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

Percentage Accurate: 93.9% → 99.8%

Time: 11.2s

Alternatives: 10

Speedup: 1.0×

• 25.5% 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

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.9%

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

   1. times-frac 99.8%

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

   2. div-sub 99.8%

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

   3. metadata-eval 99.8%

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

3. Simplified 99.8%

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

5. Final simplification 99.8%

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

Alternative 2: 97.9% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if x < -1.75 or 1.75 < x

   1. Initial program 88.3%

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

      1. associate-*l/ 99.1%

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

      2. *-commutative 99.1%

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

      3. *-rgt-identity 99.1%

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

      4. associate-*l* 99.1%

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

      5. metadata-eval 99.1%

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

      6. times-frac 99.1%

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

      7. *-commutative 99.1%

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

      8. neg-mul-1 99.1%

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

      9. distribute-rgt-neg-in 99.1%

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

      10. times-frac 99.7%

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

      11. metadata-eval 99.7%

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

      12. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 98.3%

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

      1. metadata-eval 98.3%

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

      2. distribute-lft-neg-in 98.3%

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

      3. associate-*r/ 98.3%

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

      4. associate-*l/ 98.3%

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

      5. distribute-lft-neg-in 98.3%

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

      6. distribute-neg-frac 98.3%

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

      7. metadata-eval 98.3%

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

   7. Simplified 98.3%

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

   8. Taylor expanded in y around 0 87.6%

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

      1. associate-*l/ 98.4%

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

   10. Simplified 98.4%

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

   if -1.75 < x < 1.75

   1. Initial program 99.6%

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

      1. associate-*l/ 99.4%

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

      2. *-commutative 99.4%

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

      3. *-rgt-identity 99.4%

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

      4. associate-*l* 99.4%

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

      5. metadata-eval 99.4%

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

      6. times-frac 99.4%

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

      7. *-commutative 99.4%

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

      8. neg-mul-1 99.4%

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

      9. distribute-rgt-neg-in 99.4%

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

      10. times-frac 99.6%

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

      11. metadata-eval 99.6%

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

      12. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

      1. *-commutative 99.6%

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

      2. metadata-eval 99.6%

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

      3. times-frac 99.4%

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

      4. *-un-lft-identity 99.4%

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

      5. *-commutative 99.4%

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

      6. associate-/r/ 99.8%

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

      7. *-commutative 99.8%

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

      8. *-commutative 99.8%

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

      9. *-un-lft-identity 99.8%

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

      10. times-frac 99.8%

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

      11. metadata-eval 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in x around 0 98.4%

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

4. Final simplification 98.4%

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

Alternative 3: 97.9% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.75)
		tmp = Float64(-0.3333333333333333 * Float64(Float64(3.0 - x) * Float64(x / y)));
	elseif (x <= 1.75)
		tmp = Float64(Float64(1.0 - x) / y);
	else
		tmp = Float64(Float64(3.0 - x) * 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 = -0.3333333333333333 * ((3.0 - x) * (x / y));
	elseif (x <= 1.75)
		tmp = (1.0 - x) / y;
	else
		tmp = (3.0 - x) * (x / (y * -3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.75], N[(-0.3333333333333333 * N[(N[(3.0 - x), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.75], N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision], N[(N[(3.0 - x), $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 92.0%

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

      1. associate-*l/ 98.3%

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

      2. *-commutative 98.3%

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

      3. *-rgt-identity 98.3%

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

      4. associate-*l* 98.3%

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

      5. metadata-eval 98.3%

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

      6. times-frac 98.3%

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

      7. *-commutative 98.3%

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

      8. neg-mul-1 98.3%

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

      9. distribute-rgt-neg-in 98.3%

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

      10. times-frac 99.7%

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

      11. metadata-eval 99.7%

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

      12. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 98.7%

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

      1. metadata-eval 98.7%

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

      2. distribute-lft-neg-in 98.7%

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

      3. associate-*r/ 98.7%

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

      4. associate-*l/ 98.6%

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

      5. distribute-lft-neg-in 98.6%

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

      6. distribute-neg-frac 98.6%

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

      7. metadata-eval 98.6%

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

   7. Simplified 98.6%

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

   8. Taylor expanded in y around 0 92.5%

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

      1. associate-*l/ 98.7%

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

   10. Simplified 98.7%

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

   if -1.75 < x < 1.75

   1. Initial program 99.6%

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

      1. associate-*l/ 99.4%

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

      2. *-commutative 99.4%

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

      3. *-rgt-identity 99.4%

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

      4. associate-*l* 99.4%

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

      5. metadata-eval 99.4%

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

      6. times-frac 99.4%

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

      7. *-commutative 99.4%

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

      8. neg-mul-1 99.4%

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

      9. distribute-rgt-neg-in 99.4%

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

      10. times-frac 99.6%

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

      11. metadata-eval 99.6%

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

      12. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

      1. *-commutative 99.6%

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

      2. metadata-eval 99.6%

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

      3. times-frac 99.4%

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

      4. *-un-lft-identity 99.4%

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

      5. *-commutative 99.4%

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

      6. associate-/r/ 99.8%

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

      7. *-commutative 99.8%

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

      8. *-commutative 99.8%

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

      9. *-un-lft-identity 99.8%

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

      10. times-frac 99.8%

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

      11. metadata-eval 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in x around 0 98.4%

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

   if 1.75 < x

   1. Initial program 85.1%

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

      1. associate-*l/ 99.7%

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

      2. *-commutative 99.7%

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

      3. *-rgt-identity 99.7%

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

      4. associate-*l* 99.7%

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

      5. metadata-eval 99.7%

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

      6. times-frac 99.7%

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

      7. *-commutative 99.7%

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

      8. neg-mul-1 99.7%

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

      9. distribute-rgt-neg-in 99.7%

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

      10. times-frac 99.6%

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

      11. metadata-eval 99.6%

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

      12. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around inf 98.0%

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

      1. metadata-eval 98.0%

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

      2. distribute-lft-neg-in 98.0%

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

      3. associate-*r/ 98.1%

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

      4. associate-*l/ 98.0%

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

      5. distribute-lft-neg-in 98.0%

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

      6. distribute-neg-frac 98.0%

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

      7. metadata-eval 98.0%

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

   7. Simplified 98.0%

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

      1. *-commutative 98.0%

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

      2. clear-num 98.0%

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

      3. un-div-inv 98.1%

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

      4. div-inv 98.1%

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

      5. metadata-eval 98.1%

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

   9. Applied egg-rr 98.1%

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

4. Final simplification 98.4%

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

Alternative 4: 98.0% accurate, 0.6× speedup

Math

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

FPCore

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

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.75) {
		tmp = (3.0 - x) / (-3.0 * (y / x));
	} else if (x <= 1.75) {
		tmp = (1.0 - x) / y;
	} else {
		tmp = (3.0 - x) * (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 = (3.0d0 - x) / ((-3.0d0) * (y / x))
    else if (x <= 1.75d0) then
        tmp = (1.0d0 - x) / y
    else
        tmp = (3.0d0 - x) * (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 = (3.0 - x) / (-3.0 * (y / x));
	} else if (x <= 1.75) {
		tmp = (1.0 - x) / y;
	} else {
		tmp = (3.0 - x) * (x / (y * -3.0));
	}
	return tmp;
}

Python

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

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.75)
		tmp = Float64(Float64(3.0 - x) / Float64(-3.0 * Float64(y / x)));
	elseif (x <= 1.75)
		tmp = Float64(Float64(1.0 - x) / y);
	else
		tmp = Float64(Float64(3.0 - x) * 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 = (3.0 - x) / (-3.0 * (y / x));
	elseif (x <= 1.75)
		tmp = (1.0 - x) / y;
	else
		tmp = (3.0 - x) * (x / (y * -3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.75], N[(N[(3.0 - x), $MachinePrecision] / N[(-3.0 * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.75], N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision], N[(N[(3.0 - x), $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 92.0%

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

      1. associate-*l/ 98.3%

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

      2. *-commutative 98.3%

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

      3. *-rgt-identity 98.3%

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

      4. associate-*l* 98.3%

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

      5. metadata-eval 98.3%

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

      6. times-frac 98.3%

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

      7. *-commutative 98.3%

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

      8. neg-mul-1 98.3%

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

      9. distribute-rgt-neg-in 98.3%

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

      10. times-frac 99.7%

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

      11. metadata-eval 99.7%

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

      12. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 98.7%

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

      1. metadata-eval 98.7%

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

      2. distribute-lft-neg-in 98.7%

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

      3. associate-*r/ 98.7%

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

      4. associate-*l/ 98.6%

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

      5. distribute-lft-neg-in 98.6%

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

      6. distribute-neg-frac 98.6%

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

      7. metadata-eval 98.6%

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

   7. Simplified 98.6%

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

   8. Taylor expanded in y around 0 92.5%

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

      1. associate-*l/ 98.7%

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

   10. Simplified 98.7%

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

       1. *-commutative 98.7%

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

       2. *-commutative 98.7%

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

       3. associate-*l* 98.7%

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

       4. associate-/r/ 97.9%

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

       5. associate-/l* 98.7%

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

       6. frac-2neg 98.7%

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

       7. distribute-rgt-neg-in 98.7%

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

       8. metadata-eval 98.7%

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

       9. metadata-eval 98.7%

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

       10. div-inv 98.7%

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

       11. associate-*r/ 92.4%

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

       12. div-inv 92.4%

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

       13. metadata-eval 92.4%

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

       14. *-commutative 92.4%

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

   12. Applied egg-rr 92.4%

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

       1. associate-/l* 98.7%

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

       2. neg-mul-1 98.7%

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

       3. times-frac 98.8%

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

       4. metadata-eval 98.8%

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

   14. Simplified 98.8%

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

   if -1.75 < x < 1.75

   1. Initial program 99.6%

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

      1. associate-*l/ 99.4%

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

      2. *-commutative 99.4%

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

      3. *-rgt-identity 99.4%

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

      4. associate-*l* 99.4%

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

      5. metadata-eval 99.4%

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

      6. times-frac 99.4%

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

      7. *-commutative 99.4%

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

      8. neg-mul-1 99.4%

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

      9. distribute-rgt-neg-in 99.4%

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

      10. times-frac 99.6%

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

      11. metadata-eval 99.6%

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

      12. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

      1. *-commutative 99.6%

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

      2. metadata-eval 99.6%

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

      3. times-frac 99.4%

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

      4. *-un-lft-identity 99.4%

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

      5. *-commutative 99.4%

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

      6. associate-/r/ 99.8%

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

      7. *-commutative 99.8%

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

      8. *-commutative 99.8%

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

      9. *-un-lft-identity 99.8%

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

      10. times-frac 99.8%

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

      11. metadata-eval 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in x around 0 98.4%

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

   if 1.75 < x

   1. Initial program 85.1%

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

      1. associate-*l/ 99.7%

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

      2. *-commutative 99.7%

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

      3. *-rgt-identity 99.7%

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

      4. associate-*l* 99.7%

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

      5. metadata-eval 99.7%

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

      6. times-frac 99.7%

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

      7. *-commutative 99.7%

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

      8. neg-mul-1 99.7%

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

      9. distribute-rgt-neg-in 99.7%

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

      10. times-frac 99.6%

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

      11. metadata-eval 99.6%

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

      12. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around inf 98.0%

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

      1. metadata-eval 98.0%

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

      2. distribute-lft-neg-in 98.0%

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

      3. associate-*r/ 98.1%

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

      4. associate-*l/ 98.0%

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

      5. distribute-lft-neg-in 98.0%

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

      6. distribute-neg-frac 98.0%

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

      7. metadata-eval 98.0%

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

   7. Simplified 98.0%

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

      1. *-commutative 98.0%

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

      2. clear-num 98.0%

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

      3. un-div-inv 98.1%

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

      4. div-inv 98.1%

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

      5. metadata-eval 98.1%

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

   9. Applied egg-rr 98.1%

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

4. Final simplification 98.4%

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

Alternative 5: 98.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.75:\\ \;\;\;\;\frac{3 - x}{-3 \cdot \frac{y}{x}}\\ \mathbf{elif}\;x \leq 1.7:\\ \;\;\;\;\frac{1 - x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{3 - x}{\frac{y \cdot -3}{x}}\\ \end{array} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 3 regimes

2. if x < -1.75

   1. Initial program 92.0%

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

      1. associate-*l/ 98.3%

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

      2. *-commutative 98.3%

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

      3. *-rgt-identity 98.3%

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

      4. associate-*l* 98.3%

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

      5. metadata-eval 98.3%

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

      6. times-frac 98.3%

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

      7. *-commutative 98.3%

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

      8. neg-mul-1 98.3%

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

      9. distribute-rgt-neg-in 98.3%

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

      10. times-frac 99.7%

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

      11. metadata-eval 99.7%

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

      12. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 98.7%

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

      1. metadata-eval 98.7%

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

      2. distribute-lft-neg-in 98.7%

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

      3. associate-*r/ 98.7%

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

      4. associate-*l/ 98.6%

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

      5. distribute-lft-neg-in 98.6%

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

      6. distribute-neg-frac 98.6%

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

      7. metadata-eval 98.6%

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

   7. Simplified 98.6%

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

   8. Taylor expanded in y around 0 92.5%

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

      1. associate-*l/ 98.7%

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

   10. Simplified 98.7%

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

       1. *-commutative 98.7%

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

       2. *-commutative 98.7%

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

       3. associate-*l* 98.7%

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

       4. associate-/r/ 97.9%

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

       5. associate-/l* 98.7%

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

       6. frac-2neg 98.7%

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

       7. distribute-rgt-neg-in 98.7%

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

       8. metadata-eval 98.7%

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

       9. metadata-eval 98.7%

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

       10. div-inv 98.7%

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

       11. associate-*r/ 92.4%

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

       12. div-inv 92.4%

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

       13. metadata-eval 92.4%

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

       14. *-commutative 92.4%

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

   12. Applied egg-rr 92.4%

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

       1. associate-/l* 98.7%

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

       2. neg-mul-1 98.7%

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

       3. times-frac 98.8%

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

       4. metadata-eval 98.8%

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

   14. Simplified 98.8%

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

   if -1.75 < x < 1.69999999999999996

   1. Initial program 99.6%

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

      1. associate-*l/ 99.4%

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

      2. *-commutative 99.4%

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

      3. *-rgt-identity 99.4%

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

      4. associate-*l* 99.4%

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

      5. metadata-eval 99.4%

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

      6. times-frac 99.4%

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

      7. *-commutative 99.4%

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

      8. neg-mul-1 99.4%

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

      9. distribute-rgt-neg-in 99.4%

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

      10. times-frac 99.6%

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

      11. metadata-eval 99.6%

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

      12. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

      1. *-commutative 99.6%

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

      2. metadata-eval 99.6%

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

      3. times-frac 99.4%

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

      4. *-un-lft-identity 99.4%

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

      5. *-commutative 99.4%

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

      6. associate-/r/ 99.8%

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

      7. *-commutative 99.8%

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

      8. *-commutative 99.8%

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

      9. *-un-lft-identity 99.8%

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

      10. times-frac 99.8%

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

      11. metadata-eval 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in x around 0 98.4%

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

   if 1.69999999999999996 < x

   1. Initial program 85.1%

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

      1. associate-*l/ 99.7%

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

      2. *-commutative 99.7%

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

      3. *-rgt-identity 99.7%

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

      4. associate-*l* 99.7%

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

      5. metadata-eval 99.7%

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

      6. times-frac 99.7%

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

      7. *-commutative 99.7%

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

      8. neg-mul-1 99.7%

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

      9. distribute-rgt-neg-in 99.7%

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

      10. times-frac 99.6%

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

      11. metadata-eval 99.6%

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

      12. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around inf 98.0%

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

      1. metadata-eval 98.0%

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

      2. distribute-lft-neg-in 98.0%

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

      3. associate-*r/ 98.1%

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

      4. associate-*l/ 98.0%

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

      5. distribute-lft-neg-in 98.0%

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

      6. distribute-neg-frac 98.0%

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

      7. metadata-eval 98.0%

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

   7. Simplified 98.0%

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

   8. Taylor expanded in y around 0 83.5%

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

      1. associate-*l/ 98.0%

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

   10. Simplified 98.0%

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

       1. *-commutative 98.0%

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

       2. *-commutative 98.0%

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

       3. associate-*l* 98.0%

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

       4. associate-/r/ 98.1%

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

       5. associate-/l* 98.1%

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

       6. frac-2neg 98.1%

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

       7. distribute-rgt-neg-in 98.1%

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

       8. metadata-eval 98.1%

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

       9. metadata-eval 98.1%

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

       10. div-inv 98.1%

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

       11. associate-*r/ 83.5%

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

       12. div-inv 83.4%

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

       13. metadata-eval 83.4%

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

       14. *-commutative 83.4%

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

   12. Applied egg-rr 83.4%

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

       1. associate-/l* 98.0%

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

       2. neg-mul-1 98.0%

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

       3. times-frac 98.1%

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

       4. metadata-eval 98.1%

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

   14. Simplified 98.1%

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

       1. associate-*r/ 98.1%

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

       2. *-commutative 98.1%

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

   16. Applied egg-rr 98.1%

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

4. Final simplification 98.4%

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

Alternative 6: 99.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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) * 0.3333333333333333d0)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.9%

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

   1. associate-*l/ 99.2%

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

   2. *-commutative 99.2%

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

   3. *-rgt-identity 99.2%

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

   4. associate-*l* 99.2%

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

   5. metadata-eval 99.2%

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

   6. times-frac 99.2%

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

   7. *-commutative 99.2%

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

   8. neg-mul-1 99.2%

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

   9. distribute-rgt-neg-in 99.2%

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

   10. times-frac 99.6%

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

   11. metadata-eval 99.6%

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

   12. metadata-eval 99.6%

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

3. Simplified 99.6%

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

5. Final simplification 99.6%

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

Alternative 7: 58.1% accurate, 1.1× 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 92.0%

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

   3. Taylor expanded in x around 0 37.7%

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

      1. *-commutative 37.7%

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

   5. Simplified 37.7%

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

   6. Taylor expanded in x around inf 37.7%

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

   if -0.75 < x

   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%

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

      2. *-commutative 99.5%

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

      3. *-rgt-identity 99.5%

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

      4. associate-*l* 99.5%

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

      5. metadata-eval 99.5%

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

      6. times-frac 99.5%

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

      7. *-commutative 99.5%

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

      8. neg-mul-1 99.5%

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

      9. distribute-rgt-neg-in 99.5%

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

      10. times-frac 99.6%

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

      11. metadata-eval 99.6%

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

      12. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around 0 64.9%

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

4. Final simplification 58.6%

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

Alternative 8: 58.1% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if x < -1

   1. Initial program 92.0%

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

      1. associate-*l/ 98.3%

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

      2. *-commutative 98.3%

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

      3. *-rgt-identity 98.3%

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

      4. associate-*l* 98.3%

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

      5. metadata-eval 98.3%

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

      6. times-frac 98.3%

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

      7. *-commutative 98.3%

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

      8. neg-mul-1 98.3%

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

      9. distribute-rgt-neg-in 98.3%

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

      10. times-frac 99.7%

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

      11. metadata-eval 99.7%

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

      12. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 98.7%

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

      1. metadata-eval 98.7%

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

      2. distribute-lft-neg-in 98.7%

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

      3. associate-*r/ 98.7%

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

      4. associate-*l/ 98.6%

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

      5. distribute-lft-neg-in 98.6%

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

      6. distribute-neg-frac 98.6%

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

      7. metadata-eval 98.6%

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

   7. Simplified 98.6%

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

   8. Taylor expanded in x around 0 37.7%

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

      1. associate-*r/ 37.7%

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

      2. neg-mul-1 37.7%

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

   10. Simplified 37.7%

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

   if -1 < x

   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%

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

      2. *-commutative 99.5%

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

      3. *-rgt-identity 99.5%

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

      4. associate-*l* 99.5%

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

      5. metadata-eval 99.5%

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

      6. times-frac 99.5%

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

      7. *-commutative 99.5%

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

      8. neg-mul-1 99.5%

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

      9. distribute-rgt-neg-in 99.5%

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

      10. times-frac 99.6%

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

      11. metadata-eval 99.6%

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

      12. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around 0 64.9%

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

4. Final simplification 58.6%

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

Alternative 9: 57.1% 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 93.9%

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

   1. associate-*l/ 99.2%

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

   2. *-commutative 99.2%

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

   3. *-rgt-identity 99.2%

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

   4. associate-*l* 99.2%

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

   5. metadata-eval 99.2%

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

   6. times-frac 99.2%

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

   7. *-commutative 99.2%

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

   8. neg-mul-1 99.2%

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

   9. distribute-rgt-neg-in 99.2%

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

   10. times-frac 99.6%

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

   11. metadata-eval 99.6%

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

   12. metadata-eval 99.6%

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

3. Simplified 99.6%

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

   1. *-commutative 99.6%

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

   2. metadata-eval 99.6%

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

   3. times-frac 99.2%

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

   4. *-un-lft-identity 99.2%

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

   5. *-commutative 99.2%

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

   6. associate-/r/ 99.4%

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

   7. *-commutative 99.4%

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

   8. *-commutative 99.4%

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

   9. *-un-lft-identity 99.4%

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

   10. times-frac 99.8%

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

   11. metadata-eval 99.8%

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

6. Applied egg-rr 99.8%

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

7. Taylor expanded in x around 0 57.4%

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

8. Final simplification 57.4%

   \[\leadsto \frac{1 - x}{y} \]
9. Add Preprocessing

Alternative 10: 51.5% accurate, 3.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.9%

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

   1. associate-*l/ 99.2%

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

   2. *-commutative 99.2%

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

   3. *-rgt-identity 99.2%

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

   4. associate-*l* 99.2%

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

   5. metadata-eval 99.2%

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

   6. times-frac 99.2%

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

   7. *-commutative 99.2%

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

   8. neg-mul-1 99.2%

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

   9. distribute-rgt-neg-in 99.2%

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

   10. times-frac 99.6%

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

   11. metadata-eval 99.6%

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

   12. metadata-eval 99.6%

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

3. Simplified 99.6%

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

5. Taylor expanded in x around 0 50.9%

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

6. Final simplification 50.9%

   \[\leadsto \frac{1}{y} \]
7. Add Preprocessing

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 2024020 
(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)))