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

Percentage Accurate: 93.7% → 99.8%

Time: 19.2s

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: 93.7% 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 90.3%

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

   1. associate-/l* 99.8%

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

   2. associate-/r/ 99.9%

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

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: 97.8% accurate, 0.8× speedup

Math

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

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -1.7) (not (<= x 1.7)))
   (* (* x -0.3333333333333333) (/ (- 3.0 x) y))
   (* (- 1.0 x) (/ 1.0 y))))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -1.7) || !(x <= 1.7)) {
		tmp = (x * -0.3333333333333333) * ((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 <= (-1.7d0)) .or. (.not. (x <= 1.7d0))) then
        tmp = (x * (-0.3333333333333333d0)) * ((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 <= -1.7) || !(x <= 1.7)) {
		tmp = (x * -0.3333333333333333) * ((3.0 - x) / y);
	} else {
		tmp = (1.0 - x) * (1.0 / y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -1.7) or not (x <= 1.7):
		tmp = (x * -0.3333333333333333) * ((3.0 - x) / y)
	else:
		tmp = (1.0 - x) * (1.0 / y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -1.7) || !(x <= 1.7))
		tmp = Float64(Float64(x * -0.3333333333333333) * Float64(Float64(3.0 - 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 <= -1.7) || ~((x <= 1.7)))
		tmp = (x * -0.3333333333333333) * ((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, -1.7], N[Not[LessEqual[x, 1.7]], $MachinePrecision]], N[(N[(x * -0.3333333333333333), $MachinePrecision] * N[(N[(3.0 - x), $MachinePrecision] / 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 < -1.69999999999999996 or 1.69999999999999996 < x

   1. Initial program 82.7%

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

      1. *-commutative 82.7%

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

      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 97.5%

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

   if -1.69999999999999996 < x < 1.69999999999999996

   1. Initial program 99.5%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   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 98.5%

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

      1. clear-num 98.5%

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

      2. associate-/r/ 98.5%

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

   6. Applied egg-rr 98.5%

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

4. Final simplification 97.9%

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

Alternative 3: 98.3% accurate, 0.8× speedup

Math

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

FPCore

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

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 / y) + ((x / y) * -1.3333333333333333);
	}
	return tmp;
}

Fortran

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

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -2.3) || !(x <= 1.3))
		tmp = Float64(Float64(x * -0.3333333333333333) * Float64(Float64(3.0 - x) / y));
	else
		tmp = Float64(Float64(1.0 / y) + Float64(Float64(x / y) * -1.3333333333333333));
	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 / y) + ((x / y) * -1.3333333333333333);
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if x < -2.2999999999999998 or 1.30000000000000004 < x

   1. Initial program 82.7%

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

      1. *-commutative 82.7%

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

      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 97.5%

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

   if -2.2999999999999998 < x < 1.30000000000000004

   1. Initial program 99.5%

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

      1. associate-*l/ 99.3%

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

      2. *-commutative 99.3%

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

      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. Taylor expanded in x around 0 99.0%

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

      1. *-commutative 99.0%

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

   6. Simplified 99.0%

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

4. Final simplification 98.2%

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

Alternative 4: 98.3% accurate, 0.8× speedup

Math

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

FPCore

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

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.3) {
		tmp = -0.3333333333333333 / ((y / x) / (3.0 - x));
	} else if (x <= 1.3) {
		tmp = (1.0 / y) + ((x / y) * -1.3333333333333333);
	} 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 = (-0.3333333333333333d0) / ((y / x) / (3.0d0 - x))
    else if (x <= 1.3d0) then
        tmp = (1.0d0 / y) + ((x / y) * (-1.3333333333333333d0))
    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 = -0.3333333333333333 / ((y / x) / (3.0 - x));
	} else if (x <= 1.3) {
		tmp = (1.0 / y) + ((x / y) * -1.3333333333333333);
	} else {
		tmp = (x * -0.3333333333333333) * ((3.0 - x) / y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2.3:
		tmp = -0.3333333333333333 / ((y / x) / (3.0 - x))
	elif x <= 1.3:
		tmp = (1.0 / y) + ((x / y) * -1.3333333333333333)
	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(-0.3333333333333333 / Float64(Float64(y / x) / Float64(3.0 - x)));
	elseif (x <= 1.3)
		tmp = Float64(Float64(1.0 / y) + Float64(Float64(x / y) * -1.3333333333333333));
	else
		tmp = Float64(Float64(x * -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 = -0.3333333333333333 / ((y / x) / (3.0 - x));
	elseif (x <= 1.3)
		tmp = (1.0 / y) + ((x / y) * -1.3333333333333333);
	else
		tmp = (x * -0.3333333333333333) * ((3.0 - x) / y);
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 3 regimes

2. if x < -2.2999999999999998

   1. Initial program 86.4%

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

      1. associate-*l/ 99.8%

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

      2. *-commutative 99.8%

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

      3. 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. Taylor expanded in x around inf 97.3%

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

   5. Taylor expanded in y around 0 84.0%

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

      1. clear-num 84.0%

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

      2. un-div-inv 84.0%

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

      3. *-commutative 84.0%

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

      4. associate-/r* 97.3%

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

   7. Applied egg-rr 97.3%

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

   if -2.2999999999999998 < x < 1.30000000000000004

   1. Initial program 99.5%

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

      1. associate-*l/ 99.3%

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

      2. *-commutative 99.3%

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

      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. Taylor expanded in x around 0 99.0%

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

      1. *-commutative 99.0%

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

   6. Simplified 99.0%

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

   if 1.30000000000000004 < x

   1. Initial program 79.1%

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

      1. *-commutative 79.1%

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

      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 97.6%

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

4. Final simplification 98.2%

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

Alternative 5: 98.3% accurate, 0.8× speedup

Math

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

FPCore

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

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.3) {
		tmp = (3.0 - x) / (-y / (x * 0.3333333333333333));
	} else if (x <= 1.3) {
		tmp = (1.0 / y) + ((x / y) * -1.3333333333333333);
	} 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) / (-y / (x * 0.3333333333333333d0))
    else if (x <= 1.3d0) then
        tmp = (1.0d0 / y) + ((x / y) * (-1.3333333333333333d0))
    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) / (-y / (x * 0.3333333333333333));
	} else if (x <= 1.3) {
		tmp = (1.0 / y) + ((x / y) * -1.3333333333333333);
	} 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) / (-y / (x * 0.3333333333333333))
	elif x <= 1.3:
		tmp = (1.0 / y) + ((x / y) * -1.3333333333333333)
	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(-y) / Float64(x * 0.3333333333333333)));
	elseif (x <= 1.3)
		tmp = Float64(Float64(1.0 / y) + Float64(Float64(x / y) * -1.3333333333333333));
	else
		tmp = Float64(Float64(x * -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) / (-y / (x * 0.3333333333333333));
	elseif (x <= 1.3)
		tmp = (1.0 / y) + ((x / y) * -1.3333333333333333);
	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[((-y) / N[(x * 0.3333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.3], N[(N[(1.0 / y), $MachinePrecision] + N[(N[(x / y), $MachinePrecision] * -1.3333333333333333), $MachinePrecision]), $MachinePrecision], N[(N[(x * -0.3333333333333333), $MachinePrecision] * N[(N[(3.0 - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.2999999999999998

   1. Initial program 86.4%

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

      1. associate-*l/ 99.8%

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

      2. *-commutative 99.8%

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

      3. 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. Taylor expanded in x around inf 97.3%

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

      1. associate-*r* 97.3%

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

      2. frac-2neg 97.3%

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

      3. associate-*r/ 84.0%

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

   6. Applied egg-rr 84.0%

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

      1. associate-*l* 84.0%

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

      2. *-commutative 84.0%

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

      3. distribute-lft-neg-in 84.0%

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

      4. distribute-rgt-neg-in 84.0%

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

      5. metadata-eval 84.0%

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

      6. associate-/l* 97.4%

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

      7. *-commutative 97.4%

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

   8. Simplified 97.4%

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

   if -2.2999999999999998 < x < 1.30000000000000004

   1. Initial program 99.5%

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

      1. associate-*l/ 99.3%

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

      2. *-commutative 99.3%

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

      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. Taylor expanded in x around 0 99.0%

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

      1. *-commutative 99.0%

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

   6. Simplified 99.0%

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

   if 1.30000000000000004 < x

   1. Initial program 79.1%

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

      1. *-commutative 79.1%

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

      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 97.6%

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

4. Final simplification 98.2%

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

Alternative 6: 91.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.7 \lor \neg \left(x \leq 3\right):\\ \;\;\;\;0.3333333333333333 \cdot \frac{x \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{1 - x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -3.7) (not (<= x 3.0)))
   (* 0.3333333333333333 (/ (* x x) y))
   (/ (- 1.0 x) y)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -3.7) || !(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 <= (-3.7d0)) .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 <= -3.7) || !(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 <= -3.7) 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 <= -3.7) || !(x <= 3.0))
		tmp = Float64(0.3333333333333333 * Float64(Float64(x * 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 <= -3.7) || ~((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, -3.7], N[Not[LessEqual[x, 3.0]], $MachinePrecision]], N[(0.3333333333333333 * N[(N[(x * x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.7000000000000002 or 3 < x

   1. Initial program 82.7%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   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 80.3%

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

      1. unpow2 80.3%

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

   6. Simplified 80.3%

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

   if -3.7000000000000002 < x < 3

   1. Initial program 99.5%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   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 98.5%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.7 \lor \neg \left(x \leq 3\right):\\ \;\;\;\;0.3333333333333333 \cdot \frac{x \cdot x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{1 - x}{y}\\ \end{array} \]

Alternative 7: 97.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.7 \lor \neg \left(x \leq 3\right):\\ \;\;\;\;x \cdot \left(x \cdot \frac{0.3333333333333333}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1 - x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -3.7) (not (<= x 3.0)))
   (* x (* x (/ 0.3333333333333333 y)))
   (/ (- 1.0 x) y)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -3.7) || !(x <= 3.0)) {
		tmp = x * (x * (0.3333333333333333 / 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 <= (-3.7d0)) .or. (.not. (x <= 3.0d0))) then
        tmp = x * (x * (0.3333333333333333d0 / 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 <= -3.7) || !(x <= 3.0)) {
		tmp = x * (x * (0.3333333333333333 / y));
	} else {
		tmp = (1.0 - x) / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -3.7) or not (x <= 3.0):
		tmp = x * (x * (0.3333333333333333 / y))
	else:
		tmp = (1.0 - x) / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -3.7) || !(x <= 3.0))
		tmp = Float64(x * Float64(x * Float64(0.3333333333333333 / 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 <= -3.7) || ~((x <= 3.0)))
		tmp = x * (x * (0.3333333333333333 / y));
	else
		tmp = (1.0 - x) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -3.7], N[Not[LessEqual[x, 3.0]], $MachinePrecision]], N[(x * N[(x * N[(0.3333333333333333 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.7000000000000002 or 3 < x

   1. Initial program 82.7%

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

   2. Taylor expanded in x around inf 80.3%

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

      1. unpow2 80.3%

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

   4. Simplified 80.3%

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

      1. div-inv 80.3%

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

      2. associate-*l* 97.2%

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

      3. *-commutative 97.2%

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

      4. associate-/r* 97.2%

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

      5. metadata-eval 97.2%

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

   6. Applied egg-rr 97.2%

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

   if -3.7000000000000002 < x < 3

   1. Initial program 99.5%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   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 98.5%

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

4. Final simplification 97.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.7 \lor \neg \left(x \leq 3\right):\\ \;\;\;\;x \cdot \left(x \cdot \frac{0.3333333333333333}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1 - x}{y}\\ \end{array} \]

Alternative 8: 97.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.7 \lor \neg \left(x \leq 3\right):\\ \;\;\;\;x \cdot \left(x \cdot \frac{0.3333333333333333}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(1 - x\right) \cdot \frac{1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -3.7) (not (<= x 3.0)))
   (* x (* x (/ 0.3333333333333333 y)))
   (* (- 1.0 x) (/ 1.0 y))))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -3.7) || !(x <= 3.0)) {
		tmp = x * (x * (0.3333333333333333 / 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 <= (-3.7d0)) .or. (.not. (x <= 3.0d0))) then
        tmp = x * (x * (0.3333333333333333d0 / 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 <= -3.7) || !(x <= 3.0)) {
		tmp = x * (x * (0.3333333333333333 / y));
	} else {
		tmp = (1.0 - x) * (1.0 / y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -3.7) or not (x <= 3.0):
		tmp = x * (x * (0.3333333333333333 / y))
	else:
		tmp = (1.0 - x) * (1.0 / y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -3.7) || !(x <= 3.0))
		tmp = Float64(x * Float64(x * Float64(0.3333333333333333 / 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 <= -3.7) || ~((x <= 3.0)))
		tmp = x * (x * (0.3333333333333333 / y));
	else
		tmp = (1.0 - x) * (1.0 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -3.7], N[Not[LessEqual[x, 3.0]], $MachinePrecision]], N[(x * N[(x * N[(0.3333333333333333 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 - x), $MachinePrecision] * N[(1.0 / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.7000000000000002 or 3 < x

   1. Initial program 82.7%

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

   2. Taylor expanded in x around inf 80.3%

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

      1. unpow2 80.3%

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

   4. Simplified 80.3%

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

      1. div-inv 80.3%

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

      2. associate-*l* 97.2%

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

      3. *-commutative 97.2%

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

      4. associate-/r* 97.2%

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

      5. metadata-eval 97.2%

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

   6. Applied egg-rr 97.2%

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

   if -3.7000000000000002 < x < 3

   1. Initial program 99.5%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   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 98.5%

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

      1. clear-num 98.5%

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

      2. associate-/r/ 98.5%

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

   6. Applied egg-rr 98.5%

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

4. Final simplification 97.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.7 \lor \neg \left(x \leq 3\right):\\ \;\;\;\;x \cdot \left(x \cdot \frac{0.3333333333333333}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(1 - x\right) \cdot \frac{1}{y}\\ \end{array} \]

Alternative 9: 97.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.7:\\ \;\;\;\;x \cdot \left(x \cdot \frac{0.3333333333333333}{y}\right)\\ \mathbf{elif}\;x \leq 3:\\ \;\;\;\;\left(1 - x\right) \cdot \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(x \cdot 0.3333333333333333\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -3.7)
   (* x (* x (/ 0.3333333333333333 y)))
   (if (<= x 3.0)
     (* (- 1.0 x) (/ 1.0 y))
     (* (/ x y) (* x 0.3333333333333333)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -3.7) {
		tmp = x * (x * (0.3333333333333333 / y));
	} else if (x <= 3.0) {
		tmp = (1.0 - x) * (1.0 / y);
	} else {
		tmp = (x / y) * (x * 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 <= (-3.7d0)) then
        tmp = x * (x * (0.3333333333333333d0 / y))
    else if (x <= 3.0d0) then
        tmp = (1.0d0 - x) * (1.0d0 / y)
    else
        tmp = (x / y) * (x * 0.3333333333333333d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -3.7) {
		tmp = x * (x * (0.3333333333333333 / y));
	} else if (x <= 3.0) {
		tmp = (1.0 - x) * (1.0 / y);
	} else {
		tmp = (x / y) * (x * 0.3333333333333333);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -3.7:
		tmp = x * (x * (0.3333333333333333 / y))
	elif x <= 3.0:
		tmp = (1.0 - x) * (1.0 / y)
	else:
		tmp = (x / y) * (x * 0.3333333333333333)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -3.7)
		tmp = Float64(x * Float64(x * Float64(0.3333333333333333 / y)));
	elseif (x <= 3.0)
		tmp = Float64(Float64(1.0 - x) * Float64(1.0 / y));
	else
		tmp = Float64(Float64(x / y) * Float64(x * 0.3333333333333333));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -3.7)
		tmp = x * (x * (0.3333333333333333 / y));
	elseif (x <= 3.0)
		tmp = (1.0 - x) * (1.0 / y);
	else
		tmp = (x / y) * (x * 0.3333333333333333);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -3.7], N[(x * N[(x * N[(0.3333333333333333 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.0], N[(N[(1.0 - x), $MachinePrecision] * N[(1.0 / y), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] * N[(x * 0.3333333333333333), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.7000000000000002

   1. Initial program 86.4%

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

   2. Taylor expanded in x around inf 83.8%

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

      1. unpow2 83.8%

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

   4. Simplified 83.8%

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

      1. div-inv 83.9%

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

      2. associate-*l* 97.2%

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

      3. *-commutative 97.2%

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

      4. associate-/r* 97.2%

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

      5. metadata-eval 97.2%

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

   6. Applied egg-rr 97.2%

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

   if -3.7000000000000002 < x < 3

   1. Initial program 99.5%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   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 98.5%

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

      1. clear-num 98.5%

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

      2. associate-/r/ 98.5%

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

   6. Applied egg-rr 98.5%

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

   if 3 < x

   1. Initial program 79.1%

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

   2. Taylor expanded in x around inf 76.8%

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

      1. unpow2 76.8%

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

   4. Simplified 76.8%

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

      1. times-frac 97.4%

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

      2. div-inv 97.4%

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

      3. metadata-eval 97.4%

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

   6. Applied egg-rr 97.4%

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

4. Final simplification 97.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.7:\\ \;\;\;\;x \cdot \left(x \cdot \frac{0.3333333333333333}{y}\right)\\ \mathbf{elif}\;x \leq 3:\\ \;\;\;\;\left(1 - x\right) \cdot \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(x \cdot 0.3333333333333333\right)\\ \end{array} \]

Alternative 10: 97.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.7:\\ \;\;\;\;x \cdot \frac{x}{3 \cdot y}\\ \mathbf{elif}\;x \leq 3:\\ \;\;\;\;\left(1 - x\right) \cdot \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(x \cdot 0.3333333333333333\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -3.7)
   (* x (/ x (* 3.0 y)))
   (if (<= x 3.0)
     (* (- 1.0 x) (/ 1.0 y))
     (* (/ x y) (* x 0.3333333333333333)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -3.7) {
		tmp = x * (x / (3.0 * y));
	} else if (x <= 3.0) {
		tmp = (1.0 - x) * (1.0 / y);
	} else {
		tmp = (x / y) * (x * 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 <= (-3.7d0)) then
        tmp = x * (x / (3.0d0 * y))
    else if (x <= 3.0d0) then
        tmp = (1.0d0 - x) * (1.0d0 / y)
    else
        tmp = (x / y) * (x * 0.3333333333333333d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -3.7) {
		tmp = x * (x / (3.0 * y));
	} else if (x <= 3.0) {
		tmp = (1.0 - x) * (1.0 / y);
	} else {
		tmp = (x / y) * (x * 0.3333333333333333);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -3.7:
		tmp = x * (x / (3.0 * y))
	elif x <= 3.0:
		tmp = (1.0 - x) * (1.0 / y)
	else:
		tmp = (x / y) * (x * 0.3333333333333333)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -3.7)
		tmp = Float64(x * Float64(x / Float64(3.0 * y)));
	elseif (x <= 3.0)
		tmp = Float64(Float64(1.0 - x) * Float64(1.0 / y));
	else
		tmp = Float64(Float64(x / y) * Float64(x * 0.3333333333333333));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -3.7)
		tmp = x * (x / (3.0 * y));
	elseif (x <= 3.0)
		tmp = (1.0 - x) * (1.0 / y);
	else
		tmp = (x / y) * (x * 0.3333333333333333);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -3.7], N[(x * N[(x / N[(3.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.0], N[(N[(1.0 - x), $MachinePrecision] * N[(1.0 / y), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] * N[(x * 0.3333333333333333), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.7000000000000002

   1. Initial program 86.4%

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

   2. Taylor expanded in x around inf 83.8%

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

      1. unpow2 83.8%

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

   4. Simplified 83.8%

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

      1. associate-/l* 97.2%

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

      2. associate-/r/ 97.2%

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

      3. *-commutative 97.2%

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

   6. Applied egg-rr 97.2%

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

   if -3.7000000000000002 < x < 3

   1. Initial program 99.5%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   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 98.5%

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

      1. clear-num 98.5%

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

      2. associate-/r/ 98.5%

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

   6. Applied egg-rr 98.5%

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

   if 3 < x

   1. Initial program 79.1%

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

   2. Taylor expanded in x around inf 76.8%

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

      1. unpow2 76.8%

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

   4. Simplified 76.8%

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

      1. times-frac 97.4%

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

      2. div-inv 97.4%

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

      3. metadata-eval 97.4%

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

   6. Applied egg-rr 97.4%

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

4. Final simplification 97.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.7:\\ \;\;\;\;x \cdot \frac{x}{3 \cdot y}\\ \mathbf{elif}\;x \leq 3:\\ \;\;\;\;\left(1 - x\right) \cdot \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(x \cdot 0.3333333333333333\right)\\ \end{array} \]

Alternative 11: 97.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.7:\\ \;\;\;\;x \cdot \frac{x}{3 \cdot y}\\ \mathbf{elif}\;x \leq 3:\\ \;\;\;\;\left(1 - x\right) \cdot \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{x}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -3.7)
   (* x (/ x (* 3.0 y)))
   (if (<= x 3.0)
     (* (- 1.0 x) (/ 1.0 y))
     (* 0.3333333333333333 (/ x (/ y x))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -3.7) {
		tmp = x * (x / (3.0 * y));
	} else if (x <= 3.0) {
		tmp = (1.0 - x) * (1.0 / y);
	} else {
		tmp = 0.3333333333333333 * (x / (y / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-3.7d0)) then
        tmp = x * (x / (3.0d0 * y))
    else if (x <= 3.0d0) then
        tmp = (1.0d0 - x) * (1.0d0 / y)
    else
        tmp = 0.3333333333333333d0 * (x / (y / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -3.7) {
		tmp = x * (x / (3.0 * y));
	} else if (x <= 3.0) {
		tmp = (1.0 - x) * (1.0 / y);
	} else {
		tmp = 0.3333333333333333 * (x / (y / x));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -3.7:
		tmp = x * (x / (3.0 * y))
	elif x <= 3.0:
		tmp = (1.0 - x) * (1.0 / y)
	else:
		tmp = 0.3333333333333333 * (x / (y / x))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -3.7)
		tmp = Float64(x * Float64(x / Float64(3.0 * y)));
	elseif (x <= 3.0)
		tmp = Float64(Float64(1.0 - x) * Float64(1.0 / 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 <= -3.7)
		tmp = x * (x / (3.0 * y));
	elseif (x <= 3.0)
		tmp = (1.0 - x) * (1.0 / y);
	else
		tmp = 0.3333333333333333 * (x / (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -3.7], N[(x * N[(x / N[(3.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.0], N[(N[(1.0 - x), $MachinePrecision] * N[(1.0 / y), $MachinePrecision]), $MachinePrecision], N[(0.3333333333333333 * N[(x / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.7000000000000002

   1. Initial program 86.4%

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

   2. Taylor expanded in x around inf 83.8%

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

      1. unpow2 83.8%

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

   4. Simplified 83.8%

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

      1. associate-/l* 97.2%

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

      2. associate-/r/ 97.2%

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

      3. *-commutative 97.2%

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

   6. Applied egg-rr 97.2%

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

   if -3.7000000000000002 < x < 3

   1. Initial program 99.5%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   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 98.5%

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

      1. clear-num 98.5%

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

      2. associate-/r/ 98.5%

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

   6. Applied egg-rr 98.5%

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

   if 3 < x

   1. Initial program 79.1%

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

   2. Taylor expanded in x around inf 76.8%

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

      1. unpow2 76.8%

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

   4. Simplified 76.8%

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

      1. associate-/r* 76.8%

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

      2. div-inv 76.8%

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

      3. associate-/l* 97.4%

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

      4. metadata-eval 97.4%

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

   6. Applied egg-rr 97.4%

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

4. Final simplification 97.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.7:\\ \;\;\;\;x \cdot \frac{x}{3 \cdot y}\\ \mathbf{elif}\;x \leq 3:\\ \;\;\;\;\left(1 - x\right) \cdot \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{x}{\frac{y}{x}}\\ \end{array} \]

Alternative 12: 97.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.7:\\ \;\;\;\;\frac{x}{3 \cdot \frac{y}{x}}\\ \mathbf{elif}\;x \leq 3:\\ \;\;\;\;\left(1 - x\right) \cdot \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{x}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -3.7)
   (/ x (* 3.0 (/ y x)))
   (if (<= x 3.0)
     (* (- 1.0 x) (/ 1.0 y))
     (* 0.3333333333333333 (/ x (/ y x))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -3.7) {
		tmp = x / (3.0 * (y / x));
	} else if (x <= 3.0) {
		tmp = (1.0 - x) * (1.0 / y);
	} else {
		tmp = 0.3333333333333333 * (x / (y / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-3.7d0)) then
        tmp = x / (3.0d0 * (y / x))
    else if (x <= 3.0d0) then
        tmp = (1.0d0 - x) * (1.0d0 / y)
    else
        tmp = 0.3333333333333333d0 * (x / (y / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -3.7) {
		tmp = x / (3.0 * (y / x));
	} else if (x <= 3.0) {
		tmp = (1.0 - x) * (1.0 / y);
	} else {
		tmp = 0.3333333333333333 * (x / (y / x));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -3.7:
		tmp = x / (3.0 * (y / x))
	elif x <= 3.0:
		tmp = (1.0 - x) * (1.0 / y)
	else:
		tmp = 0.3333333333333333 * (x / (y / x))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -3.7)
		tmp = Float64(x / Float64(3.0 * Float64(y / x)));
	elseif (x <= 3.0)
		tmp = Float64(Float64(1.0 - x) * Float64(1.0 / 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 <= -3.7)
		tmp = x / (3.0 * (y / x));
	elseif (x <= 3.0)
		tmp = (1.0 - x) * (1.0 / y);
	else
		tmp = 0.3333333333333333 * (x / (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -3.7], N[(x / N[(3.0 * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.0], N[(N[(1.0 - x), $MachinePrecision] * N[(1.0 / y), $MachinePrecision]), $MachinePrecision], N[(0.3333333333333333 * N[(x / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.7000000000000002

   1. Initial program 86.4%

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

   2. Taylor expanded in x around inf 83.8%

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

      1. unpow2 83.8%

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

   4. Simplified 83.8%

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

      1. associate-/l* 97.2%

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

      2. associate-/r/ 97.2%

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

      3. *-commutative 97.2%

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

   6. Applied egg-rr 97.2%

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

      1. associate-*l/ 83.8%

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

      2. associate-/l* 97.2%

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

      3. *-un-lft-identity 97.2%

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

      4. times-frac 97.2%

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

      5. metadata-eval 97.2%

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

   8. Applied egg-rr 97.2%

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

   if -3.7000000000000002 < x < 3

   1. Initial program 99.5%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   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 98.5%

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

      1. clear-num 98.5%

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

      2. associate-/r/ 98.5%

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

   6. Applied egg-rr 98.5%

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

   if 3 < x

   1. Initial program 79.1%

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

   2. Taylor expanded in x around inf 76.8%

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

      1. unpow2 76.8%

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

   4. Simplified 76.8%

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

      1. associate-/r* 76.8%

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

      2. div-inv 76.8%

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

      3. associate-/l* 97.4%

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

      4. metadata-eval 97.4%

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

   6. Applied egg-rr 97.4%

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

4. Final simplification 97.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.7:\\ \;\;\;\;\frac{x}{3 \cdot \frac{y}{x}}\\ \mathbf{elif}\;x \leq 3:\\ \;\;\;\;\left(1 - x\right) \cdot \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{x}{\frac{y}{x}}\\ \end{array} \]

Alternative 13: 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 90.3%

   \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
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* 99.7%

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

3. Simplified 99.7%

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

4. Final simplification 99.7%

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

Alternative 14: 57.6% 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 86.4%

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

      1. associate-*l/ 99.8%

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

      2. *-commutative 99.8%

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

      3. 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. Taylor expanded in x around inf 97.3%

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

   5. Taylor expanded in x around 0 34.8%

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

      1. neg-mul-1 34.8%

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

      2. distribute-neg-frac 34.8%

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

   7. Simplified 34.8%

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

   if -1 < x

   1. Initial program 91.7%

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

      1. associate-*l/ 99.4%

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

      2. *-commutative 99.4%

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

      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 0 62.7%

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

4. Final simplification 55.1%

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

Alternative 15: 56.7% 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 90.3%

   \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
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 54.0%

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

5. Final simplification 54.0%

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

Alternative 16: 51.3% accurate, 3.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 90.3%

   \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
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* 99.7%

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

3. Simplified 99.7%

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

4. Taylor expanded in x around 0 46.9%

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

5. Final simplification 46.9%

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

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 2023257 
(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)))