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

Percentage Accurate: 93.8% → 99.8%

Time: 8.8s

Alternatives: 16

Speedup: 1.0×

• 25.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 93.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 91.7%

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

   1. associate-/l* 99.6%

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

   2. *-commutative 99.6%

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

3. Simplified 99.6%

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

   1. clear-num 99.6%

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

   2. un-div-inv 99.7%

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

   3. *-commutative 99.7%

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

   4. associate-/l* 99.8%

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

6. Applied egg-rr 99.8%

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

Alternative 2: 98.3% accurate, 0.6× speedup

Math

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

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -2.3) (not (<= x 1.3)))
   (* -0.3333333333333333 (* x (/ (- 3.0 x) y)))
   (/ (+ 1.0 (* x -1.3333333333333333)) y)))

C

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

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-2.3d0)) .or. (.not. (x <= 1.3d0))) then
        tmp = (-0.3333333333333333d0) * (x * ((3.0d0 - x) / y))
    else
        tmp = (1.0d0 + (x * (-1.3333333333333333d0))) / y
    end if
    code = tmp
end function

Java

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

Python

def code(x, y):
	tmp = 0
	if (x <= -2.3) or not (x <= 1.3):
		tmp = -0.3333333333333333 * (x * ((3.0 - x) / y))
	else:
		tmp = (1.0 + (x * -1.3333333333333333)) / y
	return tmp

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if x < -2.2999999999999998 or 1.30000000000000004 < x

   1. Initial program 83.5%

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

   3. Taylor expanded in x around inf 81.8%

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

      1. neg-mul-1 81.8%

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

   5. Simplified 81.8%

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

   6. Taylor expanded in y around 0 81.8%

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

      1. associate-/l* 97.9%

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

   8. Simplified 97.9%

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

   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* 99.3%

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

      21. metadata-eval 99.3%

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

      22. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in x around 0 99.5%

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

   6. Taylor expanded in y around 0 99.5%

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

      1. *-commutative 99.5%

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

   8. Simplified 99.5%

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

4. Final simplification 98.7%

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

Alternative 3: 98.3% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 3 regimes

2. if x < -2.2999999999999998

   1. Initial program 84.2%

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

   3. Taylor expanded in x around inf 82.7%

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

      1. neg-mul-1 82.7%

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

   5. Simplified 82.7%

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

      1. *-un-lft-identity 82.7%

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

      2. times-frac 82.6%

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

      3. distribute-lft-neg-out 82.6%

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

      4. distribute-rgt-neg-in 82.6%

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

      5. sub-neg 82.6%

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

      6. distribute-neg-in 82.6%

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

      7. metadata-eval 82.6%

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

      8. add-sqr-sqrt 82.6%

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

      9. sqrt-unprod 82.6%

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

      10. sqr-neg 82.6%

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

      11. sqrt-unprod 0.0%

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

      12. add-sqr-sqrt 0.4%

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

      13. add-sqr-sqrt 0.4%

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

      14. sqrt-unprod 0.4%

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

      15. sqr-neg 0.4%

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

      16. sqrt-unprod 0.0%

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

      17. add-sqr-sqrt 82.6%

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

   7. Applied egg-rr 82.6%

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

      1. associate-*l/ 82.7%

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

      2. *-lft-identity 82.7%

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

      3. associate-/r* 82.7%

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

      4. *-commutative 82.7%

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

      5. times-frac 98.1%

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

      6. +-commutative 98.1%

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

      7. metadata-eval 98.1%

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

      8. sub-neg 98.1%

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

      9. div-sub 98.1%

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

      10. metadata-eval 98.1%

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

   9. Simplified 98.1%

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

   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* 99.3%

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

      21. metadata-eval 99.3%

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

      22. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in x around 0 99.5%

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

   6. Taylor expanded in y around 0 99.5%

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

      1. *-commutative 99.5%

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

   8. Simplified 99.5%

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

   if 1.30000000000000004 < x

   1. Initial program 82.7%

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

   3. Taylor expanded in x around inf 80.8%

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

      1. neg-mul-1 80.8%

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

   5. Simplified 80.8%

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

   6. Taylor expanded in y around 0 80.8%

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

      1. associate-/l* 97.8%

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

   8. Simplified 97.8%

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

4. Final simplification 98.7%

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

Alternative 4: 98.2% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Derivation

1. Split input into 2 regimes

2. if x < -4.5999999999999996 or 3 < x

   1. Initial program 83.5%

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

   3. Taylor expanded in x around inf 81.8%

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

      1. neg-mul-1 81.8%

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

   5. Simplified 81.8%

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

      1. *-un-lft-identity 81.8%

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

      2. times-frac 81.7%

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

      3. distribute-lft-neg-out 81.7%

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

      4. distribute-rgt-neg-in 81.7%

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

      5. sub-neg 81.7%

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

      6. distribute-neg-in 81.7%

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

      7. metadata-eval 81.7%

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

      8. add-sqr-sqrt 42.9%

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

      9. sqrt-unprod 43.2%

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

      10. sqr-neg 43.2%

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

      11. sqrt-unprod 0.2%

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

      12. add-sqr-sqrt 0.4%

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

      13. add-sqr-sqrt 0.2%

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

      14. sqrt-unprod 39.0%

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

      15. sqr-neg 39.0%

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

      16. sqrt-unprod 38.7%

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

      17. add-sqr-sqrt 81.7%

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

   7. Applied egg-rr 81.7%

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

      1. associate-*l/ 81.9%

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

      2. *-lft-identity 81.9%

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

      3. associate-/r* 81.8%

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

      4. *-commutative 81.8%

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

      5. times-frac 98.0%

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

      6. +-commutative 98.0%

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

      7. metadata-eval 98.0%

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

      8. sub-neg 98.0%

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

      9. div-sub 98.0%

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

      10. metadata-eval 98.0%

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

   9. Simplified 98.0%

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

   10. Taylor expanded in x around inf 97.8%

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

       1. *-commutative 97.8%

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

   12. Simplified 97.8%

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

   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* 99.3%

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

      21. metadata-eval 99.3%

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

      22. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in x around 0 99.5%

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

   6. Taylor expanded in y around 0 99.5%

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

      1. *-commutative 99.5%

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

   8. Simplified 99.5%

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

4. Final simplification 98.6%

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

Alternative 5: 97.6% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if x < -3.7999999999999998 or 3 < x

   1. Initial program 83.5%

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

   3. Taylor expanded in x around inf 81.8%

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

      1. neg-mul-1 81.8%

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

   5. Simplified 81.8%

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

      1. *-un-lft-identity 81.8%

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

      2. times-frac 81.7%

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

      3. distribute-lft-neg-out 81.7%

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

      4. distribute-rgt-neg-in 81.7%

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

      5. sub-neg 81.7%

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

      6. distribute-neg-in 81.7%

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

      7. metadata-eval 81.7%

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

      8. add-sqr-sqrt 42.9%

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

      9. sqrt-unprod 43.2%

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

      10. sqr-neg 43.2%

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

      11. sqrt-unprod 0.2%

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

      12. add-sqr-sqrt 0.4%

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

      13. add-sqr-sqrt 0.2%

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

      14. sqrt-unprod 39.0%

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

      15. sqr-neg 39.0%

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

      16. sqrt-unprod 38.7%

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

      17. add-sqr-sqrt 81.7%

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

   7. Applied egg-rr 81.7%

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

      1. associate-*l/ 81.9%

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

      2. *-lft-identity 81.9%

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

      3. associate-/r* 81.8%

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

      4. *-commutative 81.8%

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

      5. times-frac 98.0%

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

      6. +-commutative 98.0%

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

      7. metadata-eval 98.0%

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

      8. sub-neg 98.0%

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

      9. div-sub 98.0%

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

      10. metadata-eval 98.0%

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

   9. Simplified 98.0%

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

   10. Taylor expanded in x around inf 97.8%

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

       1. *-commutative 97.8%

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

   12. Simplified 97.8%

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

   if -3.7999999999999998 < x < 3

   1. Initial program 99.5%

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

      1. associate-/l* 99.5%

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

      2. *-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* 99.3%

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

      21. metadata-eval 99.3%

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

      22. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in x around 0 98.8%

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

4. Final simplification 98.3%

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

Alternative 6: 63.7% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-0.75d0)) then
        tmp = (x / y) * (-1.3333333333333333d0)
    else if (x <= 4.8d0) then
        tmp = 1.0d0 / y
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

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

Python

def code(x, y):
	tmp = 0
	if x <= -0.75:
		tmp = (x / y) * -1.3333333333333333
	elif x <= 4.8:
		tmp = 1.0 / y
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -0.75)
		tmp = Float64(Float64(x / y) * -1.3333333333333333);
	elseif (x <= 4.8)
		tmp = Float64(1.0 / y);
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -0.75)
		tmp = (x / y) * -1.3333333333333333;
	elseif (x <= 4.8)
		tmp = 1.0 / y;
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -0.75], N[(N[(x / y), $MachinePrecision] * -1.3333333333333333), $MachinePrecision], If[LessEqual[x, 4.8], N[(1.0 / y), $MachinePrecision], N[(x / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -0.75

   1. Initial program 84.2%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   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 26.2%

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

   6. Taylor expanded in x around inf 26.2%

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

   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. *-commutative 99.5%

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

   3. Simplified 99.5%

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

      1. clear-num 99.8%

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

      2. un-div-inv 99.8%

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

      3. *-commutative 99.8%

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

      4. associate-/l* 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in x around 0 98.7%

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

   if 4.79999999999999982 < x

   1. Initial program 82.7%

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

   3. Taylor expanded in x around inf 80.8%

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

      1. neg-mul-1 80.8%

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

   5. Simplified 80.8%

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

   6. Taylor expanded in x around 0 0.7%

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

      1. neg-mul-1 0.7%

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

      2. distribute-neg-frac2 0.7%

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

   8. Simplified 0.7%

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

      1. add-sqr-sqrt 0.5%

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

      2. sqrt-unprod 13.8%

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

      3. sqr-neg 13.8%

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

      4. sqrt-unprod 13.2%

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

      5. add-sqr-sqrt 29.8%

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

      6. div-inv 29.8%

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

   10. Applied egg-rr 29.8%

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

       1. associate-*r/ 29.8%

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

       2. *-rgt-identity 29.8%

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

   12. Simplified 29.8%

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

4. Final simplification 64.1%

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

Alternative 7: 63.7% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-1.0d0)) then
        tmp = x / -y
    else if (x <= 4.8d0) then
        tmp = 1.0d0 / y
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

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

Python

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

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.0)
		tmp = Float64(x / Float64(-y));
	elseif (x <= 4.8)
		tmp = Float64(1.0 / y);
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

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

Wolfram

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

Derivation

1. Split input into 3 regimes

2. if x < -1

   1. Initial program 84.2%

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

   3. Taylor expanded in x around inf 82.7%

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

      1. neg-mul-1 82.7%

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

   5. Simplified 82.7%

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

   6. Taylor expanded in x around 0 26.2%

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

      1. neg-mul-1 26.2%

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

      2. distribute-neg-frac2 26.2%

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

   8. Simplified 26.2%

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

   if -1 < 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. *-commutative 99.5%

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

   3. Simplified 99.5%

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

      1. clear-num 99.8%

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

      2. un-div-inv 99.8%

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

      3. *-commutative 99.8%

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

      4. associate-/l* 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in x around 0 98.7%

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

   if 4.79999999999999982 < x

   1. Initial program 82.7%

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

   3. Taylor expanded in x around inf 80.8%

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

      1. neg-mul-1 80.8%

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

   5. Simplified 80.8%

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

   6. Taylor expanded in x around 0 0.7%

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

      1. neg-mul-1 0.7%

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

      2. distribute-neg-frac2 0.7%

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

   8. Simplified 0.7%

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

      1. add-sqr-sqrt 0.5%

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

      2. sqrt-unprod 13.8%

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

      3. sqr-neg 13.8%

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

      4. sqrt-unprod 13.2%

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

      5. add-sqr-sqrt 29.8%

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

      6. div-inv 29.8%

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

   10. Applied egg-rr 29.8%

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

       1. associate-*r/ 29.8%

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

       2. *-rgt-identity 29.8%

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

   12. Simplified 29.8%

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

Alternative 8: 63.8% accurate, 0.9× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 3.0)
		tmp = Float64(Float64(1.0 - x) * 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 <= 3.0)
		tmp = (1.0 - x) * (1.0 / y);
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if x < 3

   1. Initial program 94.5%

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

      1. associate-/l* 99.5%

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

      2. *-rgt-identity 99.5%

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

      3. remove-double-neg 99.5%

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

      4. distribute-lft-neg-out 99.5%

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

      5. neg-mul-1 99.5%

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

      6. times-frac 99.4%

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

      7. *-rgt-identity 99.4%

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

      8. associate-/l* 99.4%

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

      9. metadata-eval 99.4%

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

      10. *-commutative 99.4%

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

      11. sub-neg 99.4%

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

      12. +-commutative 99.4%

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

      13. distribute-lft-in 99.4%

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

      14. neg-mul-1 99.4%

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

      15. remove-double-neg 99.4%

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

      16. metadata-eval 99.4%

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

      17. distribute-lft-neg-out 99.4%

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

      18. *-commutative 99.4%

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

      19. distribute-lft-neg-in 99.4%

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

      20. associate-/r* 99.4%

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

      21. metadata-eval 99.4%

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

      22. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x around 0 74.7%

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

   if 3 < x

   1. Initial program 82.7%

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

   3. Taylor expanded in x around inf 80.8%

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

      1. neg-mul-1 80.8%

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

   5. Simplified 80.8%

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

   6. Taylor expanded in x around 0 0.7%

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

      1. neg-mul-1 0.7%

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

      2. distribute-neg-frac2 0.7%

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

   8. Simplified 0.7%

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

      1. add-sqr-sqrt 0.5%

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

      2. sqrt-unprod 13.8%

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

      3. sqr-neg 13.8%

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

      4. sqrt-unprod 13.2%

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

      5. add-sqr-sqrt 29.8%

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

      6. div-inv 29.8%

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

   10. Applied egg-rr 29.8%

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

       1. associate-*r/ 29.8%

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

       2. *-rgt-identity 29.8%

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

   12. Simplified 29.8%

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

Alternative 9: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 91.7%

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

   1. associate-/l* 99.6%

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

   2. *-commutative 99.6%

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

3. Simplified 99.6%

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

   1. clear-num 99.6%

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

   2. un-div-inv 99.7%

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

   3. *-commutative 99.7%

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

   4. associate-/l* 99.8%

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

6. Applied egg-rr 99.8%

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

7. Taylor expanded in y around 0 99.8%

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

Alternative 10: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 91.7%

   \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
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* 91.7%

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

   3. times-frac 99.8%

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

   4. associate-*r/ 99.7%

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

6. Applied egg-rr 99.7%

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

7. Final simplification 99.7%

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

Alternative 11: 99.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 91.7%

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

   1. *-commutative 91.7%

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

   2. times-frac 99.6%

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

4. Applied egg-rr 99.6%

   \[\leadsto \color{blue}{\frac{3 - x}{y} \cdot \frac{1 - x}{3}} \]
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 91.7%

   \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
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 91.7%

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

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

   7. *-rgt-identity 99.4%

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

   8. associate-/l* 99.4%

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

   9. metadata-eval 99.4%

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

   10. *-commutative 99.4%

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

   11. sub-neg 99.4%

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

   12. +-commutative 99.4%

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

   13. distribute-lft-in 99.4%

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

   14. neg-mul-1 99.4%

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

   15. remove-double-neg 99.4%

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

   16. metadata-eval 99.4%

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

   17. distribute-lft-neg-out 99.4%

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

   18. *-commutative 99.4%

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

   19. distribute-lft-neg-in 99.4%

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

   20. associate-/r* 99.4%

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

   21. metadata-eval 99.4%

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

   22. metadata-eval 99.4%

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

3. Simplified 99.4%

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

Alternative 14: 63.8% accurate, 1.1× speedup

Math

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

FPCore

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

C

double code(double x, double y) {
	double tmp;
	if (x <= 3.0) {
		tmp = (1.0 - x) / 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 <= 3.0d0) then
        tmp = (1.0d0 - x) / y
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if x < 3

   1. Initial program 94.5%

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

      1. associate-/l* 99.5%

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

      2. *-commutative 99.5%

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

   3. Simplified 99.5%

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

      1. clear-num 99.7%

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

      2. un-div-inv 99.8%

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

      3. *-commutative 99.8%

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

      4. associate-/l* 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in x around 0 74.7%

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

   if 3 < x

   1. Initial program 82.7%

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

   3. Taylor expanded in x around inf 80.8%

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

      1. neg-mul-1 80.8%

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

   5. Simplified 80.8%

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

   6. Taylor expanded in x around 0 0.7%

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

      1. neg-mul-1 0.7%

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

      2. distribute-neg-frac2 0.7%

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

   8. Simplified 0.7%

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

      1. add-sqr-sqrt 0.5%

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

      2. sqrt-unprod 13.8%

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

      3. sqr-neg 13.8%

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

      4. sqrt-unprod 13.2%

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

      5. add-sqr-sqrt 29.8%

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

      6. div-inv 29.8%

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

   10. Applied egg-rr 29.8%

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

       1. associate-*r/ 29.8%

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

       2. *-rgt-identity 29.8%

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

   12. Simplified 29.8%

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

Alternative 15: 57.4% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= 4.8d0) then
        tmp = 1.0d0 / y
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

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

Python

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

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 4.8)
		tmp = Float64(1.0 / y);
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if x < 4.79999999999999982

   1. Initial program 94.5%

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

      1. associate-/l* 99.5%

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

      2. *-commutative 99.5%

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

   3. Simplified 99.5%

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

      1. clear-num 99.7%

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

      2. un-div-inv 99.8%

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

      3. *-commutative 99.8%

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

      4. associate-/l* 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in x around 0 67.5%

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

   if 4.79999999999999982 < x

   1. Initial program 82.7%

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

   3. Taylor expanded in x around inf 80.8%

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

      1. neg-mul-1 80.8%

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

   5. Simplified 80.8%

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

   6. Taylor expanded in x around 0 0.7%

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

      1. neg-mul-1 0.7%

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

      2. distribute-neg-frac2 0.7%

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

   8. Simplified 0.7%

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

      1. add-sqr-sqrt 0.5%

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

      2. sqrt-unprod 13.8%

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

      3. sqr-neg 13.8%

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

      4. sqrt-unprod 13.2%

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

      5. add-sqr-sqrt 29.8%

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

      6. div-inv 29.8%

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

   10. Applied egg-rr 29.8%

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

       1. associate-*r/ 29.8%

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

       2. *-rgt-identity 29.8%

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

   12. Simplified 29.8%

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

Alternative 16: 50.8% 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 91.7%

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

   1. associate-/l* 99.6%

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

   2. *-commutative 99.6%

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

3. Simplified 99.6%

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

   1. clear-num 99.6%

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

   2. un-div-inv 99.7%

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

   3. *-commutative 99.7%

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

   4. associate-/l* 99.8%

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

6. Applied egg-rr 99.8%

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

7. Taylor expanded in x around 0 52.8%

   \[\leadsto \color{blue}{\frac{1}{y}} \]
8. 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 2024137 
(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)))