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

Percentage Accurate: 93.7% → 99.8%

Time: 8.7s

Alternatives: 14

Speedup: 1.0×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 93.7% 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 91.7%

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

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

Alternative 2: 97.9% accurate, 0.8× speedup

Math

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

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -1.7) (not (<= x 1.75)))
   (* (- 3.0 x) (* (/ x y) -0.3333333333333333))
   (/ 1.0 (/ y (- 1.0 x)))))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -1.7) || !(x <= 1.75)) {
		tmp = (3.0 - x) * ((x / y) * -0.3333333333333333);
	} else {
		tmp = 1.0 / (y / (1.0 - 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 <= (-1.7d0)) .or. (.not. (x <= 1.75d0))) then
        tmp = (3.0d0 - x) * ((x / y) * (-0.3333333333333333d0))
    else
        tmp = 1.0d0 / (y / (1.0d0 - x))
    end if
    code = tmp
end function

Java

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

Python

def code(x, y):
	tmp = 0
	if (x <= -1.7) or not (x <= 1.75):
		tmp = (3.0 - x) * ((x / y) * -0.3333333333333333)
	else:
		tmp = 1.0 / (y / (1.0 - x))
	return tmp

Julia

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

MATLAB

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

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -1.7], N[Not[LessEqual[x, 1.75]], $MachinePrecision]], N[(N[(3.0 - x), $MachinePrecision] * N[(N[(x / y), $MachinePrecision] * -0.3333333333333333), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(y / N[(1.0 - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.69999999999999996 or 1.75 < x

   1. Initial program 85.4%

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

      1. associate-*l/ 99.6%

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

      2. *-commutative 99.6%

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

      3. associate-/r* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 98.0%

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

   if -1.69999999999999996 < x < 1.75

   1. Initial program 99.5%

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

      1. associate-/l* 99.7%

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

      2. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around 0 98.6%

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

      1. clear-num 98.6%

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

      2. inv-pow 98.6%

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

   6. Applied egg-rr 98.6%

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

      1. unpow-1 98.6%

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

   8. Simplified 98.6%

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

4. Final simplification 98.3%

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

Alternative 3: 98.3% accurate, 0.8× speedup

Math

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

FPCore

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

C

double code(double x, double y) {
	double tmp;
	if ((x <= -1.3) || !(x <= 2.3)) {
		tmp = (x / y) * (-1.3333333333333333 + (x * 0.3333333333333333));
	} else {
		tmp = 1.0 / (y / (1.0 - 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 <= (-1.3d0)) .or. (.not. (x <= 2.3d0))) then
        tmp = (x / y) * ((-1.3333333333333333d0) + (x * 0.3333333333333333d0))
    else
        tmp = 1.0d0 / (y / (1.0d0 - x))
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if x < -1.30000000000000004 or 2.2999999999999998 < x

   1. Initial program 85.4%

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

      1. associate-*l/ 99.6%

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

      2. *-commutative 99.6%

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

      3. associate-/r* 99.7%

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

   3. Simplified 99.7%

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

      1. associate-*r/ 99.8%

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

      2. *-commutative 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in x around inf 73.5%

      \[\leadsto \color{blue}{0.3333333333333333 \cdot \frac{{x}^{2}}{y} + -1.3333333333333333 \cdot \frac{x}{y}} \]
   7. Step-by-step derivation

      1. +-commutative 73.5%

         \[\leadsto \color{blue}{-1.3333333333333333 \cdot \frac{x}{y} + 0.3333333333333333 \cdot \frac{{x}^{2}}{y}} \]

      2. *-commutative 73.5%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot -1.3333333333333333} + 0.3333333333333333 \cdot \frac{{x}^{2}}{y} \]

      3. *-commutative 73.5%

         \[\leadsto \frac{x}{y} \cdot -1.3333333333333333 + \color{blue}{\frac{{x}^{2}}{y} \cdot 0.3333333333333333} \]

      4. unpow2 73.5%

         \[\leadsto \frac{x}{y} \cdot -1.3333333333333333 + \frac{\color{blue}{x \cdot x}}{y} \cdot 0.3333333333333333 \]

      5. associate-*l/ 87.8%

         \[\leadsto \frac{x}{y} \cdot -1.3333333333333333 + \color{blue}{\left(\frac{x}{y} \cdot x\right)} \cdot 0.3333333333333333 \]

      6. associate-*r* 87.8%

         \[\leadsto \frac{x}{y} \cdot -1.3333333333333333 + \color{blue}{\frac{x}{y} \cdot \left(x \cdot 0.3333333333333333\right)} \]

      7. distribute-lft-out 99.0%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot \left(-1.3333333333333333 + x \cdot 0.3333333333333333\right)} \]

   8. Simplified 99.0%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot \left(-1.3333333333333333 + x \cdot 0.3333333333333333\right)} \]

   if -1.30000000000000004 < x < 2.2999999999999998

   1. Initial program 99.5%

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

      1. associate-/l* 99.7%

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

      2. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around 0 98.6%

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

      1. clear-num 98.6%

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

      2. inv-pow 98.6%

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

   6. Applied egg-rr 98.6%

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

      1. unpow-1 98.6%

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

   8. Simplified 98.6%

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

4. Final simplification 98.9%

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

Alternative 4: 98.6% accurate, 0.8× speedup

Math

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

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -1.7) (not (<= x 1.75)))
   (* (/ x y) (+ -1.3333333333333333 (* x 0.3333333333333333)))
   (/ (+ 3.0 (* x -4.0)) (* y 3.0))))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -1.7) || !(x <= 1.75)) {
		tmp = (x / y) * (-1.3333333333333333 + (x * 0.3333333333333333));
	} else {
		tmp = (3.0 + (x * -4.0)) / (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 <= (-1.7d0)) .or. (.not. (x <= 1.75d0))) then
        tmp = (x / y) * ((-1.3333333333333333d0) + (x * 0.3333333333333333d0))
    else
        tmp = (3.0d0 + (x * (-4.0d0))) / (y * 3.0d0)
    end if
    code = tmp
end function

Java

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

Python

def code(x, y):
	tmp = 0
	if (x <= -1.7) or not (x <= 1.75):
		tmp = (x / y) * (-1.3333333333333333 + (x * 0.3333333333333333))
	else:
		tmp = (3.0 + (x * -4.0)) / (y * 3.0)
	return tmp

Julia

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

MATLAB

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

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -1.7], N[Not[LessEqual[x, 1.75]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] * N[(-1.3333333333333333 + N[(x * 0.3333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(3.0 + N[(x * -4.0), $MachinePrecision]), $MachinePrecision] / N[(y * 3.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.69999999999999996 or 1.75 < x

   1. Initial program 85.4%

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

      1. associate-*l/ 99.6%

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

      2. *-commutative 99.6%

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

      3. associate-/r* 99.7%

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

   3. Simplified 99.7%

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

      1. associate-*r/ 99.8%

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

      2. *-commutative 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in x around inf 73.5%

      \[\leadsto \color{blue}{0.3333333333333333 \cdot \frac{{x}^{2}}{y} + -1.3333333333333333 \cdot \frac{x}{y}} \]
   7. Step-by-step derivation

      1. +-commutative 73.5%

         \[\leadsto \color{blue}{-1.3333333333333333 \cdot \frac{x}{y} + 0.3333333333333333 \cdot \frac{{x}^{2}}{y}} \]

      2. *-commutative 73.5%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot -1.3333333333333333} + 0.3333333333333333 \cdot \frac{{x}^{2}}{y} \]

      3. *-commutative 73.5%

         \[\leadsto \frac{x}{y} \cdot -1.3333333333333333 + \color{blue}{\frac{{x}^{2}}{y} \cdot 0.3333333333333333} \]

      4. unpow2 73.5%

         \[\leadsto \frac{x}{y} \cdot -1.3333333333333333 + \frac{\color{blue}{x \cdot x}}{y} \cdot 0.3333333333333333 \]

      5. associate-*l/ 87.8%

         \[\leadsto \frac{x}{y} \cdot -1.3333333333333333 + \color{blue}{\left(\frac{x}{y} \cdot x\right)} \cdot 0.3333333333333333 \]

      6. associate-*r* 87.8%

         \[\leadsto \frac{x}{y} \cdot -1.3333333333333333 + \color{blue}{\frac{x}{y} \cdot \left(x \cdot 0.3333333333333333\right)} \]

      7. distribute-lft-out 99.0%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot \left(-1.3333333333333333 + x \cdot 0.3333333333333333\right)} \]

   8. Simplified 99.0%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot \left(-1.3333333333333333 + x \cdot 0.3333333333333333\right)} \]

   if -1.69999999999999996 < x < 1.75

   1. Initial program 99.5%

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

   2. Taylor expanded in x around 0 99.2%

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

      1. *-commutative 99.2%

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

   4. Simplified 99.2%

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

4. Final simplification 99.1%

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

Alternative 5: 91.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y) {
	double tmp;
	if ((x <= -3.8) || !(x <= 3.0)) {
		tmp = 0.3333333333333333 * ((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 <= (-3.8d0)) .or. (.not. (x <= 3.0d0))) then
        tmp = 0.3333333333333333d0 * ((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 <= -3.8) || !(x <= 3.0)) {
		tmp = 0.3333333333333333 * ((x * x) / y);
	} else {
		tmp = (1.0 - x) / y;
	}
	return tmp;
}

Python

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

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -3.8) || !(x <= 3.0))
		tmp = Float64(0.3333333333333333 * Float64(Float64(x * 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 <= -3.8) || ~((x <= 3.0)))
		tmp = 0.3333333333333333 * ((x * x) / y);
	else
		tmp = (1.0 - x) / y;
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if x < -3.7999999999999998 or 3 < x

   1. Initial program 85.4%

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

      1. associate-*l/ 99.6%

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

      2. *-commutative 99.6%

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

      3. associate-/r* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 83.5%

      \[\leadsto \color{blue}{0.3333333333333333 \cdot \frac{{x}^{2}}{y}} \]
   5. Step-by-step derivation

      1. unpow2 83.5%

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

   6. Simplified 83.5%

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

   if -3.7999999999999998 < x < 3

   1. Initial program 99.5%

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

      1. associate-/l* 99.7%

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

      2. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around 0 98.6%

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

4. Final simplification 90.2%

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

Alternative 6: 97.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y) {
	double tmp;
	if ((x <= -3.8) || !(x <= 3.0)) {
		tmp = x * (x * (0.3333333333333333 / 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 <= (-3.8d0)) .or. (.not. (x <= 3.0d0))) then
        tmp = x * (x * (0.3333333333333333d0 / 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 <= -3.8) || !(x <= 3.0)) {
		tmp = x * (x * (0.3333333333333333 / y));
	} else {
		tmp = (1.0 - x) / y;
	}
	return tmp;
}

Python

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

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -3.8) || !(x <= 3.0))
		tmp = Float64(x * Float64(x * Float64(0.3333333333333333 / 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 <= -3.8) || ~((x <= 3.0)))
		tmp = x * (x * (0.3333333333333333 / y));
	else
		tmp = (1.0 - x) / y;
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if x < -3.7999999999999998 or 3 < x

   1. Initial program 85.4%

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

   2. Taylor expanded in x around inf 83.6%

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

      1. unpow2 83.6%

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

   4. Simplified 83.6%

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

      1. div-inv 83.5%

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

      2. associate-*l* 97.8%

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

      3. *-commutative 97.8%

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

      4. associate-/r* 97.8%

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

      5. metadata-eval 97.8%

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

   6. Applied egg-rr 97.8%

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

   if -3.7999999999999998 < x < 3

   1. Initial program 99.5%

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

      1. associate-/l* 99.7%

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

      2. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around 0 98.6%

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

4. Final simplification 98.2%

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

Alternative 7: 97.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y) {
	double tmp;
	if ((x <= -3.8) || !(x <= 3.0)) {
		tmp = (x * (x / y)) / 3.0;
	} else {
		tmp = 1.0 / (y / (1.0 - 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 <= (-3.8d0)) .or. (.not. (x <= 3.0d0))) then
        tmp = (x * (x / y)) / 3.0d0
    else
        tmp = 1.0d0 / (y / (1.0d0 - x))
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if x < -3.7999999999999998 or 3 < x

   1. Initial program 85.4%

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

      1. associate-*l/ 99.6%

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

      2. *-commutative 99.6%

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

      3. associate-/r* 99.7%

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

   3. Simplified 99.7%

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

      1. associate-*r/ 99.8%

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

      2. *-commutative 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in x around inf 83.6%

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

      1. unpow2 83.6%

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

      2. associate-*r/ 97.9%

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

   8. Simplified 97.9%

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

   if -3.7999999999999998 < x < 3

   1. Initial program 99.5%

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

      1. associate-/l* 99.7%

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

      2. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around 0 98.6%

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

      1. clear-num 98.6%

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

      2. inv-pow 98.6%

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

   6. Applied egg-rr 98.6%

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

      1. unpow-1 98.6%

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

   8. Simplified 98.6%

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

4. Final simplification 98.2%

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

Alternative 8: 97.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 3 regimes

2. if x < -3.7999999999999998

   1. Initial program 84.3%

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

   2. Taylor expanded in x around inf 83.9%

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

      1. unpow2 83.9%

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

   4. Simplified 83.9%

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

      1. associate-/l* 99.2%

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

      2. associate-/r/ 99.2%

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

      3. *-commutative 99.2%

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

      4. associate-/l/ 99.3%

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

      5. div-inv 99.3%

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

      6. metadata-eval 99.3%

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

   6. Applied egg-rr 99.3%

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

   if -3.7999999999999998 < x < 3

   1. Initial program 99.5%

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

      1. associate-/l* 99.7%

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

      2. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around 0 98.6%

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

   if 3 < x

   1. Initial program 86.6%

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

   2. Taylor expanded in x around inf 83.2%

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

      1. unpow2 83.2%

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

   4. Simplified 83.2%

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

      1. div-inv 83.2%

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

      2. associate-*l* 96.4%

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

      3. *-commutative 96.4%

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

      4. associate-/r* 96.4%

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

      5. metadata-eval 96.4%

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

   6. Applied egg-rr 96.4%

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

4. Final simplification 98.2%

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

Alternative 9: 97.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 3 regimes

2. if x < -3.7999999999999998

   1. Initial program 84.3%

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

   2. Taylor expanded in x around inf 83.9%

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

      1. unpow2 83.9%

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

   4. Simplified 83.9%

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

      1. associate-/l* 99.2%

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

      2. associate-/r/ 99.2%

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

      3. *-commutative 99.2%

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

      4. associate-/l/ 99.3%

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

      5. div-inv 99.3%

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

      6. metadata-eval 99.3%

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

   6. Applied egg-rr 99.3%

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

   if -3.7999999999999998 < x < 3

   1. Initial program 99.5%

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

      1. associate-/l* 99.7%

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

      2. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around 0 98.6%

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

      1. clear-num 98.6%

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

      2. inv-pow 98.6%

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

   6. Applied egg-rr 98.6%

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

      1. unpow-1 98.6%

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

   8. Simplified 98.6%

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

   if 3 < x

   1. Initial program 86.6%

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

   2. Taylor expanded in x around inf 83.2%

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

      1. unpow2 83.2%

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

   4. Simplified 83.2%

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

      1. div-inv 83.2%

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

      2. associate-*l* 96.4%

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

      3. *-commutative 96.4%

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

      4. associate-/r* 96.4%

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

      5. metadata-eval 96.4%

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

   6. Applied egg-rr 96.4%

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

4. Final simplification 98.2%

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

Alternative 10: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 91.7%

   \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
2. 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. associate-/r* 99.8%

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

3. Simplified 99.8%

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

4. Final simplification 99.8%

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

Alternative 11: 57.1% accurate, 1.6× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -0.75)
		tmp = Float64(x * Float64(-1.3333333333333333 / y));
	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 * (-1.3333333333333333 / y);
	else
		tmp = 1.0 / y;
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if x < -0.75

   1. Initial program 84.3%

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

      1. associate-*l/ 99.7%

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

      2. *-commutative 99.7%

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

      3. associate-/r* 99.7%

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

   3. Simplified 99.7%

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

      1. associate-*r/ 99.8%

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

      2. *-commutative 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in x around inf 84.3%

      \[\leadsto \color{blue}{0.3333333333333333 \cdot \frac{{x}^{2}}{y} + -1.3333333333333333 \cdot \frac{x}{y}} \]
   7. Step-by-step derivation

      1. +-commutative 84.3%

         \[\leadsto \color{blue}{-1.3333333333333333 \cdot \frac{x}{y} + 0.3333333333333333 \cdot \frac{{x}^{2}}{y}} \]

      2. *-commutative 84.3%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot -1.3333333333333333} + 0.3333333333333333 \cdot \frac{{x}^{2}}{y} \]

      3. *-commutative 84.3%

         \[\leadsto \frac{x}{y} \cdot -1.3333333333333333 + \color{blue}{\frac{{x}^{2}}{y} \cdot 0.3333333333333333} \]

      4. unpow2 84.3%

         \[\leadsto \frac{x}{y} \cdot -1.3333333333333333 + \frac{\color{blue}{x \cdot x}}{y} \cdot 0.3333333333333333 \]

      5. associate-*l/ 99.7%

         \[\leadsto \frac{x}{y} \cdot -1.3333333333333333 + \color{blue}{\left(\frac{x}{y} \cdot x\right)} \cdot 0.3333333333333333 \]

      6. associate-*r* 99.8%

         \[\leadsto \frac{x}{y} \cdot -1.3333333333333333 + \color{blue}{\frac{x}{y} \cdot \left(x \cdot 0.3333333333333333\right)} \]

      7. distribute-lft-out 99.8%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot \left(-1.3333333333333333 + x \cdot 0.3333333333333333\right)} \]

   8. Simplified 99.8%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot \left(-1.3333333333333333 + x \cdot 0.3333333333333333\right)} \]

   9. Taylor expanded in x around 0 21.7%

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

       1. *-commutative 21.7%

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

       2. associate-*l/ 21.7%

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

       3. associate-*r/ 21.7%

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

   11. Simplified 21.7%

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

   if -0.75 < x

   1. Initial program 94.6%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   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. associate-/r* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 62.9%

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

4. Final simplification 51.1%

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

Alternative 12: 57.1% accurate, 1.8× 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 84.3%

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

      1. associate-*l/ 99.7%

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

      2. *-commutative 99.7%

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

      3. associate-/r* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 99.3%

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

      1. neg-mul-1 99.3%

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

   6. Simplified 99.3%

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

   7. Taylor expanded in x around 0 20.6%

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

      1. associate-*r/ 20.6%

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

      2. neg-mul-1 20.6%

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

   9. Simplified 20.6%

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

   if -1 < x

   1. Initial program 94.6%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   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. associate-/r* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 62.9%

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

4. Final simplification 50.8%

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

Alternative 13: 56.1% 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 91.7%

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

   1. associate-/l* 99.7%

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

   2. *-commutative 99.7%

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

3. Simplified 99.7%

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

4. Taylor expanded in x around 0 49.6%

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

5. Final simplification 49.6%

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

Alternative 14: 50.9% accurate, 3.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 91.7%

   \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
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. associate-/r* 99.8%

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

3. Simplified 99.8%

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

4. Taylor expanded in x around 0 46.2%

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

5. Final simplification 46.2%

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

Developer target: 99.9% 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 2023195 
(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)))