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

Percentage Accurate: 93.6% → 99.9%

Time: 10.4s

Alternatives: 13

Speedup: 1.0×

• 25.0% 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: 93.6% 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

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

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]

Derivation

1. Initial program 93.2%

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

   1. times-frac 99.9%

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

3. Simplified 99.9%

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

5. Final simplification 99.9%

   \[\leadsto \frac{1 - x}{y} \cdot \frac{3 - x}{3} \]
6. Add Preprocessing

Alternative 2: 99.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.75 \lor \neg \left(x \leq 1.7\right):\\ \;\;\;\;x \cdot \left(\left(4 - x\right) \cdot \frac{-0.3333333333333333}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -1.75) (not (<= x 1.7)))
   (* x (* (- 4.0 x) (/ -0.3333333333333333 y)))
   (/ (+ 1.0 (* x -1.3333333333333333)) y)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -1.75) || !(x <= 1.7)) {
		tmp = x * ((4.0 - x) * (-0.3333333333333333 / y));
	} else {
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-1.75d0)) .or. (.not. (x <= 1.7d0))) then
        tmp = x * ((4.0d0 - x) * ((-0.3333333333333333d0) / y))
    else
        tmp = (1.0d0 + (x * (-1.3333333333333333d0))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -1.75) || !(x <= 1.7)) {
		tmp = x * ((4.0 - x) * (-0.3333333333333333 / y));
	} else {
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -1.75) or not (x <= 1.7):
		tmp = x * ((4.0 - x) * (-0.3333333333333333 / y))
	else:
		tmp = (1.0 + (x * -1.3333333333333333)) / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -1.75) || !(x <= 1.7))
		tmp = Float64(x * Float64(Float64(4.0 - x) * Float64(-0.3333333333333333 / y)));
	else
		tmp = Float64(Float64(1.0 + Float64(x * -1.3333333333333333)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -1.75) || ~((x <= 1.7)))
		tmp = x * ((4.0 - x) * (-0.3333333333333333 / y));
	else
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -1.75], N[Not[LessEqual[x, 1.7]], $MachinePrecision]], N[(x * N[(N[(4.0 - x), $MachinePrecision] * N[(-0.3333333333333333 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 + N[(x * -1.3333333333333333), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.75 or 1.69999999999999996 < x

   1. Initial program 84.6%

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

   3. Taylor expanded in x around inf 83.8%

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

      1. +-commutative 83.8%

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

      2. unpow2 83.8%

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

      3. distribute-rgt-out 83.8%

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

   5. Simplified 83.8%

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

      1. frac-2neg 83.8%

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

      2. div-inv 83.7%

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

      3. distribute-rgt-neg-in 83.7%

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

      4. distribute-rgt-neg-in 83.7%

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

      5. metadata-eval 83.7%

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

   7. Applied egg-rr 83.7%

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

      1. associate-*l* 98.8%

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

      2. neg-sub0 98.8%

         \[\leadsto x \cdot \left(\color{blue}{\left(0 - \left(x + -4\right)\right)} \cdot \frac{1}{y \cdot -3}\right) \]

      3. +-commutative 98.8%

         \[\leadsto x \cdot \left(\left(0 - \color{blue}{\left(-4 + x\right)}\right) \cdot \frac{1}{y \cdot -3}\right) \]

      4. associate--r+ 98.8%

         \[\leadsto x \cdot \left(\color{blue}{\left(\left(0 - -4\right) - x\right)} \cdot \frac{1}{y \cdot -3}\right) \]

      5. metadata-eval 98.8%

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

      6. *-commutative 98.8%

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

      7. associate-/r* 98.8%

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

      8. metadata-eval 98.8%

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

   9. Simplified 98.8%

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

   if -1.75 < x < 1.69999999999999996

   1. Initial program 99.6%

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

      1. associate-*l/ 99.5%

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

      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. Add Preprocessing

   5. Taylor expanded in x around 0 99.1%

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

   6. Taylor expanded in y around 0 99.1%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.75 \lor \neg \left(x \leq 1.7\right):\\ \;\;\;\;x \cdot \left(\left(4 - x\right) \cdot \frac{-0.3333333333333333}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.75:\\ \;\;\;\;\frac{x}{3} \cdot \frac{x + -4}{y}\\ \mathbf{elif}\;x \leq 1.7:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(4 - x\right) \cdot \frac{-0.3333333333333333}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.75)
   (* (/ x 3.0) (/ (+ x -4.0) y))
   (if (<= x 1.7)
     (/ (+ 1.0 (* x -1.3333333333333333)) y)
     (* x (* (- 4.0 x) (/ -0.3333333333333333 y))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.75) {
		tmp = (x / 3.0) * ((x + -4.0) / y);
	} else if (x <= 1.7) {
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	} else {
		tmp = x * ((4.0 - x) * (-0.3333333333333333 / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-1.75d0)) then
        tmp = (x / 3.0d0) * ((x + (-4.0d0)) / y)
    else if (x <= 1.7d0) then
        tmp = (1.0d0 + (x * (-1.3333333333333333d0))) / y
    else
        tmp = x * ((4.0d0 - x) * ((-0.3333333333333333d0) / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -1.75) {
		tmp = (x / 3.0) * ((x + -4.0) / y);
	} else if (x <= 1.7) {
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	} else {
		tmp = x * ((4.0 - x) * (-0.3333333333333333 / y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.75:
		tmp = (x / 3.0) * ((x + -4.0) / y)
	elif x <= 1.7:
		tmp = (1.0 + (x * -1.3333333333333333)) / y
	else:
		tmp = x * ((4.0 - x) * (-0.3333333333333333 / y))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.75)
		tmp = Float64(Float64(x / 3.0) * Float64(Float64(x + -4.0) / y));
	elseif (x <= 1.7)
		tmp = Float64(Float64(1.0 + Float64(x * -1.3333333333333333)) / y);
	else
		tmp = Float64(x * Float64(Float64(4.0 - x) * Float64(-0.3333333333333333 / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.75)
		tmp = (x / 3.0) * ((x + -4.0) / y);
	elseif (x <= 1.7)
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	else
		tmp = x * ((4.0 - x) * (-0.3333333333333333 / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.75], N[(N[(x / 3.0), $MachinePrecision] * N[(N[(x + -4.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.7], N[(N[(1.0 + N[(x * -1.3333333333333333), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x * N[(N[(4.0 - x), $MachinePrecision] * N[(-0.3333333333333333 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.75

   1. Initial program 82.4%

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

   3. Taylor expanded in x around inf 81.1%

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

      1. +-commutative 81.1%

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

      2. unpow2 81.1%

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

      3. distribute-rgt-out 81.1%

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

   5. Simplified 81.1%

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

      1. *-commutative 81.1%

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

      2. times-frac 98.4%

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

   7. Applied egg-rr 98.4%

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

   if -1.75 < x < 1.69999999999999996

   1. Initial program 99.6%

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

      1. associate-*l/ 99.5%

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

      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. Add Preprocessing

   5. Taylor expanded in x around 0 99.1%

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

   6. Taylor expanded in y around 0 99.1%

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

   if 1.69999999999999996 < x

   1. Initial program 86.7%

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

   3. Taylor expanded in x around inf 86.3%

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

      1. +-commutative 86.3%

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

      2. unpow2 86.3%

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

      3. distribute-rgt-out 86.2%

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

   5. Simplified 86.2%

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

      1. frac-2neg 86.2%

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

      2. div-inv 86.2%

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

      3. distribute-rgt-neg-in 86.2%

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

      4. distribute-rgt-neg-in 86.2%

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

      5. metadata-eval 86.2%

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

   7. Applied egg-rr 86.2%

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

      1. associate-*l* 99.3%

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

      2. neg-sub0 99.3%

         \[\leadsto x \cdot \left(\color{blue}{\left(0 - \left(x + -4\right)\right)} \cdot \frac{1}{y \cdot -3}\right) \]

      3. +-commutative 99.3%

         \[\leadsto x \cdot \left(\left(0 - \color{blue}{\left(-4 + x\right)}\right) \cdot \frac{1}{y \cdot -3}\right) \]

      4. associate--r+ 99.3%

         \[\leadsto x \cdot \left(\color{blue}{\left(\left(0 - -4\right) - x\right)} \cdot \frac{1}{y \cdot -3}\right) \]

      5. metadata-eval 99.3%

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

      6. *-commutative 99.3%

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

      7. associate-/r* 99.3%

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

      8. metadata-eval 99.3%

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

   9. Simplified 99.3%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.75:\\ \;\;\;\;\frac{x}{3} \cdot \frac{x + -4}{y}\\ \mathbf{elif}\;x \leq 1.7:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(4 - x\right) \cdot \frac{-0.3333333333333333}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.5:\\ \;\;\;\;\frac{x + -4}{\frac{y}{x}} \cdot 0.3333333333333333\\ \mathbf{elif}\;x \leq 1.7:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(4 - x\right) \cdot \frac{-0.3333333333333333}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.5)
   (* (/ (+ x -4.0) (/ y x)) 0.3333333333333333)
   (if (<= x 1.7)
     (/ (+ 1.0 (* x -1.3333333333333333)) y)
     (* x (* (- 4.0 x) (/ -0.3333333333333333 y))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.5) {
		tmp = ((x + -4.0) / (y / x)) * 0.3333333333333333;
	} else if (x <= 1.7) {
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	} else {
		tmp = x * ((4.0 - x) * (-0.3333333333333333 / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-1.5d0)) then
        tmp = ((x + (-4.0d0)) / (y / x)) * 0.3333333333333333d0
    else if (x <= 1.7d0) then
        tmp = (1.0d0 + (x * (-1.3333333333333333d0))) / y
    else
        tmp = x * ((4.0d0 - x) * ((-0.3333333333333333d0) / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -1.5) {
		tmp = ((x + -4.0) / (y / x)) * 0.3333333333333333;
	} else if (x <= 1.7) {
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	} else {
		tmp = x * ((4.0 - x) * (-0.3333333333333333 / y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.5:
		tmp = ((x + -4.0) / (y / x)) * 0.3333333333333333
	elif x <= 1.7:
		tmp = (1.0 + (x * -1.3333333333333333)) / y
	else:
		tmp = x * ((4.0 - x) * (-0.3333333333333333 / y))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.5)
		tmp = Float64(Float64(Float64(x + -4.0) / Float64(y / x)) * 0.3333333333333333);
	elseif (x <= 1.7)
		tmp = Float64(Float64(1.0 + Float64(x * -1.3333333333333333)) / y);
	else
		tmp = Float64(x * Float64(Float64(4.0 - x) * Float64(-0.3333333333333333 / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.5)
		tmp = ((x + -4.0) / (y / x)) * 0.3333333333333333;
	elseif (x <= 1.7)
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	else
		tmp = x * ((4.0 - x) * (-0.3333333333333333 / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.5], N[(N[(N[(x + -4.0), $MachinePrecision] / N[(y / x), $MachinePrecision]), $MachinePrecision] * 0.3333333333333333), $MachinePrecision], If[LessEqual[x, 1.7], N[(N[(1.0 + N[(x * -1.3333333333333333), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x * N[(N[(4.0 - x), $MachinePrecision] * N[(-0.3333333333333333 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.5

   1. Initial program 82.4%

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

   3. Taylor expanded in x around inf 81.1%

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

      1. +-commutative 81.1%

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

      2. unpow2 81.1%

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

      3. distribute-rgt-out 81.1%

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

   5. Simplified 81.1%

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

      1. associate-/r* 81.1%

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

      2. div-inv 81.1%

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

      3. *-commutative 81.1%

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

      4. associate-/l* 98.4%

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

      5. metadata-eval 98.4%

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

   7. Applied egg-rr 98.4%

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

   if -1.5 < x < 1.69999999999999996

   1. Initial program 99.6%

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

      1. associate-*l/ 99.5%

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

      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. Add Preprocessing

   5. Taylor expanded in x around 0 99.1%

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

   6. Taylor expanded in y around 0 99.1%

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

   if 1.69999999999999996 < x

   1. Initial program 86.7%

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

   3. Taylor expanded in x around inf 86.3%

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

      1. +-commutative 86.3%

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

      2. unpow2 86.3%

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

      3. distribute-rgt-out 86.2%

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

   5. Simplified 86.2%

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

      1. frac-2neg 86.2%

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

      2. div-inv 86.2%

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

      3. distribute-rgt-neg-in 86.2%

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

      4. distribute-rgt-neg-in 86.2%

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

      5. metadata-eval 86.2%

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

   7. Applied egg-rr 86.2%

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

      1. associate-*l* 99.3%

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

      2. neg-sub0 99.3%

         \[\leadsto x \cdot \left(\color{blue}{\left(0 - \left(x + -4\right)\right)} \cdot \frac{1}{y \cdot -3}\right) \]

      3. +-commutative 99.3%

         \[\leadsto x \cdot \left(\left(0 - \color{blue}{\left(-4 + x\right)}\right) \cdot \frac{1}{y \cdot -3}\right) \]

      4. associate--r+ 99.3%

         \[\leadsto x \cdot \left(\color{blue}{\left(\left(0 - -4\right) - x\right)} \cdot \frac{1}{y \cdot -3}\right) \]

      5. metadata-eval 99.3%

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

      6. *-commutative 99.3%

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

      7. associate-/r* 99.3%

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

      8. metadata-eval 99.3%

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

   9. Simplified 99.3%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.5:\\ \;\;\;\;\frac{x + -4}{\frac{y}{x}} \cdot 0.3333333333333333\\ \mathbf{elif}\;x \leq 1.7:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(4 - x\right) \cdot \frac{-0.3333333333333333}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 99.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.75:\\ \;\;\;\;\frac{x + -4}{\frac{y}{x}} \cdot 0.3333333333333333\\ \mathbf{elif}\;x \leq 1.7:\\ \;\;\;\;-1.3333333333333333 \cdot \frac{x}{y} + \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(4 - x\right) \cdot \frac{-0.3333333333333333}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.75)
   (* (/ (+ x -4.0) (/ y x)) 0.3333333333333333)
   (if (<= x 1.7)
     (+ (* -1.3333333333333333 (/ x y)) (/ 1.0 y))
     (* x (* (- 4.0 x) (/ -0.3333333333333333 y))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.75) {
		tmp = ((x + -4.0) / (y / x)) * 0.3333333333333333;
	} else if (x <= 1.7) {
		tmp = (-1.3333333333333333 * (x / y)) + (1.0 / y);
	} else {
		tmp = x * ((4.0 - x) * (-0.3333333333333333 / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-1.75d0)) then
        tmp = ((x + (-4.0d0)) / (y / x)) * 0.3333333333333333d0
    else if (x <= 1.7d0) then
        tmp = ((-1.3333333333333333d0) * (x / y)) + (1.0d0 / y)
    else
        tmp = x * ((4.0d0 - x) * ((-0.3333333333333333d0) / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -1.75) {
		tmp = ((x + -4.0) / (y / x)) * 0.3333333333333333;
	} else if (x <= 1.7) {
		tmp = (-1.3333333333333333 * (x / y)) + (1.0 / y);
	} else {
		tmp = x * ((4.0 - x) * (-0.3333333333333333 / y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.75:
		tmp = ((x + -4.0) / (y / x)) * 0.3333333333333333
	elif x <= 1.7:
		tmp = (-1.3333333333333333 * (x / y)) + (1.0 / y)
	else:
		tmp = x * ((4.0 - x) * (-0.3333333333333333 / y))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.75)
		tmp = Float64(Float64(Float64(x + -4.0) / Float64(y / x)) * 0.3333333333333333);
	elseif (x <= 1.7)
		tmp = Float64(Float64(-1.3333333333333333 * Float64(x / y)) + Float64(1.0 / y));
	else
		tmp = Float64(x * Float64(Float64(4.0 - x) * Float64(-0.3333333333333333 / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.75)
		tmp = ((x + -4.0) / (y / x)) * 0.3333333333333333;
	elseif (x <= 1.7)
		tmp = (-1.3333333333333333 * (x / y)) + (1.0 / y);
	else
		tmp = x * ((4.0 - x) * (-0.3333333333333333 / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.75], N[(N[(N[(x + -4.0), $MachinePrecision] / N[(y / x), $MachinePrecision]), $MachinePrecision] * 0.3333333333333333), $MachinePrecision], If[LessEqual[x, 1.7], N[(N[(-1.3333333333333333 * N[(x / y), $MachinePrecision]), $MachinePrecision] + N[(1.0 / y), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(4.0 - x), $MachinePrecision] * N[(-0.3333333333333333 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.75

   1. Initial program 82.4%

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

   3. Taylor expanded in x around inf 81.1%

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

      1. +-commutative 81.1%

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

      2. unpow2 81.1%

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

      3. distribute-rgt-out 81.1%

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

   5. Simplified 81.1%

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

      1. associate-/r* 81.1%

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

      2. div-inv 81.1%

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

      3. *-commutative 81.1%

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

      4. associate-/l* 98.4%

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

      5. metadata-eval 98.4%

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

   7. Applied egg-rr 98.4%

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

   if -1.75 < x < 1.69999999999999996

   1. Initial program 99.6%

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

      1. associate-*l/ 99.5%

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

      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. Add Preprocessing

   5. Taylor expanded in x around 0 99.1%

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

   if 1.69999999999999996 < x

   1. Initial program 86.7%

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

   3. Taylor expanded in x around inf 86.3%

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

      1. +-commutative 86.3%

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

      2. unpow2 86.3%

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

      3. distribute-rgt-out 86.2%

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

   5. Simplified 86.2%

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

      1. frac-2neg 86.2%

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

      2. div-inv 86.2%

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

      3. distribute-rgt-neg-in 86.2%

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

      4. distribute-rgt-neg-in 86.2%

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

      5. metadata-eval 86.2%

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

   7. Applied egg-rr 86.2%

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

      1. associate-*l* 99.3%

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

      2. neg-sub0 99.3%

         \[\leadsto x \cdot \left(\color{blue}{\left(0 - \left(x + -4\right)\right)} \cdot \frac{1}{y \cdot -3}\right) \]

      3. +-commutative 99.3%

         \[\leadsto x \cdot \left(\left(0 - \color{blue}{\left(-4 + x\right)}\right) \cdot \frac{1}{y \cdot -3}\right) \]

      4. associate--r+ 99.3%

         \[\leadsto x \cdot \left(\color{blue}{\left(\left(0 - -4\right) - x\right)} \cdot \frac{1}{y \cdot -3}\right) \]

      5. metadata-eval 99.3%

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

      6. *-commutative 99.3%

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

      7. associate-/r* 99.3%

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

      8. metadata-eval 99.3%

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

   9. Simplified 99.3%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.75:\\ \;\;\;\;\frac{x + -4}{\frac{y}{x}} \cdot 0.3333333333333333\\ \mathbf{elif}\;x \leq 1.7:\\ \;\;\;\;-1.3333333333333333 \cdot \frac{x}{y} + \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(4 - x\right) \cdot \frac{-0.3333333333333333}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 98.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.75 \lor \neg \left(x \leq 0.58\right):\\ \;\;\;\;\frac{x}{3} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -1.75) (not (<= x 0.58))) (* (/ x 3.0) (/ x y)) (/ 1.0 y)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -1.75) || !(x <= 0.58)) {
		tmp = (x / 3.0) * (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 <= (-1.75d0)) .or. (.not. (x <= 0.58d0))) then
        tmp = (x / 3.0d0) * (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 <= -1.75) || !(x <= 0.58)) {
		tmp = (x / 3.0) * (x / y);
	} else {
		tmp = 1.0 / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -1.75) or not (x <= 0.58):
		tmp = (x / 3.0) * (x / y)
	else:
		tmp = 1.0 / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -1.75) || !(x <= 0.58))
		tmp = Float64(Float64(x / 3.0) * 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 <= -1.75) || ~((x <= 0.58)))
		tmp = (x / 3.0) * (x / y);
	else
		tmp = 1.0 / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -1.75], N[Not[LessEqual[x, 0.58]], $MachinePrecision]], N[(N[(x / 3.0), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], N[(1.0 / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.75 or 0.57999999999999996 < x

   1. Initial program 84.6%

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

   3. Taylor expanded in x around inf 83.8%

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

      1. +-commutative 83.8%

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

      2. unpow2 83.8%

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

      3. distribute-rgt-out 83.8%

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

   5. Simplified 83.8%

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

      1. *-commutative 83.8%

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

      2. times-frac 98.9%

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

   7. Applied egg-rr 98.9%

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

   8. Taylor expanded in x around inf 97.7%

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

   if -1.75 < x < 0.57999999999999996

   1. Initial program 99.6%

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

      1. associate-*l/ 99.5%

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

      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. Add Preprocessing

   5. Taylor expanded in x around 0 98.0%

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

4. Final simplification 97.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.75 \lor \neg \left(x \leq 0.58\right):\\ \;\;\;\;\frac{x}{3} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 98.1% accurate, 0.6× 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 84.6%

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

   3. Taylor expanded in x around inf 83.8%

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

      1. +-commutative 83.8%

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

      2. unpow2 83.8%

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

      3. distribute-rgt-out 83.8%

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

   5. Simplified 83.8%

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

      1. *-commutative 83.8%

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

      2. times-frac 98.9%

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

   7. Applied egg-rr 98.9%

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

   8. Taylor expanded in x around inf 97.7%

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

   if -3.7999999999999998 < x < 3

   1. Initial program 99.6%

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

      1. times-frac 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 98.2%

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

4. Final simplification 98.0%

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

Alternative 8: 98.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.8 \lor \neg \left(x \leq 3\right):\\ \;\;\;\;\frac{x}{3} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -4.8) (not (<= x 3.0)))
   (* (/ x 3.0) (/ x y))
   (/ (+ 1.0 (* x -1.3333333333333333)) y)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -4.8) || !(x <= 3.0)) {
		tmp = (x / 3.0) * (x / y);
	} else {
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-4.8d0)) .or. (.not. (x <= 3.0d0))) then
        tmp = (x / 3.0d0) * (x / y)
    else
        tmp = (1.0d0 + (x * (-1.3333333333333333d0))) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -4.8) || !(x <= 3.0)) {
		tmp = (x / 3.0) * (x / y);
	} else {
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -4.8) or not (x <= 3.0):
		tmp = (x / 3.0) * (x / y)
	else:
		tmp = (1.0 + (x * -1.3333333333333333)) / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -4.8) || !(x <= 3.0))
		tmp = Float64(Float64(x / 3.0) * Float64(x / y));
	else
		tmp = Float64(Float64(1.0 + Float64(x * -1.3333333333333333)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -4.8) || ~((x <= 3.0)))
		tmp = (x / 3.0) * (x / y);
	else
		tmp = (1.0 + (x * -1.3333333333333333)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -4.8], N[Not[LessEqual[x, 3.0]], $MachinePrecision]], N[(N[(x / 3.0), $MachinePrecision] * N[(x / y), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 + N[(x * -1.3333333333333333), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.79999999999999982 or 3 < x

   1. Initial program 84.6%

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

   3. Taylor expanded in x around inf 83.8%

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

      1. +-commutative 83.8%

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

      2. unpow2 83.8%

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

      3. distribute-rgt-out 83.8%

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

   5. Simplified 83.8%

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

      1. *-commutative 83.8%

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

      2. times-frac 98.9%

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

   7. Applied egg-rr 98.9%

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

   8. Taylor expanded in x around inf 97.7%

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

   if -4.79999999999999982 < x < 3

   1. Initial program 99.6%

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

      1. associate-*l/ 99.5%

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

      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. Add Preprocessing

   5. Taylor expanded in x around 0 99.1%

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

   6. Taylor expanded in y around 0 99.1%

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

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.8 \lor \neg \left(x \leq 3\right):\\ \;\;\;\;\frac{x}{3} \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 65.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.75:\\ \;\;\;\;-1.3333333333333333 \cdot \frac{x}{y}\\ \mathbf{elif}\;x \leq 5:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1.3333333333333333}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -0.75)
   (* -1.3333333333333333 (/ x y))
   (if (<= x 5.0) (/ 1.0 y) (* x (/ 1.3333333333333333 y)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -0.75) {
		tmp = -1.3333333333333333 * (x / y);
	} else if (x <= 5.0) {
		tmp = 1.0 / y;
	} else {
		tmp = x * (1.3333333333333333 / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-0.75d0)) then
        tmp = (-1.3333333333333333d0) * (x / y)
    else if (x <= 5.0d0) then
        tmp = 1.0d0 / y
    else
        tmp = x * (1.3333333333333333d0 / 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 if (x <= 5.0) {
		tmp = 1.0 / y;
	} else {
		tmp = x * (1.3333333333333333 / y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -0.75:
		tmp = -1.3333333333333333 * (x / y)
	elif x <= 5.0:
		tmp = 1.0 / y
	else:
		tmp = x * (1.3333333333333333 / y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -0.75)
		tmp = Float64(-1.3333333333333333 * Float64(x / y));
	elseif (x <= 5.0)
		tmp = Float64(1.0 / y);
	else
		tmp = Float64(x * Float64(1.3333333333333333 / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -0.75)
		tmp = -1.3333333333333333 * (x / y);
	elseif (x <= 5.0)
		tmp = 1.0 / y;
	else
		tmp = x * (1.3333333333333333 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -0.75], N[(-1.3333333333333333 * N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.0], N[(1.0 / y), $MachinePrecision], N[(x * N[(1.3333333333333333 / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -0.75

   1. Initial program 82.4%

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

   3. Taylor expanded in x around inf 81.1%

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

      1. +-commutative 81.1%

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

      2. unpow2 81.1%

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

      3. distribute-rgt-out 81.1%

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

   5. Simplified 81.1%

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

   6. Taylor expanded in x around 0 20.8%

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

   if -0.75 < x < 5

   1. Initial program 99.6%

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

      1. associate-*l/ 99.5%

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

      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. Add Preprocessing

   5. Taylor expanded in x around 0 98.0%

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

   if 5 < x

   1. Initial program 86.7%

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

   3. Taylor expanded in x around inf 86.3%

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

      1. +-commutative 86.3%

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

      2. unpow2 86.3%

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

      3. distribute-rgt-out 86.2%

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

   5. Simplified 86.2%

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

   6. Taylor expanded in x around 0 0.7%

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

      1. associate-*r/ 0.7%

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

   8. Simplified 0.7%

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

      1. associate-/l* 0.7%

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

      2. associate-/r/ 0.7%

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

   10. Applied egg-rr 0.7%

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

       1. add-sqr-sqrt 0.3%

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

       2. sqrt-unprod 23.1%

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

       3. sqr-neg 23.1%

          \[\leadsto \frac{-1.3333333333333333}{\sqrt{\color{blue}{\left(-y\right) \cdot \left(-y\right)}}} \cdot x \]

       4. sqrt-unprod 21.3%

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

       5. add-sqr-sqrt 34.2%

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

       6. clear-num 34.2%

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

       7. frac-2neg 34.2%

          \[\leadsto \frac{1}{\color{blue}{\frac{-\left(-y\right)}{--1.3333333333333333}}} \cdot x \]

       8. remove-double-neg 34.2%

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

       9. associate-/r/ 34.2%

          \[\leadsto \color{blue}{\left(\frac{1}{y} \cdot \left(--1.3333333333333333\right)\right)} \cdot x \]

       10. metadata-eval 34.2%

           \[\leadsto \left(\frac{1}{y} \cdot \color{blue}{1.3333333333333333}\right) \cdot x \]

   12. Applied egg-rr 34.2%

       \[\leadsto \color{blue}{\left(\frac{1}{y} \cdot 1.3333333333333333\right)} \cdot x \]
   13. Step-by-step derivation

       1. associate-*l/ 34.2%

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

       2. metadata-eval 34.2%

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

   14. Simplified 34.2%

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

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.75:\\ \;\;\;\;-1.3333333333333333 \cdot \frac{x}{y}\\ \mathbf{elif}\;x \leq 5:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1.3333333333333333}{y}\\ \end{array} \]
5. Add Preprocessing

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 93.2%

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

   1. associate-*l/ 99.6%

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

   2. *-commutative 99.6%

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

   3. *-commutative 99.6%

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

3. Simplified 99.6%

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

5. Final simplification 99.6%

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

Alternative 11: 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 93.2%

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

   1. associate-*l/ 99.6%

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

   2. *-commutative 99.6%

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

   3. *-commutative 99.6%

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

3. Simplified 99.6%

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

   1. associate-*r/ 93.2%

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

   2. frac-times 99.9%

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

   3. clear-num 99.8%

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

   4. associate-*l/ 99.9%

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

   5. *-un-lft-identity 99.9%

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

6. Applied egg-rr 99.9%

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

   1. expm1-log1p-u 65.2%

      \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{\frac{1 - x}{y}}{\frac{3}{3 - x}}\right)\right)} \]

   2. expm1-udef 37.4%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{\frac{1 - x}{y}}{\frac{3}{3 - x}}\right)} - 1} \]

   3. div-inv 37.4%

      \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{1 - x}{y} \cdot \frac{1}{\frac{3}{3 - x}}}\right)} - 1 \]

   4. clear-num 37.4%

      \[\leadsto e^{\mathsf{log1p}\left(\frac{1 - x}{y} \cdot \color{blue}{\frac{3 - x}{3}}\right)} - 1 \]

   5. div-sub 37.4%

      \[\leadsto e^{\mathsf{log1p}\left(\frac{1 - x}{y} \cdot \color{blue}{\left(\frac{3}{3} - \frac{x}{3}\right)}\right)} - 1 \]

   6. metadata-eval 37.4%

      \[\leadsto e^{\mathsf{log1p}\left(\frac{1 - x}{y} \cdot \left(\color{blue}{1} - \frac{x}{3}\right)\right)} - 1 \]

8. Applied egg-rr 37.4%

   \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{1 - x}{y} \cdot \left(1 - \frac{x}{3}\right)\right)} - 1} \]
9. Step-by-step derivation

   1. expm1-def 65.2%

      \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{1 - x}{y} \cdot \left(1 - \frac{x}{3}\right)\right)\right)} \]

   2. expm1-log1p 99.9%

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

10. Simplified 99.9%

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

11. Final simplification 99.9%

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

Alternative 12: 58.6% accurate, 1.1× 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 82.4%

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

   3. Taylor expanded in x around inf 81.1%

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

      1. +-commutative 81.1%

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

      2. unpow2 81.1%

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

      3. distribute-rgt-out 81.1%

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

   5. Simplified 81.1%

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

   6. Taylor expanded in x around 0 20.8%

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

   if -0.75 < x

   1. Initial program 96.0%

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

   5. Taylor expanded in x around 0 71.9%

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

4. Final simplification 61.3%

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

Alternative 13: 52.1% accurate, 3.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.2%

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

   1. associate-*l/ 99.6%

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

   2. *-commutative 99.6%

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

   3. *-commutative 99.6%

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

3. Simplified 99.6%

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

5. Taylor expanded in x around 0 58.0%

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

6. Final simplification 58.0%

   \[\leadsto \frac{1}{y} \]
7. Add Preprocessing

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 2024017 
(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)))