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

Percentage Accurate: 94.0% → 99.8%

Time: 10.0s

Alternatives: 14

Speedup: 1.0×

• 24.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 94.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 1.0× speedup

Math

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

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 93.9%

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

   1. times-frac 99.8%

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

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: 98.4% 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 86.1%

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

      1. associate-*l/ 99.7%

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

      2. *-commutative 99.7%

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

      3. *-rgt-identity 99.7%

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

      4. associate-*l* 99.7%

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

      5. metadata-eval 99.7%

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

      6. times-frac 99.7%

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

      7. *-commutative 99.7%

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

      8. neg-mul-1 99.7%

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

      9. distribute-rgt-neg-in 99.7%

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

      10. times-frac 99.6%

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

      11. metadata-eval 99.6%

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

      12. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around inf 95.9%

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

   if -2.2999999999999998 < x < 1.30000000000000004

   1. Initial program 99.6%

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

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

      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 98.4%

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

   6. Taylor expanded in y around 0 98.4%

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

4. Final simplification 97.3%

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

Alternative 3: 98.4% accurate, 0.6× speedup

Math

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

FPCore

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

C

double code(double x, double y) {
	double tmp;
	if ((x <= -2.3) || !(x <= 1.3)) {
		tmp = ((x / y) / 3.0) * (x + -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 <= (-2.3d0)) .or. (.not. (x <= 1.3d0))) then
        tmp = ((x / y) / 3.0d0) * (x + (-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 <= -2.3) || !(x <= 1.3)) {
		tmp = ((x / y) / 3.0) * (x + -3.0);
	} 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 = ((x / y) / 3.0) * (x + -3.0)
	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(Float64(x / y) / 3.0) * Float64(x + -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 <= -2.3) || ~((x <= 1.3)))
		tmp = ((x / y) / 3.0) * (x + -3.0);
	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[(N[(x / y), $MachinePrecision] / 3.0), $MachinePrecision] * N[(x + -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 < -2.2999999999999998 or 1.30000000000000004 < x

   1. Initial program 86.1%

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

      1. times-frac 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around inf 95.8%

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

      1. neg-mul-1 95.8%

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

      2. distribute-neg-frac 95.8%

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

   7. Simplified 95.8%

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

      1. clear-num 95.8%

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

      2. frac-2neg 95.8%

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

      3. metadata-eval 95.8%

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

      4. frac-times 95.9%

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

      5. add-sqr-sqrt 48.2%

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

      6. sqrt-unprod 42.7%

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

      7. sqr-neg 42.7%

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

      8. sqrt-unprod 0.3%

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

      9. add-sqr-sqrt 0.5%

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

      10. *-commutative 0.5%

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

      11. neg-mul-1 0.5%

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

      12. add-sqr-sqrt 0.2%

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

      13. sqrt-unprod 40.2%

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

      14. sqr-neg 40.2%

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

      15. sqrt-unprod 47.6%

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

      16. add-sqr-sqrt 95.9%

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

      17. frac-2neg 95.9%

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

      18. distribute-neg-frac 95.9%

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

      19. metadata-eval 95.9%

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

      20. metadata-eval 95.9%

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

      21. sub-neg 95.9%

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

      22. distribute-neg-in 95.9%

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

      23. metadata-eval 95.9%

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

      24. remove-double-neg 95.9%

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

   9. Applied egg-rr 95.9%

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

       1. associate-/r* 95.9%

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

       2. associate-/r/ 96.0%

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

       3. +-commutative 96.0%

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

   11. Simplified 96.0%

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

   if -2.2999999999999998 < x < 1.30000000000000004

   1. Initial program 99.6%

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

      1. associate-*l/ 99.5%

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

      2. *-commutative 99.5%

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

      3. *-rgt-identity 99.5%

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

      4. associate-*l* 99.5%

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

      5. metadata-eval 99.5%

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

      6. times-frac 99.5%

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

      7. *-commutative 99.5%

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

      8. neg-mul-1 99.5%

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

      9. distribute-rgt-neg-in 99.5%

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

      10. times-frac 99.6%

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

      11. metadata-eval 99.6%

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

      12. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around 0 98.4%

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

   6. Taylor expanded in y around 0 98.4%

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

4. Final simplification 97.4%

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

Alternative 4: 98.4% 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 87.7%

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

      1. associate-*l/ 99.8%

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

      2. *-commutative 99.8%

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

      3. *-rgt-identity 99.8%

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

      4. associate-*l* 99.8%

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

      5. metadata-eval 99.8%

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

      6. times-frac 99.8%

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

      7. *-commutative 99.8%

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

      8. neg-mul-1 99.8%

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

      9. distribute-rgt-neg-in 99.8%

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

      10. times-frac 99.7%

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

      11. metadata-eval 99.7%

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

      12. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 97.5%

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

   if -2.2999999999999998 < x < 1.30000000000000004

   1. Initial program 99.6%

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

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

      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 98.4%

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

   6. Taylor expanded in y around 0 98.4%

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

   if 1.30000000000000004 < x

   1. Initial program 84.4%

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

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

      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 94.3%

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

      1. metadata-eval 94.3%

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

      2. distribute-lft-neg-in 94.3%

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

      3. associate-*r/ 94.3%

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

      4. associate-*l/ 94.4%

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

      5. *-commutative 94.4%

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

      6. distribute-rgt-neg-in 94.4%

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

      7. distribute-neg-frac 94.4%

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

      8. metadata-eval 94.4%

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

   7. Simplified 94.4%

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

4. Final simplification 97.3%

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

Alternative 5: 97.8% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-3.8d0)) .or. (.not. (x <= 3.0d0))) then
        tmp = x / (3.0d0 * (y / x))
    else
        tmp = (1.0d0 - x) / y
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if x < -3.7999999999999998 or 3 < x

   1. Initial program 86.1%

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

      1. times-frac 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around inf 95.8%

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

      1. neg-mul-1 95.8%

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

      2. distribute-neg-frac 95.8%

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

   7. Simplified 95.8%

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

      1. *-commutative 95.8%

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

      2. clear-num 95.8%

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

      3. frac-2neg 95.8%

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

      4. metadata-eval 95.8%

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

      5. frac-times 95.9%

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

      6. neg-mul-1 95.9%

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

      7. remove-double-neg 95.9%

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

      8. frac-2neg 95.9%

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

      9. distribute-neg-frac 95.9%

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

      10. metadata-eval 95.9%

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

      11. metadata-eval 95.9%

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

      12. sub-neg 95.9%

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

      13. distribute-neg-in 95.9%

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

      14. metadata-eval 95.9%

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

      15. remove-double-neg 95.9%

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

   9. Applied egg-rr 95.9%

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

   10. Taylor expanded in x around inf 95.5%

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

   if -3.7999999999999998 < x < 3

   1. Initial program 99.6%

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

      1. associate-*l/ 99.5%

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

      2. *-commutative 99.5%

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

      3. *-rgt-identity 99.5%

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

      4. associate-*l* 99.5%

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

      5. metadata-eval 99.5%

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

      6. times-frac 99.5%

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

      7. *-commutative 99.5%

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

      8. neg-mul-1 99.5%

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

      9. distribute-rgt-neg-in 99.5%

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

      10. times-frac 99.6%

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

      11. metadata-eval 99.6%

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

      12. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

      1. *-commutative 99.6%

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

      2. *-commutative 99.6%

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

      3. metadata-eval 99.6%

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

      4. times-frac 99.5%

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

      5. *-un-lft-identity 99.5%

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

      6. associate-/r/ 99.7%

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

      7. *-commutative 99.7%

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

      8. *-commutative 99.7%

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

      9. *-un-lft-identity 99.7%

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

      10. times-frac 99.8%

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

      11. metadata-eval 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in x around 0 96.7%

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

4. Final simplification 96.2%

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

Alternative 6: 97.8% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 3 regimes

2. if x < -3.7999999999999998

   1. Initial program 87.7%

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

      1. times-frac 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around inf 97.4%

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

      1. neg-mul-1 97.4%

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

      2. distribute-neg-frac 97.4%

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

   7. Simplified 97.4%

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

      1. *-commutative 97.4%

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

      2. clear-num 97.5%

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

      3. frac-2neg 97.5%

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

      4. metadata-eval 97.5%

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

      5. frac-times 97.5%

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

      6. neg-mul-1 97.5%

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

      7. remove-double-neg 97.5%

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

      8. frac-2neg 97.5%

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

      9. distribute-neg-frac 97.5%

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

      10. metadata-eval 97.5%

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

      11. metadata-eval 97.5%

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

      12. sub-neg 97.5%

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

      13. distribute-neg-in 97.5%

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

      14. metadata-eval 97.5%

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

      15. remove-double-neg 97.5%

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

   9. Applied egg-rr 97.5%

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

   10. Taylor expanded in x around inf 97.3%

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

   if -3.7999999999999998 < x < 3

   1. Initial program 99.6%

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

      1. associate-*l/ 99.5%

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

      2. *-commutative 99.5%

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

      3. *-rgt-identity 99.5%

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

      4. associate-*l* 99.5%

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

      5. metadata-eval 99.5%

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

      6. times-frac 99.5%

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

      7. *-commutative 99.5%

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

      8. neg-mul-1 99.5%

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

      9. distribute-rgt-neg-in 99.5%

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

      10. times-frac 99.6%

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

      11. metadata-eval 99.6%

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

      12. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

      1. *-commutative 99.6%

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

      2. *-commutative 99.6%

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

      3. metadata-eval 99.6%

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

      4. times-frac 99.5%

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

      5. *-un-lft-identity 99.5%

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

      6. associate-/r/ 99.7%

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

      7. *-commutative 99.7%

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

      8. *-commutative 99.7%

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

      9. *-un-lft-identity 99.7%

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

      10. times-frac 99.8%

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

      11. metadata-eval 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in x around 0 96.7%

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

   if 3 < x

   1. Initial program 84.4%

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

      1. times-frac 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around inf 94.3%

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

      1. neg-mul-1 94.3%

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

      2. distribute-neg-frac 94.3%

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

   7. Simplified 94.3%

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

      1. *-commutative 94.3%

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

      2. clear-num 94.2%

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

      3. frac-2neg 94.2%

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

      4. metadata-eval 94.2%

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

      5. frac-times 94.4%

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

      6. neg-mul-1 94.4%

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

      7. remove-double-neg 94.4%

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

      8. frac-2neg 94.4%

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

      9. distribute-neg-frac 94.4%

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

      10. metadata-eval 94.4%

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

      11. metadata-eval 94.4%

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

      12. sub-neg 94.4%

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

      13. distribute-neg-in 94.4%

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

      14. metadata-eval 94.4%

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

      15. remove-double-neg 94.4%

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

   9. Applied egg-rr 94.4%

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

   10. Taylor expanded in x around inf 94.0%

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

4. Final simplification 96.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.8:\\ \;\;\;\;\frac{x}{y \cdot \frac{3}{x}}\\ \mathbf{elif}\;x \leq 3:\\ \;\;\;\;\frac{1 - x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{3 \cdot \frac{y}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 98.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.8:\\ \;\;\;\;\frac{x}{y \cdot \frac{3}{x}}\\ \mathbf{elif}\;x \leq 3:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{3 \cdot \frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -4.8)
   (/ x (* y (/ 3.0 x)))
   (if (<= x 3.0)
     (/ (+ 1.0 (* x -1.3333333333333333)) y)
     (/ x (* 3.0 (/ y x))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -4.8) {
		tmp = x / (y * (3.0 / x));
	} else if (x <= 3.0) {
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	} else {
		tmp = x / (3.0 * (y / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-4.8d0)) then
        tmp = x / (y * (3.0d0 / x))
    else if (x <= 3.0d0) then
        tmp = (1.0d0 + (x * (-1.3333333333333333d0))) / y
    else
        tmp = x / (3.0d0 * (y / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -4.8) {
		tmp = x / (y * (3.0 / x));
	} else if (x <= 3.0) {
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	} else {
		tmp = x / (3.0 * (y / x));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -4.8:
		tmp = x / (y * (3.0 / x))
	elif x <= 3.0:
		tmp = (1.0 + (x * -1.3333333333333333)) / y
	else:
		tmp = x / (3.0 * (y / x))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -4.8)
		tmp = Float64(x / Float64(y * Float64(3.0 / x)));
	elseif (x <= 3.0)
		tmp = Float64(Float64(1.0 + Float64(x * -1.3333333333333333)) / y);
	else
		tmp = Float64(x / Float64(3.0 * Float64(y / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -4.8)
		tmp = x / (y * (3.0 / x));
	elseif (x <= 3.0)
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	else
		tmp = x / (3.0 * (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -4.8], N[(x / N[(y * N[(3.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.0], N[(N[(1.0 + N[(x * -1.3333333333333333), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(3.0 * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.79999999999999982

   1. Initial program 87.7%

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

      1. times-frac 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around inf 97.4%

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

      1. neg-mul-1 97.4%

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

      2. distribute-neg-frac 97.4%

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

   7. Simplified 97.4%

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

      1. *-commutative 97.4%

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

      2. clear-num 97.5%

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

      3. frac-2neg 97.5%

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

      4. metadata-eval 97.5%

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

      5. frac-times 97.5%

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

      6. neg-mul-1 97.5%

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

      7. remove-double-neg 97.5%

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

      8. frac-2neg 97.5%

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

      9. distribute-neg-frac 97.5%

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

      10. metadata-eval 97.5%

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

      11. metadata-eval 97.5%

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

      12. sub-neg 97.5%

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

      13. distribute-neg-in 97.5%

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

      14. metadata-eval 97.5%

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

      15. remove-double-neg 97.5%

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

   9. Applied egg-rr 97.5%

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

   10. Taylor expanded in x around inf 97.3%

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

   if -4.79999999999999982 < x < 3

   1. Initial program 99.6%

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

      1. associate-*l/ 99.5%

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

      2. *-commutative 99.5%

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

      3. *-rgt-identity 99.5%

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

      4. associate-*l* 99.5%

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

      5. metadata-eval 99.5%

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

      6. times-frac 99.5%

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

      7. *-commutative 99.5%

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

      8. neg-mul-1 99.5%

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

      9. distribute-rgt-neg-in 99.5%

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

      10. times-frac 99.6%

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

      11. metadata-eval 99.6%

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

      12. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around 0 98.4%

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

   6. Taylor expanded in y around 0 98.4%

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

   if 3 < x

   1. Initial program 84.4%

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

      1. times-frac 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around inf 94.3%

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

      1. neg-mul-1 94.3%

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

      2. distribute-neg-frac 94.3%

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

   7. Simplified 94.3%

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

      1. *-commutative 94.3%

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

      2. clear-num 94.2%

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

      3. frac-2neg 94.2%

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

      4. metadata-eval 94.2%

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

      5. frac-times 94.4%

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

      6. neg-mul-1 94.4%

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

      7. remove-double-neg 94.4%

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

      8. frac-2neg 94.4%

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

      9. distribute-neg-frac 94.4%

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

      10. metadata-eval 94.4%

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

      11. metadata-eval 94.4%

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

      12. sub-neg 94.4%

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

      13. distribute-neg-in 94.4%

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

      14. metadata-eval 94.4%

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

      15. remove-double-neg 94.4%

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

   9. Applied egg-rr 94.4%

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

   10. Taylor expanded in x around inf 94.0%

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

4. Final simplification 97.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.8:\\ \;\;\;\;\frac{x}{y \cdot \frac{3}{x}}\\ \mathbf{elif}\;x \leq 3:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{3 \cdot \frac{y}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 98.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.8:\\ \;\;\;\;\frac{x}{y} \cdot \left(-0.3333333333333333 \cdot \left(-x\right)\right)\\ \mathbf{elif}\;x \leq 3:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{3 \cdot \frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -4.8)
   (* (/ x y) (* -0.3333333333333333 (- x)))
   (if (<= x 3.0)
     (/ (+ 1.0 (* x -1.3333333333333333)) y)
     (/ x (* 3.0 (/ y x))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -4.8) {
		tmp = (x / y) * (-0.3333333333333333 * -x);
	} else if (x <= 3.0) {
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	} else {
		tmp = x / (3.0 * (y / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-4.8d0)) then
        tmp = (x / y) * ((-0.3333333333333333d0) * -x)
    else if (x <= 3.0d0) then
        tmp = (1.0d0 + (x * (-1.3333333333333333d0))) / y
    else
        tmp = x / (3.0d0 * (y / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -4.8) {
		tmp = (x / y) * (-0.3333333333333333 * -x);
	} else if (x <= 3.0) {
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	} else {
		tmp = x / (3.0 * (y / x));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -4.8:
		tmp = (x / y) * (-0.3333333333333333 * -x)
	elif x <= 3.0:
		tmp = (1.0 + (x * -1.3333333333333333)) / y
	else:
		tmp = x / (3.0 * (y / x))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -4.8)
		tmp = Float64(Float64(x / y) * Float64(-0.3333333333333333 * Float64(-x)));
	elseif (x <= 3.0)
		tmp = Float64(Float64(1.0 + Float64(x * -1.3333333333333333)) / y);
	else
		tmp = Float64(x / Float64(3.0 * Float64(y / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -4.8)
		tmp = (x / y) * (-0.3333333333333333 * -x);
	elseif (x <= 3.0)
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	else
		tmp = x / (3.0 * (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -4.8], N[(N[(x / y), $MachinePrecision] * N[(-0.3333333333333333 * (-x)), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.0], N[(N[(1.0 + N[(x * -1.3333333333333333), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(3.0 * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.79999999999999982

   1. Initial program 87.7%

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

      1. times-frac 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around inf 97.4%

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

      1. neg-mul-1 97.4%

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

      2. distribute-neg-frac 97.4%

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

   7. Simplified 97.4%

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

   8. Taylor expanded in x around inf 97.4%

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

   if -4.79999999999999982 < x < 3

   1. Initial program 99.6%

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

      1. associate-*l/ 99.5%

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

      2. *-commutative 99.5%

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

      3. *-rgt-identity 99.5%

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

      4. associate-*l* 99.5%

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

      5. metadata-eval 99.5%

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

      6. times-frac 99.5%

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

      7. *-commutative 99.5%

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

      8. neg-mul-1 99.5%

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

      9. distribute-rgt-neg-in 99.5%

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

      10. times-frac 99.6%

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

      11. metadata-eval 99.6%

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

      12. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around 0 98.4%

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

   6. Taylor expanded in y around 0 98.4%

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

   if 3 < x

   1. Initial program 84.4%

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

      1. times-frac 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around inf 94.3%

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

      1. neg-mul-1 94.3%

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

      2. distribute-neg-frac 94.3%

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

   7. Simplified 94.3%

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

      1. *-commutative 94.3%

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

      2. clear-num 94.2%

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

      3. frac-2neg 94.2%

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

      4. metadata-eval 94.2%

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

      5. frac-times 94.4%

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

      6. neg-mul-1 94.4%

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

      7. remove-double-neg 94.4%

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

      8. frac-2neg 94.4%

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

      9. distribute-neg-frac 94.4%

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

      10. metadata-eval 94.4%

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

      11. metadata-eval 94.4%

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

      12. sub-neg 94.4%

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

      13. distribute-neg-in 94.4%

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

      14. metadata-eval 94.4%

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

      15. remove-double-neg 94.4%

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

   9. Applied egg-rr 94.4%

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

   10. Taylor expanded in x around inf 94.0%

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

4. Final simplification 97.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.8:\\ \;\;\;\;\frac{x}{y} \cdot \left(-0.3333333333333333 \cdot \left(-x\right)\right)\\ \mathbf{elif}\;x \leq 3:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{3 \cdot \frac{y}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 63.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.75:\\ \;\;\;\;\frac{x}{y} \cdot -1.3333333333333333\\ \mathbf{elif}\;x \leq 4.8:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{1.3333333333333333}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -0.75)
   (* (/ x y) -1.3333333333333333)
   (if (<= x 4.8) (/ 1.0 y) (/ x (/ y 1.3333333333333333)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -0.75) {
		tmp = (x / y) * -1.3333333333333333;
	} else if (x <= 4.8) {
		tmp = 1.0 / y;
	} else {
		tmp = x / (y / 1.3333333333333333);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-0.75d0)) then
        tmp = (x / y) * (-1.3333333333333333d0)
    else if (x <= 4.8d0) then
        tmp = 1.0d0 / y
    else
        tmp = x / (y / 1.3333333333333333d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -0.75) {
		tmp = (x / y) * -1.3333333333333333;
	} else if (x <= 4.8) {
		tmp = 1.0 / y;
	} else {
		tmp = x / (y / 1.3333333333333333);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -0.75:
		tmp = (x / y) * -1.3333333333333333
	elif x <= 4.8:
		tmp = 1.0 / y
	else:
		tmp = x / (y / 1.3333333333333333)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -0.75)
		tmp = Float64(Float64(x / y) * -1.3333333333333333);
	elseif (x <= 4.8)
		tmp = Float64(1.0 / y);
	else
		tmp = Float64(x / Float64(y / 1.3333333333333333));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -0.75)
		tmp = (x / y) * -1.3333333333333333;
	elseif (x <= 4.8)
		tmp = 1.0 / y;
	else
		tmp = x / (y / 1.3333333333333333);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -0.75], N[(N[(x / y), $MachinePrecision] * -1.3333333333333333), $MachinePrecision], If[LessEqual[x, 4.8], N[(1.0 / y), $MachinePrecision], N[(x / N[(y / 1.3333333333333333), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -0.75

   1. Initial program 87.7%

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

      1. associate-*l/ 99.8%

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

      2. *-commutative 99.8%

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

      3. *-rgt-identity 99.8%

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

      4. associate-*l* 99.8%

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

      5. metadata-eval 99.8%

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

      6. times-frac 99.8%

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

      7. *-commutative 99.8%

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

      8. neg-mul-1 99.8%

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

      9. distribute-rgt-neg-in 99.8%

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

      10. times-frac 99.7%

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

      11. metadata-eval 99.7%

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

      12. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0 39.7%

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

   6. Taylor expanded in x around inf 39.7%

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

   if -0.75 < x < 4.79999999999999982

   1. Initial program 99.6%

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

      1. associate-*l/ 99.5%

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

      2. *-commutative 99.5%

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

      3. *-rgt-identity 99.5%

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

      4. associate-*l* 99.5%

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

      5. metadata-eval 99.5%

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

      6. times-frac 99.5%

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

      7. *-commutative 99.5%

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

      8. neg-mul-1 99.5%

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

      9. distribute-rgt-neg-in 99.5%

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

      10. times-frac 99.6%

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

      11. metadata-eval 99.6%

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

      12. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around 0 96.4%

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

   if 4.79999999999999982 < x

   1. Initial program 84.4%

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

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

      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 0.8%

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

   6. Taylor expanded in x around inf 0.8%

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

      1. frac-2neg 0.8%

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

      2. associate-*r/ 0.8%

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

      3. add-sqr-sqrt 0.0%

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

      4. sqrt-unprod 43.0%

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

      5. sqr-neg 43.0%

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

      6. sqrt-unprod 22.2%

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

      7. add-sqr-sqrt 22.2%

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

      8. *-commutative 22.2%

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

   8. Applied egg-rr 22.2%

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

      1. associate-/l* 22.2%

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

      2. neg-mul-1 22.2%

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

      3. *-commutative 22.2%

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

      4. associate-/l* 22.2%

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

      5. metadata-eval 22.2%

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

   10. Simplified 22.2%

       \[\leadsto \color{blue}{\frac{x}{\frac{y}{1.3333333333333333}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.75:\\ \;\;\;\;\frac{x}{y} \cdot -1.3333333333333333\\ \mathbf{elif}\;x \leq 4.8:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{1.3333333333333333}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 99.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.9%

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

   1. associate-*l/ 99.5%

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

   2. *-commutative 99.5%

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

   3. *-rgt-identity 99.5%

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

   4. associate-*l* 99.5%

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

   5. metadata-eval 99.5%

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

   6. times-frac 99.5%

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

   7. *-commutative 99.5%

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

   8. neg-mul-1 99.5%

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

   9. distribute-rgt-neg-in 99.5%

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

   10. times-frac 99.6%

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

   11. metadata-eval 99.6%

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

   12. metadata-eval 99.6%

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

3. Simplified 99.6%

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

5. Final simplification 99.6%

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

Alternative 11: 57.5% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if x < -0.75

   1. Initial program 87.7%

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

      1. associate-*l/ 99.8%

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

      2. *-commutative 99.8%

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

      3. *-rgt-identity 99.8%

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

      4. associate-*l* 99.8%

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

      5. metadata-eval 99.8%

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

      6. times-frac 99.8%

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

      7. *-commutative 99.8%

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

      8. neg-mul-1 99.8%

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

      9. distribute-rgt-neg-in 99.8%

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

      10. times-frac 99.7%

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

      11. metadata-eval 99.7%

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

      12. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0 39.7%

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

   6. Taylor expanded in x around inf 39.7%

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

   if -0.75 < x

   1. Initial program 95.5%

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

      1. associate-*l/ 99.5%

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

      2. *-commutative 99.5%

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

      3. *-rgt-identity 99.5%

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

      4. associate-*l* 99.5%

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

      5. metadata-eval 99.5%

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

      6. times-frac 99.5%

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

      7. *-commutative 99.5%

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

      8. neg-mul-1 99.5%

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

      9. distribute-rgt-neg-in 99.5%

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

      10. times-frac 99.6%

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

      11. metadata-eval 99.6%

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

      12. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around 0 71.5%

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

4. Final simplification 64.8%

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

Alternative 12: 63.3% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if x < 3

   1. Initial program 96.4%

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

      1. associate-*l/ 99.5%

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

      2. *-commutative 99.5%

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

      3. *-rgt-identity 99.5%

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

      4. associate-*l* 99.5%

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

      5. metadata-eval 99.5%

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

      6. times-frac 99.5%

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

      7. *-commutative 99.5%

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

      8. neg-mul-1 99.5%

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

      9. distribute-rgt-neg-in 99.5%

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

      10. times-frac 99.6%

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

      11. metadata-eval 99.6%

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

      12. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

      1. *-commutative 99.6%

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

      2. *-commutative 99.6%

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

      3. metadata-eval 99.6%

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

      4. times-frac 99.5%

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

      5. *-un-lft-identity 99.5%

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

      6. associate-/r/ 99.7%

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

      7. *-commutative 99.7%

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

      8. *-commutative 99.7%

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

      9. *-un-lft-identity 99.7%

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

      10. times-frac 99.7%

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

      11. metadata-eval 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in x around 0 81.4%

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

   if 3 < x

   1. Initial program 84.4%

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

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

      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 0.8%

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

   6. Taylor expanded in x around inf 0.8%

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

      1. frac-2neg 0.8%

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

      2. associate-*r/ 0.8%

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

      3. add-sqr-sqrt 0.0%

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

      4. sqrt-unprod 43.0%

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

      5. sqr-neg 43.0%

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

      6. sqrt-unprod 22.2%

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

      7. add-sqr-sqrt 22.2%

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

      8. *-commutative 22.2%

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

   8. Applied egg-rr 22.2%

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

      1. associate-/l* 22.2%

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

      2. neg-mul-1 22.2%

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

      3. *-commutative 22.2%

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

      4. associate-/l* 22.2%

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

      5. metadata-eval 22.2%

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

   10. Simplified 22.2%

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

4. Final simplification 68.7%

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

Alternative 13: 57.5% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if x < -1

   1. Initial program 87.7%

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

      1. associate-*l/ 99.8%

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

      2. *-commutative 99.8%

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

      3. *-rgt-identity 99.8%

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

      4. associate-*l* 99.8%

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

      5. metadata-eval 99.8%

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

      6. times-frac 99.8%

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

      7. *-commutative 99.8%

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

      8. neg-mul-1 99.8%

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

      9. distribute-rgt-neg-in 99.8%

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

      10. times-frac 99.7%

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

      11. metadata-eval 99.7%

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

      12. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 97.5%

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

   6. Taylor expanded in x around 0 39.7%

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

      1. mul-1-neg 39.7%

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

      2. distribute-neg-frac 39.7%

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

   8. Simplified 39.7%

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

   if -1 < x

   1. Initial program 95.5%

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

      1. associate-*l/ 99.5%

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

      2. *-commutative 99.5%

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

      3. *-rgt-identity 99.5%

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

      4. associate-*l* 99.5%

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

      5. metadata-eval 99.5%

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

      6. times-frac 99.5%

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

      7. *-commutative 99.5%

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

      8. neg-mul-1 99.5%

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

      9. distribute-rgt-neg-in 99.5%

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

      10. times-frac 99.6%

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

      11. metadata-eval 99.6%

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

      12. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around 0 71.5%

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

4. Final simplification 64.8%

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

Alternative 14: 51.3% accurate, 3.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.9%

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

   1. associate-*l/ 99.5%

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

   2. *-commutative 99.5%

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

   3. *-rgt-identity 99.5%

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

   4. associate-*l* 99.5%

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

   5. metadata-eval 99.5%

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

   6. times-frac 99.5%

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

   7. *-commutative 99.5%

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

   8. neg-mul-1 99.5%

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

   9. distribute-rgt-neg-in 99.5%

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

   10. times-frac 99.6%

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

   11. metadata-eval 99.6%

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

   12. metadata-eval 99.6%

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

3. Simplified 99.6%

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

5. Taylor expanded in x around 0 57.4%

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

6. Final simplification 57.4%

   \[\leadsto \frac{1}{y} \]
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 2024011 
(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)))