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

Percentage Accurate: 93.8% → 99.8%

Time: 8.9s

Alternatives: 13

Speedup: 1.0×

• 25.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 93.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.7%

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

   1. *-commutative 92.7%

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

   2. associate-*l/ 99.7%

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

   3. *-commutative 99.7%

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

   4. associate-/l/ 99.9%

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

3. Simplified 99.9%

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

4. Final simplification 99.9%

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

Alternative 2: 97.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.8:\\ \;\;\;\;\frac{-x}{y} \cdot \left(x \cdot -0.3333333333333333\right)\\ \mathbf{elif}\;x \leq 1.75:\\ \;\;\;\;\left(1 - x\right) \cdot \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{x}{\frac{y}{3 - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -3.8)
   (* (/ (- x) y) (* x -0.3333333333333333))
   (if (<= x 1.75)
     (* (- 1.0 x) (/ 1.0 y))
     (* -0.3333333333333333 (/ x (/ y (- 3.0 x)))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -3.8) {
		tmp = (-x / y) * (x * -0.3333333333333333);
	} else if (x <= 1.75) {
		tmp = (1.0 - x) * (1.0 / y);
	} else {
		tmp = -0.3333333333333333 * (x / (y / (3.0 - x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-3.8d0)) then
        tmp = (-x / y) * (x * (-0.3333333333333333d0))
    else if (x <= 1.75d0) then
        tmp = (1.0d0 - x) * (1.0d0 / y)
    else
        tmp = (-0.3333333333333333d0) * (x / (y / (3.0d0 - 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) * (x * -0.3333333333333333);
	} else if (x <= 1.75) {
		tmp = (1.0 - x) * (1.0 / y);
	} else {
		tmp = -0.3333333333333333 * (x / (y / (3.0 - x)));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -3.8:
		tmp = (-x / y) * (x * -0.3333333333333333)
	elif x <= 1.75:
		tmp = (1.0 - x) * (1.0 / y)
	else:
		tmp = -0.3333333333333333 * (x / (y / (3.0 - x)))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -3.8)
		tmp = Float64(Float64(Float64(-x) / y) * Float64(x * -0.3333333333333333));
	elseif (x <= 1.75)
		tmp = Float64(Float64(1.0 - x) * Float64(1.0 / y));
	else
		tmp = Float64(-0.3333333333333333 * Float64(x / Float64(y / Float64(3.0 - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -3.8)
		tmp = (-x / y) * (x * -0.3333333333333333);
	elseif (x <= 1.75)
		tmp = (1.0 - x) * (1.0 / y);
	else
		tmp = -0.3333333333333333 * (x / (y / (3.0 - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -3.8], N[(N[((-x) / y), $MachinePrecision] * N[(x * -0.3333333333333333), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.75], N[(N[(1.0 - x), $MachinePrecision] * N[(1.0 / y), $MachinePrecision]), $MachinePrecision], N[(-0.3333333333333333 * N[(x / N[(y / N[(3.0 - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.7999999999999998

   1. Initial program 83.0%

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

      1. times-frac 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 98.2%

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

      1. neg-mul-1 98.2%

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

      2. distribute-neg-frac 98.2%

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

   6. Simplified 98.2%

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

   7. Taylor expanded in x around inf 98.1%

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

      1. *-commutative 98.1%

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

   9. Simplified 98.1%

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

   if -3.7999999999999998 < x < 1.75

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

      2. associate-*l/ 99.6%

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

      3. *-commutative 99.6%

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

      4. associate-/l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 99.3%

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

   if 1.75 < x

   1. Initial program 88.3%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   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. Taylor expanded in x around inf 97.9%

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

      1. neg-mul-1 97.9%

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

      2. distribute-neg-frac 97.9%

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

   6. Simplified 97.9%

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

   7. Taylor expanded in y around 0 86.3%

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

      1. associate-/l* 97.9%

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

   9. Simplified 97.9%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.8:\\ \;\;\;\;\frac{-x}{y} \cdot \left(x \cdot -0.3333333333333333\right)\\ \mathbf{elif}\;x \leq 1.75:\\ \;\;\;\;\left(1 - x\right) \cdot \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{x}{\frac{y}{3 - x}}\\ \end{array} \]

Alternative 3: 97.8% accurate, 0.8× speedup

Math

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

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.7)
   (* x (* -0.3333333333333333 (/ (- 3.0 x) y)))
   (if (<= x 1.75)
     (* (- 1.0 x) (/ 1.0 y))
     (* -0.3333333333333333 (/ x (/ y (- 3.0 x)))))))

C

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

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-1.7d0)) then
        tmp = x * ((-0.3333333333333333d0) * ((3.0d0 - x) / y))
    else if (x <= 1.75d0) then
        tmp = (1.0d0 - x) * (1.0d0 / y)
    else
        tmp = (-0.3333333333333333d0) * (x / (y / (3.0d0 - x)))
    end if
    code = tmp
end function

Java

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

Python

def code(x, y):
	tmp = 0
	if x <= -1.7:
		tmp = x * (-0.3333333333333333 * ((3.0 - x) / y))
	elif x <= 1.75:
		tmp = (1.0 - x) * (1.0 / y)
	else:
		tmp = -0.3333333333333333 * (x / (y / (3.0 - x)))
	return tmp

Julia

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

MATLAB

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

Wolfram

code[x_, y_] := If[LessEqual[x, -1.7], N[(x * N[(-0.3333333333333333 * N[(N[(3.0 - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.75], N[(N[(1.0 - x), $MachinePrecision] * N[(1.0 / y), $MachinePrecision]), $MachinePrecision], N[(-0.3333333333333333 * N[(x / N[(y / N[(3.0 - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.69999999999999996

   1. Initial program 83.0%

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

      1. times-frac 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 98.2%

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

      1. neg-mul-1 98.2%

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

      2. distribute-neg-frac 98.2%

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

   6. Simplified 98.2%

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

   7. Taylor expanded in y around 0 81.4%

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

      1. associate-/l* 97.9%

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

   9. Simplified 97.9%

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

   10. Taylor expanded in y around 0 81.4%

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

       1. associate-*r/ 98.1%

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

       2. *-commutative 98.1%

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

       3. associate-*r* 98.1%

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

       4. *-commutative 98.1%

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

   12. Simplified 98.1%

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

   if -1.69999999999999996 < x < 1.75

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

      2. associate-*l/ 99.6%

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

      3. *-commutative 99.6%

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

      4. associate-/l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 99.3%

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

   if 1.75 < x

   1. Initial program 88.3%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   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. Taylor expanded in x around inf 97.9%

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

      1. neg-mul-1 97.9%

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

      2. distribute-neg-frac 97.9%

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

   6. Simplified 97.9%

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

   7. Taylor expanded in y around 0 86.3%

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

      1. associate-/l* 97.9%

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

   9. Simplified 97.9%

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

4. Final simplification 98.7%

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

Alternative 4: 97.8% accurate, 0.8× speedup

Math

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

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -3.0)
   (* (- 1.0 x) (/ (/ x -3.0) y))
   (if (<= x 1.75)
     (* (- 1.0 x) (/ 1.0 y))
     (* -0.3333333333333333 (/ x (/ y (- 3.0 x)))))))

C

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

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-3.0d0)) then
        tmp = (1.0d0 - x) * ((x / (-3.0d0)) / y)
    else if (x <= 1.75d0) then
        tmp = (1.0d0 - x) * (1.0d0 / y)
    else
        tmp = (-0.3333333333333333d0) * (x / (y / (3.0d0 - x)))
    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) * ((x / -3.0) / y);
	} else if (x <= 1.75) {
		tmp = (1.0 - x) * (1.0 / y);
	} else {
		tmp = -0.3333333333333333 * (x / (y / (3.0 - x)));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -3.0:
		tmp = (1.0 - x) * ((x / -3.0) / y)
	elif x <= 1.75:
		tmp = (1.0 - x) * (1.0 / y)
	else:
		tmp = -0.3333333333333333 * (x / (y / (3.0 - x)))
	return tmp

Julia

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

MATLAB

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

Wolfram

code[x_, y_] := If[LessEqual[x, -3.0], N[(N[(1.0 - x), $MachinePrecision] * N[(N[(x / -3.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.75], N[(N[(1.0 - x), $MachinePrecision] * N[(1.0 / y), $MachinePrecision]), $MachinePrecision], N[(-0.3333333333333333 * N[(x / N[(y / N[(3.0 - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3

   1. Initial program 83.0%

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

      1. *-commutative 83.0%

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

      2. associate-*l/ 99.7%

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

      3. *-commutative 99.7%

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

      4. associate-/l/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 97.9%

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

      1. add-sqr-sqrt 0.0%

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

      2. sqrt-unprod 0.6%

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

      3. sqr-neg 0.6%

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

      4. sqrt-unprod 0.6%

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

      5. add-sqr-sqrt 0.6%

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

      6. distribute-rgt-neg-in 0.6%

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

      7. *-commutative 0.6%

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

      8. distribute-rgt-neg-in 0.6%

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

      9. metadata-eval 0.6%

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

      10. metadata-eval 0.6%

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

      11. div-inv 0.6%

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

      12. frac-2neg 0.6%

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

      13. add-sqr-sqrt 0.6%

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

      14. sqrt-unprod 0.6%

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

      15. sqr-neg 0.6%

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

      16. sqrt-unprod 0.0%

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

      17. add-sqr-sqrt 98.2%

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

      18. metadata-eval 98.2%

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

   6. Applied egg-rr 98.2%

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

   if -3 < x < 1.75

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

      2. associate-*l/ 99.6%

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

      3. *-commutative 99.6%

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

      4. associate-/l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 99.3%

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

   if 1.75 < x

   1. Initial program 88.3%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   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. Taylor expanded in x around inf 97.9%

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

      1. neg-mul-1 97.9%

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

      2. distribute-neg-frac 97.9%

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

   6. Simplified 97.9%

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

   7. Taylor expanded in y around 0 86.3%

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

      1. associate-/l* 97.9%

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

   9. Simplified 97.9%

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

4. Final simplification 98.7%

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

Alternative 5: 98.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.8:\\ \;\;\;\;\left(1 - x\right) \cdot \frac{\frac{x}{-3}}{y}\\ \mathbf{elif}\;x \leq 1.3:\\ \;\;\;\;\frac{3 + x \cdot -4}{y \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{x}{\frac{y}{3 - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -3.8)
   (* (- 1.0 x) (/ (/ x -3.0) y))
   (if (<= x 1.3)
     (/ (+ 3.0 (* x -4.0)) (* y 3.0))
     (* -0.3333333333333333 (/ x (/ y (- 3.0 x)))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -3.8) {
		tmp = (1.0 - x) * ((x / -3.0) / y);
	} else if (x <= 1.3) {
		tmp = (3.0 + (x * -4.0)) / (y * 3.0);
	} else {
		tmp = -0.3333333333333333 * (x / (y / (3.0 - x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-3.8d0)) then
        tmp = (1.0d0 - x) * ((x / (-3.0d0)) / y)
    else if (x <= 1.3d0) then
        tmp = (3.0d0 + (x * (-4.0d0))) / (y * 3.0d0)
    else
        tmp = (-0.3333333333333333d0) * (x / (y / (3.0d0 - x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -3.8) {
		tmp = (1.0 - x) * ((x / -3.0) / y);
	} else if (x <= 1.3) {
		tmp = (3.0 + (x * -4.0)) / (y * 3.0);
	} else {
		tmp = -0.3333333333333333 * (x / (y / (3.0 - x)));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -3.8:
		tmp = (1.0 - x) * ((x / -3.0) / y)
	elif x <= 1.3:
		tmp = (3.0 + (x * -4.0)) / (y * 3.0)
	else:
		tmp = -0.3333333333333333 * (x / (y / (3.0 - x)))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -3.8)
		tmp = Float64(Float64(1.0 - x) * Float64(Float64(x / -3.0) / y));
	elseif (x <= 1.3)
		tmp = Float64(Float64(3.0 + Float64(x * -4.0)) / Float64(y * 3.0));
	else
		tmp = Float64(-0.3333333333333333 * Float64(x / Float64(y / Float64(3.0 - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -3.8)
		tmp = (1.0 - x) * ((x / -3.0) / y);
	elseif (x <= 1.3)
		tmp = (3.0 + (x * -4.0)) / (y * 3.0);
	else
		tmp = -0.3333333333333333 * (x / (y / (3.0 - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -3.8], N[(N[(1.0 - x), $MachinePrecision] * N[(N[(x / -3.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.3], N[(N[(3.0 + N[(x * -4.0), $MachinePrecision]), $MachinePrecision] / N[(y * 3.0), $MachinePrecision]), $MachinePrecision], N[(-0.3333333333333333 * N[(x / N[(y / N[(3.0 - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.7999999999999998

   1. Initial program 83.0%

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

      1. *-commutative 83.0%

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

      2. associate-*l/ 99.7%

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

      3. *-commutative 99.7%

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

      4. associate-/l/ 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 97.9%

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

      1. add-sqr-sqrt 0.0%

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

      2. sqrt-unprod 0.6%

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

      3. sqr-neg 0.6%

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

      4. sqrt-unprod 0.6%

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

      5. add-sqr-sqrt 0.6%

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

      6. distribute-rgt-neg-in 0.6%

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

      7. *-commutative 0.6%

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

      8. distribute-rgt-neg-in 0.6%

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

      9. metadata-eval 0.6%

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

      10. metadata-eval 0.6%

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

      11. div-inv 0.6%

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

      12. frac-2neg 0.6%

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

      13. add-sqr-sqrt 0.6%

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

      14. sqrt-unprod 0.6%

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

      15. sqr-neg 0.6%

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

      16. sqrt-unprod 0.0%

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

      17. add-sqr-sqrt 98.2%

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

      18. metadata-eval 98.2%

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

   6. Applied egg-rr 98.2%

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

   if -3.7999999999999998 < x < 1.30000000000000004

   1. Initial program 99.6%

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

   2. Taylor expanded in x around 0 99.5%

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

      1. *-commutative 99.5%

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

   4. Simplified 99.5%

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

   if 1.30000000000000004 < x

   1. Initial program 88.3%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   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. Taylor expanded in x around inf 97.9%

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

      1. neg-mul-1 97.9%

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

      2. distribute-neg-frac 97.9%

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

   6. Simplified 97.9%

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

   7. Taylor expanded in y around 0 86.3%

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

      1. associate-/l* 97.9%

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

   9. Simplified 97.9%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.8:\\ \;\;\;\;\left(1 - x\right) \cdot \frac{\frac{x}{-3}}{y}\\ \mathbf{elif}\;x \leq 1.3:\\ \;\;\;\;\frac{3 + x \cdot -4}{y \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{x}{\frac{y}{3 - x}}\\ \end{array} \]

Alternative 6: 98.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.3:\\ \;\;\;\;\frac{x}{y} \cdot \frac{x - 3}{3}\\ \mathbf{elif}\;x \leq 1.3:\\ \;\;\;\;\frac{3 + x \cdot -4}{y \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{x}{\frac{y}{3 - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2.3)
   (* (/ x y) (/ (- x 3.0) 3.0))
   (if (<= x 1.3)
     (/ (+ 3.0 (* x -4.0)) (* y 3.0))
     (* -0.3333333333333333 (/ x (/ y (- 3.0 x)))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.3) {
		tmp = (x / y) * ((x - 3.0) / 3.0);
	} else if (x <= 1.3) {
		tmp = (3.0 + (x * -4.0)) / (y * 3.0);
	} else {
		tmp = -0.3333333333333333 * (x / (y / (3.0 - x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-2.3d0)) then
        tmp = (x / y) * ((x - 3.0d0) / 3.0d0)
    else if (x <= 1.3d0) then
        tmp = (3.0d0 + (x * (-4.0d0))) / (y * 3.0d0)
    else
        tmp = (-0.3333333333333333d0) * (x / (y / (3.0d0 - x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -2.3) {
		tmp = (x / y) * ((x - 3.0) / 3.0);
	} else if (x <= 1.3) {
		tmp = (3.0 + (x * -4.0)) / (y * 3.0);
	} else {
		tmp = -0.3333333333333333 * (x / (y / (3.0 - x)));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2.3:
		tmp = (x / y) * ((x - 3.0) / 3.0)
	elif x <= 1.3:
		tmp = (3.0 + (x * -4.0)) / (y * 3.0)
	else:
		tmp = -0.3333333333333333 * (x / (y / (3.0 - x)))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2.3)
		tmp = Float64(Float64(x / y) * Float64(Float64(x - 3.0) / 3.0));
	elseif (x <= 1.3)
		tmp = Float64(Float64(3.0 + Float64(x * -4.0)) / Float64(y * 3.0));
	else
		tmp = Float64(-0.3333333333333333 * Float64(x / Float64(y / Float64(3.0 - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2.3)
		tmp = (x / y) * ((x - 3.0) / 3.0);
	elseif (x <= 1.3)
		tmp = (3.0 + (x * -4.0)) / (y * 3.0);
	else
		tmp = -0.3333333333333333 * (x / (y / (3.0 - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2.3], N[(N[(x / y), $MachinePrecision] * N[(N[(x - 3.0), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.3], N[(N[(3.0 + N[(x * -4.0), $MachinePrecision]), $MachinePrecision] / N[(y * 3.0), $MachinePrecision]), $MachinePrecision], N[(-0.3333333333333333 * N[(x / N[(y / N[(3.0 - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.2999999999999998

   1. Initial program 83.0%

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

      1. times-frac 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 98.2%

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

      1. neg-mul-1 98.2%

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

      2. distribute-neg-frac 98.2%

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

   6. Simplified 98.2%

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

   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. Taylor expanded in x around 0 99.5%

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

      1. *-commutative 99.5%

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

   4. Simplified 99.5%

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

   if 1.30000000000000004 < x

   1. Initial program 88.3%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   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. Taylor expanded in x around inf 97.9%

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

      1. neg-mul-1 97.9%

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

      2. distribute-neg-frac 97.9%

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

   6. Simplified 97.9%

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

   7. Taylor expanded in y around 0 86.3%

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

      1. associate-/l* 97.9%

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

   9. Simplified 97.9%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3:\\ \;\;\;\;\frac{x}{y} \cdot \frac{x - 3}{3}\\ \mathbf{elif}\;x \leq 1.3:\\ \;\;\;\;\frac{3 + x \cdot -4}{y \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{x}{\frac{y}{3 - x}}\\ \end{array} \]

Alternative 7: 97.8% accurate, 0.9× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if x < -3.7999999999999998 or 3 < x

   1. Initial program 85.4%

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

      1. times-frac 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 98.1%

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

      1. neg-mul-1 98.1%

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

      2. distribute-neg-frac 98.1%

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

   6. Simplified 98.1%

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

   7. Taylor expanded in y around 0 83.7%

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

      1. associate-/l* 97.9%

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

   9. Simplified 97.9%

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

   10. Taylor expanded in x around inf 97.8%

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

       1. mul-1-neg 97.8%

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

       2. distribute-frac-neg 97.8%

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

   12. Simplified 97.8%

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

   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. *-commutative 99.6%

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

      2. associate-*l/ 99.6%

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

      3. *-commutative 99.6%

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

      4. associate-/l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 99.3%

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

4. Final simplification 98.6%

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

Alternative 8: 97.8% accurate, 0.9× speedup

Math

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

FPCore

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

C

double code(double x, double y) {
	double tmp;
	if (x <= -3.8) {
		tmp = (-x / y) * (x * -0.3333333333333333);
	} else if (x <= 3.0) {
		tmp = (1.0 - x) * (1.0 / y);
	} else {
		tmp = -0.3333333333333333 * (x / -(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) * (x * (-0.3333333333333333d0))
    else if (x <= 3.0d0) then
        tmp = (1.0d0 - x) * (1.0d0 / y)
    else
        tmp = (-0.3333333333333333d0) * (x / -(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) * (x * -0.3333333333333333);
	} else if (x <= 3.0) {
		tmp = (1.0 - x) * (1.0 / y);
	} else {
		tmp = -0.3333333333333333 * (x / -(y / x));
	}
	return tmp;
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 3 regimes

2. if x < -3.7999999999999998

   1. Initial program 83.0%

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

      1. times-frac 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 98.2%

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

      1. neg-mul-1 98.2%

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

      2. distribute-neg-frac 98.2%

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

   6. Simplified 98.2%

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

   7. Taylor expanded in x around inf 98.1%

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

      1. *-commutative 98.1%

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

   9. Simplified 98.1%

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

   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. *-commutative 99.6%

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

      2. associate-*l/ 99.6%

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

      3. *-commutative 99.6%

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

      4. associate-/l/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 99.3%

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

   if 3 < x

   1. Initial program 88.3%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   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. Taylor expanded in x around inf 97.9%

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

      1. neg-mul-1 97.9%

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

      2. distribute-neg-frac 97.9%

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

   6. Simplified 97.9%

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

   7. Taylor expanded in y around 0 86.3%

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

      1. associate-/l* 97.9%

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

   9. Simplified 97.9%

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

   10. Taylor expanded in x around inf 97.8%

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

       1. mul-1-neg 97.8%

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

       2. distribute-frac-neg 97.8%

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

   12. Simplified 97.8%

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

4. Final simplification 98.7%

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

Alternative 9: 57.8% accurate, 1.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if x < -0.75

   1. Initial program 83.0%

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

   2. Taylor expanded in x around 0 23.0%

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

      1. *-commutative 23.0%

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

   4. Simplified 23.0%

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

   5. Taylor expanded in x around inf 23.0%

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

   if -0.75 < x

   1. Initial program 96.2%

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

      1. *-commutative 96.2%

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

      2. associate-*l/ 99.7%

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

      3. *-commutative 99.7%

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

      4. associate-/l/ 99.9%

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

   3. Simplified 99.9%

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

      1. associate-*r/ 96.4%

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

      2. *-commutative 96.4%

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

      3. frac-2neg 96.4%

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

      4. +-commutative 96.4%

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

      5. distribute-neg-in 96.4%

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

      6. metadata-eval 96.4%

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

      7. sub-neg 96.4%

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

      8. metadata-eval 96.4%

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

      9. associate-*r/ 99.9%

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

      10. clear-num 99.9%

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

      11. frac-times 99.9%

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

      12. *-un-lft-identity 99.9%

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

      13. metadata-eval 99.9%

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

      14. sub-neg 99.9%

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

      15. metadata-eval 99.9%

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

      16. distribute-neg-in 99.9%

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

      17. +-commutative 99.9%

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

      18. frac-2neg 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in x around 0 70.6%

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

4. Final simplification 58.2%

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

Alternative 10: 56.9% accurate, 1.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.7%

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

   1. *-commutative 92.7%

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

   2. associate-*l/ 99.7%

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

   3. *-commutative 99.7%

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

   4. associate-/l/ 99.9%

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

3. Simplified 99.9%

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

4. Taylor expanded in x around 0 57.4%

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

5. Final simplification 57.4%

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

Alternative 11: 57.8% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if x < -1

   1. Initial program 83.0%

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

      1. times-frac 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 98.2%

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

      1. neg-mul-1 98.2%

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

      2. distribute-neg-frac 98.2%

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

   6. Simplified 98.2%

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

   7. Taylor expanded in x around 0 23.0%

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

      1. mul-1-neg 23.0%

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

      2. distribute-neg-frac 23.0%

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

   9. Simplified 23.0%

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

   if -1 < x

   1. Initial program 96.2%

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

      1. *-commutative 96.2%

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

      2. associate-*l/ 99.7%

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

      3. *-commutative 99.7%

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

      4. associate-/l/ 99.9%

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

   3. Simplified 99.9%

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

      1. associate-*r/ 96.4%

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

      2. *-commutative 96.4%

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

      3. frac-2neg 96.4%

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

      4. +-commutative 96.4%

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

      5. distribute-neg-in 96.4%

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

      6. metadata-eval 96.4%

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

      7. sub-neg 96.4%

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

      8. metadata-eval 96.4%

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

      9. associate-*r/ 99.9%

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

      10. clear-num 99.9%

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

      11. frac-times 99.9%

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

      12. *-un-lft-identity 99.9%

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

      13. metadata-eval 99.9%

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

      14. sub-neg 99.9%

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

      15. metadata-eval 99.9%

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

      16. distribute-neg-in 99.9%

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

      17. +-commutative 99.9%

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

      18. frac-2neg 99.9%

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

   5. Applied egg-rr 99.9%

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

   6. Taylor expanded in x around 0 70.6%

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

4. Final simplification 58.2%

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

Alternative 12: 56.9% accurate, 2.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.7%

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

   1. *-commutative 92.7%

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

   2. associate-*l/ 99.7%

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

   3. *-commutative 99.7%

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

   4. associate-/l/ 99.9%

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

3. Simplified 99.9%

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

   1. associate-*r/ 92.9%

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

   2. *-commutative 92.9%

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

   3. frac-2neg 92.9%

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

   4. +-commutative 92.9%

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

   5. distribute-neg-in 92.9%

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

   6. metadata-eval 92.9%

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

   7. sub-neg 92.9%

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

   8. metadata-eval 92.9%

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

   9. associate-*r/ 99.9%

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

   10. clear-num 99.8%

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

   11. frac-times 99.8%

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

   12. *-un-lft-identity 99.8%

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

   13. metadata-eval 99.8%

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

   14. sub-neg 99.8%

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

   15. metadata-eval 99.8%

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

   16. distribute-neg-in 99.8%

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

   17. +-commutative 99.8%

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

   18. frac-2neg 99.8%

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

5. Applied egg-rr 99.8%

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

6. Taylor expanded in x around 0 57.4%

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

7. Final simplification 57.4%

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

Alternative 13: 51.5% accurate, 3.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.7%

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

   1. *-commutative 92.7%

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

   2. associate-*l/ 99.7%

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

   3. *-commutative 99.7%

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

   4. associate-/l/ 99.9%

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

3. Simplified 99.9%

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

   1. associate-*r/ 92.9%

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

   2. *-commutative 92.9%

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

   3. frac-2neg 92.9%

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

   4. +-commutative 92.9%

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

   5. distribute-neg-in 92.9%

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

   6. metadata-eval 92.9%

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

   7. sub-neg 92.9%

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

   8. metadata-eval 92.9%

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

   9. associate-*r/ 99.9%

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

   10. clear-num 99.8%

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

   11. frac-times 99.8%

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

   12. *-un-lft-identity 99.8%

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

   13. metadata-eval 99.8%

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

   14. sub-neg 99.8%

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

   15. metadata-eval 99.8%

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

   16. distribute-neg-in 99.8%

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

   17. +-commutative 99.8%

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

   18. frac-2neg 99.8%

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

5. Applied egg-rr 99.8%

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

6. Taylor expanded in x around 0 53.4%

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

7. Final simplification 53.4%

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

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 2023333 
(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)))