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

Percentage Accurate: 93.8% → 99.8%

Time: 2.4min

Alternatives: 14

Speedup: 1.0×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 93.8% 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

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.9%

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

   1. associate-*l/ 99.6%

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

   2. *-commutative 99.6%

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

   3. 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 2: 98.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.5:\\ \;\;\;\;\frac{x}{y} \cdot \frac{x}{3}\\ \mathbf{elif}\;x \leq 1.75:\\ \;\;\;\;\frac{x \cdot -1.3333333333333333 + 1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{-y}{x \cdot -0.3333333333333333 + 1.3333333333333333}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -4.5)
   (* (/ x y) (/ x 3.0))
   (if (<= x 1.75)
     (/ (+ (* x -1.3333333333333333) 1.0) y)
     (/ x (/ (- y) (+ (* x -0.3333333333333333) 1.3333333333333333))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -4.5) {
		tmp = (x / y) * (x / 3.0);
	} else if (x <= 1.75) {
		tmp = ((x * -1.3333333333333333) + 1.0) / y;
	} else {
		tmp = x / (-y / ((x * -0.3333333333333333) + 1.3333333333333333));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-4.5d0)) then
        tmp = (x / y) * (x / 3.0d0)
    else if (x <= 1.75d0) then
        tmp = ((x * (-1.3333333333333333d0)) + 1.0d0) / y
    else
        tmp = x / (-y / ((x * (-0.3333333333333333d0)) + 1.3333333333333333d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -4.5) {
		tmp = (x / y) * (x / 3.0);
	} else if (x <= 1.75) {
		tmp = ((x * -1.3333333333333333) + 1.0) / y;
	} else {
		tmp = x / (-y / ((x * -0.3333333333333333) + 1.3333333333333333));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -4.5:
		tmp = (x / y) * (x / 3.0)
	elif x <= 1.75:
		tmp = ((x * -1.3333333333333333) + 1.0) / y
	else:
		tmp = x / (-y / ((x * -0.3333333333333333) + 1.3333333333333333))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -4.5)
		tmp = Float64(Float64(x / y) * Float64(x / 3.0));
	elseif (x <= 1.75)
		tmp = Float64(Float64(Float64(x * -1.3333333333333333) + 1.0) / y);
	else
		tmp = Float64(x / Float64(Float64(-y) / Float64(Float64(x * -0.3333333333333333) + 1.3333333333333333)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -4.5)
		tmp = (x / y) * (x / 3.0);
	elseif (x <= 1.75)
		tmp = ((x * -1.3333333333333333) + 1.0) / y;
	else
		tmp = x / (-y / ((x * -0.3333333333333333) + 1.3333333333333333));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -4.5], N[(N[(x / y), $MachinePrecision] * N[(x / 3.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.75], N[(N[(N[(x * -1.3333333333333333), $MachinePrecision] + 1.0), $MachinePrecision] / y), $MachinePrecision], N[(x / N[((-y) / N[(N[(x * -0.3333333333333333), $MachinePrecision] + 1.3333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.5

   1. Initial program 96.2%

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

      1. associate-*l/ 99.8%

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

      2. *-commutative 99.8%

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

      3. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 96.0%

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

      1. unpow2 96.0%

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

   6. Simplified 96.0%

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

      1. associate-/l* 99.6%

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

      2. associate-/r/ 99.7%

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

   8. Applied egg-rr 99.7%

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

      1. associate-*r* 99.7%

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

      2. associate-*r/ 99.6%

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

      3. *-commutative 99.6%

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

      4. associate-/r/ 99.7%

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

      5. associate-/l* 99.5%

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

   10. Applied egg-rr 99.5%

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

       1. *-un-lft-identity 99.5%

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

       2. div-inv 99.7%

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

       3. metadata-eval 99.7%

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

       4. times-frac 99.6%

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

       5. clear-num 99.8%

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

   12. Applied egg-rr 99.8%

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

   if -4.5 < x < 1.75

   1. Initial program 99.6%

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

      1. associate-*l/ 99.4%

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

      2. *-commutative 99.4%

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

      3. *-commutative 99.4%

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

   3. Simplified 99.4%

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

      1. associate-/r* 99.5%

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

      2. associate-*r/ 100.0%

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

      3. *-commutative 100.0%

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

      4. div-inv 100.0%

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

      5. associate-*l* 100.0%

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

      6. metadata-eval 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in x around 0 97.9%

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

   if 1.75 < x

   1. Initial program 86.9%

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

      1. associate-*l/ 99.7%

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

      2. *-commutative 99.7%

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

      3. *-commutative 99.7%

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

   3. Simplified 99.7%

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

      1. associate-/r* 99.7%

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

      2. associate-*r/ 88.2%

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

      3. *-commutative 88.2%

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

      4. div-inv 88.1%

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

      5. associate-*l* 88.1%

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

      6. metadata-eval 88.1%

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

   5. Applied egg-rr 88.1%

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

   6. Taylor expanded in x around inf 86.8%

      \[\leadsto \frac{\color{blue}{-1.3333333333333333 \cdot x + 0.3333333333333333 \cdot {x}^{2}}}{y} \]
   7. Step-by-step derivation

      1. unpow2 86.8%

         \[\leadsto \frac{-1.3333333333333333 \cdot x + 0.3333333333333333 \cdot \color{blue}{\left(x \cdot x\right)}}{y} \]

      2. associate-*l* 88.0%

         \[\leadsto \frac{-1.3333333333333333 \cdot x + \color{blue}{\left(0.3333333333333333 \cdot x\right) \cdot x}}{y} \]

      3. distribute-rgt-out 88.0%

         \[\leadsto \frac{\color{blue}{x \cdot \left(-1.3333333333333333 + 0.3333333333333333 \cdot x\right)}}{y} \]

      4. *-commutative 88.0%

         \[\leadsto \frac{x \cdot \left(-1.3333333333333333 + \color{blue}{x \cdot 0.3333333333333333}\right)}{y} \]

   8. Simplified 88.0%

      \[\leadsto \frac{\color{blue}{x \cdot \left(-1.3333333333333333 + x \cdot 0.3333333333333333\right)}}{y} \]
   9. Step-by-step derivation

      1. frac-2neg 88.0%

         \[\leadsto \color{blue}{\frac{-x \cdot \left(-1.3333333333333333 + x \cdot 0.3333333333333333\right)}{-y}} \]

      2. div-inv 88.0%

         \[\leadsto \color{blue}{\left(-x \cdot \left(-1.3333333333333333 + x \cdot 0.3333333333333333\right)\right) \cdot \frac{1}{-y}} \]

      3. distribute-rgt-neg-in 88.0%

         \[\leadsto \color{blue}{\left(x \cdot \left(-\left(-1.3333333333333333 + x \cdot 0.3333333333333333\right)\right)\right)} \cdot \frac{1}{-y} \]

      4. +-commutative 88.0%

         \[\leadsto \left(x \cdot \left(-\color{blue}{\left(x \cdot 0.3333333333333333 + -1.3333333333333333\right)}\right)\right) \cdot \frac{1}{-y} \]

      5. fma-def 88.0%

         \[\leadsto \left(x \cdot \left(-\color{blue}{\mathsf{fma}\left(x, 0.3333333333333333, -1.3333333333333333\right)}\right)\right) \cdot \frac{1}{-y} \]

   10. Applied egg-rr 88.0%

       \[\leadsto \color{blue}{\left(x \cdot \left(-\mathsf{fma}\left(x, 0.3333333333333333, -1.3333333333333333\right)\right)\right) \cdot \frac{1}{-y}} \]
   11. Step-by-step derivation

       1. associate-*r/ 88.0%

          \[\leadsto \color{blue}{\frac{\left(x \cdot \left(-\mathsf{fma}\left(x, 0.3333333333333333, -1.3333333333333333\right)\right)\right) \cdot 1}{-y}} \]

       2. *-rgt-identity 88.0%

          \[\leadsto \frac{\color{blue}{x \cdot \left(-\mathsf{fma}\left(x, 0.3333333333333333, -1.3333333333333333\right)\right)}}{-y} \]

       3. associate-/l* 99.5%

          \[\leadsto \color{blue}{\frac{x}{\frac{-y}{-\mathsf{fma}\left(x, 0.3333333333333333, -1.3333333333333333\right)}}} \]

       4. fma-udef 99.5%

          \[\leadsto \frac{x}{\frac{-y}{-\color{blue}{\left(x \cdot 0.3333333333333333 + -1.3333333333333333\right)}}} \]

       5. distribute-neg-in 99.5%

          \[\leadsto \frac{x}{\frac{-y}{\color{blue}{\left(-x \cdot 0.3333333333333333\right) + \left(--1.3333333333333333\right)}}} \]

       6. *-commutative 99.5%

          \[\leadsto \frac{x}{\frac{-y}{\left(-\color{blue}{0.3333333333333333 \cdot x}\right) + \left(--1.3333333333333333\right)}} \]

       7. remove-double-neg 99.5%

          \[\leadsto \frac{x}{\frac{-y}{\left(-0.3333333333333333 \cdot \color{blue}{\left(-\left(-x\right)\right)}\right) + \left(--1.3333333333333333\right)}} \]

       8. neg-mul-1 99.5%

          \[\leadsto \frac{x}{\frac{-y}{\left(-0.3333333333333333 \cdot \color{blue}{\left(-1 \cdot \left(-x\right)\right)}\right) + \left(--1.3333333333333333\right)}} \]

       9. associate-*r* 99.5%

          \[\leadsto \frac{x}{\frac{-y}{\left(-\color{blue}{\left(0.3333333333333333 \cdot -1\right) \cdot \left(-x\right)}\right) + \left(--1.3333333333333333\right)}} \]

       10. metadata-eval 99.5%

           \[\leadsto \frac{x}{\frac{-y}{\left(-\color{blue}{-0.3333333333333333} \cdot \left(-x\right)\right) + \left(--1.3333333333333333\right)}} \]

       11. distribute-rgt-neg-out 99.5%

           \[\leadsto \frac{x}{\frac{-y}{\color{blue}{-0.3333333333333333 \cdot \left(-\left(-x\right)\right)} + \left(--1.3333333333333333\right)}} \]

       12. remove-double-neg 99.5%

           \[\leadsto \frac{x}{\frac{-y}{-0.3333333333333333 \cdot \color{blue}{x} + \left(--1.3333333333333333\right)}} \]

       13. *-commutative 99.5%

           \[\leadsto \frac{x}{\frac{-y}{\color{blue}{x \cdot -0.3333333333333333} + \left(--1.3333333333333333\right)}} \]

       14. metadata-eval 99.5%

           \[\leadsto \frac{x}{\frac{-y}{x \cdot -0.3333333333333333 + \color{blue}{1.3333333333333333}}} \]

   12. Simplified 99.5%

       \[\leadsto \color{blue}{\frac{x}{\frac{-y}{x \cdot -0.3333333333333333 + 1.3333333333333333}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.5:\\ \;\;\;\;\frac{x}{y} \cdot \frac{x}{3}\\ \mathbf{elif}\;x \leq 1.75:\\ \;\;\;\;\frac{x \cdot -1.3333333333333333 + 1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{-y}{x \cdot -0.3333333333333333 + 1.3333333333333333}}\\ \end{array} \]

Alternative 3: 98.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.5:\\ \;\;\;\;\frac{x}{y} \cdot \frac{x}{3}\\ \mathbf{elif}\;x \leq 0.78:\\ \;\;\;\;\frac{x \cdot -1.3333333333333333 + 1}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-0.3333333333333333 - \frac{x}{-3}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -4.5)
   (* (/ x y) (/ x 3.0))
   (if (<= x 0.78)
     (/ (+ (* x -1.3333333333333333) 1.0) y)
     (* x (/ (- -0.3333333333333333 (/ x -3.0)) y)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -4.5) {
		tmp = (x / y) * (x / 3.0);
	} else if (x <= 0.78) {
		tmp = ((x * -1.3333333333333333) + 1.0) / y;
	} else {
		tmp = x * ((-0.3333333333333333 - (x / -3.0)) / 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 <= (-4.5d0)) then
        tmp = (x / y) * (x / 3.0d0)
    else if (x <= 0.78d0) then
        tmp = ((x * (-1.3333333333333333d0)) + 1.0d0) / y
    else
        tmp = x * (((-0.3333333333333333d0) - (x / (-3.0d0))) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -4.5) {
		tmp = (x / y) * (x / 3.0);
	} else if (x <= 0.78) {
		tmp = ((x * -1.3333333333333333) + 1.0) / y;
	} else {
		tmp = x * ((-0.3333333333333333 - (x / -3.0)) / y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -4.5:
		tmp = (x / y) * (x / 3.0)
	elif x <= 0.78:
		tmp = ((x * -1.3333333333333333) + 1.0) / y
	else:
		tmp = x * ((-0.3333333333333333 - (x / -3.0)) / y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -4.5)
		tmp = Float64(Float64(x / y) * Float64(x / 3.0));
	elseif (x <= 0.78)
		tmp = Float64(Float64(Float64(x * -1.3333333333333333) + 1.0) / y);
	else
		tmp = Float64(x * Float64(Float64(-0.3333333333333333 - Float64(x / -3.0)) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -4.5)
		tmp = (x / y) * (x / 3.0);
	elseif (x <= 0.78)
		tmp = ((x * -1.3333333333333333) + 1.0) / y;
	else
		tmp = x * ((-0.3333333333333333 - (x / -3.0)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -4.5], N[(N[(x / y), $MachinePrecision] * N[(x / 3.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 0.78], N[(N[(N[(x * -1.3333333333333333), $MachinePrecision] + 1.0), $MachinePrecision] / y), $MachinePrecision], N[(x * N[(N[(-0.3333333333333333 - N[(x / -3.0), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.5

   1. Initial program 96.2%

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

      1. associate-*l/ 99.8%

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

      2. *-commutative 99.8%

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

      3. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 96.0%

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

      1. unpow2 96.0%

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

   6. Simplified 96.0%

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

      1. associate-/l* 99.6%

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

      2. associate-/r/ 99.7%

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

   8. Applied egg-rr 99.7%

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

      1. associate-*r* 99.7%

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

      2. associate-*r/ 99.6%

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

      3. *-commutative 99.6%

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

      4. associate-/r/ 99.7%

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

      5. associate-/l* 99.5%

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

   10. Applied egg-rr 99.5%

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

       1. *-un-lft-identity 99.5%

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

       2. div-inv 99.7%

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

       3. metadata-eval 99.7%

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

       4. times-frac 99.6%

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

       5. clear-num 99.8%

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

   12. Applied egg-rr 99.8%

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

   if -4.5 < x < 0.78000000000000003

   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/ 99.4%

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

      2. *-commutative 99.4%

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

      3. *-commutative 99.4%

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

   3. Simplified 99.4%

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

      1. associate-/r* 99.5%

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

      2. associate-*r/ 100.0%

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

      3. *-commutative 100.0%

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

      4. div-inv 100.0%

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

      5. associate-*l* 100.0%

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

      6. metadata-eval 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in x around 0 97.9%

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

   if 0.78000000000000003 < x

   1. Initial program 86.9%

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

      1. associate-/l* 99.7%

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

      2. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 99.1%

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

      1. associate-/r* 99.1%

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

      2. associate-/r/ 99.1%

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

      3. div-sub 99.1%

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

      4. metadata-eval 99.1%

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

   6. Applied egg-rr 99.1%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.5:\\ \;\;\;\;\frac{x}{y} \cdot \frac{x}{3}\\ \mathbf{elif}\;x \leq 0.78:\\ \;\;\;\;\frac{x \cdot -1.3333333333333333 + 1}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{-0.3333333333333333 - \frac{x}{-3}}{y}\\ \end{array} \]

Alternative 4: 98.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.5:\\ \;\;\;\;\frac{x}{y} \cdot \frac{x}{3}\\ \mathbf{elif}\;x \leq 1.3:\\ \;\;\;\;\frac{x \cdot -1.3333333333333333 + 1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{3} \cdot \left(x - 3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -4.5)
   (* (/ x y) (/ x 3.0))
   (if (<= x 1.3)
     (/ (+ (* x -1.3333333333333333) 1.0) y)
     (* (/ (/ x y) 3.0) (- x 3.0)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -4.5) {
		tmp = (x / y) * (x / 3.0);
	} else if (x <= 1.3) {
		tmp = ((x * -1.3333333333333333) + 1.0) / y;
	} else {
		tmp = ((x / y) / 3.0) * (x - 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 <= (-4.5d0)) then
        tmp = (x / y) * (x / 3.0d0)
    else if (x <= 1.3d0) then
        tmp = ((x * (-1.3333333333333333d0)) + 1.0d0) / y
    else
        tmp = ((x / y) / 3.0d0) * (x - 3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -4.5) {
		tmp = (x / y) * (x / 3.0);
	} else if (x <= 1.3) {
		tmp = ((x * -1.3333333333333333) + 1.0) / y;
	} else {
		tmp = ((x / y) / 3.0) * (x - 3.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -4.5:
		tmp = (x / y) * (x / 3.0)
	elif x <= 1.3:
		tmp = ((x * -1.3333333333333333) + 1.0) / y
	else:
		tmp = ((x / y) / 3.0) * (x - 3.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -4.5)
		tmp = Float64(Float64(x / y) * Float64(x / 3.0));
	elseif (x <= 1.3)
		tmp = Float64(Float64(Float64(x * -1.3333333333333333) + 1.0) / y);
	else
		tmp = Float64(Float64(Float64(x / y) / 3.0) * Float64(x - 3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -4.5)
		tmp = (x / y) * (x / 3.0);
	elseif (x <= 1.3)
		tmp = ((x * -1.3333333333333333) + 1.0) / y;
	else
		tmp = ((x / y) / 3.0) * (x - 3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -4.5], N[(N[(x / y), $MachinePrecision] * N[(x / 3.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.3], N[(N[(N[(x * -1.3333333333333333), $MachinePrecision] + 1.0), $MachinePrecision] / y), $MachinePrecision], N[(N[(N[(x / y), $MachinePrecision] / 3.0), $MachinePrecision] * N[(x - 3.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.5

   1. Initial program 96.2%

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

      1. associate-*l/ 99.8%

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

      2. *-commutative 99.8%

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

      3. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 96.0%

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

      1. unpow2 96.0%

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

   6. Simplified 96.0%

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

      1. associate-/l* 99.6%

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

      2. associate-/r/ 99.7%

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

   8. Applied egg-rr 99.7%

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

      1. associate-*r* 99.7%

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

      2. associate-*r/ 99.6%

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

      3. *-commutative 99.6%

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

      4. associate-/r/ 99.7%

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

      5. associate-/l* 99.5%

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

   10. Applied egg-rr 99.5%

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

       1. *-un-lft-identity 99.5%

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

       2. div-inv 99.7%

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

       3. metadata-eval 99.7%

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

       4. times-frac 99.6%

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

       5. clear-num 99.8%

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

   12. Applied egg-rr 99.8%

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

   if -4.5 < x < 1.30000000000000004

   1. Initial program 99.6%

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

      1. associate-*l/ 99.4%

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

      2. *-commutative 99.4%

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

      3. *-commutative 99.4%

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

   3. Simplified 99.4%

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

      1. associate-/r* 99.5%

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

      2. associate-*r/ 100.0%

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

      3. *-commutative 100.0%

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

      4. div-inv 100.0%

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

      5. associate-*l* 100.0%

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

      6. metadata-eval 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in x around 0 97.9%

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

   if 1.30000000000000004 < x

   1. Initial program 86.9%

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

      1. associate-*l/ 99.7%

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

      2. *-commutative 99.7%

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

      3. associate-/r* 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 99.2%

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

      1. neg-mul-1 99.2%

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

      2. distribute-neg-frac 99.2%

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

   6. Simplified 99.2%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.5:\\ \;\;\;\;\frac{x}{y} \cdot \frac{x}{3}\\ \mathbf{elif}\;x \leq 1.3:\\ \;\;\;\;\frac{x \cdot -1.3333333333333333 + 1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{3} \cdot \left(x - 3\right)\\ \end{array} \]

Alternative 5: 97.7% accurate, 1.0× speedup

Math

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

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 90.5%

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

      1. associate-*l/ 99.7%

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

      2. *-commutative 99.7%

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

      3. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 90.0%

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

      1. unpow2 90.0%

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

   6. Simplified 90.0%

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

      1. associate-/l* 99.2%

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

      2. associate-/r/ 99.2%

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

   8. Applied egg-rr 99.2%

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

   if -3.7999999999999998 < x < 3

   1. Initial program 99.6%

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

      1. associate-/l* 99.8%

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

      2. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 97.1%

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

4. Final simplification 98.2%

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

Alternative 6: 97.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y) {
	double tmp;
	if ((x <= -3.8) || !(x <= 3.0)) {
		tmp = (x / y) * (x / 3.0);
	} 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 <= (-3.8d0)) .or. (.not. (x <= 3.0d0))) then
        tmp = (x / y) * (x / 3.0d0)
    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 <= -3.8) || !(x <= 3.0)) {
		tmp = (x / y) * (x / 3.0);
	} 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 / y) * (x / 3.0)
	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 / y) * Float64(x / 3.0));
	else
		tmp = Float64(Float64(1.0 - x) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -3.8) || ~((x <= 3.0)))
		tmp = (x / y) * (x / 3.0);
	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 / y), $MachinePrecision] * N[(x / 3.0), $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 90.5%

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

      1. associate-*l/ 99.7%

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

      2. *-commutative 99.7%

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

      3. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 90.0%

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

      1. unpow2 90.0%

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

   6. Simplified 90.0%

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

      1. associate-/l* 99.2%

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

      2. associate-/r/ 99.2%

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

   8. Applied egg-rr 99.2%

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

      1. associate-*r* 99.2%

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

      2. associate-*r/ 99.2%

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

      3. *-commutative 99.2%

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

      4. associate-/r/ 99.3%

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

      5. associate-/l* 99.2%

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

   10. Applied egg-rr 99.2%

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

       1. *-un-lft-identity 99.2%

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

       2. div-inv 99.3%

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

       3. metadata-eval 99.3%

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

       4. times-frac 99.2%

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

       5. clear-num 99.3%

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

   12. Applied egg-rr 99.3%

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

   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. associate-/l* 99.8%

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

      2. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 97.1%

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

4. Final simplification 98.2%

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

Alternative 7: 97.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-3.8d0)) then
        tmp = 0.3333333333333333d0 * (x * (x / y))
    else if (x <= 3.0d0) then
        tmp = (1.0d0 - x) / y
    else
        tmp = x * (x / (y / 0.3333333333333333d0))
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 3 regimes

2. if x < -3.7999999999999998

   1. Initial program 96.2%

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

      1. associate-*l/ 99.8%

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

      2. *-commutative 99.8%

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

      3. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 96.0%

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

      1. unpow2 96.0%

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

   6. Simplified 96.0%

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

      1. associate-/l* 99.6%

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

      2. associate-/r/ 99.7%

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

   8. Applied egg-rr 99.7%

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

   if -3.7999999999999998 < x < 3

   1. Initial program 99.6%

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

      1. associate-/l* 99.8%

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

      2. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 97.1%

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

   if 3 < x

   1. Initial program 86.9%

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

      1. associate-*l/ 99.7%

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

      2. *-commutative 99.7%

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

      3. *-commutative 99.7%

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

   3. Simplified 99.7%

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

      1. associate-/r* 99.7%

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

      2. associate-*r/ 88.2%

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

      3. *-commutative 88.2%

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

      4. div-inv 88.1%

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

      5. associate-*l* 88.1%

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

      6. metadata-eval 88.1%

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

   5. Applied egg-rr 88.1%

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

   6. Taylor expanded in x around 0 86.9%

      \[\leadsto \frac{\color{blue}{1 + \left(-1.3333333333333333 \cdot x + 0.3333333333333333 \cdot {x}^{2}\right)}}{y} \]
   7. Step-by-step derivation

      1. unpow2 86.9%

         \[\leadsto \frac{1 + \left(-1.3333333333333333 \cdot x + 0.3333333333333333 \cdot \color{blue}{\left(x \cdot x\right)}\right)}{y} \]

      2. associate-*l* 88.1%

         \[\leadsto \frac{1 + \left(-1.3333333333333333 \cdot x + \color{blue}{\left(0.3333333333333333 \cdot x\right) \cdot x}\right)}{y} \]

      3. distribute-rgt-out 88.0%

         \[\leadsto \frac{1 + \color{blue}{x \cdot \left(-1.3333333333333333 + 0.3333333333333333 \cdot x\right)}}{y} \]

      4. *-commutative 88.0%

         \[\leadsto \frac{1 + x \cdot \left(-1.3333333333333333 + \color{blue}{x \cdot 0.3333333333333333}\right)}{y} \]

   8. Simplified 88.0%

      \[\leadsto \frac{\color{blue}{1 + x \cdot \left(-1.3333333333333333 + x \cdot 0.3333333333333333\right)}}{y} \]

   9. Taylor expanded in x around inf 86.3%

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

       1. unpow2 86.3%

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

       2. associate-*r/ 86.3%

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

       3. *-commutative 86.3%

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

       4. associate-*r* 87.4%

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

       5. associate-*r/ 99.0%

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

       6. associate-/l* 99.0%

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

   11. Simplified 99.0%

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

4. Final simplification 98.2%

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

Alternative 8: 97.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 3 regimes

2. if x < -3.7999999999999998

   1. Initial program 96.2%

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

      1. associate-*l/ 99.8%

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

      2. *-commutative 99.8%

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

      3. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 96.0%

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

      1. unpow2 96.0%

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

   6. Simplified 96.0%

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

      1. associate-/l* 99.6%

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

      2. associate-/r/ 99.7%

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

   8. Applied egg-rr 99.7%

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

      1. associate-*r* 99.7%

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

      2. associate-*r/ 99.6%

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

      3. *-commutative 99.6%

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

      4. associate-/r/ 99.7%

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

      5. associate-/l* 99.5%

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

   10. Applied egg-rr 99.5%

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

       1. *-un-lft-identity 99.5%

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

       2. div-inv 99.7%

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

       3. metadata-eval 99.7%

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

       4. times-frac 99.6%

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

       5. clear-num 99.8%

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

   12. Applied egg-rr 99.8%

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

   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. associate-/l* 99.8%

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

      2. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 97.1%

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

   if 3 < x

   1. Initial program 86.9%

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

      1. associate-*l/ 99.7%

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

      2. *-commutative 99.7%

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

      3. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 86.3%

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

      1. unpow2 86.3%

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

   6. Simplified 86.3%

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

      1. associate-/l* 99.0%

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

      2. associate-/r/ 99.0%

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

   8. Applied egg-rr 99.0%

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

      1. associate-*r* 99.0%

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

      2. associate-*r/ 99.0%

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

      3. *-commutative 99.0%

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

      4. associate-/r/ 99.0%

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

      5. associate-/l* 99.0%

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

   10. Applied egg-rr 99.0%

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

       1. div-inv 99.1%

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

       2. metadata-eval 99.1%

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

   12. Applied egg-rr 99.1%

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

4. Final simplification 98.3%

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

Alternative 9: 98.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.5:\\ \;\;\;\;\frac{x}{y} \cdot \frac{x}{3}\\ \mathbf{elif}\;x \leq 0.65:\\ \;\;\;\;\frac{x \cdot -1.3333333333333333 + 1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{3 \cdot \frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -4.5)
   (* (/ x y) (/ x 3.0))
   (if (<= x 0.65)
     (/ (+ (* x -1.3333333333333333) 1.0) y)
     (/ x (* 3.0 (/ y x))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -4.5) {
		tmp = (x / y) * (x / 3.0);
	} else if (x <= 0.65) {
		tmp = ((x * -1.3333333333333333) + 1.0) / y;
	} else {
		tmp = x / (3.0 * (y / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-4.5d0)) then
        tmp = (x / y) * (x / 3.0d0)
    else if (x <= 0.65d0) then
        tmp = ((x * (-1.3333333333333333d0)) + 1.0d0) / y
    else
        tmp = x / (3.0d0 * (y / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -4.5) {
		tmp = (x / y) * (x / 3.0);
	} else if (x <= 0.65) {
		tmp = ((x * -1.3333333333333333) + 1.0) / y;
	} else {
		tmp = x / (3.0 * (y / x));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -4.5:
		tmp = (x / y) * (x / 3.0)
	elif x <= 0.65:
		tmp = ((x * -1.3333333333333333) + 1.0) / y
	else:
		tmp = x / (3.0 * (y / x))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -4.5)
		tmp = Float64(Float64(x / y) * Float64(x / 3.0));
	elseif (x <= 0.65)
		tmp = Float64(Float64(Float64(x * -1.3333333333333333) + 1.0) / y);
	else
		tmp = Float64(x / Float64(3.0 * Float64(y / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -4.5)
		tmp = (x / y) * (x / 3.0);
	elseif (x <= 0.65)
		tmp = ((x * -1.3333333333333333) + 1.0) / y;
	else
		tmp = x / (3.0 * (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -4.5], N[(N[(x / y), $MachinePrecision] * N[(x / 3.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 0.65], N[(N[(N[(x * -1.3333333333333333), $MachinePrecision] + 1.0), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(3.0 * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.5

   1. Initial program 96.2%

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

      1. associate-*l/ 99.8%

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

      2. *-commutative 99.8%

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

      3. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 96.0%

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

      1. unpow2 96.0%

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

   6. Simplified 96.0%

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

      1. associate-/l* 99.6%

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

      2. associate-/r/ 99.7%

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

   8. Applied egg-rr 99.7%

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

      1. associate-*r* 99.7%

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

      2. associate-*r/ 99.6%

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

      3. *-commutative 99.6%

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

      4. associate-/r/ 99.7%

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

      5. associate-/l* 99.5%

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

   10. Applied egg-rr 99.5%

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

       1. *-un-lft-identity 99.5%

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

       2. div-inv 99.7%

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

       3. metadata-eval 99.7%

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

       4. times-frac 99.6%

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

       5. clear-num 99.8%

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

   12. Applied egg-rr 99.8%

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

   if -4.5 < x < 0.650000000000000022

   1. Initial program 99.6%

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

      1. associate-*l/ 99.4%

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

      2. *-commutative 99.4%

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

      3. *-commutative 99.4%

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

   3. Simplified 99.4%

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

      1. associate-/r* 99.5%

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

      2. associate-*r/ 100.0%

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

      3. *-commutative 100.0%

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

      4. div-inv 100.0%

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

      5. associate-*l* 100.0%

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

      6. metadata-eval 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in x around 0 97.9%

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

   if 0.650000000000000022 < x

   1. Initial program 86.9%

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

      1. associate-*l/ 99.7%

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

      2. *-commutative 99.7%

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

      3. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 86.3%

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

      1. unpow2 86.3%

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

   6. Simplified 86.3%

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

      1. associate-/l* 99.0%

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

      2. associate-/r/ 99.0%

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

   8. Applied egg-rr 99.0%

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

      1. associate-*r* 99.0%

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

      2. associate-*r/ 99.0%

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

      3. *-commutative 99.0%

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

      4. associate-/r/ 99.0%

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

      5. associate-/l* 99.0%

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

   10. Applied egg-rr 99.0%

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

       1. div-inv 99.1%

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

       2. metadata-eval 99.1%

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

   12. Applied egg-rr 99.1%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.5:\\ \;\;\;\;\frac{x}{y} \cdot \frac{x}{3}\\ \mathbf{elif}\;x \leq 0.65:\\ \;\;\;\;\frac{x \cdot -1.3333333333333333 + 1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{3 \cdot \frac{y}{x}}\\ \end{array} \]

Alternative 10: 99.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.9%

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

   1. associate-*l/ 99.6%

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

   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. Final simplification 99.6%

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

Alternative 11: 58.0% accurate, 1.6× speedup

Math

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

FPCore

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

C

double code(double x, double y) {
	double tmp;
	if (x <= -0.75) {
		tmp = (x / y) * -1.3333333333333333;
	} 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 = (x / y) * (-1.3333333333333333d0)
    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 = (x / y) * -1.3333333333333333;
	} else {
		tmp = 1.0 / y;
	}
	return tmp;
}

Python

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

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -0.75)
		tmp = Float64(Float64(x / y) * -1.3333333333333333);
	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 = (x / y) * -1.3333333333333333;
	else
		tmp = 1.0 / y;
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if x < -0.75

   1. Initial program 96.3%

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

      1. associate-*l/ 99.8%

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

      2. *-commutative 99.8%

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

      3. *-commutative 99.8%

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

   3. Simplified 99.8%

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

      1. associate-/r* 99.8%

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

      2. associate-*r/ 96.2%

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

      3. *-commutative 96.2%

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

      4. div-inv 96.1%

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

      5. associate-*l* 96.1%

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

      6. metadata-eval 96.1%

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

   5. Applied egg-rr 96.1%

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

   6. Taylor expanded in x around 0 96.3%

      \[\leadsto \frac{\color{blue}{1 + \left(-1.3333333333333333 \cdot x + 0.3333333333333333 \cdot {x}^{2}\right)}}{y} \]
   7. Step-by-step derivation

      1. unpow2 96.3%

         \[\leadsto \frac{1 + \left(-1.3333333333333333 \cdot x + 0.3333333333333333 \cdot \color{blue}{\left(x \cdot x\right)}\right)}{y} \]

      2. associate-*l* 96.1%

         \[\leadsto \frac{1 + \left(-1.3333333333333333 \cdot x + \color{blue}{\left(0.3333333333333333 \cdot x\right) \cdot x}\right)}{y} \]

      3. distribute-rgt-out 96.2%

         \[\leadsto \frac{1 + \color{blue}{x \cdot \left(-1.3333333333333333 + 0.3333333333333333 \cdot x\right)}}{y} \]

      4. *-commutative 96.2%

         \[\leadsto \frac{1 + x \cdot \left(-1.3333333333333333 + \color{blue}{x \cdot 0.3333333333333333}\right)}{y} \]

   8. Simplified 96.2%

      \[\leadsto \frac{\color{blue}{1 + x \cdot \left(-1.3333333333333333 + x \cdot 0.3333333333333333\right)}}{y} \]

   9. Taylor expanded in x around 0 39.7%

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

   10. Taylor expanded in x around inf 39.7%

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

   if -0.75 < x

   1. Initial program 94.6%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   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. Taylor expanded in x around 0 61.0%

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

4. Final simplification 56.7%

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

Alternative 12: 58.0% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if x < -1

   1. Initial program 96.3%

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

      1. associate-*l/ 99.8%

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

      2. *-commutative 99.8%

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

      3. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 96.7%

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

   5. Taylor expanded in x around 0 39.7%

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

      1. associate-*r/ 39.7%

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

      2. neg-mul-1 39.7%

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

   7. Simplified 39.7%

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

   if -1 < x

   1. Initial program 94.6%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   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. Taylor expanded in x around 0 61.0%

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

4. Final simplification 56.7%

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

Alternative 13: 57.0% accurate, 2.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.9%

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

   1. associate-/l* 99.7%

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

   2. *-commutative 99.7%

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

3. Simplified 99.7%

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

4. Taylor expanded in x around 0 55.6%

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

5. Final simplification 55.6%

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

Alternative 14: 51.6% accurate, 3.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.9%

   \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
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. Taylor expanded in x around 0 49.8%

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

5. Final simplification 49.8%

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

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 2023171 
(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)))