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

Percentage Accurate: 93.8% → 99.8%

Time: 8.7s

Alternatives: 13

Speedup: 1.0×

• 24.6% 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: 93.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.7%

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

   1. times-frac 99.9%

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

3. Simplified 99.9%

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

5. Final simplification 99.9%

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

Alternative 2: 98.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.3 \lor \neg \left(x \leq 1.35\right):\\ \;\;\;\;\left(3 - x\right) \cdot \left(\frac{x}{y} \cdot -0.3333333333333333\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot -1.3333333333333333 + 1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -2.3) (not (<= x 1.35)))
   (* (- 3.0 x) (* (/ x y) -0.3333333333333333))
   (/ (+ (* x -1.3333333333333333) 1.0) y)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -2.3) || !(x <= 1.35)) {
		tmp = (3.0 - x) * ((x / y) * -0.3333333333333333);
	} else {
		tmp = ((x * -1.3333333333333333) + 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 <= (-2.3d0)) .or. (.not. (x <= 1.35d0))) then
        tmp = (3.0d0 - x) * ((x / y) * (-0.3333333333333333d0))
    else
        tmp = ((x * (-1.3333333333333333d0)) + 1.0d0) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -2.3) || !(x <= 1.35)) {
		tmp = (3.0 - x) * ((x / y) * -0.3333333333333333);
	} else {
		tmp = ((x * -1.3333333333333333) + 1.0) / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -2.3) or not (x <= 1.35):
		tmp = (3.0 - x) * ((x / y) * -0.3333333333333333)
	else:
		tmp = ((x * -1.3333333333333333) + 1.0) / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -2.3) || !(x <= 1.35))
		tmp = Float64(Float64(3.0 - x) * Float64(Float64(x / y) * -0.3333333333333333));
	else
		tmp = Float64(Float64(Float64(x * -1.3333333333333333) + 1.0) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -2.3) || ~((x <= 1.35)))
		tmp = (3.0 - x) * ((x / y) * -0.3333333333333333);
	else
		tmp = ((x * -1.3333333333333333) + 1.0) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -2.3], N[Not[LessEqual[x, 1.35]], $MachinePrecision]], N[(N[(3.0 - x), $MachinePrecision] * N[(N[(x / y), $MachinePrecision] * -0.3333333333333333), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x * -1.3333333333333333), $MachinePrecision] + 1.0), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.2999999999999998 or 1.3500000000000001 < x

   1. Initial program 91.9%

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

      1. associate-*l/ 98.9%

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

      2. *-commutative 98.9%

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

      3. *-rgt-identity 98.9%

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

      4. associate-*l* 98.9%

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

      5. metadata-eval 98.9%

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

      6. times-frac 98.9%

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

      7. *-commutative 98.9%

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

      8. neg-mul-1 98.9%

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

      9. distribute-rgt-neg-in 98.9%

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

      10. times-frac 99.7%

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

      11. metadata-eval 99.7%

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

      12. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 98.5%

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

   if -2.2999999999999998 < x < 1.3500000000000001

   1. Initial program 99.6%

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

      1. associate-*l/ 99.3%

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

      2. *-commutative 99.3%

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

      3. *-rgt-identity 99.3%

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

      4. associate-*l* 99.3%

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

      5. metadata-eval 99.3%

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

      6. times-frac 99.3%

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

      7. *-commutative 99.3%

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

      8. neg-mul-1 99.3%

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

      9. distribute-rgt-neg-in 99.3%

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

      10. times-frac 99.5%

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

      11. metadata-eval 99.5%

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

      12. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around 0 99.8%

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

   6. Taylor expanded in y around 0 99.8%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3 \lor \neg \left(x \leq 1.35\right):\\ \;\;\;\;\left(3 - x\right) \cdot \left(\frac{x}{y} \cdot -0.3333333333333333\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot -1.3333333333333333 + 1}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.3:\\ \;\;\;\;\left(3 - x\right) \cdot \left(x \cdot \frac{-0.3333333333333333}{y}\right)\\ \mathbf{elif}\;x \leq 1.35:\\ \;\;\;\;\frac{x \cdot -1.3333333333333333 + 1}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(3 - x\right) \cdot \left(\frac{x}{y} \cdot -0.3333333333333333\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2.3)
   (* (- 3.0 x) (* x (/ -0.3333333333333333 y)))
   (if (<= x 1.35)
     (/ (+ (* x -1.3333333333333333) 1.0) y)
     (* (- 3.0 x) (* (/ x y) -0.3333333333333333)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.3) {
		tmp = (3.0 - x) * (x * (-0.3333333333333333 / y));
	} else if (x <= 1.35) {
		tmp = ((x * -1.3333333333333333) + 1.0) / y;
	} else {
		tmp = (3.0 - x) * ((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 <= (-2.3d0)) then
        tmp = (3.0d0 - x) * (x * ((-0.3333333333333333d0) / y))
    else if (x <= 1.35d0) then
        tmp = ((x * (-1.3333333333333333d0)) + 1.0d0) / y
    else
        tmp = (3.0d0 - x) * ((x / y) * (-0.3333333333333333d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -2.3) {
		tmp = (3.0 - x) * (x * (-0.3333333333333333 / y));
	} else if (x <= 1.35) {
		tmp = ((x * -1.3333333333333333) + 1.0) / y;
	} else {
		tmp = (3.0 - x) * ((x / y) * -0.3333333333333333);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2.3:
		tmp = (3.0 - x) * (x * (-0.3333333333333333 / y))
	elif x <= 1.35:
		tmp = ((x * -1.3333333333333333) + 1.0) / y
	else:
		tmp = (3.0 - x) * ((x / y) * -0.3333333333333333)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2.3)
		tmp = Float64(Float64(3.0 - x) * Float64(x * Float64(-0.3333333333333333 / y)));
	elseif (x <= 1.35)
		tmp = Float64(Float64(Float64(x * -1.3333333333333333) + 1.0) / y);
	else
		tmp = Float64(Float64(3.0 - x) * Float64(Float64(x / y) * -0.3333333333333333));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2.3)
		tmp = (3.0 - x) * (x * (-0.3333333333333333 / y));
	elseif (x <= 1.35)
		tmp = ((x * -1.3333333333333333) + 1.0) / y;
	else
		tmp = (3.0 - x) * ((x / y) * -0.3333333333333333);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2.3], N[(N[(3.0 - x), $MachinePrecision] * N[(x * N[(-0.3333333333333333 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.35], N[(N[(N[(x * -1.3333333333333333), $MachinePrecision] + 1.0), $MachinePrecision] / y), $MachinePrecision], N[(N[(3.0 - x), $MachinePrecision] * N[(N[(x / y), $MachinePrecision] * -0.3333333333333333), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.2999999999999998

   1. Initial program 93.0%

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

      1. associate-*l/ 99.7%

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

      2. *-commutative 99.7%

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

      3. *-rgt-identity 99.7%

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

      4. associate-*l* 99.7%

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

      5. metadata-eval 99.7%

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

      6. times-frac 99.7%

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

      7. *-commutative 99.7%

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

      8. neg-mul-1 99.7%

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

      9. distribute-rgt-neg-in 99.7%

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

      10. times-frac 99.6%

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

      11. metadata-eval 99.6%

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

      12. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around inf 97.9%

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

      1. metadata-eval 97.9%

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

      2. distribute-lft-neg-in 97.9%

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

      3. associate-*r/ 97.9%

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

      4. associate-*l/ 97.9%

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

      5. distribute-lft-neg-in 97.9%

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

      6. distribute-neg-frac 97.9%

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

      7. metadata-eval 97.9%

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

   7. Simplified 97.9%

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

   if -2.2999999999999998 < x < 1.3500000000000001

   1. Initial program 99.6%

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

      1. associate-*l/ 99.3%

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

      2. *-commutative 99.3%

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

      3. *-rgt-identity 99.3%

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

      4. associate-*l* 99.3%

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

      5. metadata-eval 99.3%

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

      6. times-frac 99.3%

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

      7. *-commutative 99.3%

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

      8. neg-mul-1 99.3%

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

      9. distribute-rgt-neg-in 99.3%

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

      10. times-frac 99.5%

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

      11. metadata-eval 99.5%

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

      12. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around 0 99.8%

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

   6. Taylor expanded in y around 0 99.8%

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

   if 1.3500000000000001 < x

   1. Initial program 91.1%

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

      1. associate-*l/ 98.4%

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

      2. *-commutative 98.4%

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

      3. *-rgt-identity 98.4%

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

      4. associate-*l* 98.4%

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

      5. metadata-eval 98.4%

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

      6. times-frac 98.4%

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

      7. *-commutative 98.4%

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

      8. neg-mul-1 98.4%

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

      9. distribute-rgt-neg-in 98.4%

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

      10. times-frac 99.8%

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

      11. metadata-eval 99.8%

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

      12. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 98.9%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3:\\ \;\;\;\;\left(3 - x\right) \cdot \left(x \cdot \frac{-0.3333333333333333}{y}\right)\\ \mathbf{elif}\;x \leq 1.35:\\ \;\;\;\;\frac{x \cdot -1.3333333333333333 + 1}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(3 - x\right) \cdot \left(\frac{x}{y} \cdot -0.3333333333333333\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.3:\\ \;\;\;\;\left(3 - x\right) \cdot \left(x \cdot \frac{-0.3333333333333333}{y}\right)\\ \mathbf{elif}\;x \leq 1.35:\\ \;\;\;\;\frac{x \cdot -1.3333333333333333 + 1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(-1 + x \cdot 0.3333333333333333\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2.3)
   (* (- 3.0 x) (* x (/ -0.3333333333333333 y)))
   (if (<= x 1.35)
     (/ (+ (* x -1.3333333333333333) 1.0) y)
     (* (/ x y) (+ -1.0 (* x 0.3333333333333333))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.3) {
		tmp = (3.0 - x) * (x * (-0.3333333333333333 / y));
	} else if (x <= 1.35) {
		tmp = ((x * -1.3333333333333333) + 1.0) / y;
	} else {
		tmp = (x / y) * (-1.0 + (x * 0.3333333333333333));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-2.3d0)) then
        tmp = (3.0d0 - x) * (x * ((-0.3333333333333333d0) / y))
    else if (x <= 1.35d0) then
        tmp = ((x * (-1.3333333333333333d0)) + 1.0d0) / y
    else
        tmp = (x / y) * ((-1.0d0) + (x * 0.3333333333333333d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -2.3) {
		tmp = (3.0 - x) * (x * (-0.3333333333333333 / y));
	} else if (x <= 1.35) {
		tmp = ((x * -1.3333333333333333) + 1.0) / y;
	} else {
		tmp = (x / y) * (-1.0 + (x * 0.3333333333333333));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2.3:
		tmp = (3.0 - x) * (x * (-0.3333333333333333 / y))
	elif x <= 1.35:
		tmp = ((x * -1.3333333333333333) + 1.0) / y
	else:
		tmp = (x / y) * (-1.0 + (x * 0.3333333333333333))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2.3)
		tmp = Float64(Float64(3.0 - x) * Float64(x * Float64(-0.3333333333333333 / y)));
	elseif (x <= 1.35)
		tmp = Float64(Float64(Float64(x * -1.3333333333333333) + 1.0) / y);
	else
		tmp = Float64(Float64(x / y) * Float64(-1.0 + Float64(x * 0.3333333333333333)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2.3)
		tmp = (3.0 - x) * (x * (-0.3333333333333333 / y));
	elseif (x <= 1.35)
		tmp = ((x * -1.3333333333333333) + 1.0) / y;
	else
		tmp = (x / y) * (-1.0 + (x * 0.3333333333333333));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2.3], N[(N[(3.0 - x), $MachinePrecision] * N[(x * N[(-0.3333333333333333 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.35], N[(N[(N[(x * -1.3333333333333333), $MachinePrecision] + 1.0), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / y), $MachinePrecision] * N[(-1.0 + N[(x * 0.3333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.2999999999999998

   1. Initial program 93.0%

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

      1. associate-*l/ 99.7%

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

      2. *-commutative 99.7%

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

      3. *-rgt-identity 99.7%

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

      4. associate-*l* 99.7%

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

      5. metadata-eval 99.7%

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

      6. times-frac 99.7%

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

      7. *-commutative 99.7%

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

      8. neg-mul-1 99.7%

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

      9. distribute-rgt-neg-in 99.7%

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

      10. times-frac 99.6%

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

      11. metadata-eval 99.6%

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

      12. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around inf 97.9%

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

      1. metadata-eval 97.9%

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

      2. distribute-lft-neg-in 97.9%

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

      3. associate-*r/ 97.9%

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

      4. associate-*l/ 97.9%

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

      5. distribute-lft-neg-in 97.9%

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

      6. distribute-neg-frac 97.9%

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

      7. metadata-eval 97.9%

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

   7. Simplified 97.9%

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

   if -2.2999999999999998 < x < 1.3500000000000001

   1. Initial program 99.6%

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

      1. associate-*l/ 99.3%

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

      2. *-commutative 99.3%

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

      3. *-rgt-identity 99.3%

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

      4. associate-*l* 99.3%

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

      5. metadata-eval 99.3%

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

      6. times-frac 99.3%

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

      7. *-commutative 99.3%

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

      8. neg-mul-1 99.3%

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

      9. distribute-rgt-neg-in 99.3%

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

      10. times-frac 99.5%

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

      11. metadata-eval 99.5%

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

      12. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around 0 99.8%

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

   6. Taylor expanded in y around 0 99.8%

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

   if 1.3500000000000001 < x

   1. Initial program 91.1%

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

      1. associate-*l/ 98.4%

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

      2. *-commutative 98.4%

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

      3. *-rgt-identity 98.4%

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

      4. associate-*l* 98.4%

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

      5. metadata-eval 98.4%

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

      6. times-frac 98.4%

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

      7. *-commutative 98.4%

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

      8. neg-mul-1 98.4%

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

      9. distribute-rgt-neg-in 98.4%

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

      10. times-frac 99.8%

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

      11. metadata-eval 99.8%

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

      12. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 98.9%

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

      1. metadata-eval 98.9%

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

      2. distribute-lft-neg-in 98.9%

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

      3. associate-*r/ 98.9%

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

      4. associate-*l/ 98.8%

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

      5. distribute-lft-neg-in 98.8%

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

      6. distribute-neg-frac 98.8%

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

      7. metadata-eval 98.8%

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

   7. Simplified 98.8%

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

   8. Taylor expanded in x around 0 67.9%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{y} + 0.3333333333333333 \cdot \frac{{x}^{2}}{y}} \]
   9. Step-by-step derivation

      1. metadata-eval 67.9%

         \[\leadsto \color{blue}{\left(3 \cdot -0.3333333333333333\right)} \cdot \frac{x}{y} + 0.3333333333333333 \cdot \frac{{x}^{2}}{y} \]

      2. associate-*r* 67.9%

         \[\leadsto \color{blue}{3 \cdot \left(-0.3333333333333333 \cdot \frac{x}{y}\right)} + 0.3333333333333333 \cdot \frac{{x}^{2}}{y} \]

      3. associate-*r/ 67.9%

         \[\leadsto 3 \cdot \color{blue}{\frac{-0.3333333333333333 \cdot x}{y}} + 0.3333333333333333 \cdot \frac{{x}^{2}}{y} \]

      4. *-commutative 67.9%

         \[\leadsto 3 \cdot \frac{\color{blue}{x \cdot -0.3333333333333333}}{y} + 0.3333333333333333 \cdot \frac{{x}^{2}}{y} \]

      5. associate-*r/ 67.9%

         \[\leadsto 3 \cdot \frac{x \cdot -0.3333333333333333}{y} + \color{blue}{\frac{0.3333333333333333 \cdot {x}^{2}}{y}} \]

      6. unpow2 67.9%

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

      7. associate-*r* 67.9%

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

      8. *-commutative 67.9%

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

      9. metadata-eval 67.9%

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

      10. distribute-rgt-neg-in 67.9%

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

      11. distribute-lft-neg-in 67.9%

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

      12. associate-*r* 67.9%

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

      13. *-commutative 67.9%

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

      14. associate-*r/ 76.5%

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

      15. distribute-rgt-out 98.9%

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

      16. sub-neg 98.9%

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

      17. associate-*l/ 98.9%

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

      18. associate-*l* 99.0%

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

      19. sub-neg 99.0%

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

      20. distribute-rgt-in 99.0%

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

      21. metadata-eval 99.0%

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

      22. distribute-lft-neg-in 99.0%

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

      23. distribute-rgt-neg-in 99.0%

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

      24. metadata-eval 99.0%

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

   10. Simplified 99.0%

       \[\leadsto \color{blue}{\frac{x}{y} \cdot \left(-1 + x \cdot 0.3333333333333333\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3:\\ \;\;\;\;\left(3 - x\right) \cdot \left(x \cdot \frac{-0.3333333333333333}{y}\right)\\ \mathbf{elif}\;x \leq 1.35:\\ \;\;\;\;\frac{x \cdot -1.3333333333333333 + 1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(-1 + x \cdot 0.3333333333333333\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 98.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.3:\\ \;\;\;\;\frac{3 - x}{-3 \cdot \frac{y}{x}}\\ \mathbf{elif}\;x \leq 1.35:\\ \;\;\;\;\frac{x \cdot -1.3333333333333333 + 1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(-1 + x \cdot 0.3333333333333333\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2.3)
   (/ (- 3.0 x) (* -3.0 (/ y x)))
   (if (<= x 1.35)
     (/ (+ (* x -1.3333333333333333) 1.0) y)
     (* (/ x y) (+ -1.0 (* x 0.3333333333333333))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.3) {
		tmp = (3.0 - x) / (-3.0 * (y / x));
	} else if (x <= 1.35) {
		tmp = ((x * -1.3333333333333333) + 1.0) / y;
	} else {
		tmp = (x / y) * (-1.0 + (x * 0.3333333333333333));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-2.3d0)) then
        tmp = (3.0d0 - x) / ((-3.0d0) * (y / x))
    else if (x <= 1.35d0) then
        tmp = ((x * (-1.3333333333333333d0)) + 1.0d0) / y
    else
        tmp = (x / y) * ((-1.0d0) + (x * 0.3333333333333333d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -2.3) {
		tmp = (3.0 - x) / (-3.0 * (y / x));
	} else if (x <= 1.35) {
		tmp = ((x * -1.3333333333333333) + 1.0) / y;
	} else {
		tmp = (x / y) * (-1.0 + (x * 0.3333333333333333));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2.3:
		tmp = (3.0 - x) / (-3.0 * (y / x))
	elif x <= 1.35:
		tmp = ((x * -1.3333333333333333) + 1.0) / y
	else:
		tmp = (x / y) * (-1.0 + (x * 0.3333333333333333))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2.3)
		tmp = Float64(Float64(3.0 - x) / Float64(-3.0 * Float64(y / x)));
	elseif (x <= 1.35)
		tmp = Float64(Float64(Float64(x * -1.3333333333333333) + 1.0) / y);
	else
		tmp = Float64(Float64(x / y) * Float64(-1.0 + Float64(x * 0.3333333333333333)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2.3)
		tmp = (3.0 - x) / (-3.0 * (y / x));
	elseif (x <= 1.35)
		tmp = ((x * -1.3333333333333333) + 1.0) / y;
	else
		tmp = (x / y) * (-1.0 + (x * 0.3333333333333333));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2.3], N[(N[(3.0 - x), $MachinePrecision] / N[(-3.0 * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.35], N[(N[(N[(x * -1.3333333333333333), $MachinePrecision] + 1.0), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / y), $MachinePrecision] * N[(-1.0 + N[(x * 0.3333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.2999999999999998

   1. Initial program 93.0%

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

      1. associate-*l/ 99.7%

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

      2. *-commutative 99.7%

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

      3. *-rgt-identity 99.7%

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

      4. associate-*l* 99.7%

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

      5. metadata-eval 99.7%

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

      6. times-frac 99.7%

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

      7. *-commutative 99.7%

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

      8. neg-mul-1 99.7%

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

      9. distribute-rgt-neg-in 99.7%

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

      10. times-frac 99.6%

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

      11. metadata-eval 99.6%

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

      12. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around inf 97.9%

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

      1. metadata-eval 97.9%

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

      2. distribute-lft-neg-in 97.9%

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

      3. associate-*r/ 97.9%

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

      4. associate-*l/ 97.9%

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

      5. distribute-lft-neg-in 97.9%

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

      6. distribute-neg-frac 97.9%

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

      7. metadata-eval 97.9%

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

   7. Simplified 97.9%

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

      1. *-commutative 97.9%

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

      2. associate-*r/ 97.9%

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

   9. Applied egg-rr 97.9%

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

       1. clear-num 97.8%

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

       2. un-div-inv 97.9%

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

       3. *-un-lft-identity 97.9%

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

       4. *-commutative 97.9%

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

       5. times-frac 98.0%

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

       6. metadata-eval 98.0%

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

   11. Applied egg-rr 98.0%

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

   if -2.2999999999999998 < x < 1.3500000000000001

   1. Initial program 99.6%

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

      1. associate-*l/ 99.3%

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

      2. *-commutative 99.3%

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

      3. *-rgt-identity 99.3%

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

      4. associate-*l* 99.3%

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

      5. metadata-eval 99.3%

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

      6. times-frac 99.3%

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

      7. *-commutative 99.3%

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

      8. neg-mul-1 99.3%

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

      9. distribute-rgt-neg-in 99.3%

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

      10. times-frac 99.5%

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

      11. metadata-eval 99.5%

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

      12. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around 0 99.8%

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

   6. Taylor expanded in y around 0 99.8%

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

   if 1.3500000000000001 < x

   1. Initial program 91.1%

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

      1. associate-*l/ 98.4%

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

      2. *-commutative 98.4%

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

      3. *-rgt-identity 98.4%

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

      4. associate-*l* 98.4%

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

      5. metadata-eval 98.4%

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

      6. times-frac 98.4%

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

      7. *-commutative 98.4%

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

      8. neg-mul-1 98.4%

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

      9. distribute-rgt-neg-in 98.4%

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

      10. times-frac 99.8%

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

      11. metadata-eval 99.8%

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

      12. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 98.9%

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

      1. metadata-eval 98.9%

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

      2. distribute-lft-neg-in 98.9%

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

      3. associate-*r/ 98.9%

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

      4. associate-*l/ 98.8%

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

      5. distribute-lft-neg-in 98.8%

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

      6. distribute-neg-frac 98.8%

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

      7. metadata-eval 98.8%

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

   7. Simplified 98.8%

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

   8. Taylor expanded in x around 0 67.9%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{y} + 0.3333333333333333 \cdot \frac{{x}^{2}}{y}} \]
   9. Step-by-step derivation

      1. metadata-eval 67.9%

         \[\leadsto \color{blue}{\left(3 \cdot -0.3333333333333333\right)} \cdot \frac{x}{y} + 0.3333333333333333 \cdot \frac{{x}^{2}}{y} \]

      2. associate-*r* 67.9%

         \[\leadsto \color{blue}{3 \cdot \left(-0.3333333333333333 \cdot \frac{x}{y}\right)} + 0.3333333333333333 \cdot \frac{{x}^{2}}{y} \]

      3. associate-*r/ 67.9%

         \[\leadsto 3 \cdot \color{blue}{\frac{-0.3333333333333333 \cdot x}{y}} + 0.3333333333333333 \cdot \frac{{x}^{2}}{y} \]

      4. *-commutative 67.9%

         \[\leadsto 3 \cdot \frac{\color{blue}{x \cdot -0.3333333333333333}}{y} + 0.3333333333333333 \cdot \frac{{x}^{2}}{y} \]

      5. associate-*r/ 67.9%

         \[\leadsto 3 \cdot \frac{x \cdot -0.3333333333333333}{y} + \color{blue}{\frac{0.3333333333333333 \cdot {x}^{2}}{y}} \]

      6. unpow2 67.9%

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

      7. associate-*r* 67.9%

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

      8. *-commutative 67.9%

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

      9. metadata-eval 67.9%

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

      10. distribute-rgt-neg-in 67.9%

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

      11. distribute-lft-neg-in 67.9%

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

      12. associate-*r* 67.9%

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

      13. *-commutative 67.9%

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

      14. associate-*r/ 76.5%

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

      15. distribute-rgt-out 98.9%

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

      16. sub-neg 98.9%

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

      17. associate-*l/ 98.9%

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

      18. associate-*l* 99.0%

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

      19. sub-neg 99.0%

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

      20. distribute-rgt-in 99.0%

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

      21. metadata-eval 99.0%

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

      22. distribute-lft-neg-in 99.0%

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

      23. distribute-rgt-neg-in 99.0%

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

      24. metadata-eval 99.0%

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

   10. Simplified 99.0%

       \[\leadsto \color{blue}{\frac{x}{y} \cdot \left(-1 + x \cdot 0.3333333333333333\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3:\\ \;\;\;\;\frac{3 - x}{-3 \cdot \frac{y}{x}}\\ \mathbf{elif}\;x \leq 1.35:\\ \;\;\;\;\frac{x \cdot -1.3333333333333333 + 1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(-1 + x \cdot 0.3333333333333333\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 98.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.3:\\ \;\;\;\;\frac{x}{y} \cdot \frac{x - 3}{3}\\ \mathbf{elif}\;x \leq 1.35:\\ \;\;\;\;\frac{x \cdot -1.3333333333333333 + 1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(-1 + x \cdot 0.3333333333333333\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2.3)
   (* (/ x y) (/ (- x 3.0) 3.0))
   (if (<= x 1.35)
     (/ (+ (* x -1.3333333333333333) 1.0) y)
     (* (/ x y) (+ -1.0 (* x 0.3333333333333333))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.3) {
		tmp = (x / y) * ((x - 3.0) / 3.0);
	} else if (x <= 1.35) {
		tmp = ((x * -1.3333333333333333) + 1.0) / y;
	} else {
		tmp = (x / y) * (-1.0 + (x * 0.3333333333333333));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-2.3d0)) then
        tmp = (x / y) * ((x - 3.0d0) / 3.0d0)
    else if (x <= 1.35d0) then
        tmp = ((x * (-1.3333333333333333d0)) + 1.0d0) / y
    else
        tmp = (x / y) * ((-1.0d0) + (x * 0.3333333333333333d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -2.3) {
		tmp = (x / y) * ((x - 3.0) / 3.0);
	} else if (x <= 1.35) {
		tmp = ((x * -1.3333333333333333) + 1.0) / y;
	} else {
		tmp = (x / y) * (-1.0 + (x * 0.3333333333333333));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2.3:
		tmp = (x / y) * ((x - 3.0) / 3.0)
	elif x <= 1.35:
		tmp = ((x * -1.3333333333333333) + 1.0) / y
	else:
		tmp = (x / y) * (-1.0 + (x * 0.3333333333333333))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2.3)
		tmp = Float64(Float64(x / y) * Float64(Float64(x - 3.0) / 3.0));
	elseif (x <= 1.35)
		tmp = Float64(Float64(Float64(x * -1.3333333333333333) + 1.0) / y);
	else
		tmp = Float64(Float64(x / y) * Float64(-1.0 + Float64(x * 0.3333333333333333)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2.3)
		tmp = (x / y) * ((x - 3.0) / 3.0);
	elseif (x <= 1.35)
		tmp = ((x * -1.3333333333333333) + 1.0) / y;
	else
		tmp = (x / y) * (-1.0 + (x * 0.3333333333333333));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2.3], N[(N[(x / y), $MachinePrecision] * N[(N[(x - 3.0), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.35], N[(N[(N[(x * -1.3333333333333333), $MachinePrecision] + 1.0), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / y), $MachinePrecision] * N[(-1.0 + N[(x * 0.3333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.2999999999999998

   1. Initial program 93.0%

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

      1. times-frac 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 98.1%

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

      1. neg-mul-1 98.1%

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

      2. distribute-neg-frac 98.1%

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

   7. Simplified 98.1%

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

   if -2.2999999999999998 < x < 1.3500000000000001

   1. Initial program 99.6%

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

      1. associate-*l/ 99.3%

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

      2. *-commutative 99.3%

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

      3. *-rgt-identity 99.3%

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

      4. associate-*l* 99.3%

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

      5. metadata-eval 99.3%

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

      6. times-frac 99.3%

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

      7. *-commutative 99.3%

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

      8. neg-mul-1 99.3%

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

      9. distribute-rgt-neg-in 99.3%

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

      10. times-frac 99.5%

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

      11. metadata-eval 99.5%

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

      12. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around 0 99.8%

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

   6. Taylor expanded in y around 0 99.8%

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

   if 1.3500000000000001 < x

   1. Initial program 91.1%

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

      1. associate-*l/ 98.4%

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

      2. *-commutative 98.4%

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

      3. *-rgt-identity 98.4%

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

      4. associate-*l* 98.4%

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

      5. metadata-eval 98.4%

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

      6. times-frac 98.4%

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

      7. *-commutative 98.4%

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

      8. neg-mul-1 98.4%

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

      9. distribute-rgt-neg-in 98.4%

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

      10. times-frac 99.8%

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

      11. metadata-eval 99.8%

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

      12. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 98.9%

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

      1. metadata-eval 98.9%

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

      2. distribute-lft-neg-in 98.9%

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

      3. associate-*r/ 98.9%

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

      4. associate-*l/ 98.8%

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

      5. distribute-lft-neg-in 98.8%

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

      6. distribute-neg-frac 98.8%

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

      7. metadata-eval 98.8%

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

   7. Simplified 98.8%

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

   8. Taylor expanded in x around 0 67.9%

      \[\leadsto \color{blue}{-1 \cdot \frac{x}{y} + 0.3333333333333333 \cdot \frac{{x}^{2}}{y}} \]
   9. Step-by-step derivation

      1. metadata-eval 67.9%

         \[\leadsto \color{blue}{\left(3 \cdot -0.3333333333333333\right)} \cdot \frac{x}{y} + 0.3333333333333333 \cdot \frac{{x}^{2}}{y} \]

      2. associate-*r* 67.9%

         \[\leadsto \color{blue}{3 \cdot \left(-0.3333333333333333 \cdot \frac{x}{y}\right)} + 0.3333333333333333 \cdot \frac{{x}^{2}}{y} \]

      3. associate-*r/ 67.9%

         \[\leadsto 3 \cdot \color{blue}{\frac{-0.3333333333333333 \cdot x}{y}} + 0.3333333333333333 \cdot \frac{{x}^{2}}{y} \]

      4. *-commutative 67.9%

         \[\leadsto 3 \cdot \frac{\color{blue}{x \cdot -0.3333333333333333}}{y} + 0.3333333333333333 \cdot \frac{{x}^{2}}{y} \]

      5. associate-*r/ 67.9%

         \[\leadsto 3 \cdot \frac{x \cdot -0.3333333333333333}{y} + \color{blue}{\frac{0.3333333333333333 \cdot {x}^{2}}{y}} \]

      6. unpow2 67.9%

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

      7. associate-*r* 67.9%

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

      8. *-commutative 67.9%

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

      9. metadata-eval 67.9%

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

      10. distribute-rgt-neg-in 67.9%

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

      11. distribute-lft-neg-in 67.9%

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

      12. associate-*r* 67.9%

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

      13. *-commutative 67.9%

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

      14. associate-*r/ 76.5%

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

      15. distribute-rgt-out 98.9%

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

      16. sub-neg 98.9%

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

      17. associate-*l/ 98.9%

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

      18. associate-*l* 99.0%

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

      19. sub-neg 99.0%

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

      20. distribute-rgt-in 99.0%

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

      21. metadata-eval 99.0%

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

      22. distribute-lft-neg-in 99.0%

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

      23. distribute-rgt-neg-in 99.0%

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

      24. metadata-eval 99.0%

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

   10. Simplified 99.0%

       \[\leadsto \color{blue}{\frac{x}{y} \cdot \left(-1 + x \cdot 0.3333333333333333\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3:\\ \;\;\;\;\frac{x}{y} \cdot \frac{x - 3}{3}\\ \mathbf{elif}\;x \leq 1.35:\\ \;\;\;\;\frac{x \cdot -1.3333333333333333 + 1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(-1 + x \cdot 0.3333333333333333\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 64.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.75:\\ \;\;\;\;-1.3333333333333333 \cdot \frac{x}{y}\\ \mathbf{elif}\;x \leq 0.5:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -0.75)
   (* -1.3333333333333333 (/ x y))
   (if (<= x 0.5) (/ 1.0 y) (* 0.3333333333333333 (/ x y)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -0.75) {
		tmp = -1.3333333333333333 * (x / y);
	} else if (x <= 0.5) {
		tmp = 1.0 / y;
	} else {
		tmp = 0.3333333333333333 * (x / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-0.75d0)) then
        tmp = (-1.3333333333333333d0) * (x / y)
    else if (x <= 0.5d0) then
        tmp = 1.0d0 / y
    else
        tmp = 0.3333333333333333d0 * (x / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -0.75) {
		tmp = -1.3333333333333333 * (x / y);
	} else if (x <= 0.5) {
		tmp = 1.0 / y;
	} else {
		tmp = 0.3333333333333333 * (x / y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -0.75:
		tmp = -1.3333333333333333 * (x / y)
	elif x <= 0.5:
		tmp = 1.0 / y
	else:
		tmp = 0.3333333333333333 * (x / y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -0.75)
		tmp = Float64(-1.3333333333333333 * Float64(x / y));
	elseif (x <= 0.5)
		tmp = Float64(1.0 / y);
	else
		tmp = Float64(0.3333333333333333 * Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -0.75)
		tmp = -1.3333333333333333 * (x / y);
	elseif (x <= 0.5)
		tmp = 1.0 / y;
	else
		tmp = 0.3333333333333333 * (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -0.75], N[(-1.3333333333333333 * N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 0.5], N[(1.0 / y), $MachinePrecision], N[(0.3333333333333333 * N[(x / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -0.75

   1. Initial program 93.0%

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

      1. associate-*l/ 99.7%

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

      2. *-commutative 99.7%

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

      3. *-rgt-identity 99.7%

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

      4. associate-*l* 99.7%

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

      5. metadata-eval 99.7%

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

      6. times-frac 99.7%

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

      7. *-commutative 99.7%

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

      8. neg-mul-1 99.7%

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

      9. distribute-rgt-neg-in 99.7%

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

      10. times-frac 99.6%

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

      11. metadata-eval 99.6%

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

      12. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around 0 22.1%

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

   6. Taylor expanded in x around inf 22.1%

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

   if -0.75 < x < 0.5

   1. Initial program 99.6%

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

      1. associate-*l/ 99.3%

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

      2. *-commutative 99.3%

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

      3. *-rgt-identity 99.3%

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

      4. associate-*l* 99.3%

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

      5. metadata-eval 99.3%

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

      6. times-frac 99.3%

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

      7. *-commutative 99.3%

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

      8. neg-mul-1 99.3%

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

      9. distribute-rgt-neg-in 99.3%

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

      10. times-frac 99.5%

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

      11. metadata-eval 99.5%

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

      12. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around 0 98.9%

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

   if 0.5 < x

   1. Initial program 91.1%

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

      1. associate-*l/ 98.4%

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

      2. *-commutative 98.4%

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

      3. *-rgt-identity 98.4%

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

      4. associate-*l* 98.4%

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

      5. metadata-eval 98.4%

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

      6. times-frac 98.4%

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

      7. *-commutative 98.4%

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

      8. neg-mul-1 98.4%

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

      9. distribute-rgt-neg-in 98.4%

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

      10. times-frac 99.8%

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

      11. metadata-eval 99.8%

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

      12. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0 0.7%

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

      1. add-sqr-sqrt 0.5%

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

      2. sqrt-unprod 11.5%

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

      3. frac-times 11.5%

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

      4. metadata-eval 11.5%

         \[\leadsto \left(3 - x\right) \cdot \sqrt{\frac{\color{blue}{0.1111111111111111}}{y \cdot y}} \]

      5. metadata-eval 11.5%

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

      6. frac-times 11.5%

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

      7. sqrt-unprod 10.0%

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

      8. add-sqr-sqrt 27.2%

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

      9. associate-*r/ 27.2%

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

   7. Applied egg-rr 27.2%

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

   8. Taylor expanded in x around inf 27.2%

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

      1. *-commutative 27.2%

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

   10. Simplified 27.2%

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

4. Final simplification 61.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.75:\\ \;\;\;\;-1.3333333333333333 \cdot \frac{x}{y}\\ \mathbf{elif}\;x \leq 0.5:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 63.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 3:\\ \;\;\;\;0.3333333333333333 \cdot \frac{3 - x}{y}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if x < 3

   1. Initial program 97.6%

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

      1. associate-*l/ 99.4%

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

      2. *-commutative 99.4%

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

      3. *-rgt-identity 99.4%

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

      4. associate-*l* 99.4%

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

      5. metadata-eval 99.4%

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

      6. times-frac 99.4%

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

      7. *-commutative 99.4%

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

      8. neg-mul-1 99.4%

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

      9. distribute-rgt-neg-in 99.4%

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

      10. times-frac 99.5%

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

      11. metadata-eval 99.5%

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

      12. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around 0 75.5%

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

   6. Taylor expanded in x around 0 75.9%

      \[\leadsto \color{blue}{-0.3333333333333333 \cdot \frac{x}{y} + \frac{1}{y}} \]
   7. Step-by-step derivation

      1. associate-*r/ 75.9%

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

      2. metadata-eval 75.9%

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

      3. associate-*r* 75.9%

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

      4. neg-mul-1 75.9%

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

      5. associate-*l/ 75.9%

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

      6. +-commutative 75.9%

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

      7. metadata-eval 75.9%

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

      8. associate-*l/ 75.5%

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

      9. distribute-lft-out 75.5%

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

      10. sub-neg 75.5%

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

      11. associate-*l/ 75.9%

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

      12. associate-*r/ 75.6%

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

   8. Simplified 75.6%

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

   if 3 < x

   1. Initial program 91.1%

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

      1. associate-*l/ 98.4%

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

      2. *-commutative 98.4%

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

      3. *-rgt-identity 98.4%

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

      4. associate-*l* 98.4%

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

      5. metadata-eval 98.4%

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

      6. times-frac 98.4%

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

      7. *-commutative 98.4%

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

      8. neg-mul-1 98.4%

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

      9. distribute-rgt-neg-in 98.4%

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

      10. times-frac 99.8%

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

      11. metadata-eval 99.8%

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

      12. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0 0.7%

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

      1. add-sqr-sqrt 0.5%

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

      2. sqrt-unprod 11.5%

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

      3. frac-times 11.5%

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

      4. metadata-eval 11.5%

         \[\leadsto \left(3 - x\right) \cdot \sqrt{\frac{\color{blue}{0.1111111111111111}}{y \cdot y}} \]

      5. metadata-eval 11.5%

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

      6. frac-times 11.5%

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

      7. sqrt-unprod 10.0%

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

      8. add-sqr-sqrt 27.2%

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

      9. associate-*r/ 27.2%

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

   7. Applied egg-rr 27.2%

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

   8. Taylor expanded in x around inf 27.2%

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

      1. *-commutative 27.2%

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

   10. Simplified 27.2%

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

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 3:\\ \;\;\;\;0.3333333333333333 \cdot \frac{3 - x}{y}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 64.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 3:\\ \;\;\;\;\frac{x \cdot -1.3333333333333333 + 1}{y}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if x < 3

   1. Initial program 97.6%

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

      1. associate-*l/ 99.4%

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

      2. *-commutative 99.4%

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

      3. *-rgt-identity 99.4%

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

      4. associate-*l* 99.4%

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

      5. metadata-eval 99.4%

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

      6. times-frac 99.4%

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

      7. *-commutative 99.4%

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

      8. neg-mul-1 99.4%

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

      9. distribute-rgt-neg-in 99.4%

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

      10. times-frac 99.5%

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

      11. metadata-eval 99.5%

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

      12. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around 0 76.4%

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

   6. Taylor expanded in y around 0 76.4%

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

   if 3 < x

   1. Initial program 91.1%

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

      1. associate-*l/ 98.4%

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

      2. *-commutative 98.4%

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

      3. *-rgt-identity 98.4%

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

      4. associate-*l* 98.4%

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

      5. metadata-eval 98.4%

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

      6. times-frac 98.4%

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

      7. *-commutative 98.4%

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

      8. neg-mul-1 98.4%

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

      9. distribute-rgt-neg-in 98.4%

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

      10. times-frac 99.8%

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

      11. metadata-eval 99.8%

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

      12. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0 0.7%

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

      1. add-sqr-sqrt 0.5%

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

      2. sqrt-unprod 11.5%

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

      3. frac-times 11.5%

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

      4. metadata-eval 11.5%

         \[\leadsto \left(3 - x\right) \cdot \sqrt{\frac{\color{blue}{0.1111111111111111}}{y \cdot y}} \]

      5. metadata-eval 11.5%

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

      6. frac-times 11.5%

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

      7. sqrt-unprod 10.0%

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

      8. add-sqr-sqrt 27.2%

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

      9. associate-*r/ 27.2%

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

   7. Applied egg-rr 27.2%

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

   8. Taylor expanded in x around inf 27.2%

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

      1. *-commutative 27.2%

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

   10. Simplified 27.2%

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

4. Final simplification 61.8%

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

Alternative 10: 99.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (3.0d0 - x) * (((1.0d0 - x) / y) * 0.3333333333333333d0)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.7%

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

   1. associate-*l/ 99.1%

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

   2. *-commutative 99.1%

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

   3. *-rgt-identity 99.1%

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

   4. associate-*l* 99.1%

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

   5. metadata-eval 99.1%

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

   6. times-frac 99.1%

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

   7. *-commutative 99.1%

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

   8. neg-mul-1 99.1%

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

   9. distribute-rgt-neg-in 99.1%

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

   10. times-frac 99.6%

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

   11. metadata-eval 99.6%

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

   12. metadata-eval 99.6%

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

3. Simplified 99.6%

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

5. Final simplification 99.6%

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

Alternative 11: 57.8% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if x < -0.75

   1. Initial program 93.0%

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

      1. associate-*l/ 99.7%

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

      2. *-commutative 99.7%

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

      3. *-rgt-identity 99.7%

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

      4. associate-*l* 99.7%

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

      5. metadata-eval 99.7%

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

      6. times-frac 99.7%

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

      7. *-commutative 99.7%

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

      8. neg-mul-1 99.7%

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

      9. distribute-rgt-neg-in 99.7%

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

      10. times-frac 99.6%

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

      11. metadata-eval 99.6%

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

      12. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around 0 22.1%

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

   6. Taylor expanded in x around inf 22.1%

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

   if -0.75 < x

   1. Initial program 96.4%

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

      1. associate-*l/ 99.0%

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

      2. *-commutative 99.0%

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

      3. *-rgt-identity 99.0%

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

      4. associate-*l* 99.0%

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

      5. metadata-eval 99.0%

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

      6. times-frac 99.0%

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

      7. *-commutative 99.0%

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

      8. neg-mul-1 99.0%

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

      9. distribute-rgt-neg-in 99.0%

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

      10. times-frac 99.6%

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

      11. metadata-eval 99.6%

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

      12. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around 0 63.4%

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

4. Final simplification 54.7%

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

Alternative 12: 57.7% 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 93.0%

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

      1. associate-*l/ 99.7%

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

      2. *-commutative 99.7%

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

      3. *-rgt-identity 99.7%

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

      4. associate-*l* 99.7%

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

      5. metadata-eval 99.7%

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

      6. times-frac 99.7%

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

      7. *-commutative 99.7%

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

      8. neg-mul-1 99.7%

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

      9. distribute-rgt-neg-in 99.7%

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

      10. times-frac 99.6%

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

      11. metadata-eval 99.6%

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

      12. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around inf 97.9%

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

      1. metadata-eval 97.9%

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

      2. distribute-lft-neg-in 97.9%

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

      3. associate-*r/ 97.9%

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

      4. associate-*l/ 97.9%

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

      5. distribute-lft-neg-in 97.9%

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

      6. distribute-neg-frac 97.9%

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

      7. metadata-eval 97.9%

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

   7. Simplified 97.9%

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

   8. Taylor expanded in x around 0 22.1%

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

      1. associate-*r/ 22.1%

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

      2. neg-mul-1 22.1%

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

   10. Simplified 22.1%

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

   if -1 < x

   1. Initial program 96.4%

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

      1. associate-*l/ 99.0%

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

      2. *-commutative 99.0%

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

      3. *-rgt-identity 99.0%

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

      4. associate-*l* 99.0%

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

      5. metadata-eval 99.0%

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

      6. times-frac 99.0%

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

      7. *-commutative 99.0%

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

      8. neg-mul-1 99.0%

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

      9. distribute-rgt-neg-in 99.0%

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

      10. times-frac 99.6%

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

      11. metadata-eval 99.6%

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

      12. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around 0 63.4%

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

4. Final simplification 54.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;\frac{-x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{y}\\ \end{array} \]
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 95.7%

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

   1. associate-*l/ 99.1%

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

   2. *-commutative 99.1%

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

   3. *-rgt-identity 99.1%

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

   4. associate-*l* 99.1%

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

   5. metadata-eval 99.1%

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

   6. times-frac 99.1%

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

   7. *-commutative 99.1%

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

   8. neg-mul-1 99.1%

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

   9. distribute-rgt-neg-in 99.1%

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

   10. times-frac 99.6%

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

   11. metadata-eval 99.6%

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

   12. metadata-eval 99.6%

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

3. Simplified 99.6%

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

5. Taylor expanded in x around 0 51.0%

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

6. Final simplification 51.0%

   \[\leadsto \frac{1}{y} \]
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 2024027 
(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)))