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

Percentage Accurate: 93.4% → 99.8%

Time: 10.1s

Alternatives: 17

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: 93.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% 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 94.2%

   \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
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: 98.2% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (* (- 1.0 x) (- 3.0 x)) 5.0)
   (+ (* -1.3333333333333333 (/ x y)) (/ 1.0 y))
   (* (/ x y) (+ (/ x 3.0) -1.0))))

C

double code(double x, double y) {
	double tmp;
	if (((1.0 - x) * (3.0 - x)) <= 5.0) {
		tmp = (-1.3333333333333333 * (x / y)) + (1.0 / y);
	} else {
		tmp = (x / y) * ((x / 3.0) + -1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (((1.0d0 - x) * (3.0d0 - x)) <= 5.0d0) then
        tmp = ((-1.3333333333333333d0) * (x / y)) + (1.0d0 / y)
    else
        tmp = (x / y) * ((x / 3.0d0) + (-1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (((1.0 - x) * (3.0 - x)) <= 5.0) {
		tmp = (-1.3333333333333333 * (x / y)) + (1.0 / y);
	} else {
		tmp = (x / y) * ((x / 3.0) + -1.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if ((1.0 - x) * (3.0 - x)) <= 5.0:
		tmp = (-1.3333333333333333 * (x / y)) + (1.0 / y)
	else:
		tmp = (x / y) * ((x / 3.0) + -1.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (Float64(Float64(1.0 - x) * Float64(3.0 - x)) <= 5.0)
		tmp = Float64(Float64(-1.3333333333333333 * Float64(x / y)) + Float64(1.0 / y));
	else
		tmp = Float64(Float64(x / y) * Float64(Float64(x / 3.0) + -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (((1.0 - x) * (3.0 - x)) <= 5.0)
		tmp = (-1.3333333333333333 * (x / y)) + (1.0 / y);
	else
		tmp = (x / y) * ((x / 3.0) + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[(N[(1.0 - x), $MachinePrecision] * N[(3.0 - x), $MachinePrecision]), $MachinePrecision], 5.0], N[(N[(-1.3333333333333333 * N[(x / y), $MachinePrecision]), $MachinePrecision] + N[(1.0 / y), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] * N[(N[(x / 3.0), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 3 binary64) x)) < 5

   1. Initial program 99.0%

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

      1. associate-/l* 99.0%

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

      2. *-rgt-identity 99.0%

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

      3. remove-double-neg 99.0%

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

      4. distribute-lft-neg-out 99.0%

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

      5. neg-mul-1 99.0%

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

      6. times-frac 98.9%

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

      7. *-rgt-identity 98.9%

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

      8. associate-/l* 98.9%

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

      9. metadata-eval 98.9%

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

      10. *-commutative 98.9%

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

      11. neg-mul-1 98.9%

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

      12. sub-neg 98.9%

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

      13. +-commutative 98.9%

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

      14. distribute-neg-in 98.9%

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

      15. remove-double-neg 98.9%

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

      16. metadata-eval 98.9%

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

      17. distribute-lft-neg-out 98.9%

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

      18. *-commutative 98.9%

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

      19. distribute-lft-neg-in 98.9%

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

      20. associate-/r* 99.5%

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

      21. metadata-eval 99.5%

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

      22. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around 0 98.4%

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

   if 5 < (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 3 binary64) x))

   1. Initial program 88.4%

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

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

      3. metadata-eval 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in x around inf 99.2%

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

      1. neg-mul-1 99.2%

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

   7. Simplified 99.2%

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

4. Final simplification 98.8%

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

Alternative 3: 98.1% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (* (- 1.0 x) (- 3.0 x)) 5.0)
   (+ (* -1.3333333333333333 (/ x y)) (/ 1.0 y))
   (/ (- 1.0 x) (* y (/ -3.0 x)))))

C

double code(double x, double y) {
	double tmp;
	if (((1.0 - x) * (3.0 - x)) <= 5.0) {
		tmp = (-1.3333333333333333 * (x / y)) + (1.0 / y);
	} else {
		tmp = (1.0 - x) / (y * (-3.0 / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (((1.0d0 - x) * (3.0d0 - x)) <= 5.0d0) then
        tmp = ((-1.3333333333333333d0) * (x / y)) + (1.0d0 / y)
    else
        tmp = (1.0d0 - x) / (y * ((-3.0d0) / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (((1.0 - x) * (3.0 - x)) <= 5.0) {
		tmp = (-1.3333333333333333 * (x / y)) + (1.0 / y);
	} else {
		tmp = (1.0 - x) / (y * (-3.0 / x));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if ((1.0 - x) * (3.0 - x)) <= 5.0:
		tmp = (-1.3333333333333333 * (x / y)) + (1.0 / y)
	else:
		tmp = (1.0 - x) / (y * (-3.0 / x))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (Float64(Float64(1.0 - x) * Float64(3.0 - x)) <= 5.0)
		tmp = Float64(Float64(-1.3333333333333333 * Float64(x / y)) + Float64(1.0 / y));
	else
		tmp = Float64(Float64(1.0 - x) / Float64(y * Float64(-3.0 / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (((1.0 - x) * (3.0 - x)) <= 5.0)
		tmp = (-1.3333333333333333 * (x / y)) + (1.0 / y);
	else
		tmp = (1.0 - x) / (y * (-3.0 / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[(N[(1.0 - x), $MachinePrecision] * N[(3.0 - x), $MachinePrecision]), $MachinePrecision], 5.0], N[(N[(-1.3333333333333333 * N[(x / y), $MachinePrecision]), $MachinePrecision] + N[(1.0 / y), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 - x), $MachinePrecision] / N[(y * N[(-3.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 3 binary64) x)) < 5

   1. Initial program 99.0%

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

      1. associate-/l* 99.0%

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

      2. *-rgt-identity 99.0%

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

      3. remove-double-neg 99.0%

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

      4. distribute-lft-neg-out 99.0%

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

      5. neg-mul-1 99.0%

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

      6. times-frac 98.9%

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

      7. *-rgt-identity 98.9%

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

      8. associate-/l* 98.9%

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

      9. metadata-eval 98.9%

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

      10. *-commutative 98.9%

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

      11. neg-mul-1 98.9%

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

      12. sub-neg 98.9%

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

      13. +-commutative 98.9%

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

      14. distribute-neg-in 98.9%

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

      15. remove-double-neg 98.9%

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

      16. metadata-eval 98.9%

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

      17. distribute-lft-neg-out 98.9%

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

      18. *-commutative 98.9%

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

      19. distribute-lft-neg-in 98.9%

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

      20. associate-/r* 99.5%

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

      21. metadata-eval 99.5%

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

      22. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around 0 98.4%

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

   if 5 < (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 3 binary64) x))

   1. Initial program 88.4%

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

      1. associate-/l* 99.7%

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

      2. *-commutative 99.7%

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

   3. Simplified 99.7%

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

      1. clear-num 99.7%

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

      2. un-div-inv 99.8%

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

      3. *-commutative 99.8%

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

      4. associate-/l* 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in x around inf 99.2%

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

Alternative 4: 98.1% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (* (- 1.0 x) (- 3.0 x)) 5.0)
   (+ (* -1.3333333333333333 (/ x y)) (/ 1.0 y))
   (* -0.3333333333333333 (* (- 3.0 x) (/ x y)))))

C

double code(double x, double y) {
	double tmp;
	if (((1.0 - x) * (3.0 - x)) <= 5.0) {
		tmp = (-1.3333333333333333 * (x / y)) + (1.0 / y);
	} else {
		tmp = -0.3333333333333333 * ((3.0 - x) * (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 (((1.0d0 - x) * (3.0d0 - x)) <= 5.0d0) then
        tmp = ((-1.3333333333333333d0) * (x / y)) + (1.0d0 / y)
    else
        tmp = (-0.3333333333333333d0) * ((3.0d0 - x) * (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (((1.0 - x) * (3.0 - x)) <= 5.0) {
		tmp = (-1.3333333333333333 * (x / y)) + (1.0 / y);
	} else {
		tmp = -0.3333333333333333 * ((3.0 - x) * (x / y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if ((1.0 - x) * (3.0 - x)) <= 5.0:
		tmp = (-1.3333333333333333 * (x / y)) + (1.0 / y)
	else:
		tmp = -0.3333333333333333 * ((3.0 - x) * (x / y))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (Float64(Float64(1.0 - x) * Float64(3.0 - x)) <= 5.0)
		tmp = Float64(Float64(-1.3333333333333333 * Float64(x / y)) + Float64(1.0 / y));
	else
		tmp = Float64(-0.3333333333333333 * Float64(Float64(3.0 - x) * Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (((1.0 - x) * (3.0 - x)) <= 5.0)
		tmp = (-1.3333333333333333 * (x / y)) + (1.0 / y);
	else
		tmp = -0.3333333333333333 * ((3.0 - x) * (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[(N[(1.0 - x), $MachinePrecision] * N[(3.0 - x), $MachinePrecision]), $MachinePrecision], 5.0], N[(N[(-1.3333333333333333 * N[(x / y), $MachinePrecision]), $MachinePrecision] + N[(1.0 / y), $MachinePrecision]), $MachinePrecision], N[(-0.3333333333333333 * N[(N[(3.0 - x), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 3 binary64) x)) < 5

   1. Initial program 99.0%

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

      1. associate-/l* 99.0%

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

      2. *-rgt-identity 99.0%

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

      3. remove-double-neg 99.0%

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

      4. distribute-lft-neg-out 99.0%

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

      5. neg-mul-1 99.0%

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

      6. times-frac 98.9%

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

      7. *-rgt-identity 98.9%

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

      8. associate-/l* 98.9%

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

      9. metadata-eval 98.9%

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

      10. *-commutative 98.9%

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

      11. neg-mul-1 98.9%

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

      12. sub-neg 98.9%

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

      13. +-commutative 98.9%

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

      14. distribute-neg-in 98.9%

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

      15. remove-double-neg 98.9%

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

      16. metadata-eval 98.9%

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

      17. distribute-lft-neg-out 98.9%

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

      18. *-commutative 98.9%

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

      19. distribute-lft-neg-in 98.9%

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

      20. associate-/r* 99.5%

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

      21. metadata-eval 99.5%

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

      22. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around 0 98.4%

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

   if 5 < (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 3 binary64) x))

   1. Initial program 88.4%

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

   3. Taylor expanded in x around inf 87.9%

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

      1. neg-mul-1 99.2%

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

   5. Simplified 87.9%

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

   6. Taylor expanded in y around 0 88.0%

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

      1. *-commutative 88.0%

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

      2. associate-/l* 99.2%

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

   8. Simplified 99.2%

      \[\leadsto \color{blue}{-0.3333333333333333 \cdot \left(\left(3 - x\right) \cdot \frac{x}{y}\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 98.1% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (* (- 1.0 x) (- 3.0 x)) 5.0)
   (/ (+ 1.0 (* x -1.3333333333333333)) y)
   (* -0.3333333333333333 (* (- 3.0 x) (/ x y)))))

C

double code(double x, double y) {
	double tmp;
	if (((1.0 - x) * (3.0 - x)) <= 5.0) {
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	} else {
		tmp = -0.3333333333333333 * ((3.0 - x) * (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 (((1.0d0 - x) * (3.0d0 - x)) <= 5.0d0) then
        tmp = (1.0d0 + (x * (-1.3333333333333333d0))) / y
    else
        tmp = (-0.3333333333333333d0) * ((3.0d0 - x) * (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (((1.0 - x) * (3.0 - x)) <= 5.0) {
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	} else {
		tmp = -0.3333333333333333 * ((3.0 - x) * (x / y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if ((1.0 - x) * (3.0 - x)) <= 5.0:
		tmp = (1.0 + (x * -1.3333333333333333)) / y
	else:
		tmp = -0.3333333333333333 * ((3.0 - x) * (x / y))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (Float64(Float64(1.0 - x) * Float64(3.0 - x)) <= 5.0)
		tmp = Float64(Float64(1.0 + Float64(x * -1.3333333333333333)) / y);
	else
		tmp = Float64(-0.3333333333333333 * Float64(Float64(3.0 - x) * Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (((1.0 - x) * (3.0 - x)) <= 5.0)
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	else
		tmp = -0.3333333333333333 * ((3.0 - x) * (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[(N[(1.0 - x), $MachinePrecision] * N[(3.0 - x), $MachinePrecision]), $MachinePrecision], 5.0], N[(N[(1.0 + N[(x * -1.3333333333333333), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(-0.3333333333333333 * N[(N[(3.0 - x), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 3 binary64) x)) < 5

   1. Initial program 99.0%

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

      1. associate-/l* 99.0%

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

      2. *-rgt-identity 99.0%

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

      3. remove-double-neg 99.0%

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

      4. distribute-lft-neg-out 99.0%

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

      5. neg-mul-1 99.0%

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

      6. times-frac 98.9%

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

      7. *-rgt-identity 98.9%

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

      8. associate-/l* 98.9%

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

      9. metadata-eval 98.9%

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

      10. *-commutative 98.9%

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

      11. neg-mul-1 98.9%

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

      12. sub-neg 98.9%

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

      13. +-commutative 98.9%

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

      14. distribute-neg-in 98.9%

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

      15. remove-double-neg 98.9%

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

      16. metadata-eval 98.9%

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

      17. distribute-lft-neg-out 98.9%

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

      18. *-commutative 98.9%

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

      19. distribute-lft-neg-in 98.9%

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

      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. Step-by-step derivation

      1. associate-*r* 99.5%

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

      2. associate-*r/ 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in x around 0 98.4%

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

   if 5 < (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 3 binary64) x))

   1. Initial program 88.4%

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

   3. Taylor expanded in x around inf 87.9%

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

      1. neg-mul-1 99.2%

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

   5. Simplified 87.9%

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

   6. Taylor expanded in y around 0 88.0%

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

      1. *-commutative 88.0%

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

      2. associate-/l* 99.2%

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

   8. Simplified 99.2%

      \[\leadsto \color{blue}{-0.3333333333333333 \cdot \left(\left(3 - x\right) \cdot \frac{x}{y}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.8%

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

Alternative 6: 98.0% accurate, 0.6× speedup

Math

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

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (* (- 1.0 x) (- 3.0 x)) 5.0)
   (/ (+ 1.0 (* x -1.3333333333333333)) y)
   (* x (/ (* x (- -0.3333333333333333)) y))))

C

double code(double x, double y) {
	double tmp;
	if (((1.0 - x) * (3.0 - x)) <= 5.0) {
		tmp = (1.0 + (x * -1.3333333333333333)) / 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 (((1.0d0 - x) * (3.0d0 - x)) <= 5.0d0) then
        tmp = (1.0d0 + (x * (-1.3333333333333333d0))) / 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 (((1.0 - x) * (3.0 - x)) <= 5.0) {
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	} else {
		tmp = x * ((x * -(-0.3333333333333333)) / y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if ((1.0 - x) * (3.0 - x)) <= 5.0:
		tmp = (1.0 + (x * -1.3333333333333333)) / y
	else:
		tmp = x * ((x * -(-0.3333333333333333)) / y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (Float64(Float64(1.0 - x) * Float64(3.0 - x)) <= 5.0)
		tmp = Float64(Float64(1.0 + Float64(x * -1.3333333333333333)) / y);
	else
		tmp = Float64(x * Float64(Float64(x * Float64(-(-0.3333333333333333))) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (((1.0 - x) * (3.0 - x)) <= 5.0)
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	else
		tmp = x * ((x * -(-0.3333333333333333)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[(N[(1.0 - x), $MachinePrecision] * N[(3.0 - x), $MachinePrecision]), $MachinePrecision], 5.0], N[(N[(1.0 + N[(x * -1.3333333333333333), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x * N[(N[(x * (--0.3333333333333333)), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 3 binary64) x)) < 5

   1. Initial program 99.0%

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

      1. associate-/l* 99.0%

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

      2. *-rgt-identity 99.0%

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

      3. remove-double-neg 99.0%

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

      4. distribute-lft-neg-out 99.0%

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

      5. neg-mul-1 99.0%

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

      6. times-frac 98.9%

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

      7. *-rgt-identity 98.9%

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

      8. associate-/l* 98.9%

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

      9. metadata-eval 98.9%

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

      10. *-commutative 98.9%

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

      11. neg-mul-1 98.9%

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

      12. sub-neg 98.9%

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

      13. +-commutative 98.9%

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

      14. distribute-neg-in 98.9%

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

      15. remove-double-neg 98.9%

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

      16. metadata-eval 98.9%

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

      17. distribute-lft-neg-out 98.9%

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

      18. *-commutative 98.9%

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

      19. distribute-lft-neg-in 98.9%

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

      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. Step-by-step derivation

      1. associate-*r* 99.5%

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

      2. associate-*r/ 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in x around 0 98.4%

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

   if 5 < (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 3 binary64) x))

   1. Initial program 88.4%

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

      1. associate-/l* 99.7%

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

      2. *-rgt-identity 99.7%

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

      3. remove-double-neg 99.7%

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

      4. distribute-lft-neg-out 99.7%

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

      5. neg-mul-1 99.7%

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

      6. times-frac 99.7%

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

      7. *-rgt-identity 99.7%

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

      8. associate-/l* 99.7%

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

      9. metadata-eval 99.7%

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

      10. *-commutative 99.7%

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

      11. neg-mul-1 99.7%

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

      12. sub-neg 99.7%

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

      13. +-commutative 99.7%

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

      14. distribute-neg-in 99.7%

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

      15. remove-double-neg 99.7%

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

      16. metadata-eval 99.7%

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

      17. distribute-lft-neg-out 99.7%

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

      18. *-commutative 99.7%

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

      19. distribute-lft-neg-in 99.7%

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

      20. associate-/r* 99.6%

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

      21. metadata-eval 99.6%

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

      22. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around inf 99.1%

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

      1. associate-*r/ 99.1%

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

      2. associate-*l/ 99.1%

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

      3. *-commutative 99.1%

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

      4. associate-*r/ 99.1%

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

   7. Simplified 99.1%

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

   8. Taylor expanded in x around inf 99.1%

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

      1. neg-mul-1 99.2%

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

   10. Simplified 99.1%

       \[\leadsto \color{blue}{\left(-x\right)} \cdot \frac{x \cdot -0.3333333333333333}{y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.7%

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

Alternative 7: 98.0% accurate, 0.6× speedup

Math

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

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (* (- 1.0 x) (- 3.0 x)) 5.0)
   (/ (+ 1.0 (* x -1.3333333333333333)) y)
   (* x (* x (/ -0.3333333333333333 (- y))))))

C

double code(double x, double y) {
	double tmp;
	if (((1.0 - x) * (3.0 - x)) <= 5.0) {
		tmp = (1.0 + (x * -1.3333333333333333)) / 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 (((1.0d0 - x) * (3.0d0 - x)) <= 5.0d0) then
        tmp = (1.0d0 + (x * (-1.3333333333333333d0))) / 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 (((1.0 - x) * (3.0 - x)) <= 5.0) {
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	} else {
		tmp = x * (x * (-0.3333333333333333 / -y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if ((1.0 - x) * (3.0 - x)) <= 5.0:
		tmp = (1.0 + (x * -1.3333333333333333)) / y
	else:
		tmp = x * (x * (-0.3333333333333333 / -y))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (Float64(Float64(1.0 - x) * Float64(3.0 - x)) <= 5.0)
		tmp = Float64(Float64(1.0 + Float64(x * -1.3333333333333333)) / y);
	else
		tmp = Float64(x * Float64(x * Float64(-0.3333333333333333 / Float64(-y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (((1.0 - x) * (3.0 - x)) <= 5.0)
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	else
		tmp = x * (x * (-0.3333333333333333 / -y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[(N[(1.0 - x), $MachinePrecision] * N[(3.0 - x), $MachinePrecision]), $MachinePrecision], 5.0], N[(N[(1.0 + N[(x * -1.3333333333333333), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x * N[(x * N[(-0.3333333333333333 / (-y)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 3 binary64) x)) < 5

   1. Initial program 99.0%

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

      1. associate-/l* 99.0%

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

      2. *-rgt-identity 99.0%

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

      3. remove-double-neg 99.0%

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

      4. distribute-lft-neg-out 99.0%

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

      5. neg-mul-1 99.0%

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

      6. times-frac 98.9%

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

      7. *-rgt-identity 98.9%

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

      8. associate-/l* 98.9%

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

      9. metadata-eval 98.9%

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

      10. *-commutative 98.9%

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

      11. neg-mul-1 98.9%

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

      12. sub-neg 98.9%

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

      13. +-commutative 98.9%

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

      14. distribute-neg-in 98.9%

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

      15. remove-double-neg 98.9%

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

      16. metadata-eval 98.9%

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

      17. distribute-lft-neg-out 98.9%

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

      18. *-commutative 98.9%

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

      19. distribute-lft-neg-in 98.9%

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

      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. Step-by-step derivation

      1. associate-*r* 99.5%

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

      2. associate-*r/ 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in x around 0 98.4%

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

   if 5 < (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 3 binary64) x))

   1. Initial program 88.4%

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

      1. associate-/l* 99.7%

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

      2. *-rgt-identity 99.7%

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

      3. remove-double-neg 99.7%

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

      4. distribute-lft-neg-out 99.7%

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

      5. neg-mul-1 99.7%

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

      6. times-frac 99.7%

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

      7. *-rgt-identity 99.7%

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

      8. associate-/l* 99.7%

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

      9. metadata-eval 99.7%

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

      10. *-commutative 99.7%

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

      11. neg-mul-1 99.7%

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

      12. sub-neg 99.7%

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

      13. +-commutative 99.7%

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

      14. distribute-neg-in 99.7%

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

      15. remove-double-neg 99.7%

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

      16. metadata-eval 99.7%

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

      17. distribute-lft-neg-out 99.7%

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

      18. *-commutative 99.7%

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

      19. distribute-lft-neg-in 99.7%

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

      20. associate-/r* 99.6%

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

      21. metadata-eval 99.6%

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

      22. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around inf 99.1%

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

   6. Taylor expanded in x around inf 99.1%

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

      1. neg-mul-1 99.2%

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

   8. Simplified 99.1%

      \[\leadsto \color{blue}{\left(-x\right)} \cdot \left(x \cdot \frac{-0.3333333333333333}{y}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.7%

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

Alternative 8: 63.1% accurate, 0.7× speedup

Math

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

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -0.75)
   (* x (/ -1.3333333333333333 y))
   (if (<= x 5.0) (/ 1.0 y) (* x (/ 1.3333333333333333 y)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -0.75) {
		tmp = x * (-1.3333333333333333 / y);
	} else if (x <= 5.0) {
		tmp = 1.0 / y;
	} else {
		tmp = x * (1.3333333333333333 / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-0.75d0)) then
        tmp = x * ((-1.3333333333333333d0) / y)
    else if (x <= 5.0d0) then
        tmp = 1.0d0 / y
    else
        tmp = x * (1.3333333333333333d0 / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -0.75) {
		tmp = x * (-1.3333333333333333 / y);
	} else if (x <= 5.0) {
		tmp = 1.0 / y;
	} else {
		tmp = x * (1.3333333333333333 / y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -0.75:
		tmp = x * (-1.3333333333333333 / y)
	elif x <= 5.0:
		tmp = 1.0 / y
	else:
		tmp = x * (1.3333333333333333 / y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -0.75)
		tmp = Float64(x * Float64(-1.3333333333333333 / y));
	elseif (x <= 5.0)
		tmp = Float64(1.0 / y);
	else
		tmp = Float64(x * Float64(1.3333333333333333 / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -0.75)
		tmp = x * (-1.3333333333333333 / y);
	elseif (x <= 5.0)
		tmp = 1.0 / y;
	else
		tmp = x * (1.3333333333333333 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -0.75], N[(x * N[(-1.3333333333333333 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.0], N[(1.0 / y), $MachinePrecision], N[(x * N[(1.3333333333333333 / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -0.75

   1. Initial program 89.1%

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

   3. Taylor expanded in x around 0 23.6%

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

      1. *-commutative 23.6%

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

   5. Simplified 23.6%

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

   6. Taylor expanded in x around inf 23.6%

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

      1. *-commutative 23.6%

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

   8. Simplified 23.6%

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

   9. Taylor expanded in x around 0 23.6%

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

       1. associate-*r/ 23.6%

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

       2. *-commutative 23.6%

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

       3. associate-*r/ 23.6%

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

   11. Simplified 23.6%

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

   if -0.75 < x < 5

   1. Initial program 99.0%

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

      1. associate-/l* 99.0%

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

      2. *-rgt-identity 99.0%

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

      3. remove-double-neg 99.0%

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

      4. distribute-lft-neg-out 99.0%

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

      5. neg-mul-1 99.0%

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

      6. times-frac 98.9%

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

      7. *-rgt-identity 98.9%

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

      8. associate-/l* 98.9%

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

      9. metadata-eval 98.9%

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

      10. *-commutative 98.9%

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

      11. neg-mul-1 98.9%

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

      12. sub-neg 98.9%

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

      13. +-commutative 98.9%

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

      14. distribute-neg-in 98.9%

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

      15. remove-double-neg 98.9%

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

      16. metadata-eval 98.9%

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

      17. distribute-lft-neg-out 98.9%

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

      18. *-commutative 98.9%

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

      19. distribute-lft-neg-in 98.9%

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

      20. associate-/r* 99.5%

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

      21. metadata-eval 99.5%

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

      22. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around 0 97.1%

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

   if 5 < x

   1. Initial program 87.7%

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

   3. Taylor expanded in x around 0 0.7%

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

      1. *-commutative 0.7%

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

   5. Simplified 0.7%

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

   6. Taylor expanded in x around inf 0.7%

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

      1. *-commutative 0.7%

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

   8. Simplified 0.7%

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

      1. associate-*l/ 0.7%

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

      2. clear-num 0.7%

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

   10. Applied egg-rr 0.7%

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

       1. frac-2neg 0.7%

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

       2. metadata-eval 0.7%

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

       3. div-inv 0.7%

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

       4. distribute-neg-frac 0.7%

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

       5. add-sqr-sqrt 0.4%

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

       6. sqrt-unprod 12.2%

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

       7. sqr-neg 12.2%

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

       8. sqrt-unprod 11.8%

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

       9. add-sqr-sqrt 25.1%

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

       10. clear-num 25.1%

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

   12. Applied egg-rr 25.1%

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

       1. neg-mul-1 25.1%

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

       2. associate-*l/ 25.1%

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

       3. distribute-rgt-neg-in 25.1%

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

       4. *-rgt-identity 25.1%

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

       5. associate-*r/ 25.1%

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

       6. metadata-eval 25.1%

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

       7. associate-*l* 25.1%

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

       8. associate-*l/ 25.1%

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

       9. metadata-eval 25.1%

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

   14. Simplified 25.1%

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

Alternative 9: 63.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.75:\\ \;\;\;\;x \cdot \frac{-1.3333333333333333}{y}\\ \mathbf{elif}\;x \leq 4.8:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -0.75)
   (* x (/ -1.3333333333333333 y))
   (if (<= x 4.8) (/ 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 <= 4.8) {
		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 <= 4.8d0) 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 <= 4.8) {
		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 <= 4.8:
		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 <= 4.8)
		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 <= 4.8)
		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, 4.8], N[(1.0 / y), $MachinePrecision], N[(x / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -0.75

   1. Initial program 89.1%

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

   3. Taylor expanded in x around 0 23.6%

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

      1. *-commutative 23.6%

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

   5. Simplified 23.6%

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

   6. Taylor expanded in x around inf 23.6%

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

      1. *-commutative 23.6%

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

   8. Simplified 23.6%

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

   9. Taylor expanded in x around 0 23.6%

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

       1. associate-*r/ 23.6%

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

       2. *-commutative 23.6%

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

       3. associate-*r/ 23.6%

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

   11. Simplified 23.6%

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

   if -0.75 < x < 4.79999999999999982

   1. Initial program 99.0%

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

      1. associate-/l* 99.0%

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

      2. *-rgt-identity 99.0%

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

      3. remove-double-neg 99.0%

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

      4. distribute-lft-neg-out 99.0%

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

      5. neg-mul-1 99.0%

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

      6. times-frac 98.9%

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

      7. *-rgt-identity 98.9%

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

      8. associate-/l* 98.9%

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

      9. metadata-eval 98.9%

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

      10. *-commutative 98.9%

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

      11. neg-mul-1 98.9%

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

      12. sub-neg 98.9%

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

      13. +-commutative 98.9%

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

      14. distribute-neg-in 98.9%

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

      15. remove-double-neg 98.9%

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

      16. metadata-eval 98.9%

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

      17. distribute-lft-neg-out 98.9%

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

      18. *-commutative 98.9%

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

      19. distribute-lft-neg-in 98.9%

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

      20. associate-/r* 99.5%

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

      21. metadata-eval 99.5%

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

      22. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around 0 97.1%

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

   if 4.79999999999999982 < x

   1. Initial program 87.7%

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

      1. times-frac 99.7%

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

      2. div-sub 99.7%

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

      3. metadata-eval 99.7%

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in x around 0 0.7%

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

   6. Taylor expanded in x around inf 0.7%

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

      1. neg-mul-1 0.7%

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

      2. distribute-frac-neg2 0.7%

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

   8. Simplified 0.7%

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

      1. add-sqr-sqrt 0.4%

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

      2. sqrt-unprod 12.2%

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

      3. sqr-neg 12.2%

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

      4. sqrt-unprod 11.8%

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

      5. add-sqr-sqrt 25.1%

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

      6. *-un-lft-identity 25.1%

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

   10. Applied egg-rr 25.1%

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

       1. *-lft-identity 25.1%

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

   12. Simplified 25.1%

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

Alternative 10: 63.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;\frac{-x}{y}\\ \mathbf{elif}\;x \leq 4.8:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.0) (/ (- x) y) (if (<= x 4.8) (/ 1.0 y) (/ x y))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.0) {
		tmp = -x / y;
	} else if (x <= 4.8) {
		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 <= 4.8d0) 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 <= 4.8) {
		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 <= 4.8:
		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 <= 4.8)
		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 <= 4.8)
		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, 4.8], N[(1.0 / y), $MachinePrecision], N[(x / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1

   1. Initial program 89.1%

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

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

      3. metadata-eval 99.8%

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

   4. Applied egg-rr 99.8%

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

   5. Taylor expanded in x around 0 23.6%

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

   6. Taylor expanded in x around inf 23.6%

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

      1. neg-mul-1 23.6%

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

      2. distribute-frac-neg2 23.6%

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

   8. Simplified 23.6%

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

   if -1 < x < 4.79999999999999982

   1. Initial program 99.0%

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

      1. associate-/l* 99.0%

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

      2. *-rgt-identity 99.0%

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

      3. remove-double-neg 99.0%

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

      4. distribute-lft-neg-out 99.0%

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

      5. neg-mul-1 99.0%

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

      6. times-frac 98.9%

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

      7. *-rgt-identity 98.9%

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

      8. associate-/l* 98.9%

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

      9. metadata-eval 98.9%

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

      10. *-commutative 98.9%

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

      11. neg-mul-1 98.9%

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

      12. sub-neg 98.9%

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

      13. +-commutative 98.9%

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

      14. distribute-neg-in 98.9%

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

      15. remove-double-neg 98.9%

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

      16. metadata-eval 98.9%

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

      17. distribute-lft-neg-out 98.9%

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

      18. *-commutative 98.9%

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

      19. distribute-lft-neg-in 98.9%

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

      20. associate-/r* 99.5%

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

      21. metadata-eval 99.5%

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

      22. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around 0 97.1%

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

   if 4.79999999999999982 < x

   1. Initial program 87.7%

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

      1. times-frac 99.7%

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

      2. div-sub 99.7%

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

      3. metadata-eval 99.7%

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in x around 0 0.7%

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

   6. Taylor expanded in x around inf 0.7%

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

      1. neg-mul-1 0.7%

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

      2. distribute-frac-neg2 0.7%

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

   8. Simplified 0.7%

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

      1. add-sqr-sqrt 0.4%

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

      2. sqrt-unprod 12.2%

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

      3. sqr-neg 12.2%

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

      4. sqrt-unprod 11.8%

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

      5. add-sqr-sqrt 25.1%

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

      6. *-un-lft-identity 25.1%

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

   10. Applied egg-rr 25.1%

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

       1. *-lft-identity 25.1%

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

   12. Simplified 25.1%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;\frac{-x}{y}\\ \mathbf{elif}\;x \leq 4.8:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 63.8% accurate, 0.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if x < 3

   1. Initial program 96.0%

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

      1. associate-/l* 99.2%

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

      2. *-rgt-identity 99.2%

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

      3. remove-double-neg 99.2%

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

      4. distribute-lft-neg-out 99.2%

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

      5. neg-mul-1 99.2%

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

      6. times-frac 99.1%

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

      7. *-rgt-identity 99.1%

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

      8. associate-/l* 99.1%

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

      9. metadata-eval 99.1%

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

      10. *-commutative 99.1%

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

      11. neg-mul-1 99.1%

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

      12. sub-neg 99.1%

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

      13. +-commutative 99.1%

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

      14. distribute-neg-in 99.1%

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

      15. remove-double-neg 99.1%

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

      16. metadata-eval 99.1%

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

      17. distribute-lft-neg-out 99.1%

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

      18. *-commutative 99.1%

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

      19. distribute-lft-neg-in 99.1%

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

      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. Step-by-step derivation

      1. associate-*r* 96.3%

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

      2. associate-*r/ 96.6%

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

   6. Applied egg-rr 96.6%

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

   7. Taylor expanded in x around 0 75.3%

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

   if 3 < x

   1. Initial program 87.7%

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

   3. Taylor expanded in x around 0 0.7%

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

      1. *-commutative 0.7%

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

   5. Simplified 0.7%

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

   6. Taylor expanded in x around inf 0.7%

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

      1. *-commutative 0.7%

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

   8. Simplified 0.7%

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

      1. associate-*l/ 0.7%

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

      2. clear-num 0.7%

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

   10. Applied egg-rr 0.7%

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

       1. frac-2neg 0.7%

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

       2. metadata-eval 0.7%

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

       3. div-inv 0.7%

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

       4. distribute-neg-frac 0.7%

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

       5. add-sqr-sqrt 0.4%

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

       6. sqrt-unprod 12.2%

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

       7. sqr-neg 12.2%

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

       8. sqrt-unprod 11.8%

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

       9. add-sqr-sqrt 25.1%

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

       10. clear-num 25.1%

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

   12. Applied egg-rr 25.1%

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

       1. neg-mul-1 25.1%

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

       2. associate-*l/ 25.1%

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

       3. distribute-rgt-neg-in 25.1%

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

       4. *-rgt-identity 25.1%

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

       5. associate-*r/ 25.1%

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

       6. metadata-eval 25.1%

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

       7. associate-*l* 25.1%

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

       8. associate-*l/ 25.1%

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

       9. metadata-eval 25.1%

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

   14. Simplified 25.1%

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

4. Final simplification 64.5%

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

Alternative 12: 63.2% accurate, 0.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if x < 3

   1. Initial program 96.0%

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

      1. times-frac 99.9%

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

      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. Taylor expanded in x around 0 74.6%

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

      1. *-rgt-identity 74.6%

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

      2. clear-num 74.6%

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

   7. Applied egg-rr 74.6%

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

   if 3 < x

   1. Initial program 87.7%

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

   3. Taylor expanded in x around 0 0.7%

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

      1. *-commutative 0.7%

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

   5. Simplified 0.7%

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

   6. Taylor expanded in x around inf 0.7%

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

      1. *-commutative 0.7%

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

   8. Simplified 0.7%

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

      1. associate-*l/ 0.7%

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

      2. clear-num 0.7%

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

   10. Applied egg-rr 0.7%

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

       1. frac-2neg 0.7%

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

       2. metadata-eval 0.7%

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

       3. div-inv 0.7%

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

       4. distribute-neg-frac 0.7%

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

       5. add-sqr-sqrt 0.4%

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

       6. sqrt-unprod 12.2%

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

       7. sqr-neg 12.2%

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

       8. sqrt-unprod 11.8%

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

       9. add-sqr-sqrt 25.1%

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

       10. clear-num 25.1%

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

   12. Applied egg-rr 25.1%

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

       1. neg-mul-1 25.1%

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

       2. associate-*l/ 25.1%

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

       3. distribute-rgt-neg-in 25.1%

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

       4. *-rgt-identity 25.1%

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

       5. associate-*r/ 25.1%

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

       6. metadata-eval 25.1%

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

       7. associate-*l* 25.1%

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

       8. associate-*l/ 25.1%

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

       9. metadata-eval 25.1%

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

   14. Simplified 25.1%

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

Alternative 13: 63.2% accurate, 0.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if x < 3

   1. Initial program 96.0%

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

      1. times-frac 99.9%

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

      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. Taylor expanded in x around 0 74.6%

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

      1. *-rgt-identity 74.6%

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

      2. div-sub 74.6%

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

   7. Applied egg-rr 74.6%

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

   if 3 < x

   1. Initial program 87.7%

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

   3. Taylor expanded in x around 0 0.7%

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

      1. *-commutative 0.7%

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

   5. Simplified 0.7%

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

   6. Taylor expanded in x around inf 0.7%

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

      1. *-commutative 0.7%

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

   8. Simplified 0.7%

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

      1. associate-*l/ 0.7%

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

      2. clear-num 0.7%

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

   10. Applied egg-rr 0.7%

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

       1. frac-2neg 0.7%

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

       2. metadata-eval 0.7%

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

       3. div-inv 0.7%

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

       4. distribute-neg-frac 0.7%

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

       5. add-sqr-sqrt 0.4%

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

       6. sqrt-unprod 12.2%

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

       7. sqr-neg 12.2%

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

       8. sqrt-unprod 11.8%

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

       9. add-sqr-sqrt 25.1%

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

       10. clear-num 25.1%

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

   12. Applied egg-rr 25.1%

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

       1. neg-mul-1 25.1%

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

       2. associate-*l/ 25.1%

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

       3. distribute-rgt-neg-in 25.1%

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

       4. *-rgt-identity 25.1%

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

       5. associate-*r/ 25.1%

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

       6. metadata-eval 25.1%

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

       7. associate-*l* 25.1%

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

       8. associate-*l/ 25.1%

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

       9. metadata-eval 25.1%

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

   14. Simplified 25.1%

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

Alternative 14: 99.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.2%

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

   1. associate-/l* 99.3%

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

   2. *-rgt-identity 99.3%

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

   3. remove-double-neg 99.3%

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

   4. distribute-lft-neg-out 99.3%

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

   5. neg-mul-1 99.3%

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

   6. times-frac 99.3%

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

   7. *-rgt-identity 99.3%

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

   8. associate-/l* 99.3%

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

   9. metadata-eval 99.3%

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

   10. *-commutative 99.3%

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

   11. neg-mul-1 99.3%

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

   12. sub-neg 99.3%

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

   13. +-commutative 99.3%

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

   14. distribute-neg-in 99.3%

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

   15. remove-double-neg 99.3%

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

   16. metadata-eval 99.3%

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

   17. distribute-lft-neg-out 99.3%

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

   18. *-commutative 99.3%

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

   19. distribute-lft-neg-in 99.3%

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

   20. associate-/r* 99.5%

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

   21. metadata-eval 99.5%

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

   22. metadata-eval 99.5%

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

3. Simplified 99.5%

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

Alternative 15: 63.2% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if x < 3

   1. Initial program 96.0%

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

      1. associate-/l* 99.2%

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

      2. *-commutative 99.2%

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

   3. Simplified 99.2%

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

      1. clear-num 99.4%

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

      2. un-div-inv 99.4%

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

      3. *-commutative 99.4%

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

      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 74.6%

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

   if 3 < x

   1. Initial program 87.7%

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

   3. Taylor expanded in x around 0 0.7%

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

      1. *-commutative 0.7%

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

   5. Simplified 0.7%

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

   6. Taylor expanded in x around inf 0.7%

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

      1. *-commutative 0.7%

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

   8. Simplified 0.7%

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

      1. associate-*l/ 0.7%

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

      2. clear-num 0.7%

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

   10. Applied egg-rr 0.7%

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

       1. frac-2neg 0.7%

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

       2. metadata-eval 0.7%

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

       3. div-inv 0.7%

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

       4. distribute-neg-frac 0.7%

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

       5. add-sqr-sqrt 0.4%

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

       6. sqrt-unprod 12.2%

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

       7. sqr-neg 12.2%

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

       8. sqrt-unprod 11.8%

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

       9. add-sqr-sqrt 25.1%

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

       10. clear-num 25.1%

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

   12. Applied egg-rr 25.1%

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

       1. neg-mul-1 25.1%

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

       2. associate-*l/ 25.1%

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

       3. distribute-rgt-neg-in 25.1%

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

       4. *-rgt-identity 25.1%

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

       5. associate-*r/ 25.1%

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

       6. metadata-eval 25.1%

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

       7. associate-*l* 25.1%

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

       8. associate-*l/ 25.1%

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

       9. metadata-eval 25.1%

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

   14. Simplified 25.1%

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

Alternative 16: 56.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 4.8:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= x 4.8) (/ 1.0 y) (/ x y)))

C

double code(double x, double y) {
	double tmp;
	if (x <= 4.8) {
		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 <= 4.8d0) 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 <= 4.8) {
		tmp = 1.0 / y;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 4.8:
		tmp = 1.0 / y
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 4.8)
		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 <= 4.8)
		tmp = 1.0 / y;
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 4.8], N[(1.0 / y), $MachinePrecision], N[(x / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 4.79999999999999982

   1. Initial program 96.0%

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

      1. associate-/l* 99.2%

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

      2. *-rgt-identity 99.2%

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

      3. remove-double-neg 99.2%

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

      4. distribute-lft-neg-out 99.2%

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

      5. neg-mul-1 99.2%

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

      6. times-frac 99.1%

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

      7. *-rgt-identity 99.1%

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

      8. associate-/l* 99.1%

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

      9. metadata-eval 99.1%

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

      10. *-commutative 99.1%

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

      11. neg-mul-1 99.1%

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

      12. sub-neg 99.1%

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

      13. +-commutative 99.1%

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

      14. distribute-neg-in 99.1%

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

      15. remove-double-neg 99.1%

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

      16. metadata-eval 99.1%

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

      17. distribute-lft-neg-out 99.1%

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

      18. *-commutative 99.1%

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

      19. distribute-lft-neg-in 99.1%

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

      20. associate-/r* 99.5%

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

      21. metadata-eval 99.5%

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

      22. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around 0 68.6%

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

   if 4.79999999999999982 < x

   1. Initial program 87.7%

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

      1. times-frac 99.7%

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

      2. div-sub 99.7%

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

      3. metadata-eval 99.7%

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

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in x around 0 0.7%

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

   6. Taylor expanded in x around inf 0.7%

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

      1. neg-mul-1 0.7%

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

      2. distribute-frac-neg2 0.7%

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

   8. Simplified 0.7%

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

      1. add-sqr-sqrt 0.4%

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

      2. sqrt-unprod 12.2%

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

      3. sqr-neg 12.2%

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

      4. sqrt-unprod 11.8%

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

      5. add-sqr-sqrt 25.1%

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

      6. *-un-lft-identity 25.1%

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

   10. Applied egg-rr 25.1%

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

       1. *-lft-identity 25.1%

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

   12. Simplified 25.1%

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

Alternative 17: 50.5% accurate, 3.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.2%

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

   1. associate-/l* 99.3%

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

   2. *-rgt-identity 99.3%

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

   3. remove-double-neg 99.3%

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

   4. distribute-lft-neg-out 99.3%

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

   5. neg-mul-1 99.3%

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

   6. times-frac 99.3%

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

   7. *-rgt-identity 99.3%

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

   8. associate-/l* 99.3%

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

   9. metadata-eval 99.3%

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

   10. *-commutative 99.3%

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

   11. neg-mul-1 99.3%

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

   12. sub-neg 99.3%

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

   13. +-commutative 99.3%

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

   14. distribute-neg-in 99.3%

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

   15. remove-double-neg 99.3%

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

   16. metadata-eval 99.3%

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

   17. distribute-lft-neg-out 99.3%

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

   18. *-commutative 99.3%

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

   19. distribute-lft-neg-in 99.3%

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

   20. associate-/r* 99.5%

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

   21. metadata-eval 99.5%

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

   22. metadata-eval 99.5%

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

3. Simplified 99.5%

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

5. Taylor expanded in x around 0 54.9%

   \[\leadsto \color{blue}{\frac{1}{y}} \]
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 2024191 
(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)))