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

Percentage Accurate: 93.7% → 99.8%

Time: 8.7s

Alternatives: 11

Speedup: 1.0×

• 24.4% 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

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

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 92.5%

   \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
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: 98.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.3 \lor \neg \left(x \leq 2.3\right):\\ \;\;\;\;0.3333333333333333 \cdot \left(\frac{x}{y} \cdot \left(x + -4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1 - x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -1.3) (not (<= x 2.3)))
   (* 0.3333333333333333 (* (/ x y) (+ x -4.0)))
   (/ (- 1.0 x) y)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -1.3) || !(x <= 2.3)) {
		tmp = 0.3333333333333333 * ((x / y) * (x + -4.0));
	} 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 <= (-1.3d0)) .or. (.not. (x <= 2.3d0))) then
        tmp = 0.3333333333333333d0 * ((x / y) * (x + (-4.0d0)))
    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 <= -1.3) || !(x <= 2.3)) {
		tmp = 0.3333333333333333 * ((x / y) * (x + -4.0));
	} else {
		tmp = (1.0 - x) / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -1.3) or not (x <= 2.3):
		tmp = 0.3333333333333333 * ((x / y) * (x + -4.0))
	else:
		tmp = (1.0 - x) / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -1.3) || !(x <= 2.3))
		tmp = Float64(0.3333333333333333 * Float64(Float64(x / y) * Float64(x + -4.0)));
	else
		tmp = Float64(Float64(1.0 - x) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -1.3) || ~((x <= 2.3)))
		tmp = 0.3333333333333333 * ((x / y) * (x + -4.0));
	else
		tmp = (1.0 - x) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -1.3], N[Not[LessEqual[x, 2.3]], $MachinePrecision]], N[(0.3333333333333333 * N[(N[(x / y), $MachinePrecision] * N[(x + -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.30000000000000004 or 2.2999999999999998 < x

   1. Initial program 87.0%

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

      1. times-frac 99.7%

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

      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. metadata-eval 99.7%

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

      2. div-sub 99.7%

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

      3. times-frac 87.0%

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

      4. *-commutative 87.0%

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

      5. frac-times 99.7%

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

      6. clear-num 99.6%

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

      7. frac-times 99.7%

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

      8. *-un-lft-identity 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in y around 0 87.6%

      \[\leadsto \color{blue}{0.3333333333333333 \cdot \frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y}} \]
   7. Step-by-step derivation

      1. associate-/l* 99.6%

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

      2. associate-/r/ 99.7%

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

   8. Simplified 99.7%

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

   9. Taylor expanded in x around inf 71.9%

      \[\leadsto 0.3333333333333333 \cdot \color{blue}{\left(-4 \cdot \frac{x}{y} + \frac{{x}^{2}}{y}\right)} \]
   10. Step-by-step derivation

       1. *-commutative 71.9%

          \[\leadsto 0.3333333333333333 \cdot \left(\color{blue}{\frac{x}{y} \cdot -4} + \frac{{x}^{2}}{y}\right) \]

       2. unpow2 71.9%

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

       3. associate-*l/ 83.9%

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

       4. distribute-lft-out 96.3%

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

   11. Simplified 96.3%

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

   if -1.30000000000000004 < x < 2.2999999999999998

   1. Initial program 99.7%

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

      1. metadata-eval 99.9%

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

      2. div-sub 100.0%

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

      3. times-frac 99.7%

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

      4. *-commutative 99.7%

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

      5. frac-times 99.3%

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

      6. clear-num 99.2%

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

      7. frac-times 99.8%

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

      8. *-un-lft-identity 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in x around 0 97.6%

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

4. Final simplification 96.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.3 \lor \neg \left(x \leq 2.3\right):\\ \;\;\;\;0.3333333333333333 \cdot \left(\frac{x}{y} \cdot \left(x + -4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1 - x}{y}\\ \end{array} \]

Alternative 3: 98.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.75 \lor \neg \left(x \leq 1.7\right):\\ \;\;\;\;0.3333333333333333 \cdot \left(\frac{x}{y} \cdot \left(x + -4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{3 + x \cdot -4}{y \cdot 3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -1.75) (not (<= x 1.7)))
   (* 0.3333333333333333 (* (/ x y) (+ x -4.0)))
   (/ (+ 3.0 (* x -4.0)) (* y 3.0))))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -1.75) || !(x <= 1.7)) {
		tmp = 0.3333333333333333 * ((x / y) * (x + -4.0));
	} else {
		tmp = (3.0 + (x * -4.0)) / (y * 3.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-1.75d0)) .or. (.not. (x <= 1.7d0))) then
        tmp = 0.3333333333333333d0 * ((x / y) * (x + (-4.0d0)))
    else
        tmp = (3.0d0 + (x * (-4.0d0))) / (y * 3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -1.75) || !(x <= 1.7)) {
		tmp = 0.3333333333333333 * ((x / y) * (x + -4.0));
	} else {
		tmp = (3.0 + (x * -4.0)) / (y * 3.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -1.75) or not (x <= 1.7):
		tmp = 0.3333333333333333 * ((x / y) * (x + -4.0))
	else:
		tmp = (3.0 + (x * -4.0)) / (y * 3.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -1.75) || !(x <= 1.7))
		tmp = Float64(0.3333333333333333 * Float64(Float64(x / y) * Float64(x + -4.0)));
	else
		tmp = Float64(Float64(3.0 + Float64(x * -4.0)) / Float64(y * 3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -1.75) || ~((x <= 1.7)))
		tmp = 0.3333333333333333 * ((x / y) * (x + -4.0));
	else
		tmp = (3.0 + (x * -4.0)) / (y * 3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -1.75], N[Not[LessEqual[x, 1.7]], $MachinePrecision]], N[(0.3333333333333333 * N[(N[(x / y), $MachinePrecision] * N[(x + -4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(3.0 + N[(x * -4.0), $MachinePrecision]), $MachinePrecision] / N[(y * 3.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.75 or 1.69999999999999996 < x

   1. Initial program 87.2%

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

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

      2. div-sub 99.7%

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

      3. times-frac 87.2%

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

      4. *-commutative 87.2%

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

      5. frac-times 99.7%

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

      6. clear-num 99.6%

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

      7. frac-times 99.7%

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

      8. *-un-lft-identity 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in y around 0 87.7%

      \[\leadsto \color{blue}{0.3333333333333333 \cdot \frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y}} \]
   7. Step-by-step derivation

      1. associate-/l* 99.6%

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

      2. associate-/r/ 99.7%

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

   8. Simplified 99.7%

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

   9. Taylor expanded in x around inf 71.2%

      \[\leadsto 0.3333333333333333 \cdot \color{blue}{\left(-4 \cdot \frac{x}{y} + \frac{{x}^{2}}{y}\right)} \]
   10. Step-by-step derivation

       1. *-commutative 71.2%

          \[\leadsto 0.3333333333333333 \cdot \left(\color{blue}{\frac{x}{y} \cdot -4} + \frac{{x}^{2}}{y}\right) \]

       2. unpow2 71.2%

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

       3. associate-*l/ 83.0%

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

       4. distribute-lft-out 95.2%

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

   11. Simplified 95.2%

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

   if -1.75 < x < 1.69999999999999996

   1. Initial program 99.7%

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

   2. Taylor expanded in x around 0 99.6%

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

      1. *-commutative 99.6%

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

   4. Simplified 99.6%

      \[\leadsto \frac{\color{blue}{3 + x \cdot -4}}{y \cdot 3} \]
3. Recombined 2 regimes into one program.

4. Final simplification 97.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.75 \lor \neg \left(x \leq 1.7\right):\\ \;\;\;\;0.3333333333333333 \cdot \left(\frac{x}{y} \cdot \left(x + -4\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{3 + x \cdot -4}{y \cdot 3}\\ \end{array} \]

Alternative 4: 97.7% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -3.8) (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(x * Float64(x / y)));
	else
		tmp = Float64(Float64(1.0 - x) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -3.8) || ~((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[(x * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.7999999999999998 or 3 < x

   1. Initial program 87.0%

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

      1. times-frac 99.7%

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

      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. metadata-eval 99.7%

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

      2. div-sub 99.7%

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

      3. times-frac 87.0%

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

      4. *-commutative 87.0%

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

      5. frac-times 99.7%

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

      6. clear-num 99.6%

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

      7. frac-times 99.7%

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

      8. *-un-lft-identity 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in y around 0 87.6%

      \[\leadsto \color{blue}{0.3333333333333333 \cdot \frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y}} \]
   7. Step-by-step derivation

      1. associate-/l* 99.6%

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

      2. associate-/r/ 99.7%

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

   8. Simplified 99.7%

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

   9. Taylor expanded in x around inf 82.4%

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

       1. unpow2 82.4%

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

       2. associate-*r/ 94.5%

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

   11. Simplified 94.5%

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

   if -3.7999999999999998 < x < 3

   1. Initial program 99.7%

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

      1. metadata-eval 99.9%

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

      2. div-sub 100.0%

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

      3. times-frac 99.7%

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

      4. *-commutative 99.7%

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

      5. frac-times 99.3%

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

      6. clear-num 99.2%

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

      7. frac-times 99.8%

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

      8. *-un-lft-identity 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in x around 0 97.6%

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

4. Final simplification 95.8%

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

Alternative 5: 97.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \frac{x}{y}\\ \mathbf{if}\;x \leq -3.8:\\ \;\;\;\;\frac{t_0}{3}\\ \mathbf{elif}\;x \leq 3:\\ \;\;\;\;\frac{1 - x}{y}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* x (/ x y))))
   (if (<= x -3.8)
     (/ t_0 3.0)
     (if (<= x 3.0) (/ (- 1.0 x) y) (* 0.3333333333333333 t_0)))))

C

double code(double x, double y) {
	double t_0 = x * (x / y);
	double tmp;
	if (x <= -3.8) {
		tmp = t_0 / 3.0;
	} else if (x <= 3.0) {
		tmp = (1.0 - x) / y;
	} else {
		tmp = 0.3333333333333333 * t_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 * (x / y)
    if (x <= (-3.8d0)) then
        tmp = t_0 / 3.0d0
    else if (x <= 3.0d0) then
        tmp = (1.0d0 - x) / y
    else
        tmp = 0.3333333333333333d0 * t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x * (x / y);
	double tmp;
	if (x <= -3.8) {
		tmp = t_0 / 3.0;
	} else if (x <= 3.0) {
		tmp = (1.0 - x) / y;
	} else {
		tmp = 0.3333333333333333 * t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x * (x / y)
	tmp = 0
	if x <= -3.8:
		tmp = t_0 / 3.0
	elif x <= 3.0:
		tmp = (1.0 - x) / y
	else:
		tmp = 0.3333333333333333 * t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x * Float64(x / y))
	tmp = 0.0
	if (x <= -3.8)
		tmp = Float64(t_0 / 3.0);
	elseif (x <= 3.0)
		tmp = Float64(Float64(1.0 - x) / y);
	else
		tmp = Float64(0.3333333333333333 * t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x * (x / y);
	tmp = 0.0;
	if (x <= -3.8)
		tmp = t_0 / 3.0;
	elseif (x <= 3.0)
		tmp = (1.0 - x) / y;
	else
		tmp = 0.3333333333333333 * t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x * N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.8], N[(t$95$0 / 3.0), $MachinePrecision], If[LessEqual[x, 3.0], N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision], N[(0.3333333333333333 * t$95$0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.7999999999999998

   1. Initial program 90.8%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   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 inf 86.1%

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

      1. unpow2 86.1%

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

      2. associate-*r/ 86.1%

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

   6. Simplified 86.1%

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

      1. associate-/l* 86.0%

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

      2. associate-/r/ 86.1%

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

   8. Applied egg-rr 86.1%

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

      1. associate-*l/ 86.1%

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

      2. *-un-lft-identity 86.1%

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

      3. times-frac 86.1%

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

      4. metadata-eval 86.1%

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

      5. metadata-eval 86.1%

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

      6. times-frac 86.2%

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

      7. *-un-lft-identity 86.2%

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

      8. *-commutative 86.2%

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

      9. times-frac 95.2%

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

      10. associate-*r/ 95.1%

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

   10. Applied egg-rr 95.1%

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

   if -3.7999999999999998 < x < 3

   1. Initial program 99.7%

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

      1. metadata-eval 99.9%

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

      2. div-sub 100.0%

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

      3. times-frac 99.7%

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

      4. *-commutative 99.7%

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

      5. frac-times 99.3%

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

      6. clear-num 99.2%

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

      7. frac-times 99.8%

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

      8. *-un-lft-identity 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in x around 0 97.6%

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

   if 3 < x

   1. Initial program 83.3%

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

      1. times-frac 99.6%

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

      2. div-sub 99.6%

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

      3. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

      1. metadata-eval 99.6%

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

      2. div-sub 99.6%

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

      3. times-frac 83.3%

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

      4. *-commutative 83.3%

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

      5. frac-times 99.6%

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

      6. clear-num 99.5%

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

      7. frac-times 99.7%

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

      8. *-un-lft-identity 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in y around 0 84.6%

      \[\leadsto \color{blue}{0.3333333333333333 \cdot \frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y}} \]
   7. Step-by-step derivation

      1. associate-/l* 99.6%

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

      2. associate-/r/ 99.6%

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

   8. Simplified 99.6%

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

   9. Taylor expanded in x around inf 78.8%

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

       1. unpow2 78.8%

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

       2. associate-*r/ 93.9%

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

   11. Simplified 93.9%

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

4. Final simplification 95.8%

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

Alternative 6: 99.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.5%

   \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
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 92.5%

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

   4. *-commutative 92.5%

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

   5. frac-times 99.5%

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

   6. clear-num 99.5%

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

   7. frac-times 99.8%

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

   8. *-un-lft-identity 99.8%

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

5. Applied egg-rr 99.8%

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

6. Taylor expanded in y around 0 92.6%

   \[\leadsto \color{blue}{0.3333333333333333 \cdot \frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y}} \]
7. Step-by-step derivation

   1. associate-/l* 99.4%

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

   2. associate-/r/ 99.6%

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

8. Simplified 99.6%

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

9. Final simplification 99.6%

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

Alternative 7: 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 92.5%

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

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

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 8: 63.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;\frac{-x}{y}\\ \mathbf{elif}\;x \leq 4.8:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.0) (/ (- x) y) (if (<= x 4.8) (/ 1.0 y) (/ x y))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.0) {
		tmp = -x / y;
	} else if (x <= 4.8) {
		tmp = 1.0 / y;
	} else {
		tmp = 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 <= (-1.0d0)) then
        tmp = -x / y
    else if (x <= 4.8d0) then
        tmp = 1.0d0 / y
    else
        tmp = x / 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 if (x <= 4.8) {
		tmp = 1.0 / y;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.0:
		tmp = -x / y
	elif x <= 4.8:
		tmp = 1.0 / y
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.0)
		tmp = Float64(Float64(-x) / y);
	elseif (x <= 4.8)
		tmp = Float64(1.0 / y);
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.0)
		tmp = -x / y;
	elseif (x <= 4.8)
		tmp = 1.0 / y;
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.0], N[((-x) / y), $MachinePrecision], If[LessEqual[x, 4.8], N[(1.0 / y), $MachinePrecision], N[(x / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1

   1. Initial program 90.8%

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

      1. associate-*l/ 99.9%

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

      2. *-commutative 99.9%

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

      3. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 95.2%

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

      1. metadata-eval 95.2%

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

      2. distribute-lft-neg-in 95.2%

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

      3. *-commutative 95.2%

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

      4. associate-*l/ 95.2%

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

      5. associate-*r/ 95.3%

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

      6. distribute-rgt-neg-in 95.3%

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

      7. distribute-neg-frac 95.3%

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

      8. metadata-eval 95.3%

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

   6. Simplified 95.3%

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

   7. Taylor expanded in x around 0 34.4%

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

      1. mul-1-neg 34.4%

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

      2. distribute-neg-frac 34.4%

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

   9. Simplified 34.4%

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

   if -1 < x < 4.79999999999999982

   1. Initial program 99.7%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   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 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 97.2%

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

   if 4.79999999999999982 < x

   1. Initial program 83.3%

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

      1. associate-*l/ 98.4%

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

      2. *-commutative 98.4%

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

      3. *-commutative 98.4%

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

   3. Simplified 98.4%

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

   4. Taylor expanded in x around inf 94.2%

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

      1. metadata-eval 94.2%

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

      2. distribute-lft-neg-in 94.2%

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

      3. *-commutative 94.2%

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

      4. associate-*l/ 94.2%

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

      5. associate-*r/ 94.2%

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

      6. distribute-rgt-neg-in 94.2%

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

      7. distribute-neg-frac 94.2%

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

      8. metadata-eval 94.2%

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

   6. Simplified 94.2%

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

      1. frac-2neg 94.2%

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

      2. metadata-eval 94.2%

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

      3. associate-*r/ 94.2%

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

      4. associate-*l/ 94.2%

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

      5. remove-double-neg 94.2%

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

      6. frac-2neg 94.2%

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

      7. metadata-eval 94.2%

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

      8. div-inv 94.2%

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

      9. associate-*r/ 94.2%

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

   8. Applied egg-rr 93.7%

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

   9. Taylor expanded in x around 0 29.2%

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

4. Final simplification 59.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;\frac{-x}{y}\\ \mathbf{elif}\;x \leq 4.8:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]

Alternative 9: 63.8% accurate, 1.6× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if x < 3

   1. Initial program 96.2%

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

      1. metadata-eval 99.9%

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

      2. div-sub 99.9%

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

      3. times-frac 96.2%

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

      4. *-commutative 96.2%

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

      5. frac-times 99.5%

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

      6. clear-num 99.4%

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

      7. frac-times 99.8%

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

      8. *-un-lft-identity 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in x around 0 72.6%

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

   if 3 < x

   1. Initial program 83.3%

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

      1. associate-*l/ 98.4%

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

      2. *-commutative 98.4%

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

      3. *-commutative 98.4%

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

   3. Simplified 98.4%

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

   4. Taylor expanded in x around inf 94.2%

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

      1. metadata-eval 94.2%

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

      2. distribute-lft-neg-in 94.2%

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

      3. *-commutative 94.2%

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

      4. associate-*l/ 94.2%

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

      5. associate-*r/ 94.2%

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

      6. distribute-rgt-neg-in 94.2%

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

      7. distribute-neg-frac 94.2%

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

      8. metadata-eval 94.2%

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

   6. Simplified 94.2%

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

      1. frac-2neg 94.2%

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

      2. metadata-eval 94.2%

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

      3. associate-*r/ 94.2%

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

      4. associate-*l/ 94.2%

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

      5. remove-double-neg 94.2%

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

      6. frac-2neg 94.2%

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

      7. metadata-eval 94.2%

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

      8. div-inv 94.2%

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

      9. associate-*r/ 94.2%

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

   8. Applied egg-rr 93.7%

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

   9. Taylor expanded in x around 0 29.2%

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

4. Final simplification 60.1%

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

Alternative 10: 57.7% accurate, 2.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 4.8:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= x 4.8) (/ 1.0 y) (/ x y)))

C

double code(double x, double y) {
	double tmp;
	if (x <= 4.8) {
		tmp = 1.0 / y;
	} else {
		tmp = 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 <= 4.8d0) then
        tmp = 1.0d0 / y
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 4.8) {
		tmp = 1.0 / y;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 4.8:
		tmp = 1.0 / y
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 4.8)
		tmp = Float64(1.0 / y);
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 4.8)
		tmp = 1.0 / y;
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 4.8], N[(1.0 / y), $MachinePrecision], N[(x / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 4.79999999999999982

   1. Initial program 96.2%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   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 60.9%

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

   if 4.79999999999999982 < x

   1. Initial program 83.3%

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

      1. associate-*l/ 98.4%

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

      2. *-commutative 98.4%

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

      3. *-commutative 98.4%

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

   3. Simplified 98.4%

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

   4. Taylor expanded in x around inf 94.2%

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

      1. metadata-eval 94.2%

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

      2. distribute-lft-neg-in 94.2%

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

      3. *-commutative 94.2%

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

      4. associate-*l/ 94.2%

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

      5. associate-*r/ 94.2%

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

      6. distribute-rgt-neg-in 94.2%

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

      7. distribute-neg-frac 94.2%

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

      8. metadata-eval 94.2%

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

   6. Simplified 94.2%

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

      1. frac-2neg 94.2%

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

      2. metadata-eval 94.2%

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

      3. associate-*r/ 94.2%

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

      4. associate-*l/ 94.2%

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

      5. remove-double-neg 94.2%

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

      6. frac-2neg 94.2%

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

      7. metadata-eval 94.2%

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

      8. div-inv 94.2%

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

      9. associate-*r/ 94.2%

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

   8. Applied egg-rr 93.7%

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

   9. Taylor expanded in x around 0 29.2%

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

4. Final simplification 51.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 4.8:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]

Alternative 11: 51.8% accurate, 3.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 92.5%

   \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
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 44.8%

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

5. Final simplification 44.8%

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

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 2023221 
(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)))