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

Percentage Accurate: 93.8% → 99.8%

Time: 14.1s

Alternatives: 16

Speedup: 1.0×

• 25.2% 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 92.1%

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

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

Alternative 2: 98.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.3 \lor \neg \left(x \leq 1.3\right):\\ \;\;\;\;\left(3 - x\right) \cdot \left(\frac{x}{y} \cdot -0.3333333333333333\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \end{array} \end{array} \]

FPCore

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

C

double code(double x, double y) {
	double tmp;
	if ((x <= -2.3) || !(x <= 1.3)) {
		tmp = (3.0 - x) * ((x / y) * -0.3333333333333333);
	} else {
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-2.3d0)) .or. (.not. (x <= 1.3d0))) then
        tmp = (3.0d0 - x) * ((x / y) * (-0.3333333333333333d0))
    else
        tmp = (1.0d0 + (x * (-1.3333333333333333d0))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -2.3) || !(x <= 1.3)) {
		tmp = (3.0 - x) * ((x / y) * -0.3333333333333333);
	} else {
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -2.3) or not (x <= 1.3):
		tmp = (3.0 - x) * ((x / y) * -0.3333333333333333)
	else:
		tmp = (1.0 + (x * -1.3333333333333333)) / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -2.3) || !(x <= 1.3))
		tmp = Float64(Float64(3.0 - x) * Float64(Float64(x / y) * -0.3333333333333333));
	else
		tmp = Float64(Float64(1.0 + Float64(x * -1.3333333333333333)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -2.3) || ~((x <= 1.3)))
		tmp = (3.0 - x) * ((x / y) * -0.3333333333333333);
	else
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -2.3], N[Not[LessEqual[x, 1.3]], $MachinePrecision]], N[(N[(3.0 - x), $MachinePrecision] * N[(N[(x / y), $MachinePrecision] * -0.3333333333333333), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 + N[(x * -1.3333333333333333), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.2999999999999998 or 1.30000000000000004 < x

   1. Initial program 83.4%

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

      1. associate-*l/ 99.6%

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

      2. *-commutative 99.6%

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

      3. *-rgt-identity 99.6%

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

      4. associate-*l* 99.6%

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

      5. metadata-eval 99.6%

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

      6. times-frac 99.6%

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

      7. *-commutative 99.6%

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

      8. neg-mul-1 99.6%

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

      9. distribute-rgt-neg-in 99.6%

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

      10. times-frac 99.6%

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

      11. metadata-eval 99.6%

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

      12. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around inf 98.1%

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

   if -2.2999999999999998 < x < 1.30000000000000004

   1. Initial program 99.0%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   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 99.6%

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

      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 97.9%

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

   6. Taylor expanded in y around 0 97.8%

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

4. Final simplification 97.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3 \lor \neg \left(x \leq 1.3\right):\\ \;\;\;\;\left(3 - x\right) \cdot \left(\frac{x}{y} \cdot -0.3333333333333333\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.72 \lor \neg \left(x \leq 1.72\right):\\ \;\;\;\;\frac{x}{y} \cdot \left(0.3333333333333333 \cdot \left(x + -4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -1.72) (not (<= x 1.72)))
   (* (/ x y) (* 0.3333333333333333 (+ x -4.0)))
   (/ (+ 1.0 (* x -1.3333333333333333)) y)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -1.72) || !(x <= 1.72)) {
		tmp = (x / y) * (0.3333333333333333 * (x + -4.0));
	} else {
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-1.72d0)) .or. (.not. (x <= 1.72d0))) then
        tmp = (x / y) * (0.3333333333333333d0 * (x + (-4.0d0)))
    else
        tmp = (1.0d0 + (x * (-1.3333333333333333d0))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -1.72) || !(x <= 1.72)) {
		tmp = (x / y) * (0.3333333333333333 * (x + -4.0));
	} else {
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -1.72) or not (x <= 1.72):
		tmp = (x / y) * (0.3333333333333333 * (x + -4.0))
	else:
		tmp = (1.0 + (x * -1.3333333333333333)) / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -1.72) || !(x <= 1.72))
		tmp = Float64(Float64(x / y) * Float64(0.3333333333333333 * Float64(x + -4.0)));
	else
		tmp = Float64(Float64(1.0 + Float64(x * -1.3333333333333333)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -1.72) || ~((x <= 1.72)))
		tmp = (x / y) * (0.3333333333333333 * (x + -4.0));
	else
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -1.72], N[Not[LessEqual[x, 1.72]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] * N[(0.3333333333333333 * N[(x + -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 + N[(x * -1.3333333333333333), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.71999999999999997 or 1.71999999999999997 < x

   1. Initial program 83.4%

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

   3. Taylor expanded in x around inf 82.5%

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

      1. +-commutative 82.5%

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

      2. unpow2 82.5%

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

      3. distribute-rgt-out 82.5%

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

   5. Simplified 82.5%

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

      1. times-frac 98.8%

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

      2. div-inv 98.7%

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

      3. metadata-eval 98.7%

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

   7. Applied egg-rr 98.7%

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

   if -1.71999999999999997 < x < 1.71999999999999997

   1. Initial program 99.0%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   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 99.6%

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

      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 97.9%

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

   6. Taylor expanded in y around 0 97.8%

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

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.72 \lor \neg \left(x \leq 1.72\right):\\ \;\;\;\;\frac{x}{y} \cdot \left(0.3333333333333333 \cdot \left(x + -4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.72 \lor \neg \left(x \leq 1.72\right):\\ \;\;\;\;\frac{x}{y} \cdot \frac{x + -4}{3}\\ \mathbf{else}:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -1.72) (not (<= x 1.72)))
   (* (/ x y) (/ (+ x -4.0) 3.0))
   (/ (+ 1.0 (* x -1.3333333333333333)) y)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -1.72) || !(x <= 1.72)) {
		tmp = (x / y) * ((x + -4.0) / 3.0);
	} else {
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-1.72d0)) .or. (.not. (x <= 1.72d0))) then
        tmp = (x / y) * ((x + (-4.0d0)) / 3.0d0)
    else
        tmp = (1.0d0 + (x * (-1.3333333333333333d0))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -1.72) || !(x <= 1.72)) {
		tmp = (x / y) * ((x + -4.0) / 3.0);
	} else {
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -1.72) or not (x <= 1.72):
		tmp = (x / y) * ((x + -4.0) / 3.0)
	else:
		tmp = (1.0 + (x * -1.3333333333333333)) / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -1.72) || !(x <= 1.72))
		tmp = Float64(Float64(x / y) * Float64(Float64(x + -4.0) / 3.0));
	else
		tmp = Float64(Float64(1.0 + Float64(x * -1.3333333333333333)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -1.72) || ~((x <= 1.72)))
		tmp = (x / y) * ((x + -4.0) / 3.0);
	else
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -1.72], N[Not[LessEqual[x, 1.72]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] * N[(N[(x + -4.0), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 + N[(x * -1.3333333333333333), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.71999999999999997 or 1.71999999999999997 < x

   1. Initial program 83.4%

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

   3. Taylor expanded in x around inf 82.5%

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

      1. +-commutative 82.5%

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

      2. unpow2 82.5%

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

      3. distribute-rgt-out 82.5%

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

   5. Simplified 82.5%

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

   6. Taylor expanded in y around 0 82.3%

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

      1. metadata-eval 82.3%

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

      2. sub-neg 82.3%

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

      3. metadata-eval 82.3%

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

      4. times-frac 82.5%

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

      5. *-commutative 82.5%

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

      6. *-lft-identity 82.5%

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

      7. times-frac 98.8%

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

      8. +-commutative 98.8%

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

   8. Simplified 98.8%

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

   if -1.71999999999999997 < x < 1.71999999999999997

   1. Initial program 99.0%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   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 99.6%

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

      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 97.9%

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

   6. Taylor expanded in y around 0 97.8%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.72 \lor \neg \left(x \leq 1.72\right):\\ \;\;\;\;\frac{x}{y} \cdot \frac{x + -4}{3}\\ \mathbf{else}:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 98.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.72 \lor \neg \left(x \leq 1.72\right):\\ \;\;\;\;\frac{x}{y} \cdot \frac{x + -4}{3}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot -1.3333333333333333 + \frac{1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -1.72) (not (<= x 1.72)))
   (* (/ x y) (/ (+ x -4.0) 3.0))
   (+ (* (/ x y) -1.3333333333333333) (/ 1.0 y))))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -1.72) || !(x <= 1.72)) {
		tmp = (x / y) * ((x + -4.0) / 3.0);
	} else {
		tmp = ((x / y) * -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 <= (-1.72d0)) .or. (.not. (x <= 1.72d0))) then
        tmp = (x / y) * ((x + (-4.0d0)) / 3.0d0)
    else
        tmp = ((x / y) * (-1.3333333333333333d0)) + (1.0d0 / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -1.72) || !(x <= 1.72)) {
		tmp = (x / y) * ((x + -4.0) / 3.0);
	} else {
		tmp = ((x / y) * -1.3333333333333333) + (1.0 / y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -1.72) or not (x <= 1.72):
		tmp = (x / y) * ((x + -4.0) / 3.0)
	else:
		tmp = ((x / y) * -1.3333333333333333) + (1.0 / y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -1.72) || !(x <= 1.72))
		tmp = Float64(Float64(x / y) * Float64(Float64(x + -4.0) / 3.0));
	else
		tmp = Float64(Float64(Float64(x / y) * -1.3333333333333333) + Float64(1.0 / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -1.72) || ~((x <= 1.72)))
		tmp = (x / y) * ((x + -4.0) / 3.0);
	else
		tmp = ((x / y) * -1.3333333333333333) + (1.0 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -1.72], N[Not[LessEqual[x, 1.72]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] * N[(N[(x + -4.0), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x / y), $MachinePrecision] * -1.3333333333333333), $MachinePrecision] + N[(1.0 / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.71999999999999997 or 1.71999999999999997 < x

   1. Initial program 83.4%

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

   3. Taylor expanded in x around inf 82.5%

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

      1. +-commutative 82.5%

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

      2. unpow2 82.5%

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

      3. distribute-rgt-out 82.5%

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

   5. Simplified 82.5%

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

   6. Taylor expanded in y around 0 82.3%

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

      1. metadata-eval 82.3%

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

      2. sub-neg 82.3%

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

      3. metadata-eval 82.3%

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

      4. times-frac 82.5%

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

      5. *-commutative 82.5%

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

      6. *-lft-identity 82.5%

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

      7. times-frac 98.8%

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

      8. +-commutative 98.8%

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

   8. Simplified 98.8%

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

   if -1.71999999999999997 < x < 1.71999999999999997

   1. Initial program 99.0%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   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 99.6%

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

      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 97.9%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.72 \lor \neg \left(x \leq 1.72\right):\\ \;\;\;\;\frac{x}{y} \cdot \frac{x + -4}{3}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot -1.3333333333333333 + \frac{1}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 98.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.3:\\ \;\;\;\;\left(3 - x\right) \cdot \left(\frac{x}{y} \cdot -0.3333333333333333\right)\\ \mathbf{elif}\;x \leq 1.3:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(3 - x\right) \cdot \left(x \cdot \frac{-0.3333333333333333}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2.3)
   (* (- 3.0 x) (* (/ x y) -0.3333333333333333))
   (if (<= x 1.3)
     (/ (+ 1.0 (* x -1.3333333333333333)) y)
     (* (- 3.0 x) (* x (/ -0.3333333333333333 y))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.3) {
		tmp = (3.0 - x) * ((x / y) * -0.3333333333333333);
	} else if (x <= 1.3) {
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	} else {
		tmp = (3.0 - x) * (x * (-0.3333333333333333 / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-2.3d0)) then
        tmp = (3.0d0 - x) * ((x / y) * (-0.3333333333333333d0))
    else if (x <= 1.3d0) then
        tmp = (1.0d0 + (x * (-1.3333333333333333d0))) / y
    else
        tmp = (3.0d0 - x) * (x * ((-0.3333333333333333d0) / y))
    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 / y) * -0.3333333333333333);
	} else if (x <= 1.3) {
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	} else {
		tmp = (3.0 - x) * (x * (-0.3333333333333333 / y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2.3:
		tmp = (3.0 - x) * ((x / y) * -0.3333333333333333)
	elif x <= 1.3:
		tmp = (1.0 + (x * -1.3333333333333333)) / y
	else:
		tmp = (3.0 - x) * (x * (-0.3333333333333333 / y))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2.3)
		tmp = Float64(Float64(3.0 - x) * Float64(Float64(x / y) * -0.3333333333333333));
	elseif (x <= 1.3)
		tmp = Float64(Float64(1.0 + Float64(x * -1.3333333333333333)) / y);
	else
		tmp = Float64(Float64(3.0 - x) * Float64(x * Float64(-0.3333333333333333 / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2.3)
		tmp = (3.0 - x) * ((x / y) * -0.3333333333333333);
	elseif (x <= 1.3)
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	else
		tmp = (3.0 - x) * (x * (-0.3333333333333333 / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2.3], N[(N[(3.0 - x), $MachinePrecision] * N[(N[(x / y), $MachinePrecision] * -0.3333333333333333), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.3], N[(N[(1.0 + N[(x * -1.3333333333333333), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(3.0 - x), $MachinePrecision] * N[(x * N[(-0.3333333333333333 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.2999999999999998

   1. Initial program 86.6%

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

      1. associate-*l/ 99.5%

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

      2. *-commutative 99.5%

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

      3. *-rgt-identity 99.5%

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

      4. associate-*l* 99.5%

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

      5. metadata-eval 99.5%

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

      6. times-frac 99.5%

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

      7. *-commutative 99.5%

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

      8. neg-mul-1 99.5%

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

      9. distribute-rgt-neg-in 99.5%

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

      10. times-frac 99.5%

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

      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 inf 97.3%

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

   if -2.2999999999999998 < x < 1.30000000000000004

   1. Initial program 99.0%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   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 99.6%

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

      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 97.9%

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

   6. Taylor expanded in y around 0 97.8%

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

   if 1.30000000000000004 < x

   1. Initial program 80.9%

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

      1. associate-*l/ 99.7%

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

      2. *-commutative 99.7%

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

      3. *-rgt-identity 99.7%

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

      4. associate-*l* 99.7%

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

      5. metadata-eval 99.7%

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

      6. times-frac 99.7%

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

      7. *-commutative 99.7%

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

      8. neg-mul-1 99.7%

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

      9. distribute-rgt-neg-in 99.7%

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

      10. times-frac 99.6%

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

      11. metadata-eval 99.6%

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

      12. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around inf 98.6%

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

      1. metadata-eval 98.6%

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

      2. distribute-lft-neg-in 98.6%

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

      3. associate-*r/ 98.7%

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

      4. associate-*l/ 98.7%

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

      5. distribute-lft-neg-in 98.7%

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

      6. distribute-neg-frac 98.7%

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

      7. metadata-eval 98.7%

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

   7. Simplified 98.7%

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

4. Final simplification 97.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3:\\ \;\;\;\;\left(3 - x\right) \cdot \left(\frac{x}{y} \cdot -0.3333333333333333\right)\\ \mathbf{elif}\;x \leq 1.3:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(3 - x\right) \cdot \left(x \cdot \frac{-0.3333333333333333}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 98.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.3:\\ \;\;\;\;\left(3 - x\right) \cdot \frac{-0.3333333333333333}{\frac{y}{x}}\\ \mathbf{elif}\;x \leq 1.3:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(3 - x\right) \cdot \left(x \cdot \frac{-0.3333333333333333}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2.3)
   (* (- 3.0 x) (/ -0.3333333333333333 (/ y x)))
   (if (<= x 1.3)
     (/ (+ 1.0 (* x -1.3333333333333333)) y)
     (* (- 3.0 x) (* x (/ -0.3333333333333333 y))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.3) {
		tmp = (3.0 - x) * (-0.3333333333333333 / (y / x));
	} else if (x <= 1.3) {
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	} else {
		tmp = (3.0 - x) * (x * (-0.3333333333333333 / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-2.3d0)) then
        tmp = (3.0d0 - x) * ((-0.3333333333333333d0) / (y / x))
    else if (x <= 1.3d0) then
        tmp = (1.0d0 + (x * (-1.3333333333333333d0))) / y
    else
        tmp = (3.0d0 - x) * (x * ((-0.3333333333333333d0) / y))
    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) * (-0.3333333333333333 / (y / x));
	} else if (x <= 1.3) {
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	} else {
		tmp = (3.0 - x) * (x * (-0.3333333333333333 / y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2.3:
		tmp = (3.0 - x) * (-0.3333333333333333 / (y / x))
	elif x <= 1.3:
		tmp = (1.0 + (x * -1.3333333333333333)) / y
	else:
		tmp = (3.0 - x) * (x * (-0.3333333333333333 / y))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2.3)
		tmp = Float64(Float64(3.0 - x) * Float64(-0.3333333333333333 / Float64(y / x)));
	elseif (x <= 1.3)
		tmp = Float64(Float64(1.0 + Float64(x * -1.3333333333333333)) / y);
	else
		tmp = Float64(Float64(3.0 - x) * Float64(x * Float64(-0.3333333333333333 / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2.3)
		tmp = (3.0 - x) * (-0.3333333333333333 / (y / x));
	elseif (x <= 1.3)
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	else
		tmp = (3.0 - x) * (x * (-0.3333333333333333 / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2.3], N[(N[(3.0 - x), $MachinePrecision] * N[(-0.3333333333333333 / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.3], N[(N[(1.0 + N[(x * -1.3333333333333333), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(3.0 - x), $MachinePrecision] * N[(x * N[(-0.3333333333333333 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.2999999999999998

   1. Initial program 86.6%

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

      1. associate-*l/ 99.5%

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

      2. *-commutative 99.5%

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

      3. *-rgt-identity 99.5%

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

      4. associate-*l* 99.5%

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

      5. metadata-eval 99.5%

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

      6. times-frac 99.5%

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

      7. *-commutative 99.5%

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

      8. neg-mul-1 99.5%

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

      9. distribute-rgt-neg-in 99.5%

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

      10. times-frac 99.5%

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

      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 inf 97.3%

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

      1. metadata-eval 97.3%

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

      2. distribute-lft-neg-in 97.3%

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

      3. associate-*r/ 97.3%

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

      4. associate-*l/ 97.3%

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

      5. distribute-lft-neg-in 97.3%

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

      6. distribute-neg-frac 97.3%

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

      7. metadata-eval 97.3%

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

   7. Simplified 97.3%

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

      1. associate-*l/ 97.3%

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

      2. associate-/l* 97.4%

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

   9. Applied egg-rr 97.4%

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

   if -2.2999999999999998 < x < 1.30000000000000004

   1. Initial program 99.0%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   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 99.6%

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

      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 97.9%

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

   6. Taylor expanded in y around 0 97.8%

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

   if 1.30000000000000004 < x

   1. Initial program 80.9%

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

      1. associate-*l/ 99.7%

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

      2. *-commutative 99.7%

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

      3. *-rgt-identity 99.7%

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

      4. associate-*l* 99.7%

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

      5. metadata-eval 99.7%

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

      6. times-frac 99.7%

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

      7. *-commutative 99.7%

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

      8. neg-mul-1 99.7%

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

      9. distribute-rgt-neg-in 99.7%

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

      10. times-frac 99.6%

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

      11. metadata-eval 99.6%

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

      12. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around inf 98.6%

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

      1. metadata-eval 98.6%

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

      2. distribute-lft-neg-in 98.6%

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

      3. associate-*r/ 98.7%

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

      4. associate-*l/ 98.7%

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

      5. distribute-lft-neg-in 98.7%

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

      6. distribute-neg-frac 98.7%

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

      7. metadata-eval 98.7%

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

   7. Simplified 98.7%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3:\\ \;\;\;\;\left(3 - x\right) \cdot \frac{-0.3333333333333333}{\frac{y}{x}}\\ \mathbf{elif}\;x \leq 1.3:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(3 - x\right) \cdot \left(x \cdot \frac{-0.3333333333333333}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 98.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.3:\\ \;\;\;\;\left(3 - x\right) \cdot \frac{-0.3333333333333333}{\frac{y}{x}}\\ \mathbf{elif}\;x \leq 1.3:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(3 - x\right) \cdot \frac{x \cdot -0.3333333333333333}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2.3)
   (* (- 3.0 x) (/ -0.3333333333333333 (/ y x)))
   (if (<= x 1.3)
     (/ (+ 1.0 (* x -1.3333333333333333)) y)
     (* (- 3.0 x) (/ (* x -0.3333333333333333) y)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.3) {
		tmp = (3.0 - x) * (-0.3333333333333333 / (y / x));
	} else if (x <= 1.3) {
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	} else {
		tmp = (3.0 - x) * ((x * -0.3333333333333333) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-2.3d0)) then
        tmp = (3.0d0 - x) * ((-0.3333333333333333d0) / (y / x))
    else if (x <= 1.3d0) then
        tmp = (1.0d0 + (x * (-1.3333333333333333d0))) / y
    else
        tmp = (3.0d0 - x) * ((x * (-0.3333333333333333d0)) / y)
    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) * (-0.3333333333333333 / (y / x));
	} else if (x <= 1.3) {
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	} else {
		tmp = (3.0 - x) * ((x * -0.3333333333333333) / y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2.3:
		tmp = (3.0 - x) * (-0.3333333333333333 / (y / x))
	elif x <= 1.3:
		tmp = (1.0 + (x * -1.3333333333333333)) / y
	else:
		tmp = (3.0 - x) * ((x * -0.3333333333333333) / y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2.3)
		tmp = Float64(Float64(3.0 - x) * Float64(-0.3333333333333333 / Float64(y / x)));
	elseif (x <= 1.3)
		tmp = Float64(Float64(1.0 + Float64(x * -1.3333333333333333)) / y);
	else
		tmp = Float64(Float64(3.0 - x) * Float64(Float64(x * -0.3333333333333333) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2.3)
		tmp = (3.0 - x) * (-0.3333333333333333 / (y / x));
	elseif (x <= 1.3)
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	else
		tmp = (3.0 - x) * ((x * -0.3333333333333333) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2.3], N[(N[(3.0 - x), $MachinePrecision] * N[(-0.3333333333333333 / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.3], N[(N[(1.0 + N[(x * -1.3333333333333333), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(3.0 - x), $MachinePrecision] * N[(N[(x * -0.3333333333333333), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.2999999999999998

   1. Initial program 86.6%

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

      1. associate-*l/ 99.5%

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

      2. *-commutative 99.5%

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

      3. *-rgt-identity 99.5%

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

      4. associate-*l* 99.5%

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

      5. metadata-eval 99.5%

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

      6. times-frac 99.5%

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

      7. *-commutative 99.5%

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

      8. neg-mul-1 99.5%

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

      9. distribute-rgt-neg-in 99.5%

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

      10. times-frac 99.5%

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

      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 inf 97.3%

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

      1. metadata-eval 97.3%

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

      2. distribute-lft-neg-in 97.3%

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

      3. associate-*r/ 97.3%

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

      4. associate-*l/ 97.3%

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

      5. distribute-lft-neg-in 97.3%

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

      6. distribute-neg-frac 97.3%

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

      7. metadata-eval 97.3%

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

   7. Simplified 97.3%

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

      1. associate-*l/ 97.3%

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

      2. associate-/l* 97.4%

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

   9. Applied egg-rr 97.4%

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

   if -2.2999999999999998 < x < 1.30000000000000004

   1. Initial program 99.0%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   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 99.6%

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

      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 97.9%

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

   6. Taylor expanded in y around 0 97.8%

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

   if 1.30000000000000004 < x

   1. Initial program 80.9%

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

      1. associate-*l/ 99.7%

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

      2. *-commutative 99.7%

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

      3. *-rgt-identity 99.7%

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

      4. associate-*l* 99.7%

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

      5. metadata-eval 99.7%

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

      6. times-frac 99.7%

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

      7. *-commutative 99.7%

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

      8. neg-mul-1 99.7%

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

      9. distribute-rgt-neg-in 99.7%

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

      10. times-frac 99.6%

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

      11. metadata-eval 99.6%

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

      12. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around inf 98.6%

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

      1. metadata-eval 98.6%

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

      2. distribute-lft-neg-in 98.6%

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

      3. associate-*r/ 98.7%

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

      4. associate-*l/ 98.7%

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

      5. distribute-lft-neg-in 98.7%

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

      6. distribute-neg-frac 98.7%

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

      7. metadata-eval 98.7%

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

   7. Simplified 98.7%

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

      1. *-commutative 98.7%

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

      2. associate-*r/ 98.7%

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

   9. Applied egg-rr 98.7%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3:\\ \;\;\;\;\left(3 - x\right) \cdot \frac{-0.3333333333333333}{\frac{y}{x}}\\ \mathbf{elif}\;x \leq 1.3:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(3 - x\right) \cdot \frac{x \cdot -0.3333333333333333}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 97.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.72 \lor \neg \left(x \leq 5.2\right):\\ \;\;\;\;\frac{x \cdot 0.3333333333333333}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -1.72) (not (<= x 5.2)))
   (/ (* x 0.3333333333333333) (/ y x))
   (/ 1.0 y)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -1.72) || !(x <= 5.2)) {
		tmp = (x * 0.3333333333333333) / (y / x);
	} 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 <= (-1.72d0)) .or. (.not. (x <= 5.2d0))) then
        tmp = (x * 0.3333333333333333d0) / (y / x)
    else
        tmp = 1.0d0 / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -1.72) || !(x <= 5.2)) {
		tmp = (x * 0.3333333333333333) / (y / x);
	} else {
		tmp = 1.0 / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -1.72) or not (x <= 5.2):
		tmp = (x * 0.3333333333333333) / (y / x)
	else:
		tmp = 1.0 / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -1.72) || !(x <= 5.2))
		tmp = Float64(Float64(x * 0.3333333333333333) / Float64(y / x));
	else
		tmp = Float64(1.0 / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -1.72) || ~((x <= 5.2)))
		tmp = (x * 0.3333333333333333) / (y / x);
	else
		tmp = 1.0 / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -1.72], N[Not[LessEqual[x, 5.2]], $MachinePrecision]], N[(N[(x * 0.3333333333333333), $MachinePrecision] / N[(y / x), $MachinePrecision]), $MachinePrecision], N[(1.0 / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.71999999999999997 or 5.20000000000000018 < x

   1. Initial program 83.4%

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

   3. Taylor expanded in x around inf 82.5%

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

      1. +-commutative 82.5%

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

      2. unpow2 82.5%

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

      3. distribute-rgt-out 82.5%

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

   5. Simplified 82.5%

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

      1. times-frac 98.8%

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

      2. div-inv 98.7%

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

      3. metadata-eval 98.7%

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

   7. Applied egg-rr 98.7%

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

      1. *-commutative 98.7%

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

      2. clear-num 98.6%

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

      3. un-div-inv 98.7%

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

      4. *-commutative 98.7%

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

   9. Applied egg-rr 98.7%

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

   10. Taylor expanded in x around inf 98.0%

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

       1. *-commutative 98.0%

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

   12. Simplified 98.0%

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

   if -1.71999999999999997 < x < 5.20000000000000018

   1. Initial program 99.0%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   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 99.6%

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

      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 95.9%

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

4. Final simplification 96.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.72 \lor \neg \left(x \leq 5.2\right):\\ \;\;\;\;\frac{x \cdot 0.3333333333333333}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 98.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.8 \lor \neg \left(x \leq 0.65\right):\\ \;\;\;\;\frac{x \cdot 0.3333333333333333}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -4.8) (not (<= x 0.65)))
   (/ (* x 0.3333333333333333) (/ y x))
   (/ (+ 1.0 (* x -1.3333333333333333)) y)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -4.8) || !(x <= 0.65)) {
		tmp = (x * 0.3333333333333333) / (y / x);
	} else {
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-4.8d0)) .or. (.not. (x <= 0.65d0))) then
        tmp = (x * 0.3333333333333333d0) / (y / x)
    else
        tmp = (1.0d0 + (x * (-1.3333333333333333d0))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -4.8) || !(x <= 0.65)) {
		tmp = (x * 0.3333333333333333) / (y / x);
	} else {
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -4.8) or not (x <= 0.65):
		tmp = (x * 0.3333333333333333) / (y / x)
	else:
		tmp = (1.0 + (x * -1.3333333333333333)) / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -4.8) || !(x <= 0.65))
		tmp = Float64(Float64(x * 0.3333333333333333) / Float64(y / x));
	else
		tmp = Float64(Float64(1.0 + Float64(x * -1.3333333333333333)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -4.8) || ~((x <= 0.65)))
		tmp = (x * 0.3333333333333333) / (y / x);
	else
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -4.8], N[Not[LessEqual[x, 0.65]], $MachinePrecision]], N[(N[(x * 0.3333333333333333), $MachinePrecision] / N[(y / x), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 + N[(x * -1.3333333333333333), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.79999999999999982 or 0.650000000000000022 < x

   1. Initial program 83.4%

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

   3. Taylor expanded in x around inf 82.5%

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

      1. +-commutative 82.5%

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

      2. unpow2 82.5%

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

      3. distribute-rgt-out 82.5%

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

   5. Simplified 82.5%

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

      1. times-frac 98.8%

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

      2. div-inv 98.7%

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

      3. metadata-eval 98.7%

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

   7. Applied egg-rr 98.7%

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

      1. *-commutative 98.7%

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

      2. clear-num 98.6%

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

      3. un-div-inv 98.7%

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

      4. *-commutative 98.7%

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

   9. Applied egg-rr 98.7%

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

   10. Taylor expanded in x around inf 98.0%

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

       1. *-commutative 98.0%

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

   12. Simplified 98.0%

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

   if -4.79999999999999982 < x < 0.650000000000000022

   1. Initial program 99.0%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   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 99.6%

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

      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 97.9%

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

   6. Taylor expanded in y around 0 97.8%

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

4. Final simplification 97.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.8 \lor \neg \left(x \leq 0.65\right):\\ \;\;\;\;\frac{x \cdot 0.3333333333333333}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 63.6% accurate, 0.7× speedup

Math

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

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -0.75)
   (* x (/ -1.3333333333333333 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 = x * (-1.3333333333333333 / 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 = x * ((-1.3333333333333333d0) / 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 = x * (-1.3333333333333333 / 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 = x * (-1.3333333333333333 / 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(x * Float64(-1.3333333333333333 / 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 = x * (-1.3333333333333333 / 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[(x * N[(-1.3333333333333333 / 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 86.6%

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

      1. associate-*l/ 99.5%

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

      2. *-commutative 99.5%

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

      3. *-rgt-identity 99.5%

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

      4. associate-*l* 99.5%

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

      5. metadata-eval 99.5%

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

      6. times-frac 99.5%

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

      7. *-commutative 99.5%

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

      8. neg-mul-1 99.5%

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

      9. distribute-rgt-neg-in 99.5%

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

      10. times-frac 99.5%

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

      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 23.4%

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

   6. Taylor expanded in x around inf 23.4%

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

      1. associate-*r/ 23.4%

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

      2. associate-*l/ 23.4%

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

      3. *-commutative 23.4%

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

   8. Simplified 23.4%

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

   if -0.75 < x < 0.5

   1. Initial program 99.0%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   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 99.6%

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

      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 95.9%

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

   if 0.5 < x

   1. Initial program 80.9%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   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 0.8%

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

      1. add-sqr-sqrt 0.3%

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

      2. sqrt-unprod 21.0%

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

      3. frac-times 21.0%

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

      4. metadata-eval 21.0%

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

      5. metadata-eval 21.0%

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

      6. frac-times 21.0%

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

      7. sqrt-unprod 20.9%

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

      8. add-sqr-sqrt 33.8%

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

      9. frac-2neg 33.8%

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

      10. metadata-eval 33.8%

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

      11. associate-*r/ 33.8%

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

   7. Applied egg-rr 33.8%

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

      1. *-commutative 33.8%

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

      2. neg-mul-1 33.8%

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

      3. times-frac 33.8%

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

      4. metadata-eval 33.8%

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

   9. Simplified 33.8%

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

   10. Taylor expanded in x around inf 33.8%

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

       1. *-commutative 33.8%

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

   12. Simplified 33.8%

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

4. Final simplification 66.2%

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

Alternative 12: 63.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 0.54:\\ \;\;\;\;0.3333333333333333 \cdot \frac{3 - x}{y}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 0.54)
   (* 0.3333333333333333 (/ (- 3.0 x) y))
   (* 0.3333333333333333 (/ x y))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 0.54) {
		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 <= 0.54d0) 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 <= 0.54) {
		tmp = 0.3333333333333333 * ((3.0 - x) / y);
	} else {
		tmp = 0.3333333333333333 * (x / y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 0.54:
		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 <= 0.54)
		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 <= 0.54)
		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, 0.54], 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 < 0.54000000000000004

   1. Initial program 95.8%

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

      1. associate-*l/ 99.1%

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

      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 76.7%

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

   6. Taylor expanded in y around 0 76.7%

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

   if 0.54000000000000004 < x

   1. Initial program 80.9%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   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 0.8%

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

      1. add-sqr-sqrt 0.3%

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

      2. sqrt-unprod 21.0%

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

      3. frac-times 21.0%

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

      4. metadata-eval 21.0%

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

      5. metadata-eval 21.0%

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

      6. frac-times 21.0%

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

      7. sqrt-unprod 20.9%

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

      8. add-sqr-sqrt 33.8%

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

      9. frac-2neg 33.8%

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

      10. metadata-eval 33.8%

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

      11. associate-*r/ 33.8%

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

   7. Applied egg-rr 33.8%

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

      1. *-commutative 33.8%

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

      2. neg-mul-1 33.8%

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

      3. times-frac 33.8%

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

      4. metadata-eval 33.8%

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

   9. Simplified 33.8%

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

   10. Taylor expanded in x around inf 33.8%

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

       1. *-commutative 33.8%

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

   12. Simplified 33.8%

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

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 0.54:\\ \;\;\;\;0.3333333333333333 \cdot \frac{3 - x}{y}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 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 92.1%

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

   1. associate-*l/ 99.2%

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

   2. *-commutative 99.2%

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

   3. *-rgt-identity 99.2%

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

   4. associate-*l* 99.2%

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

   5. metadata-eval 99.2%

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

   6. times-frac 99.2%

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

   7. *-commutative 99.2%

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

   8. neg-mul-1 99.2%

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

   9. distribute-rgt-neg-in 99.2%

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

   10. times-frac 99.6%

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

   11. metadata-eval 99.6%

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

   12. metadata-eval 99.6%

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

3. Simplified 99.6%

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

5. Final simplification 99.6%

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

Alternative 14: 57.2% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if x < -0.75

   1. Initial program 86.6%

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

      1. associate-*l/ 99.5%

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

      2. *-commutative 99.5%

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

      3. *-rgt-identity 99.5%

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

      4. associate-*l* 99.5%

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

      5. metadata-eval 99.5%

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

      6. times-frac 99.5%

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

      7. *-commutative 99.5%

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

      8. neg-mul-1 99.5%

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

      9. distribute-rgt-neg-in 99.5%

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

      10. times-frac 99.5%

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

      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 23.4%

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

   6. Taylor expanded in x around inf 23.4%

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

      1. associate-*r/ 23.4%

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

      2. associate-*l/ 23.4%

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

      3. *-commutative 23.4%

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

   8. Simplified 23.4%

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

   if -0.75 < x

   1. Initial program 93.4%

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

      1. associate-*l/ 99.2%

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

      2. *-commutative 99.2%

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

      3. *-rgt-identity 99.2%

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

      4. associate-*l* 99.2%

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

      5. metadata-eval 99.2%

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

      6. times-frac 99.2%

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

      7. *-commutative 99.2%

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

      8. neg-mul-1 99.2%

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

      9. distribute-rgt-neg-in 99.2%

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

      10. times-frac 99.6%

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

      11. metadata-eval 99.6%

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

      12. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around 0 67.6%

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

4. Final simplification 58.9%

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

Alternative 15: 57.2% 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 86.6%

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

      1. associate-*l/ 99.5%

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

      2. *-commutative 99.5%

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

      3. *-rgt-identity 99.5%

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

      4. associate-*l* 99.5%

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

      5. metadata-eval 99.5%

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

      6. times-frac 99.5%

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

      7. *-commutative 99.5%

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

      8. neg-mul-1 99.5%

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

      9. distribute-rgt-neg-in 99.5%

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

      10. times-frac 99.5%

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

      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 inf 97.3%

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

      1. metadata-eval 97.3%

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

      2. distribute-lft-neg-in 97.3%

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

      3. associate-*r/ 97.3%

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

      4. associate-*l/ 97.3%

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

      5. distribute-lft-neg-in 97.3%

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

      6. distribute-neg-frac 97.3%

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

      7. metadata-eval 97.3%

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

   7. Simplified 97.3%

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

   8. Taylor expanded in x around 0 23.4%

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

      1. associate-*r/ 23.4%

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

      2. neg-mul-1 23.4%

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

   10. Simplified 23.4%

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

   if -1 < x

   1. Initial program 93.4%

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

      1. associate-*l/ 99.2%

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

      2. *-commutative 99.2%

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

      3. *-rgt-identity 99.2%

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

      4. associate-*l* 99.2%

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

      5. metadata-eval 99.2%

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

      6. times-frac 99.2%

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

      7. *-commutative 99.2%

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

      8. neg-mul-1 99.2%

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

      9. distribute-rgt-neg-in 99.2%

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

      10. times-frac 99.6%

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

      11. metadata-eval 99.6%

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

      12. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around 0 67.6%

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

4. Final simplification 58.9%

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

Alternative 16: 51.1% 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 92.1%

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

   1. associate-*l/ 99.2%

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

   2. *-commutative 99.2%

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

   3. *-rgt-identity 99.2%

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

   4. associate-*l* 99.2%

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

   5. metadata-eval 99.2%

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

   6. times-frac 99.2%

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

   7. *-commutative 99.2%

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

   8. neg-mul-1 99.2%

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

   9. distribute-rgt-neg-in 99.2%

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

   10. times-frac 99.6%

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

   11. metadata-eval 99.6%

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

   12. metadata-eval 99.6%

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

3. Simplified 99.6%

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

5. Taylor expanded in x around 0 55.3%

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

6. Final simplification 55.3%

   \[\leadsto \frac{1}{y} \]
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 2024041 
(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)))