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

Percentage Accurate: 93.6% → 99.7%

Time: 8.8s

Alternatives: 15

Speedup: 1.0×

• 25.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 93.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.7% accurate, 1.0× speedup

Math

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

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(Float64(1.0 - x) / y) * 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[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision] * N[(3.0 - x), $MachinePrecision]), $MachinePrecision] / 3.0), $MachinePrecision]

Derivation

1. Initial program 91.6%

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

   1. associate-/l* 99.6%

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

   2. *-commutative 99.6%

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

3. Simplified 99.6%

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

   1. *-commutative 99.6%

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

   2. associate-/l* 91.6%

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

   3. times-frac 99.8%

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

   4. associate-*r/ 99.8%

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

6. Applied egg-rr 99.8%

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

Alternative 2: 98.3% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if x < -2.2999999999999998 or 1.30000000000000004 < x

   1. Initial program 84.3%

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

      1. associate-/l* 99.7%

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

      2. *-commutative 99.7%

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

   3. Simplified 99.7%

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

      1. *-commutative 99.7%

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

      2. associate-/l* 84.3%

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

      3. times-frac 99.7%

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

      4. associate-*r/ 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in x around inf 98.9%

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

      1. neg-mul-1 98.9%

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

   9. Simplified 98.9%

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

   if -2.2999999999999998 < x < 1.30000000000000004

   1. Initial program 99.5%

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

      1. associate-/l* 99.5%

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

      2. *-rgt-identity 99.5%

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

      3. remove-double-neg 99.5%

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

      4. distribute-lft-neg-out 99.5%

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

      5. neg-mul-1 99.5%

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

      6. times-frac 99.3%

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

      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. sub-neg 99.3%

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

      12. +-commutative 99.3%

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

      13. distribute-lft-in 99.3%

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

      14. neg-mul-1 99.3%

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

      15. remove-double-neg 99.3%

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

      16. metadata-eval 99.3%

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

      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* 99.4%

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

      21. metadata-eval 99.4%

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

      22. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x around 0 99.7%

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

4. Final simplification 99.3%

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

Alternative 3: 98.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.8:\\ \;\;\;\;\left(1 - x\right) \cdot \left(x \cdot \frac{-0.3333333333333333}{y}\right)\\ \mathbf{elif}\;x \leq 1.3:\\ \;\;\;\;-1.3333333333333333 \cdot \frac{x}{y} + \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \left(x \cdot \frac{x + -3}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -3.8)
   (* (- 1.0 x) (* x (/ -0.3333333333333333 y)))
   (if (<= x 1.3)
     (+ (* -1.3333333333333333 (/ x y)) (/ 1.0 y))
     (* 0.3333333333333333 (* x (/ (+ x -3.0) y))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -3.8) {
		tmp = (1.0 - x) * (x * (-0.3333333333333333 / y));
	} else if (x <= 1.3) {
		tmp = (-1.3333333333333333 * (x / y)) + (1.0 / y);
	} else {
		tmp = 0.3333333333333333 * (x * ((x + -3.0) / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-3.8d0)) then
        tmp = (1.0d0 - x) * (x * ((-0.3333333333333333d0) / y))
    else if (x <= 1.3d0) then
        tmp = ((-1.3333333333333333d0) * (x / y)) + (1.0d0 / y)
    else
        tmp = 0.3333333333333333d0 * (x * ((x + (-3.0d0)) / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -3.8) {
		tmp = (1.0 - x) * (x * (-0.3333333333333333 / y));
	} else if (x <= 1.3) {
		tmp = (-1.3333333333333333 * (x / y)) + (1.0 / y);
	} else {
		tmp = 0.3333333333333333 * (x * ((x + -3.0) / y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -3.8:
		tmp = (1.0 - x) * (x * (-0.3333333333333333 / y))
	elif x <= 1.3:
		tmp = (-1.3333333333333333 * (x / y)) + (1.0 / y)
	else:
		tmp = 0.3333333333333333 * (x * ((x + -3.0) / y))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -3.8)
		tmp = Float64(Float64(1.0 - x) * Float64(x * Float64(-0.3333333333333333 / y)));
	elseif (x <= 1.3)
		tmp = Float64(Float64(-1.3333333333333333 * Float64(x / y)) + Float64(1.0 / y));
	else
		tmp = Float64(0.3333333333333333 * Float64(x * Float64(Float64(x + -3.0) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -3.8)
		tmp = (1.0 - x) * (x * (-0.3333333333333333 / y));
	elseif (x <= 1.3)
		tmp = (-1.3333333333333333 * (x / y)) + (1.0 / y);
	else
		tmp = 0.3333333333333333 * (x * ((x + -3.0) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -3.8], N[(N[(1.0 - x), $MachinePrecision] * N[(x * N[(-0.3333333333333333 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.3], N[(N[(-1.3333333333333333 * N[(x / y), $MachinePrecision]), $MachinePrecision] + N[(1.0 / y), $MachinePrecision]), $MachinePrecision], N[(0.3333333333333333 * N[(x * N[(N[(x + -3.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.7999999999999998

   1. Initial program 85.1%

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

      1. associate-/l* 99.7%

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

      2. *-rgt-identity 99.7%

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

      3. remove-double-neg 99.7%

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

      4. distribute-lft-neg-out 99.7%

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

      5. neg-mul-1 99.7%

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

      6. times-frac 99.7%

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

      7. *-rgt-identity 99.7%

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

      8. associate-/l* 99.7%

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

      9. metadata-eval 99.7%

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

      10. *-commutative 99.7%

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

      11. sub-neg 99.7%

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

      12. +-commutative 99.7%

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

      13. distribute-lft-in 99.7%

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

      14. neg-mul-1 99.7%

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

      15. remove-double-neg 99.7%

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

      16. metadata-eval 99.7%

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

      17. distribute-lft-neg-out 99.7%

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

      18. *-commutative 99.7%

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

      19. distribute-lft-neg-in 99.7%

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

      20. associate-/r* 99.8%

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

      21. metadata-eval 99.8%

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

      22. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 99.0%

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

   if -3.7999999999999998 < x < 1.30000000000000004

   1. Initial program 99.5%

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

      1. associate-/l* 99.5%

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

      2. *-rgt-identity 99.5%

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

      3. remove-double-neg 99.5%

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

      4. distribute-lft-neg-out 99.5%

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

      5. neg-mul-1 99.5%

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

      6. times-frac 99.3%

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

      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. sub-neg 99.3%

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

      12. +-commutative 99.3%

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

      13. distribute-lft-in 99.3%

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

      14. neg-mul-1 99.3%

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

      15. remove-double-neg 99.3%

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

      16. metadata-eval 99.3%

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

      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* 99.4%

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

      21. metadata-eval 99.4%

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

      22. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x around 0 99.7%

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

   if 1.30000000000000004 < x

   1. Initial program 83.4%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   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. Taylor expanded in x around inf 98.6%

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

      1. neg-mul-1 98.7%

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

   7. Simplified 98.6%

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

   8. Taylor expanded in y around 0 82.3%

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

      1. associate-*r/ 82.3%

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

      2. clear-num 82.3%

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

      3. associate-*r* 82.3%

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

   10. Applied egg-rr 82.3%

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

       1. associate-/r/ 82.3%

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

       2. *-commutative 82.3%

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

       3. associate-*r* 98.5%

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

       4. *-commutative 98.5%

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

       5. associate-*r/ 98.6%

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

       6. *-commutative 98.6%

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

       7. *-lft-identity 98.6%

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

       8. *-commutative 98.6%

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

       9. associate-/l* 82.3%

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

       10. remove-double-neg 82.3%

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

       11. distribute-neg-frac2 82.3%

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

       12. associate-*l* 82.3%

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

       13. associate-/l* 82.3%

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

       14. distribute-rgt-neg-out 82.3%

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

       15. neg-mul-1 82.3%

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

       16. associate-*r* 82.3%

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

       17. metadata-eval 82.3%

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

       18. associate-/l* 98.6%

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

       19. neg-mul-1 98.6%

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

       20. associate-/r* 98.6%

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

   12. Simplified 98.6%

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

Alternative 4: 98.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.8:\\ \;\;\;\;\left(1 - x\right) \cdot \left(x \cdot \frac{-0.3333333333333333}{y}\right)\\ \mathbf{elif}\;x \leq 1.3:\\ \;\;\;\;\frac{x \cdot -1.3333333333333333 + 1}{y}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \left(x \cdot \frac{x + -3}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -3.8)
   (* (- 1.0 x) (* x (/ -0.3333333333333333 y)))
   (if (<= x 1.3)
     (/ (+ (* x -1.3333333333333333) 1.0) y)
     (* 0.3333333333333333 (* x (/ (+ x -3.0) y))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -3.8) {
		tmp = (1.0 - x) * (x * (-0.3333333333333333 / y));
	} else if (x <= 1.3) {
		tmp = ((x * -1.3333333333333333) + 1.0) / y;
	} else {
		tmp = 0.3333333333333333 * (x * ((x + -3.0) / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-3.8d0)) then
        tmp = (1.0d0 - x) * (x * ((-0.3333333333333333d0) / y))
    else if (x <= 1.3d0) then
        tmp = ((x * (-1.3333333333333333d0)) + 1.0d0) / y
    else
        tmp = 0.3333333333333333d0 * (x * ((x + (-3.0d0)) / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -3.8) {
		tmp = (1.0 - x) * (x * (-0.3333333333333333 / y));
	} else if (x <= 1.3) {
		tmp = ((x * -1.3333333333333333) + 1.0) / y;
	} else {
		tmp = 0.3333333333333333 * (x * ((x + -3.0) / y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -3.8:
		tmp = (1.0 - x) * (x * (-0.3333333333333333 / y))
	elif x <= 1.3:
		tmp = ((x * -1.3333333333333333) + 1.0) / y
	else:
		tmp = 0.3333333333333333 * (x * ((x + -3.0) / y))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -3.8)
		tmp = Float64(Float64(1.0 - x) * Float64(x * Float64(-0.3333333333333333 / y)));
	elseif (x <= 1.3)
		tmp = Float64(Float64(Float64(x * -1.3333333333333333) + 1.0) / y);
	else
		tmp = Float64(0.3333333333333333 * Float64(x * Float64(Float64(x + -3.0) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -3.8)
		tmp = (1.0 - x) * (x * (-0.3333333333333333 / y));
	elseif (x <= 1.3)
		tmp = ((x * -1.3333333333333333) + 1.0) / y;
	else
		tmp = 0.3333333333333333 * (x * ((x + -3.0) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -3.8], N[(N[(1.0 - x), $MachinePrecision] * N[(x * N[(-0.3333333333333333 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.3], N[(N[(N[(x * -1.3333333333333333), $MachinePrecision] + 1.0), $MachinePrecision] / y), $MachinePrecision], N[(0.3333333333333333 * N[(x * N[(N[(x + -3.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.7999999999999998

   1. Initial program 85.1%

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

      1. associate-/l* 99.7%

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

      2. *-rgt-identity 99.7%

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

      3. remove-double-neg 99.7%

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

      4. distribute-lft-neg-out 99.7%

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

      5. neg-mul-1 99.7%

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

      6. times-frac 99.7%

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

      7. *-rgt-identity 99.7%

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

      8. associate-/l* 99.7%

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

      9. metadata-eval 99.7%

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

      10. *-commutative 99.7%

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

      11. sub-neg 99.7%

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

      12. +-commutative 99.7%

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

      13. distribute-lft-in 99.7%

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

      14. neg-mul-1 99.7%

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

      15. remove-double-neg 99.7%

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

      16. metadata-eval 99.7%

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

      17. distribute-lft-neg-out 99.7%

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

      18. *-commutative 99.7%

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

      19. distribute-lft-neg-in 99.7%

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

      20. associate-/r* 99.8%

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

      21. metadata-eval 99.8%

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

      22. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 99.0%

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

   if -3.7999999999999998 < x < 1.30000000000000004

   1. Initial program 99.5%

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

      1. associate-/l* 99.5%

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

      2. *-rgt-identity 99.5%

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

      3. remove-double-neg 99.5%

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

      4. distribute-lft-neg-out 99.5%

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

      5. neg-mul-1 99.5%

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

      6. times-frac 99.3%

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

      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. sub-neg 99.3%

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

      12. +-commutative 99.3%

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

      13. distribute-lft-in 99.3%

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

      14. neg-mul-1 99.3%

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

      15. remove-double-neg 99.3%

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

      16. metadata-eval 99.3%

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

      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* 99.4%

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

      21. metadata-eval 99.4%

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

      22. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x around 0 99.7%

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

   6. Taylor expanded in y around 0 99.6%

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

      1. *-commutative 99.6%

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

   8. Simplified 99.6%

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

   if 1.30000000000000004 < x

   1. Initial program 83.4%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   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. Taylor expanded in x around inf 98.6%

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

      1. neg-mul-1 98.7%

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

   7. Simplified 98.6%

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

   8. Taylor expanded in y around 0 82.3%

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

      1. associate-*r/ 82.3%

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

      2. clear-num 82.3%

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

      3. associate-*r* 82.3%

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

   10. Applied egg-rr 82.3%

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

       1. associate-/r/ 82.3%

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

       2. *-commutative 82.3%

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

       3. associate-*r* 98.5%

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

       4. *-commutative 98.5%

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

       5. associate-*r/ 98.6%

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

       6. *-commutative 98.6%

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

       7. *-lft-identity 98.6%

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

       8. *-commutative 98.6%

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

       9. associate-/l* 82.3%

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

       10. remove-double-neg 82.3%

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

       11. distribute-neg-frac2 82.3%

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

       12. associate-*l* 82.3%

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

       13. associate-/l* 82.3%

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

       14. distribute-rgt-neg-out 82.3%

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

       15. neg-mul-1 82.3%

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

       16. associate-*r* 82.3%

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

       17. metadata-eval 82.3%

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

       18. associate-/l* 98.6%

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

       19. neg-mul-1 98.6%

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

       20. associate-/r* 98.6%

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

   12. Simplified 98.6%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.8:\\ \;\;\;\;\left(1 - x\right) \cdot \left(x \cdot \frac{-0.3333333333333333}{y}\right)\\ \mathbf{elif}\;x \leq 1.3:\\ \;\;\;\;\frac{x \cdot -1.3333333333333333 + 1}{y}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \left(x \cdot \frac{x + -3}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 98.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.6:\\ \;\;\;\;x \cdot \left(x \cdot \frac{-0.3333333333333333}{-y}\right)\\ \mathbf{elif}\;x \leq 1.3:\\ \;\;\;\;\frac{x \cdot -1.3333333333333333 + 1}{y}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \left(x \cdot \frac{x + -3}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -4.6)
   (* x (* x (/ -0.3333333333333333 (- y))))
   (if (<= x 1.3)
     (/ (+ (* x -1.3333333333333333) 1.0) y)
     (* 0.3333333333333333 (* x (/ (+ x -3.0) y))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -4.6) {
		tmp = x * (x * (-0.3333333333333333 / -y));
	} else if (x <= 1.3) {
		tmp = ((x * -1.3333333333333333) + 1.0) / y;
	} else {
		tmp = 0.3333333333333333 * (x * ((x + -3.0) / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-4.6d0)) then
        tmp = x * (x * ((-0.3333333333333333d0) / -y))
    else if (x <= 1.3d0) then
        tmp = ((x * (-1.3333333333333333d0)) + 1.0d0) / y
    else
        tmp = 0.3333333333333333d0 * (x * ((x + (-3.0d0)) / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -4.6) {
		tmp = x * (x * (-0.3333333333333333 / -y));
	} else if (x <= 1.3) {
		tmp = ((x * -1.3333333333333333) + 1.0) / y;
	} else {
		tmp = 0.3333333333333333 * (x * ((x + -3.0) / y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -4.6:
		tmp = x * (x * (-0.3333333333333333 / -y))
	elif x <= 1.3:
		tmp = ((x * -1.3333333333333333) + 1.0) / y
	else:
		tmp = 0.3333333333333333 * (x * ((x + -3.0) / y))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -4.6)
		tmp = Float64(x * Float64(x * Float64(-0.3333333333333333 / Float64(-y))));
	elseif (x <= 1.3)
		tmp = Float64(Float64(Float64(x * -1.3333333333333333) + 1.0) / y);
	else
		tmp = Float64(0.3333333333333333 * Float64(x * Float64(Float64(x + -3.0) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -4.6)
		tmp = x * (x * (-0.3333333333333333 / -y));
	elseif (x <= 1.3)
		tmp = ((x * -1.3333333333333333) + 1.0) / y;
	else
		tmp = 0.3333333333333333 * (x * ((x + -3.0) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -4.6], N[(x * N[(x * N[(-0.3333333333333333 / (-y)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.3], N[(N[(N[(x * -1.3333333333333333), $MachinePrecision] + 1.0), $MachinePrecision] / y), $MachinePrecision], N[(0.3333333333333333 * N[(x * N[(N[(x + -3.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.5999999999999996

   1. Initial program 85.1%

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

      1. associate-/l* 99.7%

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

      2. *-rgt-identity 99.7%

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

      3. remove-double-neg 99.7%

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

      4. distribute-lft-neg-out 99.7%

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

      5. neg-mul-1 99.7%

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

      6. times-frac 99.7%

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

      7. *-rgt-identity 99.7%

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

      8. associate-/l* 99.7%

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

      9. metadata-eval 99.7%

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

      10. *-commutative 99.7%

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

      11. sub-neg 99.7%

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

      12. +-commutative 99.7%

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

      13. distribute-lft-in 99.7%

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

      14. neg-mul-1 99.7%

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

      15. remove-double-neg 99.7%

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

      16. metadata-eval 99.7%

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

      17. distribute-lft-neg-out 99.7%

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

      18. *-commutative 99.7%

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

      19. distribute-lft-neg-in 99.7%

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

      20. associate-/r* 99.8%

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

      21. metadata-eval 99.8%

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

      22. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 99.0%

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

   6. Taylor expanded in x around inf 99.0%

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

      1. neg-mul-1 99.1%

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

   8. Simplified 99.0%

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

   if -4.5999999999999996 < x < 1.30000000000000004

   1. Initial program 99.5%

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

      1. associate-/l* 99.5%

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

      2. *-rgt-identity 99.5%

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

      3. remove-double-neg 99.5%

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

      4. distribute-lft-neg-out 99.5%

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

      5. neg-mul-1 99.5%

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

      6. times-frac 99.3%

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

      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. sub-neg 99.3%

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

      12. +-commutative 99.3%

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

      13. distribute-lft-in 99.3%

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

      14. neg-mul-1 99.3%

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

      15. remove-double-neg 99.3%

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

      16. metadata-eval 99.3%

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

      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* 99.4%

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

      21. metadata-eval 99.4%

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

      22. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x around 0 99.7%

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

   6. Taylor expanded in y around 0 99.6%

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

      1. *-commutative 99.6%

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

   8. Simplified 99.6%

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

   if 1.30000000000000004 < x

   1. Initial program 83.4%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   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. Taylor expanded in x around inf 98.6%

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

      1. neg-mul-1 98.7%

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

   7. Simplified 98.6%

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

   8. Taylor expanded in y around 0 82.3%

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

      1. associate-*r/ 82.3%

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

      2. clear-num 82.3%

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

      3. associate-*r* 82.3%

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

   10. Applied egg-rr 82.3%

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

       1. associate-/r/ 82.3%

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

       2. *-commutative 82.3%

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

       3. associate-*r* 98.5%

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

       4. *-commutative 98.5%

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

       5. associate-*r/ 98.6%

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

       6. *-commutative 98.6%

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

       7. *-lft-identity 98.6%

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

       8. *-commutative 98.6%

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

       9. associate-/l* 82.3%

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

       10. remove-double-neg 82.3%

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

       11. distribute-neg-frac2 82.3%

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

       12. associate-*l* 82.3%

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

       13. associate-/l* 82.3%

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

       14. distribute-rgt-neg-out 82.3%

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

       15. neg-mul-1 82.3%

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

       16. associate-*r* 82.3%

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

       17. metadata-eval 82.3%

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

       18. associate-/l* 98.6%

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

       19. neg-mul-1 98.6%

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

       20. associate-/r* 98.6%

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

   12. Simplified 98.6%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.6:\\ \;\;\;\;x \cdot \left(x \cdot \frac{-0.3333333333333333}{-y}\right)\\ \mathbf{elif}\;x \leq 1.3:\\ \;\;\;\;\frac{x \cdot -1.3333333333333333 + 1}{y}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \left(x \cdot \frac{x + -3}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 98.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.6 \lor \neg \left(x \leq 3\right):\\ \;\;\;\;x \cdot \left(x \cdot \frac{-0.3333333333333333}{-y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot -1.3333333333333333 + 1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -4.6) (not (<= x 3.0)))
   (* x (* x (/ -0.3333333333333333 (- y))))
   (/ (+ (* x -1.3333333333333333) 1.0) y)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -4.6) || !(x <= 3.0)) {
		tmp = x * (x * (-0.3333333333333333 / -y));
	} else {
		tmp = ((x * -1.3333333333333333) + 1.0) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-4.6d0)) .or. (.not. (x <= 3.0d0))) then
        tmp = x * (x * ((-0.3333333333333333d0) / -y))
    else
        tmp = ((x * (-1.3333333333333333d0)) + 1.0d0) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -4.6) || !(x <= 3.0)) {
		tmp = x * (x * (-0.3333333333333333 / -y));
	} else {
		tmp = ((x * -1.3333333333333333) + 1.0) / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -4.6) or not (x <= 3.0):
		tmp = x * (x * (-0.3333333333333333 / -y))
	else:
		tmp = ((x * -1.3333333333333333) + 1.0) / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -4.6) || !(x <= 3.0))
		tmp = Float64(x * Float64(x * Float64(-0.3333333333333333 / Float64(-y))));
	else
		tmp = Float64(Float64(Float64(x * -1.3333333333333333) + 1.0) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -4.6) || ~((x <= 3.0)))
		tmp = x * (x * (-0.3333333333333333 / -y));
	else
		tmp = ((x * -1.3333333333333333) + 1.0) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -4.6], N[Not[LessEqual[x, 3.0]], $MachinePrecision]], N[(x * N[(x * N[(-0.3333333333333333 / (-y)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * -1.3333333333333333), $MachinePrecision] + 1.0), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.5999999999999996 or 3 < x

   1. Initial program 84.3%

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

      1. associate-/l* 99.7%

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

      2. *-rgt-identity 99.7%

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

      3. remove-double-neg 99.7%

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

      4. distribute-lft-neg-out 99.7%

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

      5. neg-mul-1 99.7%

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

      6. times-frac 99.7%

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

      7. *-rgt-identity 99.7%

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

      8. associate-/l* 99.7%

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

      9. metadata-eval 99.7%

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

      10. *-commutative 99.7%

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

      11. sub-neg 99.7%

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

      12. +-commutative 99.7%

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

      13. distribute-lft-in 99.7%

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

      14. neg-mul-1 99.7%

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

      15. remove-double-neg 99.7%

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

      16. metadata-eval 99.7%

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

      17. distribute-lft-neg-out 99.7%

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

      18. *-commutative 99.7%

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

      19. distribute-lft-neg-in 99.7%

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

      20. associate-/r* 99.7%

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

      21. metadata-eval 99.7%

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

      22. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 98.8%

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

   6. Taylor expanded in x around inf 98.8%

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

      1. neg-mul-1 98.9%

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

   8. Simplified 98.8%

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

   if -4.5999999999999996 < x < 3

   1. Initial program 99.5%

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

      1. associate-/l* 99.5%

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

      2. *-rgt-identity 99.5%

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

      3. remove-double-neg 99.5%

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

      4. distribute-lft-neg-out 99.5%

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

      5. neg-mul-1 99.5%

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

      6. times-frac 99.3%

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

      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. sub-neg 99.3%

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

      12. +-commutative 99.3%

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

      13. distribute-lft-in 99.3%

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

      14. neg-mul-1 99.3%

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

      15. remove-double-neg 99.3%

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

      16. metadata-eval 99.3%

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

      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* 99.4%

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

      21. metadata-eval 99.4%

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

      22. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x around 0 99.7%

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

   6. Taylor expanded in y around 0 99.6%

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

      1. *-commutative 99.6%

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

   8. Simplified 99.6%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.6 \lor \neg \left(x \leq 3\right):\\ \;\;\;\;x \cdot \left(x \cdot \frac{-0.3333333333333333}{-y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot -1.3333333333333333 + 1}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 92.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.6 \lor \neg \left(x \leq 3\right):\\ \;\;\;\;\frac{x \cdot x}{y \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot -1.3333333333333333 + 1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -4.6) (not (<= x 3.0)))
   (/ (* x x) (* y 3.0))
   (/ (+ (* x -1.3333333333333333) 1.0) y)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -4.6) || !(x <= 3.0)) {
		tmp = (x * x) / (y * 3.0);
	} else {
		tmp = ((x * -1.3333333333333333) + 1.0) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-4.6d0)) .or. (.not. (x <= 3.0d0))) then
        tmp = (x * x) / (y * 3.0d0)
    else
        tmp = ((x * (-1.3333333333333333d0)) + 1.0d0) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -4.6) || !(x <= 3.0)) {
		tmp = (x * x) / (y * 3.0);
	} else {
		tmp = ((x * -1.3333333333333333) + 1.0) / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -4.6) or not (x <= 3.0):
		tmp = (x * x) / (y * 3.0)
	else:
		tmp = ((x * -1.3333333333333333) + 1.0) / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -4.6) || !(x <= 3.0))
		tmp = Float64(Float64(x * x) / Float64(y * 3.0));
	else
		tmp = Float64(Float64(Float64(x * -1.3333333333333333) + 1.0) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -4.6) || ~((x <= 3.0)))
		tmp = (x * x) / (y * 3.0);
	else
		tmp = ((x * -1.3333333333333333) + 1.0) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -4.6], N[Not[LessEqual[x, 3.0]], $MachinePrecision]], N[(N[(x * x), $MachinePrecision] / N[(y * 3.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * -1.3333333333333333), $MachinePrecision] + 1.0), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.5999999999999996 or 3 < x

   1. Initial program 84.3%

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

      1. associate-/l* 99.7%

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

      2. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 98.8%

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

      1. neg-mul-1 98.9%

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

   7. Simplified 98.8%

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

      1. associate-*r/ 83.5%

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

      2. sub-neg 83.5%

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

      3. distribute-rgt-in 83.5%

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

      4. add-sqr-sqrt 44.4%

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

      5. sqrt-unprod 83.4%

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

      6. sqr-neg 83.4%

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

      7. sqrt-unprod 39.0%

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

      8. add-sqr-sqrt 83.4%

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

      9. sqr-neg 83.4%

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

      10. +-commutative 83.4%

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

      11. distribute-rgt-out 83.4%

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

      12. *-commutative 83.4%

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

   9. Applied egg-rr 83.4%

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

   10. Taylor expanded in x around inf 83.4%

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

   if -4.5999999999999996 < x < 3

   1. Initial program 99.5%

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

      1. associate-/l* 99.5%

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

      2. *-rgt-identity 99.5%

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

      3. remove-double-neg 99.5%

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

      4. distribute-lft-neg-out 99.5%

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

      5. neg-mul-1 99.5%

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

      6. times-frac 99.3%

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

      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. sub-neg 99.3%

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

      12. +-commutative 99.3%

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

      13. distribute-lft-in 99.3%

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

      14. neg-mul-1 99.3%

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

      15. remove-double-neg 99.3%

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

      16. metadata-eval 99.3%

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

      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* 99.4%

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

      21. metadata-eval 99.4%

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

      22. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x around 0 99.7%

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

   6. Taylor expanded in y around 0 99.6%

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

      1. *-commutative 99.6%

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

   8. Simplified 99.6%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.6 \lor \neg \left(x \leq 3\right):\\ \;\;\;\;\frac{x \cdot x}{y \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot -1.3333333333333333 + 1}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 91.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.72 \lor \neg \left(x \leq 5\right):\\ \;\;\;\;\frac{x \cdot x}{y \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -1.72) (not (<= x 5.0))) (/ (* x x) (* y 3.0)) (/ 1.0 y)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -1.72) || !(x <= 5.0)) {
		tmp = (x * x) / (y * 3.0);
	} else {
		tmp = 1.0 / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-1.72d0)) .or. (.not. (x <= 5.0d0))) then
        tmp = (x * x) / (y * 3.0d0)
    else
        tmp = 1.0d0 / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -1.72) || !(x <= 5.0)) {
		tmp = (x * x) / (y * 3.0);
	} else {
		tmp = 1.0 / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -1.72) or not (x <= 5.0):
		tmp = (x * x) / (y * 3.0)
	else:
		tmp = 1.0 / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -1.72) || !(x <= 5.0))
		tmp = Float64(Float64(x * x) / Float64(y * 3.0));
	else
		tmp = Float64(1.0 / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -1.72) || ~((x <= 5.0)))
		tmp = (x * x) / (y * 3.0);
	else
		tmp = 1.0 / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -1.72], N[Not[LessEqual[x, 5.0]], $MachinePrecision]], N[(N[(x * x), $MachinePrecision] / N[(y * 3.0), $MachinePrecision]), $MachinePrecision], N[(1.0 / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.71999999999999997 or 5 < x

   1. Initial program 84.3%

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

      1. associate-/l* 99.7%

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

      2. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 98.8%

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

      1. neg-mul-1 98.9%

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

   7. Simplified 98.8%

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

      1. associate-*r/ 83.5%

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

      2. sub-neg 83.5%

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

      3. distribute-rgt-in 83.5%

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

      4. add-sqr-sqrt 44.4%

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

      5. sqrt-unprod 83.4%

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

      6. sqr-neg 83.4%

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

      7. sqrt-unprod 39.0%

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

      8. add-sqr-sqrt 83.4%

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

      9. sqr-neg 83.4%

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

      10. +-commutative 83.4%

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

      11. distribute-rgt-out 83.4%

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

      12. *-commutative 83.4%

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

   9. Applied egg-rr 83.4%

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

   10. Taylor expanded in x around inf 83.4%

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

   if -1.71999999999999997 < x < 5

   1. Initial program 99.5%

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

      1. associate-/l* 99.5%

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

      2. *-rgt-identity 99.5%

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

      3. remove-double-neg 99.5%

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

      4. distribute-lft-neg-out 99.5%

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

      5. neg-mul-1 99.5%

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

      6. times-frac 99.3%

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

      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. sub-neg 99.3%

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

      12. +-commutative 99.3%

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

      13. distribute-lft-in 99.3%

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

      14. neg-mul-1 99.3%

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

      15. remove-double-neg 99.3%

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

      16. metadata-eval 99.3%

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

      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* 99.4%

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

      21. metadata-eval 99.4%

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

      22. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x around 0 98.5%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.72 \lor \neg \left(x \leq 5\right):\\ \;\;\;\;\frac{x \cdot x}{y \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 63.5% accurate, 0.7× speedup

Math

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

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -0.75)
   (* -1.3333333333333333 (/ x y))
   (if (<= x 4.8) (/ 1.0 y) (* x (/ 1.3333333333333333 y)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -0.75) {
		tmp = -1.3333333333333333 * (x / y);
	} else if (x <= 4.8) {
		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 = (-1.3333333333333333d0) * (x / y)
    else if (x <= 4.8d0) 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 = -1.3333333333333333 * (x / y);
	} else if (x <= 4.8) {
		tmp = 1.0 / y;
	} else {
		tmp = x * (1.3333333333333333 / y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -0.75:
		tmp = -1.3333333333333333 * (x / y)
	elif x <= 4.8:
		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(-1.3333333333333333 * Float64(x / y));
	elseif (x <= 4.8)
		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 = -1.3333333333333333 * (x / y);
	elseif (x <= 4.8)
		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[(-1.3333333333333333 * N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.8], 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 85.1%

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

      1. associate-/l* 99.7%

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

      2. *-rgt-identity 99.7%

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

      3. remove-double-neg 99.7%

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

      4. distribute-lft-neg-out 99.7%

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

      5. neg-mul-1 99.7%

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

      6. times-frac 99.7%

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

      7. *-rgt-identity 99.7%

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

      8. associate-/l* 99.7%

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

      9. metadata-eval 99.7%

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

      10. *-commutative 99.7%

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

      11. sub-neg 99.7%

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

      12. +-commutative 99.7%

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

      13. distribute-lft-in 99.7%

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

      14. neg-mul-1 99.7%

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

      15. remove-double-neg 99.7%

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

      16. metadata-eval 99.7%

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

      17. distribute-lft-neg-out 99.7%

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

      18. *-commutative 99.7%

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

      19. distribute-lft-neg-in 99.7%

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

      20. associate-/r* 99.8%

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

      21. metadata-eval 99.8%

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

      22. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0 32.7%

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

   6. Taylor expanded in x around inf 32.7%

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

   if -0.75 < x < 4.79999999999999982

   1. Initial program 99.5%

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

      1. associate-/l* 99.5%

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

      2. *-rgt-identity 99.5%

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

      3. remove-double-neg 99.5%

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

      4. distribute-lft-neg-out 99.5%

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

      5. neg-mul-1 99.5%

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

      6. times-frac 99.3%

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

      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. sub-neg 99.3%

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

      12. +-commutative 99.3%

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

      13. distribute-lft-in 99.3%

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

      14. neg-mul-1 99.3%

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

      15. remove-double-neg 99.3%

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

      16. metadata-eval 99.3%

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

      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* 99.4%

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

      21. metadata-eval 99.4%

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

      22. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x around 0 98.5%

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

   if 4.79999999999999982 < x

   1. Initial program 83.4%

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

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

      12. +-commutative 99.7%

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

      13. distribute-lft-in 99.7%

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

      14. neg-mul-1 99.7%

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

      15. remove-double-neg 99.7%

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

      16. metadata-eval 99.7%

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

      17. distribute-lft-neg-out 99.7%

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

      18. *-commutative 99.7%

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

      19. distribute-lft-neg-in 99.7%

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

      20. associate-/r* 99.7%

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

      21. metadata-eval 99.7%

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

      22. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0 0.8%

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

   6. Taylor expanded in x around inf 0.8%

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

      1. frac-2neg 0.8%

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

      2. associate-*r/ 0.8%

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

      3. add-sqr-sqrt 0.0%

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

      4. sqrt-unprod 45.5%

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

      5. sqr-neg 45.5%

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

      6. sqrt-unprod 21.4%

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

      7. add-sqr-sqrt 21.4%

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

      8. *-commutative 21.4%

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

   8. Applied egg-rr 21.4%

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

      1. distribute-frac-neg2 21.4%

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

      2. distribute-frac-neg 21.4%

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

      3. distribute-rgt-neg-in 21.4%

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

      4. metadata-eval 21.4%

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

      5. associate-/l* 21.4%

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

   10. Simplified 21.4%

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

Alternative 10: 63.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.75:\\ \;\;\;\;-1.3333333333333333 \cdot \frac{x}{y}\\ \mathbf{elif}\;x \leq 4.6:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -0.75)
   (* -1.3333333333333333 (/ x y))
   (if (<= x 4.6) (/ 1.0 y) (/ x y))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -0.75) {
		tmp = -1.3333333333333333 * (x / y);
	} else if (x <= 4.6) {
		tmp = 1.0 / y;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-0.75d0)) then
        tmp = (-1.3333333333333333d0) * (x / y)
    else if (x <= 4.6d0) then
        tmp = 1.0d0 / y
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -0.75) {
		tmp = -1.3333333333333333 * (x / y);
	} else if (x <= 4.6) {
		tmp = 1.0 / y;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -0.75:
		tmp = -1.3333333333333333 * (x / y)
	elif x <= 4.6:
		tmp = 1.0 / y
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -0.75)
		tmp = Float64(-1.3333333333333333 * Float64(x / y));
	elseif (x <= 4.6)
		tmp = Float64(1.0 / y);
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -0.75)
		tmp = -1.3333333333333333 * (x / y);
	elseif (x <= 4.6)
		tmp = 1.0 / y;
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -0.75], N[(-1.3333333333333333 * N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.6], N[(1.0 / y), $MachinePrecision], N[(x / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -0.75

   1. Initial program 85.1%

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

      1. associate-/l* 99.7%

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

      2. *-rgt-identity 99.7%

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

      3. remove-double-neg 99.7%

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

      4. distribute-lft-neg-out 99.7%

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

      5. neg-mul-1 99.7%

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

      6. times-frac 99.7%

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

      7. *-rgt-identity 99.7%

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

      8. associate-/l* 99.7%

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

      9. metadata-eval 99.7%

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

      10. *-commutative 99.7%

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

      11. sub-neg 99.7%

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

      12. +-commutative 99.7%

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

      13. distribute-lft-in 99.7%

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

      14. neg-mul-1 99.7%

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

      15. remove-double-neg 99.7%

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

      16. metadata-eval 99.7%

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

      17. distribute-lft-neg-out 99.7%

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

      18. *-commutative 99.7%

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

      19. distribute-lft-neg-in 99.7%

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

      20. associate-/r* 99.8%

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

      21. metadata-eval 99.8%

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

      22. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0 32.7%

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

   6. Taylor expanded in x around inf 32.7%

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

   if -0.75 < x < 4.5999999999999996

   1. Initial program 99.5%

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

      1. associate-/l* 99.5%

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

      2. *-rgt-identity 99.5%

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

      3. remove-double-neg 99.5%

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

      4. distribute-lft-neg-out 99.5%

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

      5. neg-mul-1 99.5%

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

      6. times-frac 99.3%

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

      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. sub-neg 99.3%

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

      12. +-commutative 99.3%

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

      13. distribute-lft-in 99.3%

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

      14. neg-mul-1 99.3%

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

      15. remove-double-neg 99.3%

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

      16. metadata-eval 99.3%

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

      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* 99.4%

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

      21. metadata-eval 99.4%

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

      22. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x around 0 98.5%

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

   if 4.5999999999999996 < x

   1. Initial program 83.4%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   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. Taylor expanded in x around inf 98.6%

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

      1. neg-mul-1 98.7%

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

   7. Simplified 98.6%

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

      1. associate-*r/ 82.4%

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

      2. sub-neg 82.4%

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

      3. distribute-rgt-in 82.4%

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

      4. add-sqr-sqrt 0.0%

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

      5. sqrt-unprod 82.3%

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

      6. sqr-neg 82.3%

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

      7. sqrt-unprod 82.3%

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

      8. add-sqr-sqrt 82.3%

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

      9. sqr-neg 82.3%

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

      10. +-commutative 82.3%

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

      11. distribute-rgt-out 82.3%

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

      12. *-commutative 82.3%

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

   9. Applied egg-rr 82.3%

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

   10. Taylor expanded in x around 0 21.4%

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

Alternative 11: 63.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;\frac{x}{-y}\\ \mathbf{elif}\;x \leq 4.6:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.0) (/ x (- y)) (if (<= x 4.6) (/ 1.0 y) (/ x y))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.0) {
		tmp = x / -y;
	} else if (x <= 4.6) {
		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 <= 4.6d0) 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 <= 4.6) {
		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 <= 4.6:
		tmp = 1.0 / y
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.0)
		tmp = Float64(x / Float64(-y));
	elseif (x <= 4.6)
		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 <= 4.6)
		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, 4.6], N[(1.0 / y), $MachinePrecision], N[(x / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1

   1. Initial program 85.1%

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

      1. associate-/l* 99.7%

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

      2. *-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. Taylor expanded in x around inf 99.0%

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

      1. neg-mul-1 99.1%

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

   7. Simplified 99.0%

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

   8. Taylor expanded in y around 0 84.5%

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

   9. Taylor expanded in x around 0 32.7%

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

       1. associate-*r/ 32.7%

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

       2. neg-mul-1 32.7%

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

   11. Simplified 32.7%

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

   if -1 < x < 4.5999999999999996

   1. Initial program 99.5%

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

      1. associate-/l* 99.5%

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

      2. *-rgt-identity 99.5%

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

      3. remove-double-neg 99.5%

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

      4. distribute-lft-neg-out 99.5%

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

      5. neg-mul-1 99.5%

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

      6. times-frac 99.3%

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

      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. sub-neg 99.3%

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

      12. +-commutative 99.3%

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

      13. distribute-lft-in 99.3%

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

      14. neg-mul-1 99.3%

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

      15. remove-double-neg 99.3%

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

      16. metadata-eval 99.3%

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

      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* 99.4%

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

      21. metadata-eval 99.4%

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

      22. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x around 0 98.5%

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

   if 4.5999999999999996 < x

   1. Initial program 83.4%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   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. Taylor expanded in x around inf 98.6%

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

      1. neg-mul-1 98.7%

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

   7. Simplified 98.6%

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

      1. associate-*r/ 82.4%

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

      2. sub-neg 82.4%

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

      3. distribute-rgt-in 82.4%

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

      4. add-sqr-sqrt 0.0%

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

      5. sqrt-unprod 82.3%

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

      6. sqr-neg 82.3%

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

      7. sqrt-unprod 82.3%

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

      8. add-sqr-sqrt 82.3%

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

      9. sqr-neg 82.3%

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

      10. +-commutative 82.3%

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

      11. distribute-rgt-out 82.3%

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

      12. *-commutative 82.3%

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

   9. Applied egg-rr 82.3%

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

   10. Taylor expanded in x around 0 21.4%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;\frac{x}{-y}\\ \mathbf{elif}\;x \leq 4.6:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 99.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 91.6%

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

   1. associate-/l* 99.6%

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

   2. *-commutative 99.6%

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

3. Simplified 99.6%

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

5. Final simplification 99.6%

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

Alternative 13: 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 91.6%

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

   1. associate-/l* 99.6%

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

   2. *-rgt-identity 99.6%

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

   3. remove-double-neg 99.6%

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

   4. distribute-lft-neg-out 99.6%

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

   5. neg-mul-1 99.6%

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

   6. times-frac 99.5%

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

   7. *-rgt-identity 99.5%

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

   8. associate-/l* 99.5%

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

   9. metadata-eval 99.5%

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

   10. *-commutative 99.5%

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

   11. sub-neg 99.5%

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

   12. +-commutative 99.5%

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

   13. distribute-lft-in 99.5%

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

   14. neg-mul-1 99.5%

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

   15. remove-double-neg 99.5%

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

   16. metadata-eval 99.5%

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

   17. distribute-lft-neg-out 99.5%

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

   18. *-commutative 99.5%

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

   19. distribute-lft-neg-in 99.5%

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

   20. associate-/r* 99.6%

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

   21. metadata-eval 99.6%

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

   22. metadata-eval 99.6%

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

3. Simplified 99.6%

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

Alternative 14: 57.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 4.6:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= x 4.6) (/ 1.0 y) (/ x y)))

C

double code(double x, double y) {
	double tmp;
	if (x <= 4.6) {
		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 <= 4.6d0) 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 <= 4.6) {
		tmp = 1.0 / y;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 4.6:
		tmp = 1.0 / y
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 4.6)
		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 <= 4.6)
		tmp = 1.0 / y;
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 4.6], N[(1.0 / y), $MachinePrecision], N[(x / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 4.5999999999999996

   1. Initial program 94.3%

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

      1. associate-/l* 99.6%

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

      2. *-rgt-identity 99.6%

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

      3. remove-double-neg 99.6%

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

      4. distribute-lft-neg-out 99.6%

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

      5. neg-mul-1 99.6%

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

      6. times-frac 99.5%

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

      7. *-rgt-identity 99.5%

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

      8. associate-/l* 99.5%

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

      9. metadata-eval 99.5%

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

      10. *-commutative 99.5%

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

      11. sub-neg 99.5%

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

      12. +-commutative 99.5%

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

      13. distribute-lft-in 99.5%

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

      14. neg-mul-1 99.5%

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

      15. remove-double-neg 99.5%

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

      16. metadata-eval 99.5%

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

      17. distribute-lft-neg-out 99.5%

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

      18. *-commutative 99.5%

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

      19. distribute-lft-neg-in 99.5%

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

      20. associate-/r* 99.5%

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

      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 64.5%

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

   if 4.5999999999999996 < x

   1. Initial program 83.4%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   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. Taylor expanded in x around inf 98.6%

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

      1. neg-mul-1 98.7%

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

   7. Simplified 98.6%

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

      1. associate-*r/ 82.4%

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

      2. sub-neg 82.4%

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

      3. distribute-rgt-in 82.4%

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

      4. add-sqr-sqrt 0.0%

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

      5. sqrt-unprod 82.3%

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

      6. sqr-neg 82.3%

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

      7. sqrt-unprod 82.3%

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

      8. add-sqr-sqrt 82.3%

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

      9. sqr-neg 82.3%

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

      10. +-commutative 82.3%

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

      11. distribute-rgt-out 82.3%

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

      12. *-commutative 82.3%

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

   9. Applied egg-rr 82.3%

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

   10. Taylor expanded in x around 0 21.4%

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

Alternative 15: 50.9% accurate, 3.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 91.6%

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

   1. associate-/l* 99.6%

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

   2. *-rgt-identity 99.6%

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

   3. remove-double-neg 99.6%

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

   4. distribute-lft-neg-out 99.6%

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

   5. neg-mul-1 99.6%

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

   6. times-frac 99.5%

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

   7. *-rgt-identity 99.5%

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

   8. associate-/l* 99.5%

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

   9. metadata-eval 99.5%

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

   10. *-commutative 99.5%

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

   11. sub-neg 99.5%

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

   12. +-commutative 99.5%

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

   13. distribute-lft-in 99.5%

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

   14. neg-mul-1 99.5%

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

   15. remove-double-neg 99.5%

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

   16. metadata-eval 99.5%

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

   17. distribute-lft-neg-out 99.5%

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

   18. *-commutative 99.5%

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

   19. distribute-lft-neg-in 99.5%

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

   20. associate-/r* 99.6%

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

   21. metadata-eval 99.6%

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

   22. metadata-eval 99.6%

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

3. Simplified 99.6%

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

5. Taylor expanded in x around 0 49.8%

   \[\leadsto \color{blue}{\frac{1}{y}} \]
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 2024144 
(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)))