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

Percentage Accurate: 94.2% → 99.9%

Time: 10.0s

Alternatives: 15

Speedup: 1.0×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 94.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% 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 94.9%

   \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
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 2: 98.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{y \cdot 3}\\ \mathbf{if}\;x \leq -4.6:\\ \;\;\;\;x \cdot t_0\\ \mathbf{elif}\;x \leq 1.75:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;t_0 \cdot \left(x + -4\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ x (* y 3.0))))
   (if (<= x -4.6)
     (* x t_0)
     (if (<= x 1.75)
       (/ (+ 1.0 (* x -1.3333333333333333)) y)
       (* t_0 (+ x -4.0))))))

C

double code(double x, double y) {
	double t_0 = x / (y * 3.0);
	double tmp;
	if (x <= -4.6) {
		tmp = x * t_0;
	} else if (x <= 1.75) {
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	} else {
		tmp = t_0 * (x + -4.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x / (y * 3.0d0)
    if (x <= (-4.6d0)) then
        tmp = x * t_0
    else if (x <= 1.75d0) then
        tmp = (1.0d0 + (x * (-1.3333333333333333d0))) / y
    else
        tmp = t_0 * (x + (-4.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x / (y * 3.0);
	double tmp;
	if (x <= -4.6) {
		tmp = x * t_0;
	} else if (x <= 1.75) {
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	} else {
		tmp = t_0 * (x + -4.0);
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x / (y * 3.0)
	tmp = 0
	if x <= -4.6:
		tmp = x * t_0
	elif x <= 1.75:
		tmp = (1.0 + (x * -1.3333333333333333)) / y
	else:
		tmp = t_0 * (x + -4.0)
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x / Float64(y * 3.0))
	tmp = 0.0
	if (x <= -4.6)
		tmp = Float64(x * t_0);
	elseif (x <= 1.75)
		tmp = Float64(Float64(1.0 + Float64(x * -1.3333333333333333)) / y);
	else
		tmp = Float64(t_0 * Float64(x + -4.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x / (y * 3.0);
	tmp = 0.0;
	if (x <= -4.6)
		tmp = x * t_0;
	elseif (x <= 1.75)
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	else
		tmp = t_0 * (x + -4.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x / N[(y * 3.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.6], N[(x * t$95$0), $MachinePrecision], If[LessEqual[x, 1.75], N[(N[(1.0 + N[(x * -1.3333333333333333), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(t$95$0 * N[(x + -4.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.5999999999999996

   1. Initial program 88.7%

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

   2. Taylor expanded in x around inf 88.7%

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

      1. unpow2 88.7%

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

   4. Simplified 88.7%

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

      1. associate-/l* 99.6%

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

      2. associate-/r/ 99.7%

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

      3. *-commutative 99.7%

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

   6. Applied egg-rr 99.7%

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

   if -4.5999999999999996 < 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 100.0%

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

      2. div-sub 100.0%

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

      3. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

      1. *-commutative 100.0%

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

      2. metadata-eval 100.0%

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

      3. div-sub 100.0%

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

      4. times-frac 99.6%

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

      5. associate-*r/ 99.4%

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

      6. associate-/r* 99.4%

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

      7. associate-*r/ 100.0%

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

      8. div-sub 100.0%

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

      9. metadata-eval 100.0%

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

      10. div-inv 100.0%

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

      11. metadata-eval 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in x around 0 99.0%

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

   if 1.75 < x

   1. Initial program 90.6%

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

   2. Taylor expanded in x around inf 87.5%

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

      1. unpow2 87.5%

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

      2. +-commutative 87.5%

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

      3. distribute-rgt-in 90.3%

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

   4. Simplified 90.3%

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

   5. Taylor expanded in y around 0 90.4%

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

      1. metadata-eval 90.4%

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

      2. sub-neg 90.4%

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

      3. metadata-eval 90.4%

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

      4. *-commutative 90.4%

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

      5. times-frac 90.3%

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

      6. *-lft-identity 90.3%

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

      7. associate-*l/ 99.4%

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

      8. *-commutative 99.4%

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

   7. Simplified 99.4%

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

4. Final simplification 99.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.6:\\ \;\;\;\;x \cdot \frac{x}{y \cdot 3}\\ \mathbf{elif}\;x \leq 1.75:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot 3} \cdot \left(x + -4\right)\\ \end{array} \]

Alternative 3: 92.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y) {
	double tmp;
	if ((x <= -3.8) || !(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 <= (-3.8d0)) .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 <= -3.8) || !(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 <= -3.8) 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 <= -3.8) || !(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 <= -3.8) || ~((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, -3.8], 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 < -3.7999999999999998 or 3 < x

   1. Initial program 89.8%

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

      1. times-frac 99.7%

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

      2. div-sub 99.7%

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

      3. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 89.1%

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

      1. unpow2 89.1%

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

   6. Simplified 89.1%

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

   if -3.7999999999999998 < x < 3

   1. Initial program 99.6%

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

      1. times-frac 100.0%

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

      2. div-sub 100.0%

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

      3. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

      1. metadata-eval 100.0%

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

      2. div-sub 100.0%

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

      3. times-frac 99.6%

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

      4. associate-/l* 99.8%

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

      5. *-commutative 99.8%

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

      6. *-un-lft-identity 99.8%

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

      7. times-frac 99.8%

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

      8. metadata-eval 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in x around 0 97.4%

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

4. Final simplification 93.4%

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

Alternative 4: 97.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y) {
	double tmp;
	if ((x <= -3.8) || !(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 <= (-3.8d0)) .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 <= -3.8) || !(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 <= -3.8) 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 <= -3.8) || !(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 <= -3.8) || ~((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, -3.8], 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 < -3.7999999999999998 or 3 < x

   1. Initial program 89.8%

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

   2. Taylor expanded in x around inf 89.1%

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

      1. unpow2 89.1%

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

   4. Simplified 89.1%

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

      1. div-inv 89.1%

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

      2. associate-*l* 98.9%

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

      3. *-commutative 98.9%

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

      4. associate-/r* 98.9%

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

      5. metadata-eval 98.9%

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

   6. Applied egg-rr 98.9%

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

   if -3.7999999999999998 < x < 3

   1. Initial program 99.6%

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

      1. times-frac 100.0%

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

      2. div-sub 100.0%

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

      3. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

      1. metadata-eval 100.0%

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

      2. div-sub 100.0%

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

      3. times-frac 99.6%

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

      4. associate-/l* 99.8%

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

      5. *-commutative 99.8%

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

      6. *-un-lft-identity 99.8%

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

      7. times-frac 99.8%

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

      8. metadata-eval 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in x around 0 97.4%

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

4. Final simplification 98.1%

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

Alternative 5: 97.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if x < -3.7999999999999998 or 3 < x

   1. Initial program 89.8%

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

      1. times-frac 99.7%

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

      2. div-sub 99.7%

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

      3. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

      1. *-commutative 99.7%

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

      2. metadata-eval 99.7%

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

      3. div-sub 99.7%

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

      4. times-frac 89.8%

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

      5. associate-*r/ 99.7%

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

      6. associate-/r* 99.8%

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

      7. associate-*r/ 89.9%

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

      8. div-sub 89.9%

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

      9. metadata-eval 89.9%

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

      10. div-inv 89.9%

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

      11. metadata-eval 89.9%

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

   5. Applied egg-rr 89.9%

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

   6. Taylor expanded in x around inf 89.1%

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

      1. *-commutative 89.1%

         \[\leadsto \color{blue}{\frac{{x}^{2}}{y} \cdot 0.3333333333333333} \]

      2. unpow2 89.1%

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

      3. associate-/l* 99.0%

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

      4. metadata-eval 99.0%

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

      5. times-frac 98.9%

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

      6. *-rgt-identity 98.9%

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

      7. *-commutative 98.9%

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

      8. associate-*r/ 98.9%

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

      9. associate-/l* 89.1%

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

      10. *-commutative 89.1%

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

      11. times-frac 99.0%

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

   8. Simplified 99.0%

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

   if -3.7999999999999998 < x < 3

   1. Initial program 99.6%

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

      1. times-frac 100.0%

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

      2. div-sub 100.0%

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

      3. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

      1. metadata-eval 100.0%

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

      2. div-sub 100.0%

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

      3. times-frac 99.6%

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

      4. associate-/l* 99.8%

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

      5. *-commutative 99.8%

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

      6. *-un-lft-identity 99.8%

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

      7. times-frac 99.8%

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

      8. metadata-eval 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in x around 0 97.4%

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

4. Final simplification 98.2%

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

Alternative 6: 97.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 3 regimes

2. if x < -3.7999999999999998

   1. Initial program 88.7%

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

   2. Taylor expanded in x around inf 88.7%

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

      1. unpow2 88.7%

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

   4. Simplified 88.7%

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

      1. associate-/l* 99.6%

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

      2. associate-/r/ 99.7%

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

      3. *-commutative 99.7%

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

   6. Applied egg-rr 99.7%

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

   if -3.7999999999999998 < x < 3

   1. Initial program 99.6%

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

      1. times-frac 100.0%

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

      2. div-sub 100.0%

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

      3. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

      1. metadata-eval 100.0%

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

      2. div-sub 100.0%

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

      3. times-frac 99.6%

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

      4. associate-/l* 99.8%

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

      5. *-commutative 99.8%

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

      6. *-un-lft-identity 99.8%

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

      7. times-frac 99.8%

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

      8. metadata-eval 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in x around 0 97.4%

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

   if 3 < x

   1. Initial program 90.6%

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

      1. times-frac 99.7%

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

      2. div-sub 99.7%

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

      3. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

      1. *-commutative 99.7%

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

      2. metadata-eval 99.7%

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

      3. div-sub 99.7%

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

      4. times-frac 90.6%

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

      5. associate-*r/ 99.7%

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

      6. associate-/r* 99.8%

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

      7. associate-*r/ 90.7%

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

      8. div-sub 90.7%

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

      9. metadata-eval 90.7%

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

      10. div-inv 90.7%

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

      11. metadata-eval 90.7%

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

   5. Applied egg-rr 90.7%

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

   6. Taylor expanded in x around inf 89.5%

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

      1. *-commutative 89.5%

         \[\leadsto \color{blue}{\frac{{x}^{2}}{y} \cdot 0.3333333333333333} \]

      2. unpow2 89.5%

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

      3. associate-/l* 98.5%

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

      4. metadata-eval 98.5%

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

      5. times-frac 98.5%

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

      6. *-rgt-identity 98.5%

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

      7. *-commutative 98.5%

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

      8. associate-*r/ 98.4%

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

      9. associate-/l* 89.4%

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

      10. *-commutative 89.4%

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

      11. times-frac 98.5%

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

   8. Simplified 98.5%

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

4. Final simplification 98.2%

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

Alternative 7: 97.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 3 regimes

2. if x < -3.7999999999999998

   1. Initial program 88.7%

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

   2. Taylor expanded in x around inf 88.7%

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

      1. unpow2 88.7%

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

   4. Simplified 88.7%

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

      1. associate-/l* 99.6%

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

      2. associate-/r/ 99.7%

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

      3. *-commutative 99.7%

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

   6. Applied egg-rr 99.7%

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

   if -3.7999999999999998 < x < 3

   1. Initial program 99.6%

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

      1. times-frac 100.0%

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

      2. div-sub 100.0%

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

      3. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

      1. metadata-eval 100.0%

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

      2. div-sub 100.0%

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

      3. times-frac 99.6%

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

      4. associate-/l* 99.8%

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

      5. *-commutative 99.8%

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

      6. *-un-lft-identity 99.8%

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

      7. times-frac 99.8%

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

      8. metadata-eval 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in x around 0 97.4%

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

   if 3 < x

   1. Initial program 90.6%

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

   2. Taylor expanded in x around inf 87.5%

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

      1. unpow2 87.5%

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

      2. +-commutative 87.5%

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

      3. distribute-rgt-in 90.3%

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

   4. Simplified 90.3%

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

      1. associate-/r* 90.4%

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

      2. div-inv 90.4%

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

      3. *-commutative 90.4%

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

      4. associate-/l* 99.4%

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

      5. metadata-eval 99.4%

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

   6. Applied egg-rr 99.4%

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

   7. Taylor expanded in x around inf 89.5%

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

      1. unpow2 89.5%

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

      2. associate-/l* 98.5%

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

   9. Simplified 98.5%

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

4. Final simplification 98.2%

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

Alternative 8: 97.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 3 regimes

2. if x < -3.7999999999999998

   1. Initial program 88.7%

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

   2. Taylor expanded in x around inf 88.7%

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

      1. unpow2 88.7%

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

   4. Simplified 88.7%

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

      1. associate-/l* 99.6%

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

      2. associate-/r/ 99.7%

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

      3. *-commutative 99.7%

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

   6. Applied egg-rr 99.7%

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

   if -3.7999999999999998 < x < 3

   1. Initial program 99.6%

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

      1. times-frac 100.0%

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

      2. div-sub 100.0%

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

      3. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

      1. metadata-eval 100.0%

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

      2. div-sub 100.0%

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

      3. times-frac 99.6%

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

      4. associate-/l* 99.8%

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

      5. *-commutative 99.8%

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

      6. *-un-lft-identity 99.8%

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

      7. times-frac 99.8%

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

      8. metadata-eval 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in x around 0 97.4%

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

   if 3 < x

   1. Initial program 90.6%

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

      1. times-frac 99.7%

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

      2. div-sub 99.7%

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

      3. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

      1. *-commutative 99.7%

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

      2. metadata-eval 99.7%

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

      3. div-sub 99.7%

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

      4. times-frac 90.6%

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

      5. associate-*r/ 99.7%

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

      6. associate-/r* 99.8%

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

      7. associate-*r/ 90.7%

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

      8. div-sub 90.7%

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

      9. metadata-eval 90.7%

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

      10. div-inv 90.7%

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

      11. metadata-eval 90.7%

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

   5. Applied egg-rr 90.7%

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

   6. Taylor expanded in x around inf 89.5%

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

      1. *-commutative 89.5%

         \[\leadsto \color{blue}{\frac{{x}^{2}}{y} \cdot 0.3333333333333333} \]

      2. unpow2 89.5%

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

      3. associate-/l* 98.5%

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

      4. metadata-eval 98.5%

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

      5. times-frac 98.5%

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

      6. *-rgt-identity 98.5%

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

      7. *-commutative 98.5%

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

      8. associate-*r/ 98.4%

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

      9. associate-/l* 89.4%

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

      10. *-commutative 89.4%

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

      11. times-frac 98.5%

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

   8. Simplified 98.5%

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

      1. *-commutative 98.5%

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

      2. clear-num 98.4%

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

      3. frac-times 98.6%

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

      4. *-un-lft-identity 98.6%

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

   10. Applied egg-rr 98.6%

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

4. Final simplification 98.2%

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

Alternative 9: 98.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.6:\\ \;\;\;\;x \cdot \frac{x}{y \cdot 3}\\ \mathbf{elif}\;x \leq 0.65:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \frac{3}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -4.6)
   (* x (/ x (* y 3.0)))
   (if (<= x 0.65)
     (/ (+ 1.0 (* x -1.3333333333333333)) y)
     (/ x (* y (/ 3.0 x))))))

C

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

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-4.6d0)) then
        tmp = x * (x / (y * 3.0d0))
    else if (x <= 0.65d0) then
        tmp = (1.0d0 + (x * (-1.3333333333333333d0))) / y
    else
        tmp = x / (y * (3.0d0 / x))
    end if
    code = tmp
end function

Java

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

Python

def code(x, y):
	tmp = 0
	if x <= -4.6:
		tmp = x * (x / (y * 3.0))
	elif x <= 0.65:
		tmp = (1.0 + (x * -1.3333333333333333)) / y
	else:
		tmp = x / (y * (3.0 / x))
	return tmp

Julia

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

MATLAB

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

Wolfram

code[x_, y_] := If[LessEqual[x, -4.6], N[(x * N[(x / N[(y * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 0.65], N[(N[(1.0 + N[(x * -1.3333333333333333), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(y * N[(3.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.5999999999999996

   1. Initial program 88.7%

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

   2. Taylor expanded in x around inf 88.7%

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

      1. unpow2 88.7%

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

   4. Simplified 88.7%

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

      1. associate-/l* 99.6%

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

      2. associate-/r/ 99.7%

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

      3. *-commutative 99.7%

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

   6. Applied egg-rr 99.7%

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

   if -4.5999999999999996 < x < 0.650000000000000022

   1. Initial program 99.6%

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

      1. times-frac 100.0%

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

      2. div-sub 100.0%

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

      3. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

      1. *-commutative 100.0%

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

      2. metadata-eval 100.0%

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

      3. div-sub 100.0%

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

      4. times-frac 99.6%

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

      5. associate-*r/ 99.4%

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

      6. associate-/r* 99.4%

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

      7. associate-*r/ 100.0%

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

      8. div-sub 100.0%

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

      9. metadata-eval 100.0%

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

      10. div-inv 100.0%

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

      11. metadata-eval 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in x around 0 99.0%

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

   if 0.650000000000000022 < x

   1. Initial program 90.6%

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

      1. times-frac 99.7%

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

      2. div-sub 99.7%

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

      3. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

      1. *-commutative 99.7%

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

      2. metadata-eval 99.7%

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

      3. div-sub 99.7%

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

      4. times-frac 90.6%

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

      5. associate-*r/ 99.7%

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

      6. associate-/r* 99.8%

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

      7. associate-*r/ 90.7%

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

      8. div-sub 90.7%

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

      9. metadata-eval 90.7%

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

      10. div-inv 90.7%

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

      11. metadata-eval 90.7%

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

   5. Applied egg-rr 90.7%

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

   6. Taylor expanded in x around inf 89.5%

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

      1. *-commutative 89.5%

         \[\leadsto \color{blue}{\frac{{x}^{2}}{y} \cdot 0.3333333333333333} \]

      2. unpow2 89.5%

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

      3. associate-/l* 98.5%

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

      4. metadata-eval 98.5%

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

      5. times-frac 98.5%

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

      6. *-rgt-identity 98.5%

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

      7. *-commutative 98.5%

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

      8. associate-*r/ 98.4%

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

      9. associate-/l* 89.4%

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

      10. *-commutative 89.4%

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

      11. times-frac 98.5%

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

   8. Simplified 98.5%

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

      1. *-commutative 98.5%

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

      2. clear-num 98.4%

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

      3. frac-times 98.6%

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

      4. *-un-lft-identity 98.6%

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

   10. Applied egg-rr 98.6%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.6:\\ \;\;\;\;x \cdot \frac{x}{y \cdot 3}\\ \mathbf{elif}\;x \leq 0.65:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \frac{3}{x}}\\ \end{array} \]

Alternative 10: 99.5% accurate, 1.0× speedup

Math

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

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(1.0 - x) / Float64(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[(1.0 - x), $MachinePrecision] / N[(y * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 94.9%

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

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

3. Simplified 99.5%

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

4. Final simplification 99.5%

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

Alternative 11: 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 94.9%

   \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
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 12: 57.6% 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 88.7%

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

   2. Taylor expanded in x around inf 88.7%

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

      1. unpow2 88.7%

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

      2. +-commutative 88.7%

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

      3. distribute-rgt-in 88.7%

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

   4. Simplified 88.7%

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

   5. Taylor expanded in x around 0 30.4%

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

   if -0.75 < x

   1. Initial program 96.4%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   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 64.6%

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

4. Final simplification 57.9%

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

Alternative 13: 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 88.7%

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

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 99.5%

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

      1. *-commutative 99.5%

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

   6. Simplified 99.5%

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

   7. Taylor expanded in x around 0 30.4%

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

      1. associate-*r/ 30.4%

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

      2. neg-mul-1 30.4%

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

   9. Simplified 30.4%

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

   if -1 < x

   1. Initial program 96.4%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   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 64.6%

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

4. Final simplification 57.9%

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

Alternative 14: 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 94.9%

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

   1. metadata-eval 99.8%

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

   2. div-sub 99.8%

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

   3. times-frac 94.9%

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

   4. associate-/l* 99.7%

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

   5. *-commutative 99.7%

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

   6. *-un-lft-identity 99.7%

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

   7. times-frac 99.7%

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

   8. metadata-eval 99.7%

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

5. Applied egg-rr 99.7%

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

6. Taylor expanded in x around 0 56.8%

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

7. Final simplification 56.8%

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

Alternative 15: 51.4% 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 94.9%

   \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
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: 99.9% 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 2023214 
(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)))