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

Percentage Accurate: 94.2% → 99.8%

Time: 7.5s

Alternatives: 16

Speedup: 1.0×

• 25.4% 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: 94.2% 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

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.7%

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

   1. times-frac 99.8%

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

3. Simplified 99.8%

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

4. Final simplification 99.8%

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

Alternative 2: 98.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.8 \lor \neg \left(x \leq 3\right):\\ \;\;\;\;\left(1 - x\right) \cdot \left(\frac{x}{y} \cdot -0.3333333333333333\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -3.8) (not (<= x 3.0)))
   (* (- 1.0 x) (* (/ x y) -0.3333333333333333))
   (/ (+ 1.0 (* x -1.3333333333333333)) y)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -3.8) || !(x <= 3.0)) {
		tmp = (1.0 - 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 <= (-3.8d0)) .or. (.not. (x <= 3.0d0))) then
        tmp = (1.0d0 - 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 <= -3.8) || !(x <= 3.0)) {
		tmp = (1.0 - x) * ((x / y) * -0.3333333333333333);
	} else {
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -3.8) or not (x <= 3.0):
		tmp = (1.0 - 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 <= -3.8) || !(x <= 3.0))
		tmp = Float64(Float64(1.0 - 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 <= -3.8) || ~((x <= 3.0)))
		tmp = (1.0 - 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, -3.8], N[Not[LessEqual[x, 3.0]], $MachinePrecision]], N[(N[(1.0 - 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 < -3.7999999999999998 or 3 < x

   1. Initial program 91.8%

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

      1. *-commutative 91.8%

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

      2. associate-*l/ 99.8%

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

      3. *-commutative 99.8%

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

      4. *-lft-identity 99.8%

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

      5. associate-*l/ 99.7%

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

      6. *-commutative 99.7%

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

      7. *-commutative 99.7%

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

      8. associate-/r* 99.6%

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

      9. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in x around inf 96.9%

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

   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/ 99.7%

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

      3. *-commutative 99.7%

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

      4. *-lft-identity 99.7%

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

      5. associate-*l/ 99.4%

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

      6. *-commutative 99.4%

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

      7. *-commutative 99.4%

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

      8. associate-/r* 99.4%

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

      9. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in x around 0 98.8%

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

   5. Taylor expanded in y around 0 98.8%

      \[\leadsto \color{blue}{\frac{1 + -1.3333333333333333 \cdot x}{y}} \]
   6. Step-by-step derivation

      1. *-commutative 98.8%

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

   7. Simplified 98.8%

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

4. Final simplification 97.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.8 \lor \neg \left(x \leq 3\right):\\ \;\;\;\;\left(1 - x\right) \cdot \left(\frac{x}{y} \cdot -0.3333333333333333\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \end{array} \]

Alternative 3: 98.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.8 \lor \neg \left(x \leq 3\right):\\ \;\;\;\;\left(1 - x\right) \cdot \frac{x}{\frac{y}{-0.3333333333333333}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -3.8) (not (<= x 3.0)))
   (* (- 1.0 x) (/ x (/ y -0.3333333333333333)))
   (/ (+ 1.0 (* x -1.3333333333333333)) y)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -3.8) || !(x <= 3.0)) {
		tmp = (1.0 - 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 <= (-3.8d0)) .or. (.not. (x <= 3.0d0))) then
        tmp = (1.0d0 - 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 <= -3.8) || !(x <= 3.0)) {
		tmp = (1.0 - x) * (x / (y / -0.3333333333333333));
	} else {
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -3.8) or not (x <= 3.0):
		tmp = (1.0 - 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 <= -3.8) || !(x <= 3.0))
		tmp = Float64(Float64(1.0 - x) * Float64(x / Float64(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 <= -3.8) || ~((x <= 3.0)))
		tmp = (1.0 - 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, -3.8], N[Not[LessEqual[x, 3.0]], $MachinePrecision]], N[(N[(1.0 - x), $MachinePrecision] * N[(x / N[(y / -0.3333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 + N[(x * -1.3333333333333333), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.7999999999999998 or 3 < x

   1. Initial program 91.8%

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

      1. *-commutative 91.8%

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

      2. associate-*l/ 99.8%

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

      3. *-commutative 99.8%

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

      4. *-lft-identity 99.8%

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

      5. associate-*l/ 99.7%

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

      6. *-commutative 99.7%

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

      7. *-commutative 99.7%

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

      8. associate-/r* 99.6%

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

      9. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in x around inf 96.9%

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

      1. associate-*r/ 96.9%

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

      2. *-commutative 96.9%

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

      3. associate-/l* 97.0%

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

   6. Simplified 97.0%

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

   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/ 99.7%

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

      3. *-commutative 99.7%

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

      4. *-lft-identity 99.7%

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

      5. associate-*l/ 99.4%

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

      6. *-commutative 99.4%

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

      7. *-commutative 99.4%

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

      8. associate-/r* 99.4%

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

      9. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in x around 0 98.8%

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

   5. Taylor expanded in y around 0 98.8%

      \[\leadsto \color{blue}{\frac{1 + -1.3333333333333333 \cdot x}{y}} \]
   6. Step-by-step derivation

      1. *-commutative 98.8%

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

   7. Simplified 98.8%

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

4. Final simplification 97.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.8 \lor \neg \left(x \leq 3\right):\\ \;\;\;\;\left(1 - x\right) \cdot \frac{x}{\frac{y}{-0.3333333333333333}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \end{array} \]

Alternative 4: 98.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.75 \lor \neg \left(x \leq 1.75\right):\\ \;\;\;\;\frac{x}{y} \cdot \left(0.3333333333333333 \cdot \left(x + -4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -1.75) (not (<= x 1.75)))
   (* (/ x y) (* 0.3333333333333333 (+ x -4.0)))
   (/ (+ 1.0 (* x -1.3333333333333333)) y)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -1.75) || !(x <= 1.75)) {
		tmp = (x / y) * (0.3333333333333333 * (x + -4.0));
	} else {
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-1.75d0)) .or. (.not. (x <= 1.75d0))) then
        tmp = (x / y) * (0.3333333333333333d0 * (x + (-4.0d0)))
    else
        tmp = (1.0d0 + (x * (-1.3333333333333333d0))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -1.75) || !(x <= 1.75)) {
		tmp = (x / y) * (0.3333333333333333 * (x + -4.0));
	} else {
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -1.75) or not (x <= 1.75):
		tmp = (x / y) * (0.3333333333333333 * (x + -4.0))
	else:
		tmp = (1.0 + (x * -1.3333333333333333)) / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -1.75) || !(x <= 1.75))
		tmp = Float64(Float64(x / y) * Float64(0.3333333333333333 * Float64(x + -4.0)));
	else
		tmp = Float64(Float64(1.0 + Float64(x * -1.3333333333333333)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -1.75) || ~((x <= 1.75)))
		tmp = (x / y) * (0.3333333333333333 * (x + -4.0));
	else
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -1.75], N[Not[LessEqual[x, 1.75]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] * N[(0.3333333333333333 * N[(x + -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 + N[(x * -1.3333333333333333), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.75 or 1.75 < x

   1. Initial program 91.8%

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

   2. Taylor expanded in x around inf 90.9%

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

      1. +-commutative 90.9%

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

      2. unpow2 90.9%

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

      3. distribute-rgt-out 90.9%

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

   4. Simplified 90.9%

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

      1. times-frac 98.8%

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

      2. div-inv 98.8%

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

      3. metadata-eval 98.8%

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

   6. Applied egg-rr 98.8%

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

   if -1.75 < 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/ 99.7%

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

      3. *-commutative 99.7%

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

      4. *-lft-identity 99.7%

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

      5. associate-*l/ 99.4%

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

      6. *-commutative 99.4%

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

      7. *-commutative 99.4%

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

      8. associate-/r* 99.4%

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

      9. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in x around 0 98.8%

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

   5. Taylor expanded in y around 0 98.8%

      \[\leadsto \color{blue}{\frac{1 + -1.3333333333333333 \cdot x}{y}} \]
   6. Step-by-step derivation

      1. *-commutative 98.8%

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

   7. Simplified 98.8%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.75 \lor \neg \left(x \leq 1.75\right):\\ \;\;\;\;\frac{x}{y} \cdot \left(0.3333333333333333 \cdot \left(x + -4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \end{array} \]

Alternative 5: 98.3% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 3 regimes

2. if x < -4.5999999999999996

   1. Initial program 91.6%

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

   2. Taylor expanded in x around inf 91.0%

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

      1. +-commutative 91.0%

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

      2. unpow2 91.0%

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

      3. distribute-rgt-out 91.0%

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

   4. Simplified 91.0%

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

      1. *-commutative 91.0%

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

      2. times-frac 99.0%

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

   6. Applied egg-rr 99.0%

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

   7. Taylor expanded in x around inf 97.7%

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

   if -4.5999999999999996 < 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/ 99.7%

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

      3. *-commutative 99.7%

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

      4. *-lft-identity 99.7%

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

      5. associate-*l/ 99.4%

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

      6. *-commutative 99.4%

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

      7. *-commutative 99.4%

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

      8. associate-/r* 99.4%

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

      9. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in x around 0 98.8%

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

   5. Taylor expanded in y around 0 98.8%

      \[\leadsto \color{blue}{\frac{1 + -1.3333333333333333 \cdot x}{y}} \]
   6. Step-by-step derivation

      1. *-commutative 98.8%

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

   7. Simplified 98.8%

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

   if 3 < x

   1. Initial program 92.0%

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

      1. *-commutative 92.0%

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

      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. *-lft-identity 99.7%

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

      5. associate-*l/ 99.7%

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

      6. *-commutative 99.7%

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

      7. *-commutative 99.7%

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

      8. associate-/r* 99.6%

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

      9. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in x around inf 95.9%

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

      1. associate-*r/ 95.9%

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

      2. *-commutative 95.9%

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

      3. associate-/l* 96.0%

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

   6. Simplified 96.0%

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

   7. Taylor expanded in y around 0 88.2%

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

      1. associate-/l* 95.9%

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

   9. Simplified 95.9%

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

4. Final simplification 97.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.6:\\ \;\;\;\;\frac{x}{3} \cdot \frac{x}{y}\\ \mathbf{elif}\;x \leq 3:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{x}{\frac{y}{1 - x}}\\ \end{array} \]

Alternative 6: 98.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.75:\\ \;\;\;\;\frac{x}{y} \cdot \left(0.3333333333333333 \cdot \left(x + -4\right)\right)\\ \mathbf{elif}\;x \leq 1.75:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + -4}{y} \cdot \frac{x}{3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.75)
   (* (/ x y) (* 0.3333333333333333 (+ x -4.0)))
   (if (<= x 1.75)
     (/ (+ 1.0 (* x -1.3333333333333333)) y)
     (* (/ (+ x -4.0) y) (/ x 3.0)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.75) {
		tmp = (x / y) * (0.3333333333333333 * (x + -4.0));
	} else if (x <= 1.75) {
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	} else {
		tmp = ((x + -4.0) / y) * (x / 3.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-1.75d0)) then
        tmp = (x / y) * (0.3333333333333333d0 * (x + (-4.0d0)))
    else if (x <= 1.75d0) then
        tmp = (1.0d0 + (x * (-1.3333333333333333d0))) / y
    else
        tmp = ((x + (-4.0d0)) / y) * (x / 3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -1.75) {
		tmp = (x / y) * (0.3333333333333333 * (x + -4.0));
	} else if (x <= 1.75) {
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	} else {
		tmp = ((x + -4.0) / y) * (x / 3.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.75:
		tmp = (x / y) * (0.3333333333333333 * (x + -4.0))
	elif x <= 1.75:
		tmp = (1.0 + (x * -1.3333333333333333)) / y
	else:
		tmp = ((x + -4.0) / y) * (x / 3.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.75)
		tmp = Float64(Float64(x / y) * Float64(0.3333333333333333 * Float64(x + -4.0)));
	elseif (x <= 1.75)
		tmp = Float64(Float64(1.0 + Float64(x * -1.3333333333333333)) / y);
	else
		tmp = Float64(Float64(Float64(x + -4.0) / y) * Float64(x / 3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.75)
		tmp = (x / y) * (0.3333333333333333 * (x + -4.0));
	elseif (x <= 1.75)
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	else
		tmp = ((x + -4.0) / y) * (x / 3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.75], N[(N[(x / y), $MachinePrecision] * N[(0.3333333333333333 * N[(x + -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.75], N[(N[(1.0 + N[(x * -1.3333333333333333), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(N[(x + -4.0), $MachinePrecision] / y), $MachinePrecision] * N[(x / 3.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.75

   1. Initial program 91.6%

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

   2. Taylor expanded in x around inf 91.0%

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

      1. +-commutative 91.0%

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

      2. unpow2 91.0%

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

      3. distribute-rgt-out 91.0%

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

   4. Simplified 91.0%

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

      1. times-frac 99.1%

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

      2. div-inv 99.1%

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

      3. metadata-eval 99.1%

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

   6. Applied egg-rr 99.1%

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

   if -1.75 < 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/ 99.7%

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

      3. *-commutative 99.7%

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

      4. *-lft-identity 99.7%

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

      5. associate-*l/ 99.4%

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

      6. *-commutative 99.4%

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

      7. *-commutative 99.4%

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

      8. associate-/r* 99.4%

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

      9. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in x around 0 98.8%

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

   5. Taylor expanded in y around 0 98.8%

      \[\leadsto \color{blue}{\frac{1 + -1.3333333333333333 \cdot x}{y}} \]
   6. Step-by-step derivation

      1. *-commutative 98.8%

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

   7. Simplified 98.8%

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

   if 1.75 < x

   1. Initial program 92.0%

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

   2. Taylor expanded in x around inf 90.8%

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

      1. +-commutative 90.8%

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

      2. unpow2 90.8%

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

      3. distribute-rgt-out 90.8%

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

   4. Simplified 90.8%

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

      1. *-commutative 90.8%

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

      2. times-frac 98.6%

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

   6. Applied egg-rr 98.6%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.75:\\ \;\;\;\;\frac{x}{y} \cdot \left(0.3333333333333333 \cdot \left(x + -4\right)\right)\\ \mathbf{elif}\;x \leq 1.75:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + -4}{y} \cdot \frac{x}{3}\\ \end{array} \]

Alternative 7: 98.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + -4}{y}\\ \mathbf{if}\;x \leq -1.75:\\ \;\;\;\;\frac{x \cdot t_0}{3}\\ \mathbf{elif}\;x \leq 1.75:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;t_0 \cdot \frac{x}{3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (+ x -4.0) y)))
   (if (<= x -1.75)
     (/ (* x t_0) 3.0)
     (if (<= x 1.75)
       (/ (+ 1.0 (* x -1.3333333333333333)) y)
       (* t_0 (/ x 3.0))))))

C

double code(double x, double y) {
	double t_0 = (x + -4.0) / y;
	double tmp;
	if (x <= -1.75) {
		tmp = (x * t_0) / 3.0;
	} else if (x <= 1.75) {
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	} else {
		tmp = t_0 * (x / 3.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x + (-4.0d0)) / y
    if (x <= (-1.75d0)) then
        tmp = (x * t_0) / 3.0d0
    else if (x <= 1.75d0) then
        tmp = (1.0d0 + (x * (-1.3333333333333333d0))) / y
    else
        tmp = t_0 * (x / 3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (x + -4.0) / y;
	double tmp;
	if (x <= -1.75) {
		tmp = (x * t_0) / 3.0;
	} else if (x <= 1.75) {
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	} else {
		tmp = t_0 * (x / 3.0);
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (x + -4.0) / y
	tmp = 0
	if x <= -1.75:
		tmp = (x * t_0) / 3.0
	elif x <= 1.75:
		tmp = (1.0 + (x * -1.3333333333333333)) / y
	else:
		tmp = t_0 * (x / 3.0)
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(x + -4.0) / y)
	tmp = 0.0
	if (x <= -1.75)
		tmp = Float64(Float64(x * t_0) / 3.0);
	elseif (x <= 1.75)
		tmp = Float64(Float64(1.0 + Float64(x * -1.3333333333333333)) / y);
	else
		tmp = Float64(t_0 * Float64(x / 3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (x + -4.0) / y;
	tmp = 0.0;
	if (x <= -1.75)
		tmp = (x * t_0) / 3.0;
	elseif (x <= 1.75)
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	else
		tmp = t_0 * (x / 3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(x + -4.0), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[x, -1.75], N[(N[(x * t$95$0), $MachinePrecision] / 3.0), $MachinePrecision], If[LessEqual[x, 1.75], N[(N[(1.0 + N[(x * -1.3333333333333333), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(t$95$0 * N[(x / 3.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.75

   1. Initial program 91.6%

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

   2. Taylor expanded in x around inf 91.0%

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

      1. +-commutative 91.0%

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

      2. unpow2 91.0%

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

      3. distribute-rgt-out 91.0%

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

   4. Simplified 91.0%

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

      1. *-commutative 91.0%

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

      2. times-frac 99.0%

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

   6. Applied egg-rr 99.0%

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

      1. *-commutative 99.0%

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

      2. associate-*l/ 99.1%

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

   8. Applied egg-rr 99.1%

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

   if -1.75 < 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/ 99.7%

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

      3. *-commutative 99.7%

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

      4. *-lft-identity 99.7%

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

      5. associate-*l/ 99.4%

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

      6. *-commutative 99.4%

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

      7. *-commutative 99.4%

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

      8. associate-/r* 99.4%

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

      9. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in x around 0 98.8%

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

   5. Taylor expanded in y around 0 98.8%

      \[\leadsto \color{blue}{\frac{1 + -1.3333333333333333 \cdot x}{y}} \]
   6. Step-by-step derivation

      1. *-commutative 98.8%

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

   7. Simplified 98.8%

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

   if 1.75 < x

   1. Initial program 92.0%

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

   2. Taylor expanded in x around inf 90.8%

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

      1. +-commutative 90.8%

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

      2. unpow2 90.8%

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

      3. distribute-rgt-out 90.8%

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

   4. Simplified 90.8%

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

      1. *-commutative 90.8%

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

      2. times-frac 98.6%

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

   6. Applied egg-rr 98.6%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.75:\\ \;\;\;\;\frac{x \cdot \frac{x + -4}{y}}{3}\\ \mathbf{elif}\;x \leq 1.75:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + -4}{y} \cdot \frac{x}{3}\\ \end{array} \]

Alternative 8: 98.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.75:\\ \;\;\;\;\frac{x + -4}{\frac{y \cdot 3}{x}}\\ \mathbf{elif}\;x \leq 1.75:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + -4}{y} \cdot \frac{x}{3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.75)
   (/ (+ x -4.0) (/ (* y 3.0) x))
   (if (<= x 1.75)
     (/ (+ 1.0 (* x -1.3333333333333333)) y)
     (* (/ (+ x -4.0) y) (/ x 3.0)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.75) {
		tmp = (x + -4.0) / ((y * 3.0) / x);
	} else if (x <= 1.75) {
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	} else {
		tmp = ((x + -4.0) / y) * (x / 3.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-1.75d0)) then
        tmp = (x + (-4.0d0)) / ((y * 3.0d0) / x)
    else if (x <= 1.75d0) then
        tmp = (1.0d0 + (x * (-1.3333333333333333d0))) / y
    else
        tmp = ((x + (-4.0d0)) / y) * (x / 3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -1.75) {
		tmp = (x + -4.0) / ((y * 3.0) / x);
	} else if (x <= 1.75) {
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	} else {
		tmp = ((x + -4.0) / y) * (x / 3.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.75:
		tmp = (x + -4.0) / ((y * 3.0) / x)
	elif x <= 1.75:
		tmp = (1.0 + (x * -1.3333333333333333)) / y
	else:
		tmp = ((x + -4.0) / y) * (x / 3.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.75)
		tmp = Float64(Float64(x + -4.0) / Float64(Float64(y * 3.0) / x));
	elseif (x <= 1.75)
		tmp = Float64(Float64(1.0 + Float64(x * -1.3333333333333333)) / y);
	else
		tmp = Float64(Float64(Float64(x + -4.0) / y) * Float64(x / 3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.75)
		tmp = (x + -4.0) / ((y * 3.0) / x);
	elseif (x <= 1.75)
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	else
		tmp = ((x + -4.0) / y) * (x / 3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.75], N[(N[(x + -4.0), $MachinePrecision] / N[(N[(y * 3.0), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.75], N[(N[(1.0 + N[(x * -1.3333333333333333), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(N[(x + -4.0), $MachinePrecision] / y), $MachinePrecision] * N[(x / 3.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.75

   1. Initial program 91.6%

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

   2. Taylor expanded in x around inf 91.0%

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

      1. +-commutative 91.0%

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

      2. unpow2 91.0%

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

      3. distribute-rgt-out 91.0%

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

   4. Simplified 91.0%

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

      1. *-commutative 91.0%

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

      2. times-frac 99.0%

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

   6. Applied egg-rr 99.0%

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

      1. frac-times 91.0%

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

      2. associate-/l* 99.1%

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

      3. *-commutative 99.1%

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

   8. Applied egg-rr 99.1%

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

   if -1.75 < 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/ 99.7%

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

      3. *-commutative 99.7%

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

      4. *-lft-identity 99.7%

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

      5. associate-*l/ 99.4%

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

      6. *-commutative 99.4%

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

      7. *-commutative 99.4%

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

      8. associate-/r* 99.4%

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

      9. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in x around 0 98.8%

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

   5. Taylor expanded in y around 0 98.8%

      \[\leadsto \color{blue}{\frac{1 + -1.3333333333333333 \cdot x}{y}} \]
   6. Step-by-step derivation

      1. *-commutative 98.8%

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

   7. Simplified 98.8%

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

   if 1.75 < x

   1. Initial program 92.0%

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

   2. Taylor expanded in x around inf 90.8%

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

      1. +-commutative 90.8%

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

      2. unpow2 90.8%

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

      3. distribute-rgt-out 90.8%

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

   4. Simplified 90.8%

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

      1. *-commutative 90.8%

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

      2. times-frac 98.6%

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

   6. Applied egg-rr 98.6%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.75:\\ \;\;\;\;\frac{x + -4}{\frac{y \cdot 3}{x}}\\ \mathbf{elif}\;x \leq 1.75:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + -4}{y} \cdot \frac{x}{3}\\ \end{array} \]

Alternative 9: 97.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y) {
	double tmp;
	if ((x <= -3.8) || !(x <= 3.0)) {
		tmp = (x / 3.0) * (x / y);
	} 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 = (x / 3.0d0) * (x / y)
    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 = (x / 3.0) * (x / y);
	} 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 = (x / 3.0) * (x / y)
	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(Float64(x / 3.0) * Float64(x / y));
	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 = (x / 3.0) * (x / y);
	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[(N[(x / 3.0), $MachinePrecision] * N[(x / y), $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 91.8%

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

   2. Taylor expanded in x around inf 90.9%

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

      1. +-commutative 90.9%

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

      2. unpow2 90.9%

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

      3. distribute-rgt-out 90.9%

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

   4. Simplified 90.9%

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

      1. *-commutative 90.9%

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

      2. times-frac 98.8%

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

   6. Applied egg-rr 98.8%

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

   7. Taylor expanded in x around inf 96.8%

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

   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/ 99.7%

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

      3. *-commutative 99.7%

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

      4. *-lft-identity 99.7%

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

      5. associate-*l/ 99.4%

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

      6. *-commutative 99.4%

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

      7. *-commutative 99.4%

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

      8. associate-/r* 99.4%

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

      9. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in x around 0 97.5%

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

4. Final simplification 97.2%

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

Alternative 10: 97.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y) {
	double tmp;
	if ((x <= -3.8) || !(x <= 3.0)) {
		tmp = (x / 3.0) * (x / y);
	} 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) * (x / y)
    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) * (x / y);
	} 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) * (x / y)
	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(Float64(x / 3.0) * Float64(x / y));
	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) * (x / y);
	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[(N[(x / 3.0), $MachinePrecision] * N[(x / y), $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 91.8%

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

   2. Taylor expanded in x around inf 90.9%

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

      1. +-commutative 90.9%

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

      2. unpow2 90.9%

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

      3. distribute-rgt-out 90.9%

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

   4. Simplified 90.9%

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

      1. *-commutative 90.9%

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

      2. times-frac 98.8%

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

   6. Applied egg-rr 98.8%

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

   7. Taylor expanded in x around inf 96.8%

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

   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. times-frac 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 97.5%

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

4. Final simplification 97.2%

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

Alternative 11: 98.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.6 \lor \neg \left(x \leq 0.65\right):\\ \;\;\;\;\frac{x}{3} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -4.6) (not (<= x 0.65)))
   (* (/ x 3.0) (/ x y))
   (/ (+ 1.0 (* x -1.3333333333333333)) y)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -4.6) || !(x <= 0.65)) {
		tmp = (x / 3.0) * (x / y);
	} else {
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-4.6d0)) .or. (.not. (x <= 0.65d0))) then
        tmp = (x / 3.0d0) * (x / y)
    else
        tmp = (1.0d0 + (x * (-1.3333333333333333d0))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -4.6) || !(x <= 0.65)) {
		tmp = (x / 3.0) * (x / y);
	} else {
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -4.6) or not (x <= 0.65):
		tmp = (x / 3.0) * (x / y)
	else:
		tmp = (1.0 + (x * -1.3333333333333333)) / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -4.6) || !(x <= 0.65))
		tmp = Float64(Float64(x / 3.0) * Float64(x / y));
	else
		tmp = Float64(Float64(1.0 + Float64(x * -1.3333333333333333)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -4.6) || ~((x <= 0.65)))
		tmp = (x / 3.0) * (x / y);
	else
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -4.6], N[Not[LessEqual[x, 0.65]], $MachinePrecision]], N[(N[(x / 3.0), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 + N[(x * -1.3333333333333333), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.5999999999999996 or 0.650000000000000022 < x

   1. Initial program 91.8%

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

   2. Taylor expanded in x around inf 90.9%

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

      1. +-commutative 90.9%

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

      2. unpow2 90.9%

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

      3. distribute-rgt-out 90.9%

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

   4. Simplified 90.9%

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

      1. *-commutative 90.9%

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

      2. times-frac 98.8%

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

   6. Applied egg-rr 98.8%

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

   7. Taylor expanded in x around inf 96.8%

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

   if -4.5999999999999996 < x < 0.650000000000000022

   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/ 99.7%

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

      3. *-commutative 99.7%

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

      4. *-lft-identity 99.7%

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

      5. associate-*l/ 99.4%

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

      6. *-commutative 99.4%

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

      7. *-commutative 99.4%

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

      8. associate-/r* 99.4%

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

      9. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in x around 0 98.8%

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

   5. Taylor expanded in y around 0 98.8%

      \[\leadsto \color{blue}{\frac{1 + -1.3333333333333333 \cdot x}{y}} \]
   6. Step-by-step derivation

      1. *-commutative 98.8%

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

   7. Simplified 98.8%

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

4. Final simplification 97.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.6 \lor \neg \left(x \leq 0.65\right):\\ \;\;\;\;\frac{x}{3} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \end{array} \]

Alternative 12: 99.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.7%

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

   1. *-commutative 95.7%

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

   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. *-lft-identity 99.7%

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

   5. associate-*l/ 99.6%

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

   6. *-commutative 99.6%

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

   7. *-commutative 99.6%

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

   8. associate-/r* 99.5%

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

   9. metadata-eval 99.5%

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

3. Simplified 99.5%

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

4. Final simplification 99.5%

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

Alternative 13: 57.6% accurate, 1.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if x < -0.75

   1. Initial program 91.6%

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

      1. *-commutative 91.6%

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

      2. associate-*l/ 99.8%

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

      3. *-commutative 99.8%

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

      4. *-lft-identity 99.8%

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

      5. associate-*l/ 99.8%

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

      6. *-commutative 99.8%

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

      7. *-commutative 99.8%

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

      8. associate-/r* 99.7%

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

      9. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around 0 30.0%

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

   5. Taylor expanded in x around inf 30.0%

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

      1. associate-*r/ 30.0%

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

      2. associate-*l/ 30.0%

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

      3. *-commutative 30.0%

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

   7. Simplified 30.0%

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

   if -0.75 < x

   1. Initial program 97.2%

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

      1. *-commutative 97.2%

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

      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. *-lft-identity 99.7%

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

      5. associate-*l/ 99.5%

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

      6. *-commutative 99.5%

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

      7. *-commutative 99.5%

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

      8. associate-/r* 99.5%

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

      9. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in x around 0 67.1%

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

   5. Taylor expanded in y around 0 67.1%

      \[\leadsto \color{blue}{\frac{1 + -1.3333333333333333 \cdot x}{y}} \]
   6. Step-by-step derivation

      1. *-commutative 67.1%

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

   7. Simplified 67.1%

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

   8. Taylor expanded in x around 0 67.5%

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

4. Final simplification 57.6%

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

Alternative 14: 56.6% 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 95.7%

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

   1. *-commutative 95.7%

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

   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. *-lft-identity 99.7%

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

   5. associate-*l/ 99.6%

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

   6. *-commutative 99.6%

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

   7. *-commutative 99.6%

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

   8. associate-/r* 99.5%

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

   9. metadata-eval 99.5%

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

3. Simplified 99.5%

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

4. Taylor expanded in x around 0 56.6%

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

5. Final simplification 56.6%

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

Alternative 15: 1.7% accurate, 3.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.7%

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

2. Taylor expanded in x around 0 50.8%

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

   1. div-inv 50.7%

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

   2. add-sqr-sqrt 29.4%

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

   3. sqrt-unprod 24.3%

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

   4. swap-sqr 24.3%

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

   5. metadata-eval 24.3%

      \[\leadsto 3 \cdot \frac{1}{\sqrt{\left(y \cdot y\right) \cdot \color{blue}{9}}} \]

   6. metadata-eval 24.3%

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

   7. metadata-eval 24.3%

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

   8. metadata-eval 24.3%

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

   9. swap-sqr 24.3%

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

   10. metadata-eval 24.3%

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

   11. metadata-eval 24.3%

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

   12. div-inv 24.3%

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

   13. metadata-eval 24.3%

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

   14. metadata-eval 24.3%

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

   15. div-inv 24.3%

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

   16. sqrt-unprod 0.9%

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

   17. add-sqr-sqrt 1.8%

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

   18. clear-num 1.8%

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

4. Applied egg-rr 1.8%

   \[\leadsto \color{blue}{3 \cdot \frac{-0.3333333333333333}{y}} \]
5. Step-by-step derivation

   1. associate-*r/ 1.8%

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

   2. metadata-eval 1.8%

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

6. Simplified 1.8%

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

7. Final simplification 1.8%

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

Alternative 16: 51.0% accurate, 3.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.7%

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

   1. *-commutative 95.7%

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

   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. *-lft-identity 99.7%

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

   5. associate-*l/ 99.6%

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

   6. *-commutative 99.6%

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

   7. *-commutative 99.6%

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

   8. associate-/r* 99.5%

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

   9. metadata-eval 99.5%

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

3. Simplified 99.5%

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

4. Taylor expanded in x around 0 57.3%

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

5. Taylor expanded in y around 0 57.3%

   \[\leadsto \color{blue}{\frac{1 + -1.3333333333333333 \cdot x}{y}} \]
6. Step-by-step derivation

   1. *-commutative 57.3%

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

7. Simplified 57.3%

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

8. Taylor expanded in x around 0 50.9%

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

9. Final simplification 50.9%

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

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 2023309 
(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)))