10. Simplified 95.6%

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

Alternative 9: 97.9% accurate, 0.6× speedup

Math

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

FPCore

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

C

double code(double x, double y) {
	double tmp;
	if ((x <= -3.8) || !(x <= 3.0)) {
		tmp = (x / y) * (x * 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 / y) * (x * 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 / y) * (x * 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 / y) * (x * 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(Float64(x / y) * Float64(x * 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 / y) * (x * 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[(N[(x / y), $MachinePrecision] * N[(x * 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 92.6%

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

      1. associate-/l* 99.6%

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

      2. *-rgt-identity 99.6%

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

      3. remove-double-neg 99.6%

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

      4. distribute-lft-neg-out 99.6%

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

      5. neg-mul-1 99.6%

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

      6. times-frac 99.6%

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

      7. *-rgt-identity 99.6%

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

      8. associate-/l* 99.6%

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

      9. metadata-eval 99.6%

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

      10. *-commutative 99.6%

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

      11. sub-neg 99.6%

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

      12. +-commutative 99.6%

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

      13. distribute-lft-in 99.6%

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

      14. neg-mul-1 99.6%

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

      15. remove-double-neg 99.6%

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

      16. metadata-eval 99.6%

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

      17. distribute-lft-neg-out 99.6%

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

      18. *-commutative 99.6%

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

      19. distribute-lft-neg-in 99.6%

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

      20. associate-/r* 99.5%

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

      21. metadata-eval 99.5%

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

      22. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around inf 95.8%

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

      1. neg-mul-1 95.8%

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

   7. Simplified 95.8%

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

   8. Taylor expanded in x around inf 95.5%

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

      1. distribute-lft-neg-out 95.5%

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

      2. *-commutative 95.5%

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

      3. *-commutative 95.5%

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

      4. add-sqr-sqrt 45.6%

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

      5. sqrt-unprod 42.2%

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

      6. sqr-neg 42.2%

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

      7. sqrt-unprod 0.4%

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

      8. add-sqr-sqrt 0.6%

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

      9. associate-*l* 0.6%

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

      10. add-sqr-sqrt 0.4%

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

      11. sqrt-unprod 42.3%

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

      12. sqr-neg 42.3%

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

      13. sqrt-unprod 45.6%

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

      14. add-sqr-sqrt 95.6%

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

      15. *-commutative 95.6%

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

   10. Applied egg-rr 95.6%

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

       1. distribute-rgt-neg-in 95.6%

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

       2. distribute-rgt-neg-in 95.6%

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

       3. metadata-eval 95.6%

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

   12. Applied egg-rr 95.6%

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

   if -3.7999999999999998 < x < 3

   1. Initial program 99.7%

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

      1. associate-/l* 99.7%

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

      2. *-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 99.8%

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

      2. un-div-inv 99.8%

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

      3. *-commutative 99.8%

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

      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 98.5%

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

4. Final simplification 97.2%

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

Alternative 10: 92.2% accurate, 0.6× speedup

Math

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

FPCore

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

C

double code(double x, double y) {
	double tmp;
	if ((x <= -3.8) || !(x <= 3.0)) {
		tmp = 0.3333333333333333 * ((x * x) / 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 = 0.3333333333333333d0 * ((x * x) / 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 = 0.3333333333333333 * ((x * x) / 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 = 0.3333333333333333 * ((x * x) / 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(0.3333333333333333 * Float64(Float64(x * x) / 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 = 0.3333333333333333 * ((x * x) / 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[(0.3333333333333333 * N[(N[(x * x), $MachinePrecision] / y), $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 92.6%

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

      1. associate-/l* 99.6%

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

      2. *-rgt-identity 99.6%

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

      3. remove-double-neg 99.6%

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

      4. distribute-lft-neg-out 99.6%

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

      5. neg-mul-1 99.6%

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

      6. times-frac 99.6%

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

      7. *-rgt-identity 99.6%

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

      8. associate-/l* 99.6%

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

      9. metadata-eval 99.6%

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

      10. *-commutative 99.6%

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

      11. sub-neg 99.6%

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

      12. +-commutative 99.6%

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

      13. distribute-lft-in 99.6%

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

      14. neg-mul-1 99.6%

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

      15. remove-double-neg 99.6%

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

      16. metadata-eval 99.6%

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

      17. distribute-lft-neg-out 99.6%

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

      18. *-commutative 99.6%

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

      19. distribute-lft-neg-in 99.6%

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

      20. associate-/r* 99.5%

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

      21. metadata-eval 99.5%

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

      22. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around inf 95.8%

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

      1. neg-mul-1 95.8%

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

   7. Simplified 95.8%

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

   8. Taylor expanded in y around 0 88.9%

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

   9. Taylor expanded in x around inf 88.6%

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

   if -3.7999999999999998 < x < 3

   1. Initial program 99.7%

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

      1. associate-/l* 99.7%

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

      2. *-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 99.8%

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

      2. un-div-inv 99.8%

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

      3. *-commutative 99.8%

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

      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 98.5%

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

4. Final simplification 93.9%

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

Alternative 11: 97.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.8:\\ \;\;\;\;\frac{x \cdot 0.3333333333333333}{\frac{y}{x}}\\ \mathbf{elif}\;x \leq 3:\\ \;\;\;\;\frac{\left(2 - x\right) + -1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(x \cdot 0.3333333333333333\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -3.8)
   (/ (* x 0.3333333333333333) (/ y x))
   (if (<= x 3.0)
     (/ (+ (- 2.0 x) -1.0) y)
     (* (/ x y) (* x 0.3333333333333333)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -3.8) {
		tmp = (x * 0.3333333333333333) / (y / x);
	} else if (x <= 3.0) {
		tmp = ((2.0 - x) + -1.0) / y;
	} else {
		tmp = (x / y) * (x * 0.3333333333333333);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-3.8d0)) then
        tmp = (x * 0.3333333333333333d0) / (y / x)
    else if (x <= 3.0d0) then
        tmp = ((2.0d0 - x) + (-1.0d0)) / y
    else
        tmp = (x / y) * (x * 0.3333333333333333d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -3.8) {
		tmp = (x * 0.3333333333333333) / (y / x);
	} else if (x <= 3.0) {
		tmp = ((2.0 - x) + -1.0) / y;
	} else {
		tmp = (x / y) * (x * 0.3333333333333333);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -3.8:
		tmp = (x * 0.3333333333333333) / (y / x)
	elif x <= 3.0:
		tmp = ((2.0 - x) + -1.0) / y
	else:
		tmp = (x / y) * (x * 0.3333333333333333)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -3.8)
		tmp = Float64(Float64(x * 0.3333333333333333) / Float64(y / x));
	elseif (x <= 3.0)
		tmp = Float64(Float64(Float64(2.0 - x) + -1.0) / y);
	else
		tmp = Float64(Float64(x / y) * Float64(x * 0.3333333333333333));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -3.8)
		tmp = (x * 0.3333333333333333) / (y / x);
	elseif (x <= 3.0)
		tmp = ((2.0 - x) + -1.0) / y;
	else
		tmp = (x / y) * (x * 0.3333333333333333);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -3.8], N[(N[(x * 0.3333333333333333), $MachinePrecision] / N[(y / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.0], N[(N[(N[(2.0 - x), $MachinePrecision] + -1.0), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / y), $MachinePrecision] * N[(x * 0.3333333333333333), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.7999999999999998

   1. Initial program 93.6%

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

      1. associate-/l* 99.6%

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

      2. *-rgt-identity 99.6%

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

      3. remove-double-neg 99.6%

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

      4. distribute-lft-neg-out 99.6%

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

      5. neg-mul-1 99.6%

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

      6. times-frac 99.6%

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

      7. *-rgt-identity 99.6%

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

      8. associate-/l* 99.6%

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

      9. metadata-eval 99.6%

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

      10. *-commutative 99.6%

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

      11. sub-neg 99.6%

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

      12. +-commutative 99.6%

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

      13. distribute-lft-in 99.6%

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

      14. neg-mul-1 99.6%

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

      15. remove-double-neg 99.6%

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

      16. metadata-eval 99.6%

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

      17. distribute-lft-neg-out 99.6%

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

      18. *-commutative 99.6%

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

      19. distribute-lft-neg-in 99.6%

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

      20. associate-/r* 99.5%

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

      21. metadata-eval 99.5%

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

      22. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around inf 96.0%

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

      1. neg-mul-1 96.0%

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

   7. Simplified 96.0%

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

   8. Taylor expanded in x around inf 95.6%

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

      1. distribute-lft-neg-out 95.6%

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

      2. *-commutative 95.6%

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

      3. *-commutative 95.6%

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

      4. add-sqr-sqrt 0.0%

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

      5. sqrt-unprod 0.7%

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

      6. sqr-neg 0.7%

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

      7. sqrt-unprod 0.7%

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

      8. add-sqr-sqrt 0.7%

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

      9. associate-*l* 0.7%

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

      10. add-sqr-sqrt 0.7%

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

      11. sqrt-unprod 0.7%

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

      12. sqr-neg 0.7%

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

      13. sqrt-unprod 0.0%

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

      14. add-sqr-sqrt 95.7%

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

      15. *-commutative 95.7%

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

   10. Applied egg-rr 95.7%

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

       1. distribute-rgt-neg-in 95.7%

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

       2. clear-num 95.7%

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

       3. associate-*l/ 95.7%

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

       4. *-un-lft-identity 95.7%

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

       5. distribute-rgt-neg-in 95.7%

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

       6. metadata-eval 95.7%

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

   12. Applied egg-rr 95.7%

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

   if -3.7999999999999998 < x < 3

   1. Initial program 99.7%

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

      1. associate-/l* 99.7%

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

      2. *-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 99.8%

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

      2. un-div-inv 99.8%

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

      3. *-commutative 99.8%

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

      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 98.5%

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

      1. expm1-log1p-u 98.5%

         \[\leadsto \frac{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(1 - x\right)\right)}}{y} \]

   9. Applied egg-rr 98.5%

      \[\leadsto \frac{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(1 - x\right)\right)}}{y} \]
   10. Step-by-step derivation

       1. expm1-undefine 98.5%

          \[\leadsto \frac{\color{blue}{e^{\mathsf{log1p}\left(1 - x\right)} - 1}}{y} \]

       2. sub-neg 98.5%

          \[\leadsto \frac{\color{blue}{e^{\mathsf{log1p}\left(1 - x\right)} + \left(-1\right)}}{y} \]

       3. log1p-undefine 98.5%

          \[\leadsto \frac{e^{\color{blue}{\log \left(1 + \left(1 - x\right)\right)}} + \left(-1\right)}{y} \]

       4. rem-exp-log 98.5%

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

       5. associate-+r- 98.5%

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

       6. metadata-eval 98.5%

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

       7. metadata-eval 98.5%

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

   11. Simplified 98.5%

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

   if 3 < x

   1. Initial program 91.6%

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

      1. associate-/l* 99.6%

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

      2. *-rgt-identity 99.6%

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

      3. remove-double-neg 99.6%

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

      4. distribute-lft-neg-out 99.6%

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

      5. neg-mul-1 99.6%

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

      6. times-frac 99.5%

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

      7. *-rgt-identity 99.5%

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

      8. associate-/l* 99.5%

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

      9. metadata-eval 99.5%

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

      10. *-commutative 99.5%

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

      11. sub-neg 99.5%

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

      12. +-commutative 99.5%

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

      13. distribute-lft-in 99.5%

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

      14. neg-mul-1 99.5%

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

      15. remove-double-neg 99.5%

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

      16. metadata-eval 99.5%

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

      17. distribute-lft-neg-out 99.5%

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

      18. *-commutative 99.5%

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

      19. distribute-lft-neg-in 99.5%

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

      20. associate-/r* 99.4%

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

      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 inf 95.7%

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

      1. neg-mul-1 95.7%

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

   7. Simplified 95.7%

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

   8. Taylor expanded in x around inf 95.4%

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

      1. distribute-lft-neg-out 95.4%

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

      2. *-commutative 95.4%

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

      3. *-commutative 95.4%

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

      4. add-sqr-sqrt 95.2%

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

      5. sqrt-unprod 87.4%

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

      6. sqr-neg 87.4%

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

      7. sqrt-unprod 0.0%

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

      8. add-sqr-sqrt 0.6%

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

      9. associate-*l* 0.6%

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

      10. add-sqr-sqrt 0.0%

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

      11. sqrt-unprod 87.6%

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

      12. sqr-neg 87.6%

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

      13. sqrt-unprod 95.2%

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

      14. add-sqr-sqrt 95.6%

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

      15. *-commutative 95.6%

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

   10. Applied egg-rr 95.6%

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

       1. distribute-rgt-neg-in 95.6%

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

       2. distribute-rgt-neg-in 95.6%

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

       3. metadata-eval 95.6%

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

   12. Applied egg-rr 95.6%

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

Alternative 12: 97.9% accurate, 0.6× speedup

Math

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

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -3.8)
   (/ (* x 0.3333333333333333) (/ y x))
   (if (<= x 3.0) (/ (- 1.0 x) y) (* (/ x y) (* x 0.3333333333333333)))))

C

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

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-3.8d0)) then
        tmp = (x * 0.3333333333333333d0) / (y / x)
    else if (x <= 3.0d0) then
        tmp = (1.0d0 - x) / y
    else
        tmp = (x / y) * (x * 0.3333333333333333d0)
    end if
    code = tmp
end function

Java

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

Python

def code(x, y):
	tmp = 0
	if x <= -3.8:
		tmp = (x * 0.3333333333333333) / (y / x)
	elif x <= 3.0:
		tmp = (1.0 - x) / y
	else:
		tmp = (x / y) * (x * 0.3333333333333333)
	return tmp

Julia

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

MATLAB

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

Wolfram

code[x_, y_] := If[LessEqual[x, -3.8], N[(N[(x * 0.3333333333333333), $MachinePrecision] / N[(y / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.0], N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / y), $MachinePrecision] * N[(x * 0.3333333333333333), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.7999999999999998

   1. Initial program 93.6%

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

      1. associate-/l* 99.6%

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

      2. *-rgt-identity 99.6%

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

      3. remove-double-neg 99.6%

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

      4. distribute-lft-neg-out 99.6%

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

      5. neg-mul-1 99.6%

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

      6. times-frac 99.6%

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

      7. *-rgt-identity 99.6%

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

      8. associate-/l* 99.6%

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

      9. metadata-eval 99.6%

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

      10. *-commutative 99.6%

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

      11. sub-neg 99.6%

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

      12. +-commutative 99.6%

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

      13. distribute-lft-in 99.6%

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

      14. neg-mul-1 99.6%

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

      15. remove-double-neg 99.6%

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

      16. metadata-eval 99.6%

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

      17. distribute-lft-neg-out 99.6%

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

      18. *-commutative 99.6%

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

      19. distribute-lft-neg-in 99.6%

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

      20. associate-/r* 99.5%

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

      21. metadata-eval 99.5%

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

      22. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around inf 96.0%

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

      1. neg-mul-1 96.0%

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

   7. Simplified 96.0%

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

   8. Taylor expanded in x around inf 95.6%

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

      1. distribute-lft-neg-out 95.6%

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

      2. *-commutative 95.6%

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

      3. *-commutative 95.6%

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

      4. add-sqr-sqrt 0.0%

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

      5. sqrt-unprod 0.7%

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

      6. sqr-neg 0.7%

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

      7. sqrt-unprod 0.7%

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

      8. add-sqr-sqrt 0.7%

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

      9. associate-*l* 0.7%

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

      10. add-sqr-sqrt 0.7%

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

      11. sqrt-unprod 0.7%

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

      12. sqr-neg 0.7%

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

      13. sqrt-unprod 0.0%

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

      14. add-sqr-sqrt 95.7%

          \[\leadsto -\frac{x}{y} \cdot \left(-0.3333333333333333 \cdot \color{blue}{x}\right) \]

      15. *-commutative 95.7%

          \[\leadsto -\frac{x}{y} \cdot \color{blue}{\left(x \cdot -0.3333333333333333\right)} \]

   10. Applied egg-rr 95.7%

       \[\leadsto \color{blue}{-\frac{x}{y} \cdot \left(x \cdot -0.3333333333333333\right)} \]
   11. Step-by-step derivation

       1. distribute-rgt-neg-in 95.7%

          \[\leadsto \color{blue}{\frac{x}{y} \cdot \left(-x \cdot -0.3333333333333333\right)} \]

       2. clear-num 95.7%

          \[\leadsto \color{blue}{\frac{1}{\frac{y}{x}}} \cdot \left(-x \cdot -0.3333333333333333\right) \]

       3. associate-*l/ 95.7%

          \[\leadsto \color{blue}{\frac{1 \cdot \left(-x \cdot -0.3333333333333333\right)}{\frac{y}{x}}} \]

       4. *-un-lft-identity 95.7%

          \[\leadsto \frac{\color{blue}{-x \cdot -0.3333333333333333}}{\frac{y}{x}} \]

       5. distribute-rgt-neg-in 95.7%

          \[\leadsto \frac{\color{blue}{x \cdot \left(--0.3333333333333333\right)}}{\frac{y}{x}} \]

       6. metadata-eval 95.7%

          \[\leadsto \frac{x \cdot \color{blue}{0.3333333333333333}}{\frac{y}{x}} \]

   12. Applied egg-rr 95.7%

       \[\leadsto \color{blue}{\frac{x \cdot 0.3333333333333333}{\frac{y}{x}}} \]

   if -3.7999999999999998 < x < 3

   1. Initial program 99.7%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   2. Step-by-step derivation

      1. associate-/l* 99.7%

         \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{3 - x}{y \cdot 3}} \]

      2. *-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 99.8%

         \[\leadsto \left(1 - x\right) \cdot \color{blue}{\frac{1}{\frac{3 \cdot y}{3 - x}}} \]

      2. un-div-inv 99.8%

         \[\leadsto \color{blue}{\frac{1 - x}{\frac{3 \cdot y}{3 - x}}} \]

      3. *-commutative 99.8%

         \[\leadsto \frac{1 - x}{\frac{\color{blue}{y \cdot 3}}{3 - x}} \]

      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 98.5%

      \[\leadsto \frac{1 - x}{\color{blue}{y}} \]

   if 3 < x

   1. Initial program 91.6%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   2. Step-by-step derivation

      1. associate-/l* 99.6%

         \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{3 - x}{y \cdot 3}} \]

      2. *-rgt-identity 99.6%

         \[\leadsto \left(1 - x\right) \cdot \frac{\color{blue}{\left(3 - x\right) \cdot 1}}{y \cdot 3} \]

      3. remove-double-neg 99.6%

         \[\leadsto \left(1 - x\right) \cdot \frac{\left(3 - x\right) \cdot 1}{\color{blue}{-\left(-y \cdot 3\right)}} \]

      4. distribute-lft-neg-out 99.6%

         \[\leadsto \left(1 - x\right) \cdot \frac{\left(3 - x\right) \cdot 1}{-\color{blue}{\left(-y\right) \cdot 3}} \]

      5. neg-mul-1 99.6%

         \[\leadsto \left(1 - x\right) \cdot \frac{\left(3 - x\right) \cdot 1}{\color{blue}{-1 \cdot \left(\left(-y\right) \cdot 3\right)}} \]

      6. times-frac 99.5%

         \[\leadsto \left(1 - x\right) \cdot \color{blue}{\left(\frac{3 - x}{-1} \cdot \frac{1}{\left(-y\right) \cdot 3}\right)} \]

      7. *-rgt-identity 99.5%

         \[\leadsto \left(1 - x\right) \cdot \left(\frac{\color{blue}{\left(3 - x\right) \cdot 1}}{-1} \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      8. associate-/l* 99.5%

         \[\leadsto \left(1 - x\right) \cdot \left(\color{blue}{\left(\left(3 - x\right) \cdot \frac{1}{-1}\right)} \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      9. metadata-eval 99.5%

         \[\leadsto \left(1 - x\right) \cdot \left(\left(\left(3 - x\right) \cdot \color{blue}{-1}\right) \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      10. *-commutative 99.5%

          \[\leadsto \left(1 - x\right) \cdot \left(\color{blue}{\left(-1 \cdot \left(3 - x\right)\right)} \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      11. sub-neg 99.5%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(-1 \cdot \color{blue}{\left(3 + \left(-x\right)\right)}\right) \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      12. +-commutative 99.5%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(-1 \cdot \color{blue}{\left(\left(-x\right) + 3\right)}\right) \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      13. distribute-lft-in 99.5%

          \[\leadsto \left(1 - x\right) \cdot \left(\color{blue}{\left(-1 \cdot \left(-x\right) + -1 \cdot 3\right)} \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      14. neg-mul-1 99.5%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(\color{blue}{\left(-\left(-x\right)\right)} + -1 \cdot 3\right) \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      15. remove-double-neg 99.5%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(\color{blue}{x} + -1 \cdot 3\right) \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      16. metadata-eval 99.5%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(x + \color{blue}{-3}\right) \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      17. distribute-lft-neg-out 99.5%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(x + -3\right) \cdot \frac{1}{\color{blue}{-y \cdot 3}}\right) \]

      18. *-commutative 99.5%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(x + -3\right) \cdot \frac{1}{-\color{blue}{3 \cdot y}}\right) \]

      19. distribute-lft-neg-in 99.5%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(x + -3\right) \cdot \frac{1}{\color{blue}{\left(-3\right) \cdot y}}\right) \]

      20. associate-/r* 99.4%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(x + -3\right) \cdot \color{blue}{\frac{\frac{1}{-3}}{y}}\right) \]

      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 inf 95.7%

      \[\leadsto \color{blue}{\left(-1 \cdot x\right)} \cdot \left(\left(x + -3\right) \cdot \frac{-0.3333333333333333}{y}\right) \]
   6. Step-by-step derivation

      1. neg-mul-1 95.7%

         \[\leadsto \color{blue}{\left(-x\right)} \cdot \left(\left(x + -3\right) \cdot \frac{-0.3333333333333333}{y}\right) \]

   7. Simplified 95.7%

      \[\leadsto \color{blue}{\left(-x\right)} \cdot \left(\left(x + -3\right) \cdot \frac{-0.3333333333333333}{y}\right) \]

   8. Taylor expanded in x around inf 95.4%

      \[\leadsto \left(-x\right) \cdot \color{blue}{\left(-0.3333333333333333 \cdot \frac{x}{y}\right)} \]
   9. Step-by-step derivation

      1. distribute-lft-neg-out 95.4%

         \[\leadsto \color{blue}{-x \cdot \left(-0.3333333333333333 \cdot \frac{x}{y}\right)} \]

      2. *-commutative 95.4%

         \[\leadsto -\color{blue}{\left(-0.3333333333333333 \cdot \frac{x}{y}\right) \cdot x} \]

      3. *-commutative 95.4%

         \[\leadsto -\color{blue}{\left(\frac{x}{y} \cdot -0.3333333333333333\right)} \cdot x \]

      4. add-sqr-sqrt 95.2%

         \[\leadsto -\left(\frac{x}{y} \cdot -0.3333333333333333\right) \cdot \color{blue}{\left(\sqrt{x} \cdot \sqrt{x}\right)} \]

      5. sqrt-unprod 87.4%

         \[\leadsto -\left(\frac{x}{y} \cdot -0.3333333333333333\right) \cdot \color{blue}{\sqrt{x \cdot x}} \]

      6. sqr-neg 87.4%

         \[\leadsto -\left(\frac{x}{y} \cdot -0.3333333333333333\right) \cdot \sqrt{\color{blue}{\left(-x\right) \cdot \left(-x\right)}} \]

      7. sqrt-unprod 0.0%

         \[\leadsto -\left(\frac{x}{y} \cdot -0.3333333333333333\right) \cdot \color{blue}{\left(\sqrt{-x} \cdot \sqrt{-x}\right)} \]

      8. add-sqr-sqrt 0.6%

         \[\leadsto -\left(\frac{x}{y} \cdot -0.3333333333333333\right) \cdot \color{blue}{\left(-x\right)} \]

      9. associate-*l* 0.6%

         \[\leadsto -\color{blue}{\frac{x}{y} \cdot \left(-0.3333333333333333 \cdot \left(-x\right)\right)} \]

      10. add-sqr-sqrt 0.0%

          \[\leadsto -\frac{x}{y} \cdot \left(-0.3333333333333333 \cdot \color{blue}{\left(\sqrt{-x} \cdot \sqrt{-x}\right)}\right) \]

      11. sqrt-unprod 87.6%

          \[\leadsto -\frac{x}{y} \cdot \left(-0.3333333333333333 \cdot \color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}}\right) \]

      12. sqr-neg 87.6%

          \[\leadsto -\frac{x}{y} \cdot \left(-0.3333333333333333 \cdot \sqrt{\color{blue}{x \cdot x}}\right) \]

      13. sqrt-unprod 95.2%

          \[\leadsto -\frac{x}{y} \cdot \left(-0.3333333333333333 \cdot \color{blue}{\left(\sqrt{x} \cdot \sqrt{x}\right)}\right) \]

      14. add-sqr-sqrt 95.6%

          \[\leadsto -\frac{x}{y} \cdot \left(-0.3333333333333333 \cdot \color{blue}{x}\right) \]

      15. *-commutative 95.6%

          \[\leadsto -\frac{x}{y} \cdot \color{blue}{\left(x \cdot -0.3333333333333333\right)} \]

   10. Applied egg-rr 95.6%

       \[\leadsto \color{blue}{-\frac{x}{y} \cdot \left(x \cdot -0.3333333333333333\right)} \]
   11. Step-by-step derivation

       1. distribute-rgt-neg-in 95.6%

          \[\leadsto \color{blue}{\frac{x}{y} \cdot \left(-x \cdot -0.3333333333333333\right)} \]

       2. distribute-rgt-neg-in 95.6%

          \[\leadsto \frac{x}{y} \cdot \color{blue}{\left(x \cdot \left(--0.3333333333333333\right)\right)} \]

       3. metadata-eval 95.6%

          \[\leadsto \frac{x}{y} \cdot \left(x \cdot \color{blue}{0.3333333333333333}\right) \]

   12. Applied egg-rr 95.6%

       \[\leadsto \color{blue}{\frac{x}{y} \cdot \left(x \cdot 0.3333333333333333\right)} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 13: 63.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.75:\\ \;\;\;\;x \cdot \frac{-1.3333333333333333}{y}\\ \mathbf{elif}\;x \leq 4.7:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -0.75)
   (* x (/ -1.3333333333333333 y))
   (if (<= x 4.7) (/ 1.0 y) (/ x y))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -0.75) {
		tmp = x * (-1.3333333333333333 / y);
	} else if (x <= 4.7) {
		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 * ((-1.3333333333333333d0) / y)
    else if (x <= 4.7d0) 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 * (-1.3333333333333333 / y);
	} else if (x <= 4.7) {
		tmp = 1.0 / y;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -0.75:
		tmp = x * (-1.3333333333333333 / y)
	elif x <= 4.7:
		tmp = 1.0 / y
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -0.75)
		tmp = Float64(x * Float64(-1.3333333333333333 / y));
	elseif (x <= 4.7)
		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 * (-1.3333333333333333 / y);
	elseif (x <= 4.7)
		tmp = 1.0 / y;
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -0.75], N[(x * N[(-1.3333333333333333 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.7], N[(1.0 / y), $MachinePrecision], N[(x / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -0.75

   1. Initial program 93.6%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 25.0%

      \[\leadsto \frac{\color{blue}{3 + -4 \cdot x}}{y \cdot 3} \]
   4. Step-by-step derivation

      1. *-commutative 25.0%

         \[\leadsto \frac{3 + \color{blue}{x \cdot -4}}{y \cdot 3} \]

   5. Simplified 25.0%

      \[\leadsto \frac{\color{blue}{3 + x \cdot -4}}{y \cdot 3} \]

   6. Taylor expanded in x around inf 25.0%

      \[\leadsto \color{blue}{-1.3333333333333333 \cdot \frac{x}{y}} \]
   7. Step-by-step derivation

      1. *-commutative 25.0%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot -1.3333333333333333} \]

      2. *-rgt-identity 25.0%

         \[\leadsto \frac{\color{blue}{x \cdot 1}}{y} \cdot -1.3333333333333333 \]

      3. associate-*r/ 25.0%

         \[\leadsto \color{blue}{\left(x \cdot \frac{1}{y}\right)} \cdot -1.3333333333333333 \]

      4. associate-*l* 25.0%

         \[\leadsto \color{blue}{x \cdot \left(\frac{1}{y} \cdot -1.3333333333333333\right)} \]

      5. metadata-eval 25.0%

         \[\leadsto x \cdot \left(\frac{1}{y} \cdot \color{blue}{\left(-1.3333333333333333\right)}\right) \]

      6. distribute-rgt-neg-in 25.0%

         \[\leadsto x \cdot \color{blue}{\left(-\frac{1}{y} \cdot 1.3333333333333333\right)} \]

      7. *-commutative 25.0%

         \[\leadsto x \cdot \left(-\color{blue}{1.3333333333333333 \cdot \frac{1}{y}}\right) \]

      8. associate-*r/ 25.0%

         \[\leadsto x \cdot \left(-\color{blue}{\frac{1.3333333333333333 \cdot 1}{y}}\right) \]

      9. metadata-eval 25.0%

         \[\leadsto x \cdot \left(-\frac{\color{blue}{1.3333333333333333}}{y}\right) \]

      10. distribute-neg-frac 25.0%

          \[\leadsto x \cdot \color{blue}{\frac{-1.3333333333333333}{y}} \]

      11. metadata-eval 25.0%

          \[\leadsto x \cdot \frac{\color{blue}{-1.3333333333333333}}{y} \]

   8. Simplified 25.0%

      \[\leadsto \color{blue}{x \cdot \frac{-1.3333333333333333}{y}} \]

   if -0.75 < x < 4.70000000000000018

   1. Initial program 99.7%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   2. Step-by-step derivation

      1. associate-/l* 99.7%

         \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{3 - x}{y \cdot 3}} \]

      2. *-rgt-identity 99.7%

         \[\leadsto \left(1 - x\right) \cdot \frac{\color{blue}{\left(3 - x\right) \cdot 1}}{y \cdot 3} \]

      3. remove-double-neg 99.7%

         \[\leadsto \left(1 - x\right) \cdot \frac{\left(3 - x\right) \cdot 1}{\color{blue}{-\left(-y \cdot 3\right)}} \]

      4. distribute-lft-neg-out 99.7%

         \[\leadsto \left(1 - x\right) \cdot \frac{\left(3 - x\right) \cdot 1}{-\color{blue}{\left(-y\right) \cdot 3}} \]

      5. neg-mul-1 99.7%

         \[\leadsto \left(1 - x\right) \cdot \frac{\left(3 - x\right) \cdot 1}{\color{blue}{-1 \cdot \left(\left(-y\right) \cdot 3\right)}} \]

      6. times-frac 99.5%

         \[\leadsto \left(1 - x\right) \cdot \color{blue}{\left(\frac{3 - x}{-1} \cdot \frac{1}{\left(-y\right) \cdot 3}\right)} \]

      7. *-rgt-identity 99.5%

         \[\leadsto \left(1 - x\right) \cdot \left(\frac{\color{blue}{\left(3 - x\right) \cdot 1}}{-1} \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      8. associate-/l* 99.5%

         \[\leadsto \left(1 - x\right) \cdot \left(\color{blue}{\left(\left(3 - x\right) \cdot \frac{1}{-1}\right)} \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      9. metadata-eval 99.5%

         \[\leadsto \left(1 - x\right) \cdot \left(\left(\left(3 - x\right) \cdot \color{blue}{-1}\right) \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      10. *-commutative 99.5%

          \[\leadsto \left(1 - x\right) \cdot \left(\color{blue}{\left(-1 \cdot \left(3 - x\right)\right)} \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      11. sub-neg 99.5%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(-1 \cdot \color{blue}{\left(3 + \left(-x\right)\right)}\right) \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      12. +-commutative 99.5%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(-1 \cdot \color{blue}{\left(\left(-x\right) + 3\right)}\right) \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      13. distribute-lft-in 99.5%

          \[\leadsto \left(1 - x\right) \cdot \left(\color{blue}{\left(-1 \cdot \left(-x\right) + -1 \cdot 3\right)} \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      14. neg-mul-1 99.5%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(\color{blue}{\left(-\left(-x\right)\right)} + -1 \cdot 3\right) \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      15. remove-double-neg 99.5%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(\color{blue}{x} + -1 \cdot 3\right) \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      16. metadata-eval 99.5%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(x + \color{blue}{-3}\right) \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      17. distribute-lft-neg-out 99.5%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(x + -3\right) \cdot \frac{1}{\color{blue}{-y \cdot 3}}\right) \]

      18. *-commutative 99.5%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(x + -3\right) \cdot \frac{1}{-\color{blue}{3 \cdot y}}\right) \]

      19. distribute-lft-neg-in 99.5%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(x + -3\right) \cdot \frac{1}{\color{blue}{\left(-3\right) \cdot y}}\right) \]

      20. associate-/r* 99.4%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(x + -3\right) \cdot \color{blue}{\frac{\frac{1}{-3}}{y}}\right) \]

      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 98.4%

      \[\leadsto \color{blue}{\frac{1}{y}} \]

   if 4.70000000000000018 < x

   1. Initial program 91.6%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   2. Step-by-step derivation

      1. associate-/l* 99.6%

         \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{3 - x}{y \cdot 3}} \]

      2. *-rgt-identity 99.6%

         \[\leadsto \left(1 - x\right) \cdot \frac{\color{blue}{\left(3 - x\right) \cdot 1}}{y \cdot 3} \]

      3. remove-double-neg 99.6%

         \[\leadsto \left(1 - x\right) \cdot \frac{\left(3 - x\right) \cdot 1}{\color{blue}{-\left(-y \cdot 3\right)}} \]

      4. distribute-lft-neg-out 99.6%

         \[\leadsto \left(1 - x\right) \cdot \frac{\left(3 - x\right) \cdot 1}{-\color{blue}{\left(-y\right) \cdot 3}} \]

      5. neg-mul-1 99.6%

         \[\leadsto \left(1 - x\right) \cdot \frac{\left(3 - x\right) \cdot 1}{\color{blue}{-1 \cdot \left(\left(-y\right) \cdot 3\right)}} \]

      6. times-frac 99.5%

         \[\leadsto \left(1 - x\right) \cdot \color{blue}{\left(\frac{3 - x}{-1} \cdot \frac{1}{\left(-y\right) \cdot 3}\right)} \]

      7. *-rgt-identity 99.5%

         \[\leadsto \left(1 - x\right) \cdot \left(\frac{\color{blue}{\left(3 - x\right) \cdot 1}}{-1} \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      8. associate-/l* 99.5%

         \[\leadsto \left(1 - x\right) \cdot \left(\color{blue}{\left(\left(3 - x\right) \cdot \frac{1}{-1}\right)} \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      9. metadata-eval 99.5%

         \[\leadsto \left(1 - x\right) \cdot \left(\left(\left(3 - x\right) \cdot \color{blue}{-1}\right) \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      10. *-commutative 99.5%

          \[\leadsto \left(1 - x\right) \cdot \left(\color{blue}{\left(-1 \cdot \left(3 - x\right)\right)} \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      11. sub-neg 99.5%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(-1 \cdot \color{blue}{\left(3 + \left(-x\right)\right)}\right) \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      12. +-commutative 99.5%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(-1 \cdot \color{blue}{\left(\left(-x\right) + 3\right)}\right) \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      13. distribute-lft-in 99.5%

          \[\leadsto \left(1 - x\right) \cdot \left(\color{blue}{\left(-1 \cdot \left(-x\right) + -1 \cdot 3\right)} \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      14. neg-mul-1 99.5%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(\color{blue}{\left(-\left(-x\right)\right)} + -1 \cdot 3\right) \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      15. remove-double-neg 99.5%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(\color{blue}{x} + -1 \cdot 3\right) \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      16. metadata-eval 99.5%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(x + \color{blue}{-3}\right) \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      17. distribute-lft-neg-out 99.5%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(x + -3\right) \cdot \frac{1}{\color{blue}{-y \cdot 3}}\right) \]

      18. *-commutative 99.5%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(x + -3\right) \cdot \frac{1}{-\color{blue}{3 \cdot y}}\right) \]

      19. distribute-lft-neg-in 99.5%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(x + -3\right) \cdot \frac{1}{\color{blue}{\left(-3\right) \cdot y}}\right) \]

      20. associate-/r* 99.4%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(x + -3\right) \cdot \color{blue}{\frac{\frac{1}{-3}}{y}}\right) \]

      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 inf 95.7%

      \[\leadsto \color{blue}{\left(-1 \cdot x\right)} \cdot \left(\left(x + -3\right) \cdot \frac{-0.3333333333333333}{y}\right) \]
   6. Step-by-step derivation

      1. neg-mul-1 95.7%

         \[\leadsto \color{blue}{\left(-x\right)} \cdot \left(\left(x + -3\right) \cdot \frac{-0.3333333333333333}{y}\right) \]

   7. Simplified 95.7%

      \[\leadsto \color{blue}{\left(-x\right)} \cdot \left(\left(x + -3\right) \cdot \frac{-0.3333333333333333}{y}\right) \]

   8. Taylor expanded in y around 0 87.8%

      \[\leadsto \color{blue}{0.3333333333333333 \cdot \frac{x \cdot \left(x - 3\right)}{y}} \]

   9. Taylor expanded in x around 0 0.8%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{y}} \]
   10. Step-by-step derivation

       1. neg-mul-1 0.8%

          \[\leadsto \color{blue}{-\frac{x}{y}} \]

       2. distribute-neg-frac2 0.8%

          \[\leadsto \color{blue}{\frac{x}{-y}} \]

   11. Simplified 0.8%

       \[\leadsto \color{blue}{\frac{x}{-y}} \]
   12. Step-by-step derivation

       1. add-sqr-sqrt 0.4%

          \[\leadsto \frac{x}{\color{blue}{\sqrt{-y} \cdot \sqrt{-y}}} \]

       2. sqrt-unprod 18.1%

          \[\leadsto \frac{x}{\color{blue}{\sqrt{\left(-y\right) \cdot \left(-y\right)}}} \]

       3. sqr-neg 18.1%

          \[\leadsto \frac{x}{\sqrt{\color{blue}{y \cdot y}}} \]

       4. sqrt-unprod 16.4%

          \[\leadsto \frac{x}{\color{blue}{\sqrt{y} \cdot \sqrt{y}}} \]

       5. add-sqr-sqrt 29.9%

          \[\leadsto \frac{x}{\color{blue}{y}} \]

       6. div-inv 29.9%

          \[\leadsto \color{blue}{x \cdot \frac{1}{y}} \]

   13. Applied egg-rr 29.9%

       \[\leadsto \color{blue}{x \cdot \frac{1}{y}} \]
   14. Step-by-step derivation

       1. associate-*r/ 29.9%

          \[\leadsto \color{blue}{\frac{x \cdot 1}{y}} \]

       2. *-rgt-identity 29.9%

          \[\leadsto \frac{\color{blue}{x}}{y} \]

   15. Simplified 29.9%

       \[\leadsto \color{blue}{\frac{x}{y}} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 14: 63.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;\frac{-x}{y}\\ \mathbf{elif}\;x \leq 4.7:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.0) (/ (- x) y) (if (<= x 4.7) (/ 1.0 y) (/ x y))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.0) {
		tmp = -x / y;
	} else if (x <= 4.7) {
		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 <= 4.7d0) 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 <= 4.7) {
		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 <= 4.7:
		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 <= 4.7)
		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 <= 4.7)
		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, 4.7], N[(1.0 / y), $MachinePrecision], N[(x / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1

   1. Initial program 93.6%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   2. Step-by-step derivation

      1. associate-/l* 99.6%

         \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{3 - x}{y \cdot 3}} \]

      2. *-rgt-identity 99.6%

         \[\leadsto \left(1 - x\right) \cdot \frac{\color{blue}{\left(3 - x\right) \cdot 1}}{y \cdot 3} \]

      3. remove-double-neg 99.6%

         \[\leadsto \left(1 - x\right) \cdot \frac{\left(3 - x\right) \cdot 1}{\color{blue}{-\left(-y \cdot 3\right)}} \]

      4. distribute-lft-neg-out 99.6%

         \[\leadsto \left(1 - x\right) \cdot \frac{\left(3 - x\right) \cdot 1}{-\color{blue}{\left(-y\right) \cdot 3}} \]

      5. neg-mul-1 99.6%

         \[\leadsto \left(1 - x\right) \cdot \frac{\left(3 - x\right) \cdot 1}{\color{blue}{-1 \cdot \left(\left(-y\right) \cdot 3\right)}} \]

      6. times-frac 99.6%

         \[\leadsto \left(1 - x\right) \cdot \color{blue}{\left(\frac{3 - x}{-1} \cdot \frac{1}{\left(-y\right) \cdot 3}\right)} \]

      7. *-rgt-identity 99.6%

         \[\leadsto \left(1 - x\right) \cdot \left(\frac{\color{blue}{\left(3 - x\right) \cdot 1}}{-1} \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      8. associate-/l* 99.6%

         \[\leadsto \left(1 - x\right) \cdot \left(\color{blue}{\left(\left(3 - x\right) \cdot \frac{1}{-1}\right)} \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      9. metadata-eval 99.6%

         \[\leadsto \left(1 - x\right) \cdot \left(\left(\left(3 - x\right) \cdot \color{blue}{-1}\right) \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      10. *-commutative 99.6%

          \[\leadsto \left(1 - x\right) \cdot \left(\color{blue}{\left(-1 \cdot \left(3 - x\right)\right)} \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      11. sub-neg 99.6%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(-1 \cdot \color{blue}{\left(3 + \left(-x\right)\right)}\right) \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      12. +-commutative 99.6%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(-1 \cdot \color{blue}{\left(\left(-x\right) + 3\right)}\right) \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      13. distribute-lft-in 99.6%

          \[\leadsto \left(1 - x\right) \cdot \left(\color{blue}{\left(-1 \cdot \left(-x\right) + -1 \cdot 3\right)} \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      14. neg-mul-1 99.6%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(\color{blue}{\left(-\left(-x\right)\right)} + -1 \cdot 3\right) \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      15. remove-double-neg 99.6%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(\color{blue}{x} + -1 \cdot 3\right) \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      16. metadata-eval 99.6%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(x + \color{blue}{-3}\right) \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      17. distribute-lft-neg-out 99.6%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(x + -3\right) \cdot \frac{1}{\color{blue}{-y \cdot 3}}\right) \]

      18. *-commutative 99.6%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(x + -3\right) \cdot \frac{1}{-\color{blue}{3 \cdot y}}\right) \]

      19. distribute-lft-neg-in 99.6%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(x + -3\right) \cdot \frac{1}{\color{blue}{\left(-3\right) \cdot y}}\right) \]

      20. associate-/r* 99.5%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(x + -3\right) \cdot \color{blue}{\frac{\frac{1}{-3}}{y}}\right) \]

      21. metadata-eval 99.5%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(x + -3\right) \cdot \frac{\frac{1}{\color{blue}{-3}}}{y}\right) \]

      22. metadata-eval 99.5%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(x + -3\right) \cdot \frac{\color{blue}{-0.3333333333333333}}{y}\right) \]

   3. Simplified 99.5%

      \[\leadsto \color{blue}{\left(1 - x\right) \cdot \left(\left(x + -3\right) \cdot \frac{-0.3333333333333333}{y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 96.0%

      \[\leadsto \color{blue}{\left(-1 \cdot x\right)} \cdot \left(\left(x + -3\right) \cdot \frac{-0.3333333333333333}{y}\right) \]
   6. Step-by-step derivation

      1. neg-mul-1 96.0%

         \[\leadsto \color{blue}{\left(-x\right)} \cdot \left(\left(x + -3\right) \cdot \frac{-0.3333333333333333}{y}\right) \]

   7. Simplified 96.0%

      \[\leadsto \color{blue}{\left(-x\right)} \cdot \left(\left(x + -3\right) \cdot \frac{-0.3333333333333333}{y}\right) \]

   8. Taylor expanded in y around 0 90.0%

      \[\leadsto \color{blue}{0.3333333333333333 \cdot \frac{x \cdot \left(x - 3\right)}{y}} \]

   9. Taylor expanded in x around 0 25.0%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{y}} \]
   10. Step-by-step derivation

       1. neg-mul-1 25.0%

          \[\leadsto \color{blue}{-\frac{x}{y}} \]

       2. distribute-neg-frac2 25.0%

          \[\leadsto \color{blue}{\frac{x}{-y}} \]

   11. Simplified 25.0%

       \[\leadsto \color{blue}{\frac{x}{-y}} \]

   if -1 < x < 4.70000000000000018

   1. Initial program 99.7%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   2. Step-by-step derivation

      1. associate-/l* 99.7%

         \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{3 - x}{y \cdot 3}} \]

      2. *-rgt-identity 99.7%

         \[\leadsto \left(1 - x\right) \cdot \frac{\color{blue}{\left(3 - x\right) \cdot 1}}{y \cdot 3} \]

      3. remove-double-neg 99.7%

         \[\leadsto \left(1 - x\right) \cdot \frac{\left(3 - x\right) \cdot 1}{\color{blue}{-\left(-y \cdot 3\right)}} \]

      4. distribute-lft-neg-out 99.7%

         \[\leadsto \left(1 - x\right) \cdot \frac{\left(3 - x\right) \cdot 1}{-\color{blue}{\left(-y\right) \cdot 3}} \]

      5. neg-mul-1 99.7%

         \[\leadsto \left(1 - x\right) \cdot \frac{\left(3 - x\right) \cdot 1}{\color{blue}{-1 \cdot \left(\left(-y\right) \cdot 3\right)}} \]

      6. times-frac 99.5%

         \[\leadsto \left(1 - x\right) \cdot \color{blue}{\left(\frac{3 - x}{-1} \cdot \frac{1}{\left(-y\right) \cdot 3}\right)} \]

      7. *-rgt-identity 99.5%

         \[\leadsto \left(1 - x\right) \cdot \left(\frac{\color{blue}{\left(3 - x\right) \cdot 1}}{-1} \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      8. associate-/l* 99.5%

         \[\leadsto \left(1 - x\right) \cdot \left(\color{blue}{\left(\left(3 - x\right) \cdot \frac{1}{-1}\right)} \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      9. metadata-eval 99.5%

         \[\leadsto \left(1 - x\right) \cdot \left(\left(\left(3 - x\right) \cdot \color{blue}{-1}\right) \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      10. *-commutative 99.5%

          \[\leadsto \left(1 - x\right) \cdot \left(\color{blue}{\left(-1 \cdot \left(3 - x\right)\right)} \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      11. sub-neg 99.5%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(-1 \cdot \color{blue}{\left(3 + \left(-x\right)\right)}\right) \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      12. +-commutative 99.5%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(-1 \cdot \color{blue}{\left(\left(-x\right) + 3\right)}\right) \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      13. distribute-lft-in 99.5%

          \[\leadsto \left(1 - x\right) \cdot \left(\color{blue}{\left(-1 \cdot \left(-x\right) + -1 \cdot 3\right)} \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      14. neg-mul-1 99.5%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(\color{blue}{\left(-\left(-x\right)\right)} + -1 \cdot 3\right) \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      15. remove-double-neg 99.5%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(\color{blue}{x} + -1 \cdot 3\right) \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      16. metadata-eval 99.5%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(x + \color{blue}{-3}\right) \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      17. distribute-lft-neg-out 99.5%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(x + -3\right) \cdot \frac{1}{\color{blue}{-y \cdot 3}}\right) \]

      18. *-commutative 99.5%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(x + -3\right) \cdot \frac{1}{-\color{blue}{3 \cdot y}}\right) \]

      19. distribute-lft-neg-in 99.5%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(x + -3\right) \cdot \frac{1}{\color{blue}{\left(-3\right) \cdot y}}\right) \]

      20. associate-/r* 99.4%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(x + -3\right) \cdot \color{blue}{\frac{\frac{1}{-3}}{y}}\right) \]

      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 98.4%

      \[\leadsto \color{blue}{\frac{1}{y}} \]

   if 4.70000000000000018 < x

   1. Initial program 91.6%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   2. Step-by-step derivation

      1. associate-/l* 99.6%

         \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{3 - x}{y \cdot 3}} \]

      2. *-rgt-identity 99.6%

         \[\leadsto \left(1 - x\right) \cdot \frac{\color{blue}{\left(3 - x\right) \cdot 1}}{y \cdot 3} \]

      3. remove-double-neg 99.6%

         \[\leadsto \left(1 - x\right) \cdot \frac{\left(3 - x\right) \cdot 1}{\color{blue}{-\left(-y \cdot 3\right)}} \]

      4. distribute-lft-neg-out 99.6%

         \[\leadsto \left(1 - x\right) \cdot \frac{\left(3 - x\right) \cdot 1}{-\color{blue}{\left(-y\right) \cdot 3}} \]

      5. neg-mul-1 99.6%

         \[\leadsto \left(1 - x\right) \cdot \frac{\left(3 - x\right) \cdot 1}{\color{blue}{-1 \cdot \left(\left(-y\right) \cdot 3\right)}} \]

      6. times-frac 99.5%

         \[\leadsto \left(1 - x\right) \cdot \color{blue}{\left(\frac{3 - x}{-1} \cdot \frac{1}{\left(-y\right) \cdot 3}\right)} \]

      7. *-rgt-identity 99.5%

         \[\leadsto \left(1 - x\right) \cdot \left(\frac{\color{blue}{\left(3 - x\right) \cdot 1}}{-1} \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      8. associate-/l* 99.5%

         \[\leadsto \left(1 - x\right) \cdot \left(\color{blue}{\left(\left(3 - x\right) \cdot \frac{1}{-1}\right)} \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      9. metadata-eval 99.5%

         \[\leadsto \left(1 - x\right) \cdot \left(\left(\left(3 - x\right) \cdot \color{blue}{-1}\right) \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      10. *-commutative 99.5%

          \[\leadsto \left(1 - x\right) \cdot \left(\color{blue}{\left(-1 \cdot \left(3 - x\right)\right)} \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      11. sub-neg 99.5%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(-1 \cdot \color{blue}{\left(3 + \left(-x\right)\right)}\right) \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      12. +-commutative 99.5%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(-1 \cdot \color{blue}{\left(\left(-x\right) + 3\right)}\right) \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      13. distribute-lft-in 99.5%

          \[\leadsto \left(1 - x\right) \cdot \left(\color{blue}{\left(-1 \cdot \left(-x\right) + -1 \cdot 3\right)} \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      14. neg-mul-1 99.5%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(\color{blue}{\left(-\left(-x\right)\right)} + -1 \cdot 3\right) \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      15. remove-double-neg 99.5%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(\color{blue}{x} + -1 \cdot 3\right) \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      16. metadata-eval 99.5%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(x + \color{blue}{-3}\right) \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      17. distribute-lft-neg-out 99.5%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(x + -3\right) \cdot \frac{1}{\color{blue}{-y \cdot 3}}\right) \]

      18. *-commutative 99.5%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(x + -3\right) \cdot \frac{1}{-\color{blue}{3 \cdot y}}\right) \]

      19. distribute-lft-neg-in 99.5%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(x + -3\right) \cdot \frac{1}{\color{blue}{\left(-3\right) \cdot y}}\right) \]

      20. associate-/r* 99.4%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(x + -3\right) \cdot \color{blue}{\frac{\frac{1}{-3}}{y}}\right) \]

      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 inf 95.7%

      \[\leadsto \color{blue}{\left(-1 \cdot x\right)} \cdot \left(\left(x + -3\right) \cdot \frac{-0.3333333333333333}{y}\right) \]
   6. Step-by-step derivation

      1. neg-mul-1 95.7%

         \[\leadsto \color{blue}{\left(-x\right)} \cdot \left(\left(x + -3\right) \cdot \frac{-0.3333333333333333}{y}\right) \]

   7. Simplified 95.7%

      \[\leadsto \color{blue}{\left(-x\right)} \cdot \left(\left(x + -3\right) \cdot \frac{-0.3333333333333333}{y}\right) \]

   8. Taylor expanded in y around 0 87.8%

      \[\leadsto \color{blue}{0.3333333333333333 \cdot \frac{x \cdot \left(x - 3\right)}{y}} \]

   9. Taylor expanded in x around 0 0.8%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{y}} \]
   10. Step-by-step derivation

       1. neg-mul-1 0.8%

          \[\leadsto \color{blue}{-\frac{x}{y}} \]

       2. distribute-neg-frac2 0.8%

          \[\leadsto \color{blue}{\frac{x}{-y}} \]

   11. Simplified 0.8%

       \[\leadsto \color{blue}{\frac{x}{-y}} \]
   12. Step-by-step derivation

       1. add-sqr-sqrt 0.4%

          \[\leadsto \frac{x}{\color{blue}{\sqrt{-y} \cdot \sqrt{-y}}} \]

       2. sqrt-unprod 18.1%

          \[\leadsto \frac{x}{\color{blue}{\sqrt{\left(-y\right) \cdot \left(-y\right)}}} \]

       3. sqr-neg 18.1%

          \[\leadsto \frac{x}{\sqrt{\color{blue}{y \cdot y}}} \]

       4. sqrt-unprod 16.4%

          \[\leadsto \frac{x}{\color{blue}{\sqrt{y} \cdot \sqrt{y}}} \]

       5. add-sqr-sqrt 29.9%

          \[\leadsto \frac{x}{\color{blue}{y}} \]

       6. div-inv 29.9%

          \[\leadsto \color{blue}{x \cdot \frac{1}{y}} \]

   13. Applied egg-rr 29.9%

       \[\leadsto \color{blue}{x \cdot \frac{1}{y}} \]
   14. Step-by-step derivation

       1. associate-*r/ 29.9%

          \[\leadsto \color{blue}{\frac{x \cdot 1}{y}} \]

       2. *-rgt-identity 29.9%

          \[\leadsto \frac{\color{blue}{x}}{y} \]

   15. Simplified 29.9%

       \[\leadsto \color{blue}{\frac{x}{y}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;\frac{-x}{y}\\ \mathbf{elif}\;x \leq 4.7:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 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 96.4%

   \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
2. Step-by-step derivation

   1. associate-/l* 99.6%

      \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{3 - x}{y \cdot 3}} \]

   2. *-commutative 99.6%

      \[\leadsto \left(1 - x\right) \cdot \frac{3 - x}{\color{blue}{3 \cdot y}} \]

3. Simplified 99.6%

   \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{3 - x}{3 \cdot y}} \]
4. Add Preprocessing

5. Final simplification 99.6%

   \[\leadsto \left(1 - x\right) \cdot \frac{3 - x}{y \cdot 3} \]
6. Add Preprocessing

Alternative 16: 99.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(1 - x\right) \cdot \left(\left(x + -3\right) \cdot \frac{-0.3333333333333333}{y}\right) \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (* (- 1.0 x) (* (+ x -3.0) (/ -0.3333333333333333 y))))

C

double code(double x, double y) {
	return (1.0 - x) * ((x + -3.0) * (-0.3333333333333333 / y));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (1.0d0 - x) * ((x + (-3.0d0)) * ((-0.3333333333333333d0) / y))
end function

Java

public static double code(double x, double y) {
	return (1.0 - x) * ((x + -3.0) * (-0.3333333333333333 / y));
}

Python

def code(x, y):
	return (1.0 - x) * ((x + -3.0) * (-0.3333333333333333 / y))

Julia

function code(x, y)
	return Float64(Float64(1.0 - x) * Float64(Float64(x + -3.0) * Float64(-0.3333333333333333 / y)))
end

MATLAB

function tmp = code(x, y)
	tmp = (1.0 - x) * ((x + -3.0) * (-0.3333333333333333 / y));
end

Wolfram

code[x_, y_] := N[(N[(1.0 - x), $MachinePrecision] * N[(N[(x + -3.0), $MachinePrecision] * N[(-0.3333333333333333 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 96.4%

   \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
2. Step-by-step derivation

   1. associate-/l* 99.6%

      \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{3 - x}{y \cdot 3}} \]

   2. *-rgt-identity 99.6%

      \[\leadsto \left(1 - x\right) \cdot \frac{\color{blue}{\left(3 - x\right) \cdot 1}}{y \cdot 3} \]

   3. remove-double-neg 99.6%

      \[\leadsto \left(1 - x\right) \cdot \frac{\left(3 - x\right) \cdot 1}{\color{blue}{-\left(-y \cdot 3\right)}} \]

   4. distribute-lft-neg-out 99.6%

      \[\leadsto \left(1 - x\right) \cdot \frac{\left(3 - x\right) \cdot 1}{-\color{blue}{\left(-y\right) \cdot 3}} \]

   5. neg-mul-1 99.6%

      \[\leadsto \left(1 - x\right) \cdot \frac{\left(3 - x\right) \cdot 1}{\color{blue}{-1 \cdot \left(\left(-y\right) \cdot 3\right)}} \]

   6. times-frac 99.5%

      \[\leadsto \left(1 - x\right) \cdot \color{blue}{\left(\frac{3 - x}{-1} \cdot \frac{1}{\left(-y\right) \cdot 3}\right)} \]

   7. *-rgt-identity 99.5%

      \[\leadsto \left(1 - x\right) \cdot \left(\frac{\color{blue}{\left(3 - x\right) \cdot 1}}{-1} \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

   8. associate-/l* 99.5%

      \[\leadsto \left(1 - x\right) \cdot \left(\color{blue}{\left(\left(3 - x\right) \cdot \frac{1}{-1}\right)} \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

   9. metadata-eval 99.5%

      \[\leadsto \left(1 - x\right) \cdot \left(\left(\left(3 - x\right) \cdot \color{blue}{-1}\right) \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

   10. *-commutative 99.5%

       \[\leadsto \left(1 - x\right) \cdot \left(\color{blue}{\left(-1 \cdot \left(3 - x\right)\right)} \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

   11. sub-neg 99.5%

       \[\leadsto \left(1 - x\right) \cdot \left(\left(-1 \cdot \color{blue}{\left(3 + \left(-x\right)\right)}\right) \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

   12. +-commutative 99.5%

       \[\leadsto \left(1 - x\right) \cdot \left(\left(-1 \cdot \color{blue}{\left(\left(-x\right) + 3\right)}\right) \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

   13. distribute-lft-in 99.5%

       \[\leadsto \left(1 - x\right) \cdot \left(\color{blue}{\left(-1 \cdot \left(-x\right) + -1 \cdot 3\right)} \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

   14. neg-mul-1 99.5%

       \[\leadsto \left(1 - x\right) \cdot \left(\left(\color{blue}{\left(-\left(-x\right)\right)} + -1 \cdot 3\right) \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

   15. remove-double-neg 99.5%

       \[\leadsto \left(1 - x\right) \cdot \left(\left(\color{blue}{x} + -1 \cdot 3\right) \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

   16. metadata-eval 99.5%

       \[\leadsto \left(1 - x\right) \cdot \left(\left(x + \color{blue}{-3}\right) \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

   17. distribute-lft-neg-out 99.5%

       \[\leadsto \left(1 - x\right) \cdot \left(\left(x + -3\right) \cdot \frac{1}{\color{blue}{-y \cdot 3}}\right) \]

   18. *-commutative 99.5%

       \[\leadsto \left(1 - x\right) \cdot \left(\left(x + -3\right) \cdot \frac{1}{-\color{blue}{3 \cdot y}}\right) \]

   19. distribute-lft-neg-in 99.5%

       \[\leadsto \left(1 - x\right) \cdot \left(\left(x + -3\right) \cdot \frac{1}{\color{blue}{\left(-3\right) \cdot y}}\right) \]

   20. associate-/r* 99.4%

       \[\leadsto \left(1 - x\right) \cdot \left(\left(x + -3\right) \cdot \color{blue}{\frac{\frac{1}{-3}}{y}}\right) \]

   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. Add Preprocessing

Alternative 17: 63.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 3:\\ \;\;\;\;\frac{1 - x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + 1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 3.0) (/ (- 1.0 x) y) (/ (+ x 1.0) y)))

C

double code(double x, double y) {
	double tmp;
	if (x <= 3.0) {
		tmp = (1.0 - x) / y;
	} else {
		tmp = (x + 1.0) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= 3.0d0) then
        tmp = (1.0d0 - x) / y
    else
        tmp = (x + 1.0d0) / 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 + 1.0) / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 3.0:
		tmp = (1.0 - x) / y
	else:
		tmp = (x + 1.0) / 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(Float64(x + 1.0) / 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 + 1.0) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 3.0], N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision], N[(N[(x + 1.0), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 3

   1. Initial program 97.8%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   2. Step-by-step derivation

      1. associate-/l* 99.6%

         \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{3 - x}{y \cdot 3}} \]

      2. *-commutative 99.6%

         \[\leadsto \left(1 - x\right) \cdot \frac{3 - x}{\color{blue}{3 \cdot y}} \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{3 - x}{3 \cdot y}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. 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 75.6%

      \[\leadsto \frac{1 - x}{\color{blue}{y}} \]

   if 3 < x

   1. Initial program 91.6%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   2. Step-by-step derivation

      1. associate-/l* 99.6%

         \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{3 - x}{y \cdot 3}} \]

      2. *-commutative 99.6%

         \[\leadsto \left(1 - x\right) \cdot \frac{3 - x}{\color{blue}{3 \cdot y}} \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{3 - x}{3 \cdot y}} \]
   4. Add Preprocessing
   5. 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 0.8%

      \[\leadsto \frac{1 - x}{\color{blue}{y}} \]
   8. Step-by-step derivation

      1. *-un-lft-identity 0.8%

         \[\leadsto \color{blue}{1 \cdot \frac{1 - x}{y}} \]

      2. *-un-lft-identity 0.8%

         \[\leadsto 1 \cdot \frac{\color{blue}{1 \cdot \left(1 - x\right)}}{y} \]

      3. *-un-lft-identity 0.8%

         \[\leadsto 1 \cdot \frac{\color{blue}{1 - x}}{y} \]

      4. sub-neg 0.8%

         \[\leadsto 1 \cdot \frac{\color{blue}{1 + \left(-x\right)}}{y} \]

      5. add-sqr-sqrt 0.0%

         \[\leadsto 1 \cdot \frac{1 + \color{blue}{\sqrt{-x} \cdot \sqrt{-x}}}{y} \]

      6. sqrt-unprod 41.9%

         \[\leadsto 1 \cdot \frac{1 + \color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}}}{y} \]

      7. sqr-neg 41.9%

         \[\leadsto 1 \cdot \frac{1 + \sqrt{\color{blue}{x \cdot x}}}{y} \]

      8. sqrt-unprod 29.9%

         \[\leadsto 1 \cdot \frac{1 + \color{blue}{\sqrt{x} \cdot \sqrt{x}}}{y} \]

      9. add-sqr-sqrt 29.9%

         \[\leadsto 1 \cdot \frac{1 + \color{blue}{x}}{y} \]

   9. Applied egg-rr 29.9%

      \[\leadsto \color{blue}{1 \cdot \frac{1 + x}{y}} \]
   10. Step-by-step derivation

       1. *-lft-identity 29.9%

          \[\leadsto \color{blue}{\frac{1 + x}{y}} \]

   11. Simplified 29.9%

       \[\leadsto \color{blue}{\frac{1 + x}{y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 3:\\ \;\;\;\;\frac{1 - x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + 1}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 63.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.43:\\ \;\;\;\;x \cdot \frac{-1.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + 1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -0.43) (* x (/ -1.3333333333333333 y)) (/ (+ x 1.0) y)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -0.43) {
		tmp = x * (-1.3333333333333333 / y);
	} else {
		tmp = (x + 1.0) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-0.43d0)) then
        tmp = x * ((-1.3333333333333333d0) / y)
    else
        tmp = (x + 1.0d0) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -0.43) {
		tmp = x * (-1.3333333333333333 / y);
	} else {
		tmp = (x + 1.0) / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -0.43:
		tmp = x * (-1.3333333333333333 / y)
	else:
		tmp = (x + 1.0) / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -0.43)
		tmp = Float64(x * Float64(-1.3333333333333333 / y));
	else
		tmp = Float64(Float64(x + 1.0) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -0.43)
		tmp = x * (-1.3333333333333333 / y);
	else
		tmp = (x + 1.0) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -0.43], N[(x * N[(-1.3333333333333333 / y), $MachinePrecision]), $MachinePrecision], N[(N[(x + 1.0), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -0.429999999999999993

   1. Initial program 93.6%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 25.0%

      \[\leadsto \frac{\color{blue}{3 + -4 \cdot x}}{y \cdot 3} \]
   4. Step-by-step derivation

      1. *-commutative 25.0%

         \[\leadsto \frac{3 + \color{blue}{x \cdot -4}}{y \cdot 3} \]

   5. Simplified 25.0%

      \[\leadsto \frac{\color{blue}{3 + x \cdot -4}}{y \cdot 3} \]

   6. Taylor expanded in x around inf 25.0%

      \[\leadsto \color{blue}{-1.3333333333333333 \cdot \frac{x}{y}} \]
   7. Step-by-step derivation

      1. *-commutative 25.0%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot -1.3333333333333333} \]

      2. *-rgt-identity 25.0%

         \[\leadsto \frac{\color{blue}{x \cdot 1}}{y} \cdot -1.3333333333333333 \]

      3. associate-*r/ 25.0%

         \[\leadsto \color{blue}{\left(x \cdot \frac{1}{y}\right)} \cdot -1.3333333333333333 \]

      4. associate-*l* 25.0%

         \[\leadsto \color{blue}{x \cdot \left(\frac{1}{y} \cdot -1.3333333333333333\right)} \]

      5. metadata-eval 25.0%

         \[\leadsto x \cdot \left(\frac{1}{y} \cdot \color{blue}{\left(-1.3333333333333333\right)}\right) \]

      6. distribute-rgt-neg-in 25.0%

         \[\leadsto x \cdot \color{blue}{\left(-\frac{1}{y} \cdot 1.3333333333333333\right)} \]

      7. *-commutative 25.0%

         \[\leadsto x \cdot \left(-\color{blue}{1.3333333333333333 \cdot \frac{1}{y}}\right) \]

      8. associate-*r/ 25.0%

         \[\leadsto x \cdot \left(-\color{blue}{\frac{1.3333333333333333 \cdot 1}{y}}\right) \]

      9. metadata-eval 25.0%

         \[\leadsto x \cdot \left(-\frac{\color{blue}{1.3333333333333333}}{y}\right) \]

      10. distribute-neg-frac 25.0%

          \[\leadsto x \cdot \color{blue}{\frac{-1.3333333333333333}{y}} \]

      11. metadata-eval 25.0%

          \[\leadsto x \cdot \frac{\color{blue}{-1.3333333333333333}}{y} \]

   8. Simplified 25.0%

      \[\leadsto \color{blue}{x \cdot \frac{-1.3333333333333333}{y}} \]

   if -0.429999999999999993 < x

   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* 99.6%

         \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{3 - x}{y \cdot 3}} \]

      2. *-commutative 99.6%

         \[\leadsto \left(1 - x\right) \cdot \frac{3 - x}{\color{blue}{3 \cdot y}} \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{3 - x}{3 \cdot y}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 99.7%

         \[\leadsto \left(1 - x\right) \cdot \color{blue}{\frac{1}{\frac{3 \cdot y}{3 - x}}} \]

      2. un-div-inv 99.8%

         \[\leadsto \color{blue}{\frac{1 - x}{\frac{3 \cdot y}{3 - x}}} \]

      3. *-commutative 99.8%

         \[\leadsto \frac{1 - x}{\frac{\color{blue}{y \cdot 3}}{3 - x}} \]

      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 69.8%

      \[\leadsto \frac{1 - x}{\color{blue}{y}} \]
   8. Step-by-step derivation

      1. *-un-lft-identity 69.8%

         \[\leadsto \color{blue}{1 \cdot \frac{1 - x}{y}} \]

      2. *-un-lft-identity 69.8%

         \[\leadsto 1 \cdot \frac{\color{blue}{1 \cdot \left(1 - x\right)}}{y} \]

      3. *-un-lft-identity 69.8%

         \[\leadsto 1 \cdot \frac{\color{blue}{1 - x}}{y} \]

      4. sub-neg 69.8%

         \[\leadsto 1 \cdot \frac{\color{blue}{1 + \left(-x\right)}}{y} \]

      5. add-sqr-sqrt 39.5%

         \[\leadsto 1 \cdot \frac{1 + \color{blue}{\sqrt{-x} \cdot \sqrt{-x}}}{y} \]

      6. sqrt-unprod 81.9%

         \[\leadsto 1 \cdot \frac{1 + \color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}}}{y} \]

      7. sqr-neg 81.9%

         \[\leadsto 1 \cdot \frac{1 + \sqrt{\color{blue}{x \cdot x}}}{y} \]

      8. sqrt-unprod 38.9%

         \[\leadsto 1 \cdot \frac{1 + \color{blue}{\sqrt{x} \cdot \sqrt{x}}}{y} \]

      9. add-sqr-sqrt 78.2%

         \[\leadsto 1 \cdot \frac{1 + \color{blue}{x}}{y} \]

   9. Applied egg-rr 78.2%

      \[\leadsto \color{blue}{1 \cdot \frac{1 + x}{y}} \]
   10. Step-by-step derivation

       1. *-lft-identity 78.2%

          \[\leadsto \color{blue}{\frac{1 + x}{y}} \]

   11. Simplified 78.2%

       \[\leadsto \color{blue}{\frac{1 + x}{y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.43:\\ \;\;\;\;x \cdot \frac{-1.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + 1}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 57.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 4.7:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= x 4.7) (/ 1.0 y) (/ x y)))

C

double code(double x, double y) {
	double tmp;
	if (x <= 4.7) {
		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 <= 4.7d0) 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 <= 4.7) {
		tmp = 1.0 / y;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 4.7:
		tmp = 1.0 / y
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 4.7)
		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 <= 4.7)
		tmp = 1.0 / y;
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 4.7], N[(1.0 / y), $MachinePrecision], N[(x / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 4.70000000000000018

   1. Initial program 97.8%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   2. Step-by-step derivation

      1. associate-/l* 99.6%

         \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{3 - x}{y \cdot 3}} \]

      2. *-rgt-identity 99.6%

         \[\leadsto \left(1 - x\right) \cdot \frac{\color{blue}{\left(3 - x\right) \cdot 1}}{y \cdot 3} \]

      3. remove-double-neg 99.6%

         \[\leadsto \left(1 - x\right) \cdot \frac{\left(3 - x\right) \cdot 1}{\color{blue}{-\left(-y \cdot 3\right)}} \]

      4. distribute-lft-neg-out 99.6%

         \[\leadsto \left(1 - x\right) \cdot \frac{\left(3 - x\right) \cdot 1}{-\color{blue}{\left(-y\right) \cdot 3}} \]

      5. neg-mul-1 99.6%

         \[\leadsto \left(1 - x\right) \cdot \frac{\left(3 - x\right) \cdot 1}{\color{blue}{-1 \cdot \left(\left(-y\right) \cdot 3\right)}} \]

      6. times-frac 99.5%

         \[\leadsto \left(1 - x\right) \cdot \color{blue}{\left(\frac{3 - x}{-1} \cdot \frac{1}{\left(-y\right) \cdot 3}\right)} \]

      7. *-rgt-identity 99.5%

         \[\leadsto \left(1 - x\right) \cdot \left(\frac{\color{blue}{\left(3 - x\right) \cdot 1}}{-1} \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      8. associate-/l* 99.5%

         \[\leadsto \left(1 - x\right) \cdot \left(\color{blue}{\left(\left(3 - x\right) \cdot \frac{1}{-1}\right)} \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      9. metadata-eval 99.5%

         \[\leadsto \left(1 - x\right) \cdot \left(\left(\left(3 - x\right) \cdot \color{blue}{-1}\right) \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      10. *-commutative 99.5%

          \[\leadsto \left(1 - x\right) \cdot \left(\color{blue}{\left(-1 \cdot \left(3 - x\right)\right)} \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      11. sub-neg 99.5%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(-1 \cdot \color{blue}{\left(3 + \left(-x\right)\right)}\right) \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      12. +-commutative 99.5%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(-1 \cdot \color{blue}{\left(\left(-x\right) + 3\right)}\right) \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      13. distribute-lft-in 99.5%

          \[\leadsto \left(1 - x\right) \cdot \left(\color{blue}{\left(-1 \cdot \left(-x\right) + -1 \cdot 3\right)} \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      14. neg-mul-1 99.5%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(\color{blue}{\left(-\left(-x\right)\right)} + -1 \cdot 3\right) \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      15. remove-double-neg 99.5%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(\color{blue}{x} + -1 \cdot 3\right) \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      16. metadata-eval 99.5%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(x + \color{blue}{-3}\right) \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      17. distribute-lft-neg-out 99.5%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(x + -3\right) \cdot \frac{1}{\color{blue}{-y \cdot 3}}\right) \]

      18. *-commutative 99.5%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(x + -3\right) \cdot \frac{1}{-\color{blue}{3 \cdot y}}\right) \]

      19. distribute-lft-neg-in 99.5%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(x + -3\right) \cdot \frac{1}{\color{blue}{\left(-3\right) \cdot y}}\right) \]

      20. associate-/r* 99.4%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(x + -3\right) \cdot \color{blue}{\frac{\frac{1}{-3}}{y}}\right) \]

      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 69.5%

      \[\leadsto \color{blue}{\frac{1}{y}} \]

   if 4.70000000000000018 < x

   1. Initial program 91.6%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   2. Step-by-step derivation

      1. associate-/l* 99.6%

         \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{3 - x}{y \cdot 3}} \]

      2. *-rgt-identity 99.6%

         \[\leadsto \left(1 - x\right) \cdot \frac{\color{blue}{\left(3 - x\right) \cdot 1}}{y \cdot 3} \]

      3. remove-double-neg 99.6%

         \[\leadsto \left(1 - x\right) \cdot \frac{\left(3 - x\right) \cdot 1}{\color{blue}{-\left(-y \cdot 3\right)}} \]

      4. distribute-lft-neg-out 99.6%

         \[\leadsto \left(1 - x\right) \cdot \frac{\left(3 - x\right) \cdot 1}{-\color{blue}{\left(-y\right) \cdot 3}} \]

      5. neg-mul-1 99.6%

         \[\leadsto \left(1 - x\right) \cdot \frac{\left(3 - x\right) \cdot 1}{\color{blue}{-1 \cdot \left(\left(-y\right) \cdot 3\right)}} \]

      6. times-frac 99.5%

         \[\leadsto \left(1 - x\right) \cdot \color{blue}{\left(\frac{3 - x}{-1} \cdot \frac{1}{\left(-y\right) \cdot 3}\right)} \]

      7. *-rgt-identity 99.5%

         \[\leadsto \left(1 - x\right) \cdot \left(\frac{\color{blue}{\left(3 - x\right) \cdot 1}}{-1} \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      8. associate-/l* 99.5%

         \[\leadsto \left(1 - x\right) \cdot \left(\color{blue}{\left(\left(3 - x\right) \cdot \frac{1}{-1}\right)} \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      9. metadata-eval 99.5%

         \[\leadsto \left(1 - x\right) \cdot \left(\left(\left(3 - x\right) \cdot \color{blue}{-1}\right) \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      10. *-commutative 99.5%

          \[\leadsto \left(1 - x\right) \cdot \left(\color{blue}{\left(-1 \cdot \left(3 - x\right)\right)} \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      11. sub-neg 99.5%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(-1 \cdot \color{blue}{\left(3 + \left(-x\right)\right)}\right) \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      12. +-commutative 99.5%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(-1 \cdot \color{blue}{\left(\left(-x\right) + 3\right)}\right) \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      13. distribute-lft-in 99.5%

          \[\leadsto \left(1 - x\right) \cdot \left(\color{blue}{\left(-1 \cdot \left(-x\right) + -1 \cdot 3\right)} \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      14. neg-mul-1 99.5%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(\color{blue}{\left(-\left(-x\right)\right)} + -1 \cdot 3\right) \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      15. remove-double-neg 99.5%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(\color{blue}{x} + -1 \cdot 3\right) \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      16. metadata-eval 99.5%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(x + \color{blue}{-3}\right) \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

      17. distribute-lft-neg-out 99.5%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(x + -3\right) \cdot \frac{1}{\color{blue}{-y \cdot 3}}\right) \]

      18. *-commutative 99.5%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(x + -3\right) \cdot \frac{1}{-\color{blue}{3 \cdot y}}\right) \]

      19. distribute-lft-neg-in 99.5%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(x + -3\right) \cdot \frac{1}{\color{blue}{\left(-3\right) \cdot y}}\right) \]

      20. associate-/r* 99.4%

          \[\leadsto \left(1 - x\right) \cdot \left(\left(x + -3\right) \cdot \color{blue}{\frac{\frac{1}{-3}}{y}}\right) \]

      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 inf 95.7%

      \[\leadsto \color{blue}{\left(-1 \cdot x\right)} \cdot \left(\left(x + -3\right) \cdot \frac{-0.3333333333333333}{y}\right) \]
   6. Step-by-step derivation

      1. neg-mul-1 95.7%

         \[\leadsto \color{blue}{\left(-x\right)} \cdot \left(\left(x + -3\right) \cdot \frac{-0.3333333333333333}{y}\right) \]

   7. Simplified 95.7%

      \[\leadsto \color{blue}{\left(-x\right)} \cdot \left(\left(x + -3\right) \cdot \frac{-0.3333333333333333}{y}\right) \]

   8. Taylor expanded in y around 0 87.8%

      \[\leadsto \color{blue}{0.3333333333333333 \cdot \frac{x \cdot \left(x - 3\right)}{y}} \]

   9. Taylor expanded in x around 0 0.8%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{y}} \]
   10. Step-by-step derivation

       1. neg-mul-1 0.8%

          \[\leadsto \color{blue}{-\frac{x}{y}} \]

       2. distribute-neg-frac2 0.8%

          \[\leadsto \color{blue}{\frac{x}{-y}} \]

   11. Simplified 0.8%

       \[\leadsto \color{blue}{\frac{x}{-y}} \]
   12. Step-by-step derivation

       1. add-sqr-sqrt 0.4%

          \[\leadsto \frac{x}{\color{blue}{\sqrt{-y} \cdot \sqrt{-y}}} \]

       2. sqrt-unprod 18.1%

          \[\leadsto \frac{x}{\color{blue}{\sqrt{\left(-y\right) \cdot \left(-y\right)}}} \]

       3. sqr-neg 18.1%

          \[\leadsto \frac{x}{\sqrt{\color{blue}{y \cdot y}}} \]

       4. sqrt-unprod 16.4%

          \[\leadsto \frac{x}{\color{blue}{\sqrt{y} \cdot \sqrt{y}}} \]

       5. add-sqr-sqrt 29.9%

          \[\leadsto \frac{x}{\color{blue}{y}} \]

       6. div-inv 29.9%

          \[\leadsto \color{blue}{x \cdot \frac{1}{y}} \]

   13. Applied egg-rr 29.9%

       \[\leadsto \color{blue}{x \cdot \frac{1}{y}} \]
   14. Step-by-step derivation

       1. associate-*r/ 29.9%

          \[\leadsto \color{blue}{\frac{x \cdot 1}{y}} \]

       2. *-rgt-identity 29.9%

          \[\leadsto \frac{\color{blue}{x}}{y} \]

   15. Simplified 29.9%

       \[\leadsto \color{blue}{\frac{x}{y}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 20: 51.0% accurate, 3.7× speedup

Math

\[\begin{array}{l} \\ \frac{1}{y} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ 1.0 y))

C

double code(double x, double y) {
	return 1.0 / y;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 1.0d0 / y
end function

Java

public static double code(double x, double y) {
	return 1.0 / y;
}

Python

def code(x, y):
	return 1.0 / y

Julia

function code(x, y)
	return Float64(1.0 / y)
end

MATLAB

function tmp = code(x, y)
	tmp = 1.0 / y;
end

Wolfram

code[x_, y_] := N[(1.0 / y), $MachinePrecision]

Derivation

1. Initial program 96.4%

   \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
2. Step-by-step derivation

   1. associate-/l* 99.6%

      \[\leadsto \color{blue}{\left(1 - x\right) \cdot \frac{3 - x}{y \cdot 3}} \]

   2. *-rgt-identity 99.6%

      \[\leadsto \left(1 - x\right) \cdot \frac{\color{blue}{\left(3 - x\right) \cdot 1}}{y \cdot 3} \]

   3. remove-double-neg 99.6%

      \[\leadsto \left(1 - x\right) \cdot \frac{\left(3 - x\right) \cdot 1}{\color{blue}{-\left(-y \cdot 3\right)}} \]

   4. distribute-lft-neg-out 99.6%

      \[\leadsto \left(1 - x\right) \cdot \frac{\left(3 - x\right) \cdot 1}{-\color{blue}{\left(-y\right) \cdot 3}} \]

   5. neg-mul-1 99.6%

      \[\leadsto \left(1 - x\right) \cdot \frac{\left(3 - x\right) \cdot 1}{\color{blue}{-1 \cdot \left(\left(-y\right) \cdot 3\right)}} \]

   6. times-frac 99.5%

      \[\leadsto \left(1 - x\right) \cdot \color{blue}{\left(\frac{3 - x}{-1} \cdot \frac{1}{\left(-y\right) \cdot 3}\right)} \]

   7. *-rgt-identity 99.5%

      \[\leadsto \left(1 - x\right) \cdot \left(\frac{\color{blue}{\left(3 - x\right) \cdot 1}}{-1} \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

   8. associate-/l* 99.5%

      \[\leadsto \left(1 - x\right) \cdot \left(\color{blue}{\left(\left(3 - x\right) \cdot \frac{1}{-1}\right)} \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

   9. metadata-eval 99.5%

      \[\leadsto \left(1 - x\right) \cdot \left(\left(\left(3 - x\right) \cdot \color{blue}{-1}\right) \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

   10. *-commutative 99.5%

       \[\leadsto \left(1 - x\right) \cdot \left(\color{blue}{\left(-1 \cdot \left(3 - x\right)\right)} \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

   11. sub-neg 99.5%

       \[\leadsto \left(1 - x\right) \cdot \left(\left(-1 \cdot \color{blue}{\left(3 + \left(-x\right)\right)}\right) \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

   12. +-commutative 99.5%

       \[\leadsto \left(1 - x\right) \cdot \left(\left(-1 \cdot \color{blue}{\left(\left(-x\right) + 3\right)}\right) \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

   13. distribute-lft-in 99.5%

       \[\leadsto \left(1 - x\right) \cdot \left(\color{blue}{\left(-1 \cdot \left(-x\right) + -1 \cdot 3\right)} \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

   14. neg-mul-1 99.5%

       \[\leadsto \left(1 - x\right) \cdot \left(\left(\color{blue}{\left(-\left(-x\right)\right)} + -1 \cdot 3\right) \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

   15. remove-double-neg 99.5%

       \[\leadsto \left(1 - x\right) \cdot \left(\left(\color{blue}{x} + -1 \cdot 3\right) \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

   16. metadata-eval 99.5%

       \[\leadsto \left(1 - x\right) \cdot \left(\left(x + \color{blue}{-3}\right) \cdot \frac{1}{\left(-y\right) \cdot 3}\right) \]

   17. distribute-lft-neg-out 99.5%

       \[\leadsto \left(1 - x\right) \cdot \left(\left(x + -3\right) \cdot \frac{1}{\color{blue}{-y \cdot 3}}\right) \]

   18. *-commutative 99.5%

       \[\leadsto \left(1 - x\right) \cdot \left(\left(x + -3\right) \cdot \frac{1}{-\color{blue}{3 \cdot y}}\right) \]

   19. distribute-lft-neg-in 99.5%

       \[\leadsto \left(1 - x\right) \cdot \left(\left(x + -3\right) \cdot \frac{1}{\color{blue}{\left(-3\right) \cdot y}}\right) \]

   20. associate-/r* 99.4%

       \[\leadsto \left(1 - x\right) \cdot \left(\left(x + -3\right) \cdot \color{blue}{\frac{\frac{1}{-3}}{y}}\right) \]

   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 55.2%

   \[\leadsto \color{blue}{\frac{1}{y}} \]
6. Add Preprocessing

Developer Target 1: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{1 - x}{y} \cdot \frac{3 - x}{3} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* (/ (- 1.0 x) y) (/ (- 3.0 x) 3.0)))

C

double code(double x, double y) {
	return ((1.0 - x) / y) * ((3.0 - x) / 3.0);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = ((1.0d0 - x) / y) * ((3.0d0 - x) / 3.0d0)
end function

Java

public static double code(double x, double y) {
	return ((1.0 - x) / y) * ((3.0 - x) / 3.0);
}

Python

def code(x, y):
	return ((1.0 - x) / y) * ((3.0 - x) / 3.0)

Julia

function code(x, y)
	return Float64(Float64(Float64(1.0 - x) / y) * Float64(Float64(3.0 - x) / 3.0))
end

MATLAB

function tmp = code(x, y)
	tmp = ((1.0 - x) / y) * ((3.0 - x) / 3.0);
end

Wolfram

code[x_, y_] := N[(N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision] * N[(N[(3.0 - x), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024163 
(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)))