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

Percentage Accurate: 94.1% → 99.8%

Time: 9.0s

Alternatives: 15

Speedup: 1.0×

• 25.3% 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: 94.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.9%

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

   1. associate-/l* 99.7%

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

   2. *-commutative 99.7%

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

3. Simplified 99.7%

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

   1. associate-/l* 99.5%

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

   2. associate-/r/ 99.9%

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

5. Applied egg-rr 99.9%

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

6. Final simplification 99.9%

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

Alternative 2: 98.3% accurate, 0.8× speedup

Math

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

FPCore

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

C

double code(double x, double y) {
	double tmp;
	if ((x <= -2.3) || !(x <= 1.3)) {
		tmp = x * (-0.3333333333333333 * ((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 <= (-2.3d0)) .or. (.not. (x <= 1.3d0))) then
        tmp = x * ((-0.3333333333333333d0) * ((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 <= -2.3) || !(x <= 1.3)) {
		tmp = x * (-0.3333333333333333 * ((3.0 - x) / y));
	} else {
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	}
	return tmp;
}

Python

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

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -2.3) || !(x <= 1.3))
		tmp = Float64(x * Float64(-0.3333333333333333 * Float64(Float64(3.0 - 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 <= -2.3) || ~((x <= 1.3)))
		tmp = x * (-0.3333333333333333 * ((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, -2.3], N[Not[LessEqual[x, 1.3]], $MachinePrecision]], N[(x * N[(-0.3333333333333333 * N[(N[(3.0 - x), $MachinePrecision] / y), $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 < -2.2999999999999998 or 1.30000000000000004 < x

   1. Initial program 87.5%

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

      1. *-commutative 87.5%

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

      2. times-frac 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 95.1%

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

      1. *-commutative 95.1%

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

   6. Simplified 95.1%

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

   7. Taylor expanded in y around 0 82.9%

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

      1. associate-*r/ 95.2%

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

      2. associate-*r* 95.1%

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

      3. *-commutative 95.1%

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

      4. associate-*l* 95.1%

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

   9. Simplified 95.1%

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

   if -2.2999999999999998 < x < 1.30000000000000004

   1. Initial program 99.6%

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

      1. times-frac 99.9%

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

      2. div-sub 99.9%

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

      3. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around 0 98.2%

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

   5. Taylor expanded in y around 0 98.2%

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

4. Final simplification 96.8%

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

Alternative 3: 98.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.72 \lor \neg \left(x \leq 1.75\right):\\ \;\;\;\;\frac{x}{y} \cdot \left(\left(x + -4\right) \cdot 0.3333333333333333\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -1.72) (not (<= x 1.75)))
   (* (/ x y) (* (+ x -4.0) 0.3333333333333333))
   (/ (+ 1.0 (* x -1.3333333333333333)) y)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -1.72) || !(x <= 1.75)) {
		tmp = (x / y) * ((x + -4.0) * 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 <= (-1.72d0)) .or. (.not. (x <= 1.75d0))) then
        tmp = (x / y) * ((x + (-4.0d0)) * 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 <= -1.72) || !(x <= 1.75)) {
		tmp = (x / y) * ((x + -4.0) * 0.3333333333333333);
	} else {
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -1.72) or not (x <= 1.75):
		tmp = (x / y) * ((x + -4.0) * 0.3333333333333333)
	else:
		tmp = (1.0 + (x * -1.3333333333333333)) / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -1.72) || !(x <= 1.75))
		tmp = Float64(Float64(x / y) * Float64(Float64(x + -4.0) * 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 <= -1.72) || ~((x <= 1.75)))
		tmp = (x / y) * ((x + -4.0) * 0.3333333333333333);
	else
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -1.72], N[Not[LessEqual[x, 1.75]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] * N[(N[(x + -4.0), $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 < -1.71999999999999997 or 1.75 < x

   1. Initial program 87.5%

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

   2. Taylor expanded in x around inf 84.4%

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

      1. +-commutative 84.4%

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

      2. unpow2 84.4%

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

      3. distribute-rgt-out 84.4%

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

   4. Simplified 84.4%

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

      1. times-frac 96.7%

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

      2. div-inv 96.6%

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

      3. metadata-eval 96.6%

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

   6. Applied egg-rr 96.6%

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

   if -1.71999999999999997 < 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. times-frac 99.9%

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

      2. div-sub 99.9%

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

      3. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around 0 98.2%

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

   5. Taylor expanded in y around 0 98.2%

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

4. Final simplification 97.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.72 \lor \neg \left(x \leq 1.75\right):\\ \;\;\;\;\frac{x}{y} \cdot \left(\left(x + -4\right) \cdot 0.3333333333333333\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \end{array} \]

Alternative 4: 98.3% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 3 regimes

2. if x < -2.2999999999999998

   1. Initial program 88.3%

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

      1. associate-*l/ 99.7%

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

      2. *-commutative 99.7%

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

      3. associate-/r* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 95.9%

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

      1. *-commutative 95.9%

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

   6. Simplified 95.9%

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

   if -2.2999999999999998 < x < 1.3500000000000001

   1. Initial program 99.6%

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

      1. times-frac 99.9%

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

      2. div-sub 99.9%

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

      3. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around 0 98.2%

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

   5. Taylor expanded in y around 0 98.2%

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

   if 1.3500000000000001 < x

   1. Initial program 86.6%

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

      1. *-commutative 86.6%

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

      2. times-frac 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 94.2%

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

      1. *-commutative 94.2%

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

   6. Simplified 94.2%

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

   7. Taylor expanded in y around 0 81.2%

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

      1. associate-*r/ 94.3%

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

      2. associate-*r* 94.2%

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

      3. *-commutative 94.2%

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

      4. associate-*l* 94.3%

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

   9. Simplified 94.3%

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

4. Final simplification 96.8%

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

Alternative 5: 98.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.72:\\ \;\;\;\;\frac{x + -4}{y} \cdot \left(x \cdot 0.3333333333333333\right)\\ \mathbf{elif}\;x \leq 1.75:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(\left(x + -4\right) \cdot 0.3333333333333333\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.72)
   (* (/ (+ x -4.0) y) (* x 0.3333333333333333))
   (if (<= x 1.75)
     (/ (+ 1.0 (* x -1.3333333333333333)) y)
     (* (/ x y) (* (+ x -4.0) 0.3333333333333333)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.72) {
		tmp = ((x + -4.0) / y) * (x * 0.3333333333333333);
	} else if (x <= 1.75) {
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	} else {
		tmp = (x / y) * ((x + -4.0) * 0.3333333333333333);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-1.72d0)) then
        tmp = ((x + (-4.0d0)) / y) * (x * 0.3333333333333333d0)
    else if (x <= 1.75d0) then
        tmp = (1.0d0 + (x * (-1.3333333333333333d0))) / y
    else
        tmp = (x / y) * ((x + (-4.0d0)) * 0.3333333333333333d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -1.72) {
		tmp = ((x + -4.0) / y) * (x * 0.3333333333333333);
	} else if (x <= 1.75) {
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	} else {
		tmp = (x / y) * ((x + -4.0) * 0.3333333333333333);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.72:
		tmp = ((x + -4.0) / y) * (x * 0.3333333333333333)
	elif x <= 1.75:
		tmp = (1.0 + (x * -1.3333333333333333)) / y
	else:
		tmp = (x / y) * ((x + -4.0) * 0.3333333333333333)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.72)
		tmp = Float64(Float64(Float64(x + -4.0) / y) * Float64(x * 0.3333333333333333));
	elseif (x <= 1.75)
		tmp = Float64(Float64(1.0 + Float64(x * -1.3333333333333333)) / y);
	else
		tmp = Float64(Float64(x / y) * Float64(Float64(x + -4.0) * 0.3333333333333333));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.72)
		tmp = ((x + -4.0) / y) * (x * 0.3333333333333333);
	elseif (x <= 1.75)
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	else
		tmp = (x / y) * ((x + -4.0) * 0.3333333333333333);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.72], N[(N[(N[(x + -4.0), $MachinePrecision] / y), $MachinePrecision] * N[(x * 0.3333333333333333), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.75], N[(N[(1.0 + N[(x * -1.3333333333333333), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(N[(x / y), $MachinePrecision] * N[(N[(x + -4.0), $MachinePrecision] * 0.3333333333333333), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.71999999999999997

   1. Initial program 88.3%

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

   2. Taylor expanded in x around inf 86.0%

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

      1. +-commutative 86.0%

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

      2. unpow2 86.0%

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

      3. distribute-rgt-out 86.0%

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

   4. Simplified 86.0%

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

      1. *-commutative 86.0%

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

      2. times-frac 97.5%

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

      3. div-inv 97.4%

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

      4. metadata-eval 97.4%

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

   6. Applied egg-rr 97.4%

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

   if -1.71999999999999997 < 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. times-frac 99.9%

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

      2. div-sub 99.9%

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

      3. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around 0 98.2%

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

   5. Taylor expanded in y around 0 98.2%

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

   if 1.75 < x

   1. Initial program 86.6%

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

   2. Taylor expanded in x around inf 82.7%

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

      1. +-commutative 82.7%

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

      2. unpow2 82.7%

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

      3. distribute-rgt-out 82.7%

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

   4. Simplified 82.7%

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

      1. times-frac 95.8%

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

      2. div-inv 95.7%

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

      3. metadata-eval 95.7%

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

   6. Applied egg-rr 95.7%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot \left(\left(x + -4\right) \cdot 0.3333333333333333\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 97.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.72:\\ \;\;\;\;\frac{x + -4}{y} \cdot \left(x \cdot 0.3333333333333333\right)\\ \mathbf{elif}\;x \leq 1.75:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(\left(x + -4\right) \cdot 0.3333333333333333\right)\\ \end{array} \]

Alternative 6: 97.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.75 \lor \neg \left(x \leq 3\right):\\ \;\;\;\;0.3333333333333333 \cdot \left(x \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1 - x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -3.75) (not (<= x 3.0)))
   (* 0.3333333333333333 (* x (/ x y)))
   (/ (- 1.0 x) y)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -3.75) || !(x <= 3.0)) {
		tmp = 0.3333333333333333 * (x * (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 <= (-3.75d0)) .or. (.not. (x <= 3.0d0))) then
        tmp = 0.3333333333333333d0 * (x * (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 <= -3.75) || !(x <= 3.0)) {
		tmp = 0.3333333333333333 * (x * (x / y));
	} else {
		tmp = (1.0 - x) / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -3.75) or not (x <= 3.0):
		tmp = 0.3333333333333333 * (x * (x / y))
	else:
		tmp = (1.0 - x) / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -3.75) || !(x <= 3.0))
		tmp = Float64(0.3333333333333333 * Float64(x * 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 <= -3.75) || ~((x <= 3.0)))
		tmp = 0.3333333333333333 * (x * (x / y));
	else
		tmp = (1.0 - x) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -3.75], N[Not[LessEqual[x, 3.0]], $MachinePrecision]], N[(0.3333333333333333 * N[(x * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.75 or 3 < x

   1. Initial program 87.5%

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

      1. associate-/l* 99.7%

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

      2. *-commutative 99.7%

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

   3. Simplified 99.7%

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

      1. associate-/l* 99.7%

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

      2. associate-/r/ 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in x around inf 82.6%

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

      1. unpow2 82.6%

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

      2. associate-/l* 94.7%

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

   8. Simplified 94.7%

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

      1. associate-/r/ 94.8%

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

   10. Applied egg-rr 94.8%

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

   if -3.75 < x < 3

   1. Initial program 99.6%

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

      1. associate-/l* 99.8%

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

      2. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 96.7%

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

4. Final simplification 95.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.75 \lor \neg \left(x \leq 3\right):\\ \;\;\;\;0.3333333333333333 \cdot \left(x \cdot \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1 - x}{y}\\ \end{array} \]

Alternative 7: 97.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.75:\\ \;\;\;\;0.3333333333333333 \cdot \left(x \cdot \frac{x}{y}\right)\\ \mathbf{elif}\;x \leq 3:\\ \;\;\;\;\frac{1 - x}{y}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{x}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -3.75)
   (* 0.3333333333333333 (* x (/ x y)))
   (if (<= x 3.0) (/ (- 1.0 x) y) (* 0.3333333333333333 (/ x (/ y x))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -3.75) {
		tmp = 0.3333333333333333 * (x * (x / y));
	} else if (x <= 3.0) {
		tmp = (1.0 - x) / 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 <= (-3.75d0)) then
        tmp = 0.3333333333333333d0 * (x * (x / y))
    else if (x <= 3.0d0) then
        tmp = (1.0d0 - x) / 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 <= -3.75) {
		tmp = 0.3333333333333333 * (x * (x / y));
	} else if (x <= 3.0) {
		tmp = (1.0 - x) / y;
	} else {
		tmp = 0.3333333333333333 * (x / (y / x));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -3.75:
		tmp = 0.3333333333333333 * (x * (x / y))
	elif x <= 3.0:
		tmp = (1.0 - x) / y
	else:
		tmp = 0.3333333333333333 * (x / (y / x))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -3.75)
		tmp = Float64(0.3333333333333333 * Float64(x * Float64(x / y)));
	elseif (x <= 3.0)
		tmp = Float64(Float64(1.0 - x) / y);
	else
		tmp = Float64(0.3333333333333333 * Float64(x / Float64(y / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -3.75)
		tmp = 0.3333333333333333 * (x * (x / y));
	elseif (x <= 3.0)
		tmp = (1.0 - x) / y;
	else
		tmp = 0.3333333333333333 * (x / (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -3.75], N[(0.3333333333333333 * N[(x * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.0], N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision], N[(0.3333333333333333 * N[(x / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.75

   1. Initial program 88.3%

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

      1. associate-/l* 99.7%

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

      2. *-commutative 99.7%

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

   3. Simplified 99.7%

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

      1. associate-/l* 99.8%

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

      2. associate-/r/ 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in x around inf 84.1%

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

      1. unpow2 84.1%

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

      2. associate-/l* 95.4%

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

   8. Simplified 95.4%

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

      1. associate-/r/ 95.6%

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

   10. Applied egg-rr 95.6%

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

   if -3.75 < x < 3

   1. Initial program 99.6%

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

      1. associate-/l* 99.8%

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

      2. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 96.7%

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

   if 3 < x

   1. Initial program 86.6%

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

      1. associate-/l* 99.6%

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

      2. *-commutative 99.6%

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

   3. Simplified 99.6%

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

      1. associate-/l* 99.7%

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

      2. associate-/r/ 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in x around inf 80.8%

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

      1. unpow2 80.8%

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

      2. associate-/l* 94.0%

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

   8. Simplified 94.0%

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

4. Final simplification 95.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.75:\\ \;\;\;\;0.3333333333333333 \cdot \left(x \cdot \frac{x}{y}\right)\\ \mathbf{elif}\;x \leq 3:\\ \;\;\;\;\frac{1 - x}{y}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{x}{\frac{y}{x}}\\ \end{array} \]

Alternative 8: 97.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.75:\\ \;\;\;\;x \cdot \left(0.3333333333333333 \cdot \frac{x}{y}\right)\\ \mathbf{elif}\;x \leq 3:\\ \;\;\;\;\frac{1 - x}{y}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{x}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -3.75)
   (* x (* 0.3333333333333333 (/ x y)))
   (if (<= x 3.0) (/ (- 1.0 x) y) (* 0.3333333333333333 (/ x (/ y x))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -3.75) {
		tmp = x * (0.3333333333333333 * (x / y));
	} else if (x <= 3.0) {
		tmp = (1.0 - x) / 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 <= (-3.75d0)) then
        tmp = x * (0.3333333333333333d0 * (x / y))
    else if (x <= 3.0d0) then
        tmp = (1.0d0 - x) / 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 <= -3.75) {
		tmp = x * (0.3333333333333333 * (x / y));
	} else if (x <= 3.0) {
		tmp = (1.0 - x) / y;
	} else {
		tmp = 0.3333333333333333 * (x / (y / x));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -3.75:
		tmp = x * (0.3333333333333333 * (x / y))
	elif x <= 3.0:
		tmp = (1.0 - x) / y
	else:
		tmp = 0.3333333333333333 * (x / (y / x))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -3.75)
		tmp = Float64(x * Float64(0.3333333333333333 * Float64(x / y)));
	elseif (x <= 3.0)
		tmp = Float64(Float64(1.0 - x) / y);
	else
		tmp = Float64(0.3333333333333333 * Float64(x / Float64(y / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -3.75)
		tmp = x * (0.3333333333333333 * (x / y));
	elseif (x <= 3.0)
		tmp = (1.0 - x) / y;
	else
		tmp = 0.3333333333333333 * (x / (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -3.75], N[(x * N[(0.3333333333333333 * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.0], N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision], N[(0.3333333333333333 * N[(x / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.75

   1. Initial program 88.3%

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

   2. Taylor expanded in x around inf 84.2%

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

      1. unpow2 84.2%

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

   4. Simplified 84.2%

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

      1. div-inv 84.1%

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

      2. associate-*l* 95.5%

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

      3. add-sqr-sqrt 0.0%

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

      4. sqrt-prod 0.6%

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

      5. sqr-neg 0.6%

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

      6. sqrt-unprod 0.6%

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

      7. add-sqr-sqrt 0.6%

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

      8. div-inv 0.6%

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

      9. *-commutative 0.6%

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

      10. associate-/l/ 0.6%

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

      11. div-inv 0.6%

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

      12. add-sqr-sqrt 0.6%

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

      13. sqrt-unprod 0.6%

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

      14. sqr-neg 0.6%

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

      15. sqrt-prod 0.0%

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

      16. add-sqr-sqrt 95.6%

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

      17. metadata-eval 95.6%

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

   6. Applied egg-rr 95.6%

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

   if -3.75 < x < 3

   1. Initial program 99.6%

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

      1. associate-/l* 99.8%

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

      2. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 96.7%

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

   if 3 < x

   1. Initial program 86.6%

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

      1. associate-/l* 99.6%

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

      2. *-commutative 99.6%

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

   3. Simplified 99.6%

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

      1. associate-/l* 99.7%

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

      2. associate-/r/ 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in x around inf 80.8%

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

      1. unpow2 80.8%

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

      2. associate-/l* 94.0%

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

   8. Simplified 94.0%

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

4. Final simplification 95.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.75:\\ \;\;\;\;x \cdot \left(0.3333333333333333 \cdot \frac{x}{y}\right)\\ \mathbf{elif}\;x \leq 3:\\ \;\;\;\;\frac{1 - x}{y}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{x}{\frac{y}{x}}\\ \end{array} \]

Alternative 9: 98.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -4.6)
		tmp = Float64(x * Float64(0.3333333333333333 * 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 / x)));
	end
	return tmp
end

MATLAB

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

Wolfram

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

Derivation

1. Split input into 3 regimes

2. if x < -4.5999999999999996

   1. Initial program 88.3%

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

   2. Taylor expanded in x around inf 84.2%

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

      1. unpow2 84.2%

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

   4. Simplified 84.2%

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

      1. div-inv 84.1%

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

      2. associate-*l* 95.5%

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

      3. add-sqr-sqrt 0.0%

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

      4. sqrt-prod 0.6%

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

      5. sqr-neg 0.6%

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

      6. sqrt-unprod 0.6%

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

      7. add-sqr-sqrt 0.6%

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

      8. div-inv 0.6%

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

      9. *-commutative 0.6%

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

      10. associate-/l/ 0.6%

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

      11. div-inv 0.6%

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

      12. add-sqr-sqrt 0.6%

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

      13. sqrt-unprod 0.6%

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

      14. sqr-neg 0.6%

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

      15. sqrt-prod 0.0%

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

      16. add-sqr-sqrt 95.6%

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

      17. metadata-eval 95.6%

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

   6. Applied egg-rr 95.6%

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

   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. times-frac 99.9%

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

      2. div-sub 99.9%

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

      3. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around 0 98.2%

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

   5. Taylor expanded in y around 0 98.2%

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

   if 3 < x

   1. Initial program 86.6%

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

      1. associate-/l* 99.6%

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

      2. *-commutative 99.6%

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

   3. Simplified 99.6%

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

      1. associate-/l* 99.7%

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

      2. associate-/r/ 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in x around inf 80.8%

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

      1. unpow2 80.8%

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

      2. associate-/l* 94.0%

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

   8. Simplified 94.0%

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

4. Final simplification 96.6%

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

Alternative 10: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.9%

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

   1. associate-*l/ 99.5%

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

   2. *-commutative 99.5%

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

   3. associate-/r* 99.8%

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

3. Simplified 99.8%

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

4. Final simplification 99.8%

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

Alternative 11: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y) {
	return ((1.0 - x) / y) * (1.0 - (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) * (1.0d0 - (x / 3.0d0))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.9%

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

   1. times-frac 99.8%

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

   2. div-sub 99.8%

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

   3. metadata-eval 99.8%

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

3. Simplified 99.8%

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

4. Final simplification 99.8%

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

Alternative 12: 58.1% 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 88.3%

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

   2. Taylor expanded in x around inf 86.0%

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

      1. +-commutative 86.0%

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

      2. unpow2 86.0%

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

      3. distribute-rgt-out 86.0%

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

   4. Simplified 86.0%

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

   5. Taylor expanded in x around 0 32.5%

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

   if -0.75 < x

   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%

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

      2. div-sub 99.8%

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

      3. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 69.2%

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

4. Final simplification 59.9%

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

Alternative 13: 58.1% 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 88.3%

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

      1. associate-*l/ 99.7%

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

      2. *-commutative 99.7%

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

      3. associate-/r* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 95.9%

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

      1. neg-mul-1 95.9%

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

      2. distribute-neg-frac 95.9%

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

   6. Simplified 95.9%

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

   7. Taylor expanded in x around 0 32.5%

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

      1. mul-1-neg 32.5%

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

      2. distribute-neg-frac 32.5%

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

   9. Simplified 32.5%

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

   if -1 < x

   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%

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

      2. div-sub 99.8%

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

      3. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 69.2%

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

4. Final simplification 59.9%

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

Alternative 14: 57.2% 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 93.9%

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

   1. associate-/l* 99.7%

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

   2. *-commutative 99.7%

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

3. Simplified 99.7%

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

4. Taylor expanded in x around 0 59.1%

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

5. Final simplification 59.1%

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

Alternative 15: 51.6% accurate, 3.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.9%

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

   1. times-frac 99.8%

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

   2. div-sub 99.8%

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

   3. metadata-eval 99.8%

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

3. Simplified 99.8%

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

4. Taylor expanded in x around 0 52.9%

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

5. Final simplification 52.9%

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

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 2023187 
(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)))