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

Percentage Accurate: 94.0% → 99.8%

Time: 9.7s

Alternatives: 13

Speedup: 1.0×

• 25.0% 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: 94.0% 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: 98.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.64 \lor \neg \left(x \leq 4.6\right):\\ \;\;\;\;\left(x + -4\right) \cdot \left(x \cdot \frac{0.3333333333333333}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -0.64) (not (<= x 4.6)))
   (* (+ x -4.0) (* x (/ 0.3333333333333333 y)))
   (/ 1.0 y)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -0.64) || !(x <= 4.6)) {
		tmp = (x + -4.0) * (x * (0.3333333333333333 / 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 <= (-0.64d0)) .or. (.not. (x <= 4.6d0))) then
        tmp = (x + (-4.0d0)) * (x * (0.3333333333333333d0 / 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 <= -0.64) || !(x <= 4.6)) {
		tmp = (x + -4.0) * (x * (0.3333333333333333 / y));
	} else {
		tmp = 1.0 / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -0.64) or not (x <= 4.6):
		tmp = (x + -4.0) * (x * (0.3333333333333333 / y))
	else:
		tmp = 1.0 / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -0.64) || !(x <= 4.6))
		tmp = Float64(Float64(x + -4.0) * Float64(x * Float64(0.3333333333333333 / y)));
	else
		tmp = Float64(1.0 / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -0.64) || ~((x <= 4.6)))
		tmp = (x + -4.0) * (x * (0.3333333333333333 / y));
	else
		tmp = 1.0 / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -0.64], N[Not[LessEqual[x, 4.6]], $MachinePrecision]], N[(N[(x + -4.0), $MachinePrecision] * N[(x * N[(0.3333333333333333 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -0.640000000000000013 or 4.5999999999999996 < x

   1. Initial program 88.4%

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

   3. Taylor expanded in x around inf 86.4%

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

      1. +-commutative 86.4%

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

      2. unpow2 86.4%

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

      3. distribute-rgt-out 86.3%

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

   5. Simplified 86.3%

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

      1. div-inv 86.3%

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

      2. *-commutative 86.3%

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

      3. associate-*l* 97.6%

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

      4. *-commutative 97.6%

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

      5. associate-/r* 97.7%

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

      6. metadata-eval 97.7%

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

   7. Applied egg-rr 97.7%

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

   if -0.640000000000000013 < x < 4.5999999999999996

   1. Initial program 99.5%

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

      1. associate-*l/ 99.2%

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

      2. *-commutative 99.2%

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

      3. *-commutative 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in x around 0 98.8%

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

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.64 \lor \neg \left(x \leq 4.6\right):\\ \;\;\;\;\left(x + -4\right) \cdot \left(x \cdot \frac{0.3333333333333333}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.64:\\ \;\;\;\;\frac{x}{y} \cdot \left(\left(x + -4\right) \cdot 0.3333333333333333\right)\\ \mathbf{elif}\;x \leq 4.6:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(x + -4\right) \cdot \left(x \cdot \frac{0.3333333333333333}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -0.64)
   (* (/ x y) (* (+ x -4.0) 0.3333333333333333))
   (if (<= x 4.6) (/ 1.0 y) (* (+ x -4.0) (* x (/ 0.3333333333333333 y))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -0.64) {
		tmp = (x / y) * ((x + -4.0) * 0.3333333333333333);
	} else if (x <= 4.6) {
		tmp = 1.0 / y;
	} else {
		tmp = (x + -4.0) * (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 <= (-0.64d0)) then
        tmp = (x / y) * ((x + (-4.0d0)) * 0.3333333333333333d0)
    else if (x <= 4.6d0) then
        tmp = 1.0d0 / y
    else
        tmp = (x + (-4.0d0)) * (x * (0.3333333333333333d0 / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -0.64) {
		tmp = (x / y) * ((x + -4.0) * 0.3333333333333333);
	} else if (x <= 4.6) {
		tmp = 1.0 / y;
	} else {
		tmp = (x + -4.0) * (x * (0.3333333333333333 / y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -0.64:
		tmp = (x / y) * ((x + -4.0) * 0.3333333333333333)
	elif x <= 4.6:
		tmp = 1.0 / y
	else:
		tmp = (x + -4.0) * (x * (0.3333333333333333 / y))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -0.64)
		tmp = Float64(Float64(x / y) * Float64(Float64(x + -4.0) * 0.3333333333333333));
	elseif (x <= 4.6)
		tmp = Float64(1.0 / y);
	else
		tmp = Float64(Float64(x + -4.0) * Float64(x * Float64(0.3333333333333333 / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -0.64)
		tmp = (x / y) * ((x + -4.0) * 0.3333333333333333);
	elseif (x <= 4.6)
		tmp = 1.0 / y;
	else
		tmp = (x + -4.0) * (x * (0.3333333333333333 / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -0.64], N[(N[(x / y), $MachinePrecision] * N[(N[(x + -4.0), $MachinePrecision] * 0.3333333333333333), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.6], N[(1.0 / y), $MachinePrecision], N[(N[(x + -4.0), $MachinePrecision] * N[(x * N[(0.3333333333333333 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -0.640000000000000013

   1. Initial program 87.9%

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

   3. Taylor expanded in x around inf 86.0%

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

      1. +-commutative 86.0%

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

      2. unpow2 86.0%

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

      3. distribute-rgt-out 86.0%

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

   5. Simplified 86.0%

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

      1. times-frac 97.8%

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

      2. div-inv 97.8%

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

      3. metadata-eval 97.8%

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

   7. Applied egg-rr 97.8%

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

   if -0.640000000000000013 < x < 4.5999999999999996

   1. Initial program 99.5%

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

      1. associate-*l/ 99.2%

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

      2. *-commutative 99.2%

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

      3. *-commutative 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in x around 0 98.8%

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

   if 4.5999999999999996 < x

   1. Initial program 88.8%

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

   3. Taylor expanded in x around inf 86.7%

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

      1. +-commutative 86.7%

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

      2. unpow2 86.7%

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

      3. distribute-rgt-out 86.7%

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

   5. Simplified 86.7%

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

      1. div-inv 86.6%

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

      2. *-commutative 86.6%

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

      3. associate-*l* 97.6%

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

      4. *-commutative 97.6%

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

      5. associate-/r* 97.6%

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

      6. metadata-eval 97.6%

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

   7. Applied egg-rr 97.6%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.64:\\ \;\;\;\;\frac{x}{y} \cdot \left(\left(x + -4\right) \cdot 0.3333333333333333\right)\\ \mathbf{elif}\;x \leq 4.6:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(x + -4\right) \cdot \left(x \cdot \frac{0.3333333333333333}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.64:\\ \;\;\;\;\frac{x}{y} \cdot \left(x \cdot 0.3333333333333333 - 1.3333333333333333\right)\\ \mathbf{elif}\;x \leq 4.6:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(x + -4\right) \cdot \left(x \cdot \frac{0.3333333333333333}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -0.64)
   (* (/ x y) (- (* x 0.3333333333333333) 1.3333333333333333))
   (if (<= x 4.6) (/ 1.0 y) (* (+ x -4.0) (* x (/ 0.3333333333333333 y))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -0.64) {
		tmp = (x / y) * ((x * 0.3333333333333333) - 1.3333333333333333);
	} else if (x <= 4.6) {
		tmp = 1.0 / y;
	} else {
		tmp = (x + -4.0) * (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 <= (-0.64d0)) then
        tmp = (x / y) * ((x * 0.3333333333333333d0) - 1.3333333333333333d0)
    else if (x <= 4.6d0) then
        tmp = 1.0d0 / y
    else
        tmp = (x + (-4.0d0)) * (x * (0.3333333333333333d0 / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -0.64) {
		tmp = (x / y) * ((x * 0.3333333333333333) - 1.3333333333333333);
	} else if (x <= 4.6) {
		tmp = 1.0 / y;
	} else {
		tmp = (x + -4.0) * (x * (0.3333333333333333 / y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -0.64:
		tmp = (x / y) * ((x * 0.3333333333333333) - 1.3333333333333333)
	elif x <= 4.6:
		tmp = 1.0 / y
	else:
		tmp = (x + -4.0) * (x * (0.3333333333333333 / y))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -0.64)
		tmp = Float64(Float64(x / y) * Float64(Float64(x * 0.3333333333333333) - 1.3333333333333333));
	elseif (x <= 4.6)
		tmp = Float64(1.0 / y);
	else
		tmp = Float64(Float64(x + -4.0) * Float64(x * Float64(0.3333333333333333 / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -0.64)
		tmp = (x / y) * ((x * 0.3333333333333333) - 1.3333333333333333);
	elseif (x <= 4.6)
		tmp = 1.0 / y;
	else
		tmp = (x + -4.0) * (x * (0.3333333333333333 / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -0.64], N[(N[(x / y), $MachinePrecision] * N[(N[(x * 0.3333333333333333), $MachinePrecision] - 1.3333333333333333), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.6], N[(1.0 / y), $MachinePrecision], N[(N[(x + -4.0), $MachinePrecision] * N[(x * N[(0.3333333333333333 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -0.640000000000000013

   1. Initial program 87.9%

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

   3. Taylor expanded in x around inf 86.0%

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

      1. +-commutative 86.0%

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

      2. unpow2 86.0%

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

      3. distribute-rgt-out 86.0%

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

   5. Simplified 86.0%

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

      1. div-inv 85.9%

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

      2. *-commutative 85.9%

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

      3. associate-*l* 97.7%

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

      4. *-commutative 97.7%

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

      5. associate-/r* 97.7%

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

      6. metadata-eval 97.7%

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

   7. Applied egg-rr 97.7%

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

   8. Taylor expanded in x around 0 86.0%

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

      1. +-commutative 86.0%

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

      2. unpow2 86.0%

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

      3. fma-define 86.0%

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

      4. associate-*l/ 97.7%

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

      5. fma-define 97.7%

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

      6. associate-*l* 97.7%

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

      7. metadata-eval 97.7%

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

      8. associate-*r* 97.7%

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

      9. *-commutative 97.7%

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

      10. distribute-lft-in 97.7%

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

      11. associate-*r/ 97.8%

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

      12. associate-*l/ 85.9%

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

      13. associate-*l* 85.9%

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

      14. *-commutative 85.9%

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

      15. associate-/l* 86.0%

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

      16. metadata-eval 86.0%

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

      17. associate-/l* 86.0%

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

      18. /-rgt-identity 86.0%

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

      19. times-frac 97.8%

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

      20. metadata-eval 97.8%

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

      21. sub-neg 97.8%

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

      22. div-sub 97.9%

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

   10. Simplified 97.8%

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

   if -0.640000000000000013 < x < 4.5999999999999996

   1. Initial program 99.5%

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

      1. associate-*l/ 99.2%

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

      2. *-commutative 99.2%

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

      3. *-commutative 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in x around 0 98.8%

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

   if 4.5999999999999996 < x

   1. Initial program 88.8%

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

   3. Taylor expanded in x around inf 86.7%

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

      1. +-commutative 86.7%

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

      2. unpow2 86.7%

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

      3. distribute-rgt-out 86.7%

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

   5. Simplified 86.7%

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

      1. div-inv 86.6%

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

      2. *-commutative 86.6%

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

      3. associate-*l* 97.6%

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

      4. *-commutative 97.6%

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

      5. associate-/r* 97.6%

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

      6. metadata-eval 97.6%

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

   7. Applied egg-rr 97.6%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.64:\\ \;\;\;\;\frac{x}{y} \cdot \left(x \cdot 0.3333333333333333 - 1.3333333333333333\right)\\ \mathbf{elif}\;x \leq 4.6:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(x + -4\right) \cdot \left(x \cdot \frac{0.3333333333333333}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 98.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.64:\\ \;\;\;\;\frac{x}{y} \cdot \left(\frac{x}{3} - 1.3333333333333333\right)\\ \mathbf{elif}\;x \leq 4.6:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(x + -4\right) \cdot \left(x \cdot \frac{0.3333333333333333}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -0.64)
   (* (/ x y) (- (/ x 3.0) 1.3333333333333333))
   (if (<= x 4.6) (/ 1.0 y) (* (+ x -4.0) (* x (/ 0.3333333333333333 y))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -0.64) {
		tmp = (x / y) * ((x / 3.0) - 1.3333333333333333);
	} else if (x <= 4.6) {
		tmp = 1.0 / y;
	} else {
		tmp = (x + -4.0) * (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 <= (-0.64d0)) then
        tmp = (x / y) * ((x / 3.0d0) - 1.3333333333333333d0)
    else if (x <= 4.6d0) then
        tmp = 1.0d0 / y
    else
        tmp = (x + (-4.0d0)) * (x * (0.3333333333333333d0 / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -0.64) {
		tmp = (x / y) * ((x / 3.0) - 1.3333333333333333);
	} else if (x <= 4.6) {
		tmp = 1.0 / y;
	} else {
		tmp = (x + -4.0) * (x * (0.3333333333333333 / y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -0.64:
		tmp = (x / y) * ((x / 3.0) - 1.3333333333333333)
	elif x <= 4.6:
		tmp = 1.0 / y
	else:
		tmp = (x + -4.0) * (x * (0.3333333333333333 / y))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -0.64)
		tmp = Float64(Float64(x / y) * Float64(Float64(x / 3.0) - 1.3333333333333333));
	elseif (x <= 4.6)
		tmp = Float64(1.0 / y);
	else
		tmp = Float64(Float64(x + -4.0) * Float64(x * Float64(0.3333333333333333 / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -0.64)
		tmp = (x / y) * ((x / 3.0) - 1.3333333333333333);
	elseif (x <= 4.6)
		tmp = 1.0 / y;
	else
		tmp = (x + -4.0) * (x * (0.3333333333333333 / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -0.64], N[(N[(x / y), $MachinePrecision] * N[(N[(x / 3.0), $MachinePrecision] - 1.3333333333333333), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.6], N[(1.0 / y), $MachinePrecision], N[(N[(x + -4.0), $MachinePrecision] * N[(x * N[(0.3333333333333333 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -0.640000000000000013

   1. Initial program 87.9%

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

   3. Taylor expanded in x around inf 86.0%

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

      1. +-commutative 86.0%

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

      2. unpow2 86.0%

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

      3. distribute-rgt-out 86.0%

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

   5. Simplified 86.0%

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

      1. div-inv 85.9%

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

      2. *-commutative 85.9%

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

      3. associate-*l* 97.7%

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

      4. *-commutative 97.7%

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

      5. associate-/r* 97.7%

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

      6. metadata-eval 97.7%

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

   7. Applied egg-rr 97.7%

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

   8. Taylor expanded in x around 0 86.0%

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

      1. +-commutative 86.0%

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

      2. unpow2 86.0%

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

      3. fma-define 86.0%

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

      4. associate-*l/ 97.7%

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

      5. fma-define 97.7%

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

      6. associate-*l* 97.7%

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

      7. metadata-eval 97.7%

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

      8. associate-*r* 97.7%

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

      9. *-commutative 97.7%

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

      10. distribute-lft-in 97.7%

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

      11. associate-*r/ 97.8%

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

      12. associate-*l/ 85.9%

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

      13. associate-*l* 85.9%

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

      14. *-commutative 85.9%

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

      15. associate-/l* 86.0%

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

      16. metadata-eval 86.0%

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

      17. associate-/l* 86.0%

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

      18. /-rgt-identity 86.0%

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

      19. times-frac 97.8%

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

      20. metadata-eval 97.8%

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

      21. sub-neg 97.8%

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

      22. div-sub 97.9%

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

   10. Simplified 97.8%

       \[\leadsto \color{blue}{\frac{x}{y} \cdot \left(0.3333333333333333 \cdot x - 1.3333333333333333\right)} \]
   11. Step-by-step derivation

       1. *-commutative 97.8%

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

       2. metadata-eval 97.8%

          \[\leadsto \frac{x}{y} \cdot \left(x \cdot \color{blue}{\frac{1}{3}} - 1.3333333333333333\right) \]

       3. div-inv 97.9%

          \[\leadsto \frac{x}{y} \cdot \left(\color{blue}{\frac{x}{3}} - 1.3333333333333333\right) \]

   12. Applied egg-rr 97.9%

       \[\leadsto \frac{x}{y} \cdot \left(\color{blue}{\frac{x}{3}} - 1.3333333333333333\right) \]

   if -0.640000000000000013 < x < 4.5999999999999996

   1. Initial program 99.5%

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

      1. associate-*l/ 99.2%

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

      2. *-commutative 99.2%

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

      3. *-commutative 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in x around 0 98.8%

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

   if 4.5999999999999996 < x

   1. Initial program 88.8%

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

   3. Taylor expanded in x around inf 86.7%

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

      1. +-commutative 86.7%

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

      2. unpow2 86.7%

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

      3. distribute-rgt-out 86.7%

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

   5. Simplified 86.7%

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

      1. div-inv 86.6%

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

      2. *-commutative 86.6%

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

      3. associate-*l* 97.6%

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

      4. *-commutative 97.6%

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

      5. associate-/r* 97.6%

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

      6. metadata-eval 97.6%

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

   7. Applied egg-rr 97.6%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.64:\\ \;\;\;\;\frac{x}{y} \cdot \left(\frac{x}{3} - 1.3333333333333333\right)\\ \mathbf{elif}\;x \leq 4.6:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(x + -4\right) \cdot \left(x \cdot \frac{0.3333333333333333}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 98.5% accurate, 0.6× speedup

Math

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

FPCore

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

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.75) {
		tmp = (x / y) * ((x / 3.0) - 1.3333333333333333);
	} else if (x <= 1.7) {
		tmp = (3.0 + (x * -4.0)) / (y * 3.0);
	} else {
		tmp = (x + -4.0) * (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 <= (-1.75d0)) then
        tmp = (x / y) * ((x / 3.0d0) - 1.3333333333333333d0)
    else if (x <= 1.7d0) then
        tmp = (3.0d0 + (x * (-4.0d0))) / (y * 3.0d0)
    else
        tmp = (x + (-4.0d0)) * (x * (0.3333333333333333d0 / y))
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 3 regimes

2. if x < -1.75

   1. Initial program 87.9%

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

   3. Taylor expanded in x around inf 86.0%

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

      1. +-commutative 86.0%

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

      2. unpow2 86.0%

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

      3. distribute-rgt-out 86.0%

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

   5. Simplified 86.0%

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

      1. div-inv 85.9%

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

      2. *-commutative 85.9%

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

      3. associate-*l* 97.7%

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

      4. *-commutative 97.7%

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

      5. associate-/r* 97.7%

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

      6. metadata-eval 97.7%

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

   7. Applied egg-rr 97.7%

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

   8. Taylor expanded in x around 0 86.0%

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

      1. +-commutative 86.0%

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

      2. unpow2 86.0%

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

      3. fma-define 86.0%

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

      4. associate-*l/ 97.7%

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

      5. fma-define 97.7%

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

      6. associate-*l* 97.7%

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

      7. metadata-eval 97.7%

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

      8. associate-*r* 97.7%

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

      9. *-commutative 97.7%

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

      10. distribute-lft-in 97.7%

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

      11. associate-*r/ 97.8%

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

      12. associate-*l/ 85.9%

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

      13. associate-*l* 85.9%

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

      14. *-commutative 85.9%

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

      15. associate-/l* 86.0%

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

      16. metadata-eval 86.0%

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

      17. associate-/l* 86.0%

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

      18. /-rgt-identity 86.0%

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

      19. times-frac 97.8%

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

      20. metadata-eval 97.8%

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

      21. sub-neg 97.8%

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

      22. div-sub 97.9%

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

   10. Simplified 97.8%

       \[\leadsto \color{blue}{\frac{x}{y} \cdot \left(0.3333333333333333 \cdot x - 1.3333333333333333\right)} \]
   11. Step-by-step derivation

       1. *-commutative 97.8%

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

       2. metadata-eval 97.8%

          \[\leadsto \frac{x}{y} \cdot \left(x \cdot \color{blue}{\frac{1}{3}} - 1.3333333333333333\right) \]

       3. div-inv 97.9%

          \[\leadsto \frac{x}{y} \cdot \left(\color{blue}{\frac{x}{3}} - 1.3333333333333333\right) \]

   12. Applied egg-rr 97.9%

       \[\leadsto \frac{x}{y} \cdot \left(\color{blue}{\frac{x}{3}} - 1.3333333333333333\right) \]

   if -1.75 < x < 1.69999999999999996

   1. Initial program 99.5%

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

   3. Taylor expanded in x around 0 99.2%

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

      1. *-commutative 99.2%

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

   5. Simplified 99.2%

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

   if 1.69999999999999996 < x

   1. Initial program 88.8%

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

   3. Taylor expanded in x around inf 86.7%

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

      1. +-commutative 86.7%

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

      2. unpow2 86.7%

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

      3. distribute-rgt-out 86.7%

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

   5. Simplified 86.7%

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

      1. div-inv 86.6%

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

      2. *-commutative 86.6%

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

      3. associate-*l* 97.6%

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

      4. *-commutative 97.6%

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

      5. associate-/r* 97.6%

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

      6. metadata-eval 97.6%

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

   7. Applied egg-rr 97.6%

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

4. Final simplification 98.4%

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

Alternative 7: 64.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.75:\\ \;\;\;\;\frac{x}{y} \cdot -1.3333333333333333\\ \mathbf{elif}\;x \leq 4.2:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot 0.3333333333333333\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -0.75)
   (* (/ x y) -1.3333333333333333)
   (if (<= x 4.2) (/ 1.0 y) (* (/ x y) 0.3333333333333333))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -0.75) {
		tmp = (x / y) * -1.3333333333333333;
	} else if (x <= 4.2) {
		tmp = 1.0 / y;
	} else {
		tmp = (x / y) * 0.3333333333333333;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-0.75d0)) then
        tmp = (x / y) * (-1.3333333333333333d0)
    else if (x <= 4.2d0) then
        tmp = 1.0d0 / y
    else
        tmp = (x / y) * 0.3333333333333333d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -0.75) {
		tmp = (x / y) * -1.3333333333333333;
	} else if (x <= 4.2) {
		tmp = 1.0 / y;
	} else {
		tmp = (x / y) * 0.3333333333333333;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -0.75:
		tmp = (x / y) * -1.3333333333333333
	elif x <= 4.2:
		tmp = 1.0 / y
	else:
		tmp = (x / y) * 0.3333333333333333
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -0.75)
		tmp = Float64(Float64(x / y) * -1.3333333333333333);
	elseif (x <= 4.2)
		tmp = Float64(1.0 / y);
	else
		tmp = Float64(Float64(x / y) * 0.3333333333333333);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -0.75)
		tmp = (x / y) * -1.3333333333333333;
	elseif (x <= 4.2)
		tmp = 1.0 / y;
	else
		tmp = (x / y) * 0.3333333333333333;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -0.75], N[(N[(x / y), $MachinePrecision] * -1.3333333333333333), $MachinePrecision], If[LessEqual[x, 4.2], N[(1.0 / y), $MachinePrecision], N[(N[(x / y), $MachinePrecision] * 0.3333333333333333), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -0.75

   1. Initial program 87.9%

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

   3. Taylor expanded in x around 0 28.7%

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

      1. *-commutative 28.7%

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

   5. Simplified 28.7%

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

   6. Taylor expanded in x around inf 28.7%

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

   if -0.75 < x < 4.20000000000000018

   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/ 99.2%

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

      2. *-commutative 99.2%

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

      3. *-commutative 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in x around 0 98.8%

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

   if 4.20000000000000018 < x

   1. Initial program 88.8%

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

      1. *-lft-identity 88.8%

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

      2. metadata-eval 88.8%

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

      3. times-frac 88.8%

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

      4. neg-mul-1 88.8%

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

      5. distribute-lft-neg-out 88.8%

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

      6. associate-/l* 88.8%

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

      7. associate-/r* 99.7%

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

      8. associate-/l* 99.7%

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

      9. neg-mul-1 99.7%

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

      10. sub-neg 99.7%

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

      11. +-commutative 99.7%

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

      12. distribute-neg-in 99.7%

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

      13. remove-double-neg 99.7%

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

      14. metadata-eval 99.7%

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

      15. distribute-lft-neg-out 99.7%

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

      16. distribute-rgt-neg-in 99.7%

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

      17. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0 0.6%

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

      1. *-commutative 0.6%

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

   7. Simplified 0.6%

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

      1. frac-2neg 0.6%

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

      2. div-inv 0.6%

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

      3. +-commutative 0.6%

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

      4. distribute-neg-in 0.6%

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

      5. metadata-eval 0.6%

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

      6. add-sqr-sqrt 0.0%

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

      7. sqrt-unprod 53.5%

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

      8. sqr-neg 53.5%

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

      9. sqrt-unprod 37.5%

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

      10. add-sqr-sqrt 37.5%

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

      11. *-commutative 37.5%

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

      12. distribute-lft-neg-in 37.5%

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

      13. metadata-eval 37.5%

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

      14. associate-/r* 37.5%

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

      15. metadata-eval 37.5%

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

   9. Applied egg-rr 37.5%

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

       1. *-commutative 37.5%

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

       2. +-commutative 37.5%

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

   11. Simplified 37.5%

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

   12. Taylor expanded in x around inf 37.5%

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

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.75:\\ \;\;\;\;\frac{x}{y} \cdot -1.3333333333333333\\ \mathbf{elif}\;x \leq 4.2:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot 0.3333333333333333\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 63.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.6:\\ \;\;\;\;\frac{x}{y} \cdot -1.3333333333333333\\ \mathbf{else}:\\ \;\;\;\;\frac{0.3333333333333333}{y} \cdot \left(x + 3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -0.6)
   (* (/ x y) -1.3333333333333333)
   (* (/ 0.3333333333333333 y) (+ x 3.0))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -0.6) {
		tmp = (x / y) * -1.3333333333333333;
	} else {
		tmp = (0.3333333333333333 / y) * (x + 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 <= (-0.6d0)) then
        tmp = (x / y) * (-1.3333333333333333d0)
    else
        tmp = (0.3333333333333333d0 / y) * (x + 3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -0.6) {
		tmp = (x / y) * -1.3333333333333333;
	} else {
		tmp = (0.3333333333333333 / y) * (x + 3.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -0.6:
		tmp = (x / y) * -1.3333333333333333
	else:
		tmp = (0.3333333333333333 / y) * (x + 3.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -0.6)
		tmp = Float64(Float64(x / y) * -1.3333333333333333);
	else
		tmp = Float64(Float64(0.3333333333333333 / y) * Float64(x + 3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -0.6)
		tmp = (x / y) * -1.3333333333333333;
	else
		tmp = (0.3333333333333333 / y) * (x + 3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -0.6], N[(N[(x / y), $MachinePrecision] * -1.3333333333333333), $MachinePrecision], N[(N[(0.3333333333333333 / y), $MachinePrecision] * N[(x + 3.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -0.599999999999999978

   1. Initial program 87.9%

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

   3. Taylor expanded in x around 0 28.7%

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

      1. *-commutative 28.7%

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

   5. Simplified 28.7%

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

   6. Taylor expanded in x around inf 28.7%

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

   if -0.599999999999999978 < x

   1. Initial program 95.8%

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

      1. *-lft-identity 95.8%

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

      2. metadata-eval 95.8%

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

      3. times-frac 95.8%

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

      4. neg-mul-1 95.8%

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

      5. distribute-lft-neg-out 95.8%

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

      6. associate-/l* 95.9%

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

      7. associate-/r* 99.7%

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

      8. associate-/l* 99.6%

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

      9. neg-mul-1 99.6%

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

      10. sub-neg 99.6%

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

      11. +-commutative 99.6%

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

      12. distribute-neg-in 99.6%

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

      13. remove-double-neg 99.6%

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

      14. metadata-eval 99.6%

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

      15. distribute-lft-neg-out 99.6%

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

      16. distribute-rgt-neg-in 99.6%

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

      17. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around 0 64.4%

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

      1. *-commutative 64.4%

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

   7. Simplified 64.4%

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

      1. frac-2neg 64.4%

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

      2. div-inv 64.2%

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

      3. +-commutative 64.2%

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

      4. distribute-neg-in 64.2%

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

      5. metadata-eval 64.2%

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

      6. add-sqr-sqrt 30.1%

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

      7. sqrt-unprod 82.6%

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

      8. sqr-neg 82.6%

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

      9. sqrt-unprod 47.0%

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

      10. add-sqr-sqrt 77.0%

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

      11. *-commutative 77.0%

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

      12. distribute-lft-neg-in 77.0%

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

      13. metadata-eval 77.0%

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

      14. associate-/r* 77.1%

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

      15. metadata-eval 77.1%

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

   9. Applied egg-rr 77.1%

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

       1. *-commutative 77.1%

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

       2. +-commutative 77.1%

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

   11. Simplified 77.1%

       \[\leadsto \color{blue}{\frac{0.3333333333333333}{y} \cdot \left(x + 3\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.6:\\ \;\;\;\;\frac{x}{y} \cdot -1.3333333333333333\\ \mathbf{else}:\\ \;\;\;\;\frac{0.3333333333333333}{y} \cdot \left(x + 3\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 64.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.6:\\ \;\;\;\;\frac{x}{y} \cdot -1.3333333333333333\\ \mathbf{else}:\\ \;\;\;\;\frac{1 + x \cdot 0.3333333333333333}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -0.6)
   (* (/ x y) -1.3333333333333333)
   (/ (+ 1.0 (* x 0.3333333333333333)) y)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -0.6) {
		tmp = (x / y) * -1.3333333333333333;
	} else {
		tmp = (1.0 + (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 <= (-0.6d0)) then
        tmp = (x / y) * (-1.3333333333333333d0)
    else
        tmp = (1.0d0 + (x * 0.3333333333333333d0)) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -0.6) {
		tmp = (x / y) * -1.3333333333333333;
	} else {
		tmp = (1.0 + (x * 0.3333333333333333)) / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -0.6:
		tmp = (x / y) * -1.3333333333333333
	else:
		tmp = (1.0 + (x * 0.3333333333333333)) / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -0.6)
		tmp = Float64(Float64(x / y) * -1.3333333333333333);
	else
		tmp = Float64(Float64(1.0 + Float64(x * 0.3333333333333333)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -0.6)
		tmp = (x / y) * -1.3333333333333333;
	else
		tmp = (1.0 + (x * 0.3333333333333333)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -0.6], N[(N[(x / y), $MachinePrecision] * -1.3333333333333333), $MachinePrecision], N[(N[(1.0 + N[(x * 0.3333333333333333), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -0.599999999999999978

   1. Initial program 87.9%

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

   3. Taylor expanded in x around 0 28.7%

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

      1. *-commutative 28.7%

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

   5. Simplified 28.7%

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

   6. Taylor expanded in x around inf 28.7%

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

   if -0.599999999999999978 < x

   1. Initial program 95.8%

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

      1. *-lft-identity 95.8%

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

      2. metadata-eval 95.8%

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

      3. times-frac 95.8%

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

      4. neg-mul-1 95.8%

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

      5. distribute-lft-neg-out 95.8%

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

      6. associate-/l* 95.9%

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

      7. associate-/r* 99.7%

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

      8. associate-/l* 99.6%

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

      9. neg-mul-1 99.6%

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

      10. sub-neg 99.6%

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

      11. +-commutative 99.6%

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

      12. distribute-neg-in 99.6%

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

      13. remove-double-neg 99.6%

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

      14. metadata-eval 99.6%

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

      15. distribute-lft-neg-out 99.6%

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

      16. distribute-rgt-neg-in 99.6%

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

      17. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around 0 64.4%

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

      1. *-commutative 64.4%

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

   7. Simplified 64.4%

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

      1. frac-2neg 64.4%

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

      2. div-inv 64.2%

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

      3. +-commutative 64.2%

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

      4. distribute-neg-in 64.2%

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

      5. metadata-eval 64.2%

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

      6. add-sqr-sqrt 30.1%

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

      7. sqrt-unprod 82.6%

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

      8. sqr-neg 82.6%

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

      9. sqrt-unprod 47.0%

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

      10. add-sqr-sqrt 77.0%

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

      11. *-commutative 77.0%

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

      12. distribute-lft-neg-in 77.0%

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

      13. metadata-eval 77.0%

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

      14. associate-/r* 77.1%

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

      15. metadata-eval 77.1%

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

   9. Applied egg-rr 77.1%

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

       1. *-commutative 77.1%

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

       2. +-commutative 77.1%

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

   11. Simplified 77.1%

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

       1. associate-*l/ 77.5%

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

       2. +-commutative 77.5%

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

       3. distribute-lft-in 77.5%

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

       4. metadata-eval 77.5%

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

   13. Applied egg-rr 77.5%

       \[\leadsto \color{blue}{\frac{1 + 0.3333333333333333 \cdot x}{y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.6:\\ \;\;\;\;\frac{x}{y} \cdot -1.3333333333333333\\ \mathbf{else}:\\ \;\;\;\;\frac{1 + x \cdot 0.3333333333333333}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 99.5% accurate, 1.0× speedup

Math

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

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(1.0 - x) / Float64(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[(1.0 - x), $MachinePrecision] / N[(y * 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. 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. *-commutative 99.5%

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

3. Simplified 99.5%

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

5. Final simplification 99.5%

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

Alternative 11: 58.0% 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 87.9%

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

   3. Taylor expanded in x around 0 28.7%

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

      1. *-commutative 28.7%

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

   5. Simplified 28.7%

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

   6. Taylor expanded in x around inf 28.7%

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

   if -0.75 < x

   1. Initial program 95.8%

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

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x around 0 66.4%

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

4. Final simplification 57.1%

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

Alternative 12: 58.0% 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 87.9%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   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. Taylor expanded in x around inf 97.6%

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

      1. neg-mul-1 97.6%

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

      2. distribute-neg-frac 97.6%

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

   7. Simplified 97.6%

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

   8. Taylor expanded in x around 0 28.7%

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

      1. mul-1-neg 28.7%

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

      2. distribute-neg-frac 28.7%

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

   10. Simplified 28.7%

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

   if -1 < x

   1. Initial program 95.8%

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

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x around 0 66.4%

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

4. Final simplification 57.1%

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

Alternative 13: 51.8% accurate, 3.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.9%

   \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
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. *-commutative 99.5%

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

3. Simplified 99.5%

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

5. Taylor expanded in x around 0 51.2%

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

6. Final simplification 51.2%

   \[\leadsto \frac{1}{y} \]
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 2024034 
(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)))