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

Percentage Accurate: 93.9% → 99.8%

Time: 8.3s

Alternatives: 11

Speedup: 1.0×

• 24.9% 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: 93.9% 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

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

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]

Derivation

1. Initial program 96.3%

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

   1. times-frac 99.9%

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

3. Simplified 99.9%

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

4. Final simplification 99.9%

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

Alternative 2: 98.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.75:\\ \;\;\;\;\left(\frac{x}{y} \cdot \left(x + -4\right)\right) \cdot 0.3333333333333333\\ \mathbf{elif}\;x \leq 1.7:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(x + -4\right) \cdot \frac{x}{y \cdot 3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.75)
   (* (* (/ x y) (+ x -4.0)) 0.3333333333333333)
   (if (<= x 1.7)
     (/ (+ 1.0 (* x -1.3333333333333333)) y)
     (* (+ x -4.0) (/ x (* y 3.0))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.75) {
		tmp = ((x / y) * (x + -4.0)) * 0.3333333333333333;
	} else if (x <= 1.7) {
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	} else {
		tmp = (x + -4.0) * (x / (y * 3.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-1.75d0)) then
        tmp = ((x / y) * (x + (-4.0d0))) * 0.3333333333333333d0
    else if (x <= 1.7d0) then
        tmp = (1.0d0 + (x * (-1.3333333333333333d0))) / y
    else
        tmp = (x + (-4.0d0)) * (x / (y * 3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -1.75) {
		tmp = ((x / y) * (x + -4.0)) * 0.3333333333333333;
	} else if (x <= 1.7) {
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	} else {
		tmp = (x + -4.0) * (x / (y * 3.0));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.75:
		tmp = ((x / y) * (x + -4.0)) * 0.3333333333333333
	elif x <= 1.7:
		tmp = (1.0 + (x * -1.3333333333333333)) / y
	else:
		tmp = (x + -4.0) * (x / (y * 3.0))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.75)
		tmp = Float64(Float64(Float64(x / y) * Float64(x + -4.0)) * 0.3333333333333333);
	elseif (x <= 1.7)
		tmp = Float64(Float64(1.0 + Float64(x * -1.3333333333333333)) / y);
	else
		tmp = Float64(Float64(x + -4.0) * Float64(x / Float64(y * 3.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.75)
		tmp = ((x / y) * (x + -4.0)) * 0.3333333333333333;
	elseif (x <= 1.7)
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	else
		tmp = (x + -4.0) * (x / (y * 3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.75], N[(N[(N[(x / y), $MachinePrecision] * N[(x + -4.0), $MachinePrecision]), $MachinePrecision] * 0.3333333333333333), $MachinePrecision], If[LessEqual[x, 1.7], N[(N[(1.0 + N[(x * -1.3333333333333333), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x + -4.0), $MachinePrecision] * N[(x / N[(y * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.75

   1. Initial program 91.4%

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

   2. Taylor expanded in x around inf 89.6%

      \[\leadsto \frac{\color{blue}{-4 \cdot x + {x}^{2}}}{y \cdot 3} \]
   3. Step-by-step derivation

      1. +-commutative 89.6%

         \[\leadsto \frac{\color{blue}{{x}^{2} + -4 \cdot x}}{y \cdot 3} \]

      2. unpow2 89.6%

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

      3. distribute-rgt-out 89.6%

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

   4. Simplified 89.6%

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

      1. associate-/r* 89.7%

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

      2. div-inv 89.7%

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

      3. *-commutative 89.7%

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

      4. associate-/l* 98.0%

         \[\leadsto \color{blue}{\frac{x + -4}{\frac{y}{x}}} \cdot \frac{1}{3} \]

      5. metadata-eval 98.0%

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

   6. Applied egg-rr 98.0%

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

   7. Taylor expanded in x around 0 89.7%

      \[\leadsto \color{blue}{\left(-4 \cdot \frac{x}{y} + \frac{{x}^{2}}{y}\right)} \cdot 0.3333333333333333 \]
   8. Step-by-step derivation

      1. unpow2 89.7%

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

      2. associate-*r/ 98.0%

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

      3. distribute-rgt-in 98.0%

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

      4. +-commutative 98.0%

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

   9. Simplified 98.0%

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

   if -1.75 < x < 1.69999999999999996

   1. Initial program 99.4%

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

      1. *-commutative 99.4%

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

      2. associate-*l/ 99.5%

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

      3. *-commutative 99.5%

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

      4. sub-neg 99.5%

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

      5. +-commutative 99.5%

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

      6. neg-sub0 99.5%

         \[\leadsto \left(1 - x\right) \cdot \frac{\color{blue}{\left(0 - x\right)} + 3}{y \cdot 3} \]

      7. associate-+l- 99.5%

         \[\leadsto \left(1 - x\right) \cdot \frac{\color{blue}{0 - \left(x - 3\right)}}{y \cdot 3} \]

      8. sub0-neg 99.5%

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

      9. distribute-frac-neg 99.5%

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

      10. sub-neg 99.5%

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

      11. remove-double-neg 99.5%

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

      12. distribute-neg-in 99.5%

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

      13. +-commutative 99.5%

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

      14. sub-neg 99.5%

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

      15. distribute-frac-neg 99.5%

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

      16. mul-1-neg 99.5%

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

      17. metadata-eval 99.5%

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

      18. times-frac 99.5%

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

      19. *-lft-identity 99.5%

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

      20. neg-mul-1 99.5%

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

      21. distribute-lft-neg-out 99.5%

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

      22. distribute-frac-neg 99.5%

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

   3. Simplified 99.5%

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

      1. associate-*r/ 99.4%

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

      2. *-commutative 99.4%

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

      3. associate-/r* 99.9%

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

      4. *-commutative 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in x around 0 98.2%

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

   if 1.69999999999999996 < x

   1. Initial program 95.3%

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

   2. Taylor expanded in x around inf 95.3%

      \[\leadsto \frac{\color{blue}{-4 \cdot x + {x}^{2}}}{y \cdot 3} \]
   3. Step-by-step derivation

      1. +-commutative 95.3%

         \[\leadsto \frac{\color{blue}{{x}^{2} + -4 \cdot x}}{y \cdot 3} \]

      2. unpow2 95.3%

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

      3. distribute-rgt-out 95.3%

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

   4. Simplified 95.3%

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

      1. associate-/l* 99.7%

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

      2. associate-/r/ 99.7%

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

      3. *-commutative 99.7%

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

   6. Applied egg-rr 99.7%

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

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.75:\\ \;\;\;\;\left(\frac{x}{y} \cdot \left(x + -4\right)\right) \cdot 0.3333333333333333\\ \mathbf{elif}\;x \leq 1.7:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(x + -4\right) \cdot \frac{x}{y \cdot 3}\\ \end{array} \]

Alternative 3: 98.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.75:\\ \;\;\;\;\left(\frac{x}{y} \cdot \left(x + -4\right)\right) \cdot 0.3333333333333333\\ \mathbf{elif}\;x \leq 1.7:\\ \;\;\;\;\frac{x}{y} \cdot -1.3333333333333333 + \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(x + -4\right) \cdot \frac{x}{y \cdot 3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.75)
   (* (* (/ x y) (+ x -4.0)) 0.3333333333333333)
   (if (<= x 1.7)
     (+ (* (/ x y) -1.3333333333333333) (/ 1.0 y))
     (* (+ x -4.0) (/ x (* y 3.0))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.75) {
		tmp = ((x / y) * (x + -4.0)) * 0.3333333333333333;
	} else if (x <= 1.7) {
		tmp = ((x / y) * -1.3333333333333333) + (1.0 / y);
	} else {
		tmp = (x + -4.0) * (x / (y * 3.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-1.75d0)) then
        tmp = ((x / y) * (x + (-4.0d0))) * 0.3333333333333333d0
    else if (x <= 1.7d0) then
        tmp = ((x / y) * (-1.3333333333333333d0)) + (1.0d0 / y)
    else
        tmp = (x + (-4.0d0)) * (x / (y * 3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -1.75) {
		tmp = ((x / y) * (x + -4.0)) * 0.3333333333333333;
	} else if (x <= 1.7) {
		tmp = ((x / y) * -1.3333333333333333) + (1.0 / y);
	} else {
		tmp = (x + -4.0) * (x / (y * 3.0));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.75:
		tmp = ((x / y) * (x + -4.0)) * 0.3333333333333333
	elif x <= 1.7:
		tmp = ((x / y) * -1.3333333333333333) + (1.0 / y)
	else:
		tmp = (x + -4.0) * (x / (y * 3.0))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.75)
		tmp = Float64(Float64(Float64(x / y) * Float64(x + -4.0)) * 0.3333333333333333);
	elseif (x <= 1.7)
		tmp = Float64(Float64(Float64(x / y) * -1.3333333333333333) + Float64(1.0 / y));
	else
		tmp = Float64(Float64(x + -4.0) * Float64(x / Float64(y * 3.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.75)
		tmp = ((x / y) * (x + -4.0)) * 0.3333333333333333;
	elseif (x <= 1.7)
		tmp = ((x / y) * -1.3333333333333333) + (1.0 / y);
	else
		tmp = (x + -4.0) * (x / (y * 3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.75], N[(N[(N[(x / y), $MachinePrecision] * N[(x + -4.0), $MachinePrecision]), $MachinePrecision] * 0.3333333333333333), $MachinePrecision], If[LessEqual[x, 1.7], N[(N[(N[(x / y), $MachinePrecision] * -1.3333333333333333), $MachinePrecision] + N[(1.0 / y), $MachinePrecision]), $MachinePrecision], N[(N[(x + -4.0), $MachinePrecision] * N[(x / N[(y * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.75

   1. Initial program 91.4%

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

   2. Taylor expanded in x around inf 89.6%

      \[\leadsto \frac{\color{blue}{-4 \cdot x + {x}^{2}}}{y \cdot 3} \]
   3. Step-by-step derivation

      1. +-commutative 89.6%

         \[\leadsto \frac{\color{blue}{{x}^{2} + -4 \cdot x}}{y \cdot 3} \]

      2. unpow2 89.6%

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

      3. distribute-rgt-out 89.6%

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

   4. Simplified 89.6%

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

      1. associate-/r* 89.7%

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

      2. div-inv 89.7%

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

      3. *-commutative 89.7%

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

      4. associate-/l* 98.0%

         \[\leadsto \color{blue}{\frac{x + -4}{\frac{y}{x}}} \cdot \frac{1}{3} \]

      5. metadata-eval 98.0%

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

   6. Applied egg-rr 98.0%

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

   7. Taylor expanded in x around 0 89.7%

      \[\leadsto \color{blue}{\left(-4 \cdot \frac{x}{y} + \frac{{x}^{2}}{y}\right)} \cdot 0.3333333333333333 \]
   8. Step-by-step derivation

      1. unpow2 89.7%

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

      2. associate-*r/ 98.0%

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

      3. distribute-rgt-in 98.0%

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

      4. +-commutative 98.0%

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

   9. Simplified 98.0%

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

   if -1.75 < x < 1.69999999999999996

   1. Initial program 99.4%

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

      1. *-commutative 99.4%

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

      2. associate-*l/ 99.5%

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

      3. *-commutative 99.5%

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

      4. sub-neg 99.5%

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

      5. +-commutative 99.5%

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

      6. neg-sub0 99.5%

         \[\leadsto \left(1 - x\right) \cdot \frac{\color{blue}{\left(0 - x\right)} + 3}{y \cdot 3} \]

      7. associate-+l- 99.5%

         \[\leadsto \left(1 - x\right) \cdot \frac{\color{blue}{0 - \left(x - 3\right)}}{y \cdot 3} \]

      8. sub0-neg 99.5%

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

      9. distribute-frac-neg 99.5%

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

      10. sub-neg 99.5%

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

      11. remove-double-neg 99.5%

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

      12. distribute-neg-in 99.5%

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

      13. +-commutative 99.5%

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

      14. sub-neg 99.5%

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

      15. distribute-frac-neg 99.5%

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

      16. mul-1-neg 99.5%

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

      17. metadata-eval 99.5%

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

      18. times-frac 99.5%

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

      19. *-lft-identity 99.5%

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

      20. neg-mul-1 99.5%

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

      21. distribute-lft-neg-out 99.5%

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

      22. distribute-frac-neg 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in x around 0 98.2%

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

   if 1.69999999999999996 < x

   1. Initial program 95.3%

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

   2. Taylor expanded in x around inf 95.3%

      \[\leadsto \frac{\color{blue}{-4 \cdot x + {x}^{2}}}{y \cdot 3} \]
   3. Step-by-step derivation

      1. +-commutative 95.3%

         \[\leadsto \frac{\color{blue}{{x}^{2} + -4 \cdot x}}{y \cdot 3} \]

      2. unpow2 95.3%

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

      3. distribute-rgt-out 95.3%

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

   4. Simplified 95.3%

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

      1. associate-/l* 99.7%

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

      2. associate-/r/ 99.7%

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

      3. *-commutative 99.7%

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

   6. Applied egg-rr 99.7%

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

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.75:\\ \;\;\;\;\left(\frac{x}{y} \cdot \left(x + -4\right)\right) \cdot 0.3333333333333333\\ \mathbf{elif}\;x \leq 1.7:\\ \;\;\;\;\frac{x}{y} \cdot -1.3333333333333333 + \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(x + -4\right) \cdot \frac{x}{y \cdot 3}\\ \end{array} \]

Alternative 4: 98.0% accurate, 0.9× speedup

Math

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

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(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 93.4%

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

      1. times-frac 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 98.6%

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

   5. Taylor expanded in x around inf 98.6%

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

      1. neg-mul-1 98.6%

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

      2. distribute-neg-frac 98.6%

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

   7. Simplified 98.6%

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

   if -4.5999999999999996 < x < 3

   1. Initial program 99.4%

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

      1. *-commutative 99.4%

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

      2. associate-*l/ 99.5%

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

      3. *-commutative 99.5%

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

      4. sub-neg 99.5%

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

      5. +-commutative 99.5%

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

      6. neg-sub0 99.5%

         \[\leadsto \left(1 - x\right) \cdot \frac{\color{blue}{\left(0 - x\right)} + 3}{y \cdot 3} \]

      7. associate-+l- 99.5%

         \[\leadsto \left(1 - x\right) \cdot \frac{\color{blue}{0 - \left(x - 3\right)}}{y \cdot 3} \]

      8. sub0-neg 99.5%

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

      9. distribute-frac-neg 99.5%

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

      10. sub-neg 99.5%

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

      11. remove-double-neg 99.5%

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

      12. distribute-neg-in 99.5%

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

      13. +-commutative 99.5%

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

      14. sub-neg 99.5%

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

      15. distribute-frac-neg 99.5%

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

      16. mul-1-neg 99.5%

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

      17. metadata-eval 99.5%

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

      18. times-frac 99.5%

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

      19. *-lft-identity 99.5%

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

      20. neg-mul-1 99.5%

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

      21. distribute-lft-neg-out 99.5%

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

      22. distribute-frac-neg 99.5%

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

   3. Simplified 99.5%

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

      1. associate-*r/ 99.4%

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

      2. *-commutative 99.4%

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

      3. associate-/r* 99.9%

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

      4. *-commutative 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in x around 0 98.2%

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

4. Final simplification 98.4%

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

Alternative 5: 98.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.75:\\ \;\;\;\;\left(\frac{x}{y} \cdot \left(x + -4\right)\right) \cdot 0.3333333333333333\\ \mathbf{elif}\;x \leq 3:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(\left(-x\right) \cdot -0.3333333333333333\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.75)
   (* (* (/ x y) (+ x -4.0)) 0.3333333333333333)
   (if (<= x 3.0)
     (/ (+ 1.0 (* x -1.3333333333333333)) y)
     (* (/ x y) (* (- x) -0.3333333333333333)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.75) {
		tmp = ((x / y) * (x + -4.0)) * 0.3333333333333333;
	} else if (x <= 3.0) {
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	} else {
		tmp = (x / y) * (-x * -0.3333333333333333);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-1.75d0)) then
        tmp = ((x / y) * (x + (-4.0d0))) * 0.3333333333333333d0
    else if (x <= 3.0d0) then
        tmp = (1.0d0 + (x * (-1.3333333333333333d0))) / y
    else
        tmp = (x / y) * (-x * (-0.3333333333333333d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -1.75) {
		tmp = ((x / y) * (x + -4.0)) * 0.3333333333333333;
	} else if (x <= 3.0) {
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	} else {
		tmp = (x / y) * (-x * -0.3333333333333333);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.75:
		tmp = ((x / y) * (x + -4.0)) * 0.3333333333333333
	elif x <= 3.0:
		tmp = (1.0 + (x * -1.3333333333333333)) / y
	else:
		tmp = (x / y) * (-x * -0.3333333333333333)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.75)
		tmp = Float64(Float64(Float64(x / y) * Float64(x + -4.0)) * 0.3333333333333333);
	elseif (x <= 3.0)
		tmp = Float64(Float64(1.0 + Float64(x * -1.3333333333333333)) / y);
	else
		tmp = Float64(Float64(x / y) * Float64(Float64(-x) * -0.3333333333333333));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.75)
		tmp = ((x / y) * (x + -4.0)) * 0.3333333333333333;
	elseif (x <= 3.0)
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	else
		tmp = (x / y) * (-x * -0.3333333333333333);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.75], N[(N[(N[(x / y), $MachinePrecision] * N[(x + -4.0), $MachinePrecision]), $MachinePrecision] * 0.3333333333333333), $MachinePrecision], If[LessEqual[x, 3.0], N[(N[(1.0 + N[(x * -1.3333333333333333), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / y), $MachinePrecision] * N[((-x) * -0.3333333333333333), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.75

   1. Initial program 91.4%

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

   2. Taylor expanded in x around inf 89.6%

      \[\leadsto \frac{\color{blue}{-4 \cdot x + {x}^{2}}}{y \cdot 3} \]
   3. Step-by-step derivation

      1. +-commutative 89.6%

         \[\leadsto \frac{\color{blue}{{x}^{2} + -4 \cdot x}}{y \cdot 3} \]

      2. unpow2 89.6%

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

      3. distribute-rgt-out 89.6%

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

   4. Simplified 89.6%

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

      1. associate-/r* 89.7%

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

      2. div-inv 89.7%

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

      3. *-commutative 89.7%

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

      4. associate-/l* 98.0%

         \[\leadsto \color{blue}{\frac{x + -4}{\frac{y}{x}}} \cdot \frac{1}{3} \]

      5. metadata-eval 98.0%

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

   6. Applied egg-rr 98.0%

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

   7. Taylor expanded in x around 0 89.7%

      \[\leadsto \color{blue}{\left(-4 \cdot \frac{x}{y} + \frac{{x}^{2}}{y}\right)} \cdot 0.3333333333333333 \]
   8. Step-by-step derivation

      1. unpow2 89.7%

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

      2. associate-*r/ 98.0%

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

      3. distribute-rgt-in 98.0%

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

      4. +-commutative 98.0%

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

   9. Simplified 98.0%

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

   if -1.75 < x < 3

   1. Initial program 99.4%

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

      1. *-commutative 99.4%

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

      2. associate-*l/ 99.5%

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

      3. *-commutative 99.5%

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

      4. sub-neg 99.5%

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

      5. +-commutative 99.5%

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

      6. neg-sub0 99.5%

         \[\leadsto \left(1 - x\right) \cdot \frac{\color{blue}{\left(0 - x\right)} + 3}{y \cdot 3} \]

      7. associate-+l- 99.5%

         \[\leadsto \left(1 - x\right) \cdot \frac{\color{blue}{0 - \left(x - 3\right)}}{y \cdot 3} \]

      8. sub0-neg 99.5%

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

      9. distribute-frac-neg 99.5%

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

      10. sub-neg 99.5%

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

      11. remove-double-neg 99.5%

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

      12. distribute-neg-in 99.5%

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

      13. +-commutative 99.5%

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

      14. sub-neg 99.5%

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

      15. distribute-frac-neg 99.5%

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

      16. mul-1-neg 99.5%

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

      17. metadata-eval 99.5%

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

      18. times-frac 99.5%

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

      19. *-lft-identity 99.5%

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

      20. neg-mul-1 99.5%

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

      21. distribute-lft-neg-out 99.5%

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

      22. distribute-frac-neg 99.5%

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

   3. Simplified 99.5%

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

      1. associate-*r/ 99.4%

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

      2. *-commutative 99.4%

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

      3. associate-/r* 99.9%

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

      4. *-commutative 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in x around 0 98.2%

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

   if 3 < x

   1. Initial program 95.3%

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

      1. times-frac 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 99.7%

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

   5. Taylor expanded in x around inf 99.7%

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

      1. neg-mul-1 99.7%

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

      2. distribute-neg-frac 99.7%

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

   7. Simplified 99.7%

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

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.75:\\ \;\;\;\;\left(\frac{x}{y} \cdot \left(x + -4\right)\right) \cdot 0.3333333333333333\\ \mathbf{elif}\;x \leq 3:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(\left(-x\right) \cdot -0.3333333333333333\right)\\ \end{array} \]

Alternative 6: 99.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.3%

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

   1. *-commutative 96.3%

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

   2. associate-*l/ 99.2%

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

   3. *-commutative 99.2%

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

   4. sub-neg 99.2%

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

   5. +-commutative 99.2%

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

   6. neg-sub0 99.2%

      \[\leadsto \left(1 - x\right) \cdot \frac{\color{blue}{\left(0 - x\right)} + 3}{y \cdot 3} \]

   7. associate-+l- 99.2%

      \[\leadsto \left(1 - x\right) \cdot \frac{\color{blue}{0 - \left(x - 3\right)}}{y \cdot 3} \]

   8. sub0-neg 99.2%

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

   9. distribute-frac-neg 99.2%

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

   10. sub-neg 99.2%

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

   11. remove-double-neg 99.2%

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

   12. distribute-neg-in 99.2%

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

   13. +-commutative 99.2%

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

   14. sub-neg 99.2%

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

   15. distribute-frac-neg 99.2%

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

   16. mul-1-neg 99.2%

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

   17. metadata-eval 99.2%

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

   18. times-frac 99.2%

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

   19. *-lft-identity 99.2%

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

   20. neg-mul-1 99.2%

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

   21. distribute-lft-neg-out 99.2%

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

   22. distribute-frac-neg 99.2%

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

3. Simplified 99.2%

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

4. Final simplification 99.2%

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

Alternative 7: 57.3% accurate, 1.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if x < -0.75

   1. Initial program 91.4%

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

   2. Taylor expanded in x around inf 89.6%

      \[\leadsto \frac{\color{blue}{-4 \cdot x + {x}^{2}}}{y \cdot 3} \]
   3. Step-by-step derivation

      1. +-commutative 89.6%

         \[\leadsto \frac{\color{blue}{{x}^{2} + -4 \cdot x}}{y \cdot 3} \]

      2. unpow2 89.6%

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

      3. distribute-rgt-out 89.6%

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

   4. Simplified 89.6%

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

   5. Taylor expanded in x around 0 42.2%

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

   if -0.75 < x

   1. Initial program 98.0%

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

      1. *-commutative 98.0%

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

      2. associate-*l/ 99.6%

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

      3. *-commutative 99.6%

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

      4. sub-neg 99.6%

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

      5. +-commutative 99.6%

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

      6. neg-sub0 99.6%

         \[\leadsto \left(1 - x\right) \cdot \frac{\color{blue}{\left(0 - x\right)} + 3}{y \cdot 3} \]

      7. associate-+l- 99.6%

         \[\leadsto \left(1 - x\right) \cdot \frac{\color{blue}{0 - \left(x - 3\right)}}{y \cdot 3} \]

      8. sub0-neg 99.6%

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

      9. distribute-frac-neg 99.6%

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

      10. sub-neg 99.6%

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

      11. remove-double-neg 99.6%

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

      12. distribute-neg-in 99.6%

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

      13. +-commutative 99.6%

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

      14. sub-neg 99.6%

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

      15. distribute-frac-neg 99.6%

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

      16. mul-1-neg 99.6%

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

      17. metadata-eval 99.6%

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

      18. times-frac 99.6%

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

      19. *-lft-identity 99.6%

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

      20. neg-mul-1 99.6%

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

      21. distribute-lft-neg-out 99.6%

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

      22. distribute-frac-neg 99.6%

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

   3. Simplified 99.6%

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

      1. frac-2neg 99.6%

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

      2. +-commutative 99.6%

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

      3. distribute-neg-in 99.6%

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

      4. metadata-eval 99.6%

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

      5. sub-neg 99.6%

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

      6. distribute-rgt-neg-in 99.6%

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

      7. metadata-eval 99.6%

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

      8. associate-*r/ 98.0%

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

      9. frac-times 99.9%

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

      10. clear-num 99.8%

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

      11. frac-times 99.6%

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

      12. *-un-lft-identity 99.6%

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

   5. Applied egg-rr 99.6%

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

      1. *-commutative 99.6%

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

      2. associate-*r/ 99.5%

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

   7. Simplified 99.5%

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

   8. Taylor expanded in x around 0 65.1%

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

4. Final simplification 59.0%

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

Alternative 8: 56.3% accurate, 1.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.3%

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

   1. *-commutative 96.3%

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

   2. associate-*l/ 99.2%

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

   3. *-commutative 99.2%

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

   4. sub-neg 99.2%

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

   5. +-commutative 99.2%

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

   6. neg-sub0 99.2%

      \[\leadsto \left(1 - x\right) \cdot \frac{\color{blue}{\left(0 - x\right)} + 3}{y \cdot 3} \]

   7. associate-+l- 99.2%

      \[\leadsto \left(1 - x\right) \cdot \frac{\color{blue}{0 - \left(x - 3\right)}}{y \cdot 3} \]

   8. sub0-neg 99.2%

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

   9. distribute-frac-neg 99.2%

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

   10. sub-neg 99.2%

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

   11. remove-double-neg 99.2%

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

   12. distribute-neg-in 99.2%

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

   13. +-commutative 99.2%

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

   14. sub-neg 99.2%

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

   15. distribute-frac-neg 99.2%

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

   16. mul-1-neg 99.2%

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

   17. metadata-eval 99.2%

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

   18. times-frac 99.2%

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

   19. *-lft-identity 99.2%

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

   20. neg-mul-1 99.2%

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

   21. distribute-lft-neg-out 99.2%

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

   22. distribute-frac-neg 99.2%

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

3. Simplified 99.2%

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

4. Taylor expanded in x around 0 58.2%

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

5. Final simplification 58.2%

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

Alternative 9: 56.8% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \frac{1 + x \cdot -1.3333333333333333}{y} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (+ 1.0 (* x -1.3333333333333333)) y))

C

double code(double x, double y) {
	return (1.0 + (x * -1.3333333333333333)) / y;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (1.0d0 + (x * (-1.3333333333333333d0))) / y
end function

Java

public static double code(double x, double y) {
	return (1.0 + (x * -1.3333333333333333)) / y;
}

Python

def code(x, y):
	return (1.0 + (x * -1.3333333333333333)) / y

Julia

function code(x, y)
	return Float64(Float64(1.0 + Float64(x * -1.3333333333333333)) / y)
end

MATLAB

function tmp = code(x, y)
	tmp = (1.0 + (x * -1.3333333333333333)) / y;
end

Wolfram

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

Derivation

1. Initial program 96.3%

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

   1. *-commutative 96.3%

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

   2. associate-*l/ 99.2%

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

   3. *-commutative 99.2%

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

   4. sub-neg 99.2%

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

   5. +-commutative 99.2%

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

   6. neg-sub0 99.2%

      \[\leadsto \left(1 - x\right) \cdot \frac{\color{blue}{\left(0 - x\right)} + 3}{y \cdot 3} \]

   7. associate-+l- 99.2%

      \[\leadsto \left(1 - x\right) \cdot \frac{\color{blue}{0 - \left(x - 3\right)}}{y \cdot 3} \]

   8. sub0-neg 99.2%

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

   9. distribute-frac-neg 99.2%

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

   10. sub-neg 99.2%

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

   11. remove-double-neg 99.2%

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

   12. distribute-neg-in 99.2%

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

   13. +-commutative 99.2%

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

   14. sub-neg 99.2%

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

   15. distribute-frac-neg 99.2%

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

   16. mul-1-neg 99.2%

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

   17. metadata-eval 99.2%

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

   18. times-frac 99.2%

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

   19. *-lft-identity 99.2%

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

   20. neg-mul-1 99.2%

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

   21. distribute-lft-neg-out 99.2%

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

   22. distribute-frac-neg 99.2%

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

3. Simplified 99.2%

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

   1. associate-*r/ 96.3%

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

   2. *-commutative 96.3%

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

   3. associate-/r* 96.6%

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

   4. *-commutative 96.6%

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

5. Applied egg-rr 96.6%

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

6. Taylor expanded in x around 0 58.6%

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

7. Final simplification 58.6%

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

Alternative 10: 56.3% accurate, 2.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.3%

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

   1. times-frac 99.9%

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

3. Simplified 99.9%

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

4. Taylor expanded in x around 0 58.2%

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

5. Final simplification 58.2%

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

Alternative 11: 51.2% accurate, 3.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.3%

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

   1. *-commutative 96.3%

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

   2. associate-*l/ 99.2%

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

   3. *-commutative 99.2%

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

   4. sub-neg 99.2%

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

   5. +-commutative 99.2%

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

   6. neg-sub0 99.2%

      \[\leadsto \left(1 - x\right) \cdot \frac{\color{blue}{\left(0 - x\right)} + 3}{y \cdot 3} \]

   7. associate-+l- 99.2%

      \[\leadsto \left(1 - x\right) \cdot \frac{\color{blue}{0 - \left(x - 3\right)}}{y \cdot 3} \]

   8. sub0-neg 99.2%

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

   9. distribute-frac-neg 99.2%

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

   10. sub-neg 99.2%

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

   11. remove-double-neg 99.2%

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

   12. distribute-neg-in 99.2%

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

   13. +-commutative 99.2%

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

   14. sub-neg 99.2%

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

   15. distribute-frac-neg 99.2%

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

   16. mul-1-neg 99.2%

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

   17. metadata-eval 99.2%

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

   18. times-frac 99.2%

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

   19. *-lft-identity 99.2%

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

   20. neg-mul-1 99.2%

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

   21. distribute-lft-neg-out 99.2%

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

   22. distribute-frac-neg 99.2%

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

3. Simplified 99.2%

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

   1. frac-2neg 99.2%

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

   2. +-commutative 99.2%

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

   3. distribute-neg-in 99.2%

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

   4. metadata-eval 99.2%

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

   5. sub-neg 99.2%

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

   6. distribute-rgt-neg-in 99.2%

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

   7. metadata-eval 99.2%

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

   8. associate-*r/ 96.3%

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

   9. frac-times 99.9%

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

   10. clear-num 99.8%

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

   11. frac-times 99.6%

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

   12. *-un-lft-identity 99.6%

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

5. Applied egg-rr 99.6%

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

   1. *-commutative 99.6%

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

   2. associate-*r/ 99.2%

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

7. Simplified 99.2%

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

8. Taylor expanded in x around 0 49.1%

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

9. Final simplification 49.1%

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

Developer target: 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 2023310 
(FPCore (x y)
  :name "Diagrams.TwoD.Arc:bezierFromSweepQ1 from diagrams-lib-1.3.0.3"
  :precision binary64

  :herbie-target
  (* (/ (- 1.0 x) y) (/ (- 3.0 x) 3.0))

  (/ (* (- 1.0 x) (- 3.0 x)) (* y 3.0)))