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

1. Initial program 92.1%

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

   1. times-frac99.8%

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

   2. div-sub99.8%

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

   3. metadata-eval99.8%

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

3. Simplified99.8%

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

4. Final simplification99.8%

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

1. Split input into 2 regimes

2. if x < -1.75 or 1.71999999999999997 < x

   1. Initial program 83.8%

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

   2. Taylor expanded in x around inf 83.3%

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

      1. +-commutative83.3%

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

      2. unpow283.3%

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

      3. distribute-rgt-out83.3%

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

   4. Simplified83.3%

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

      1. div-inv83.3%

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

      2. *-commutative83.3%

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

      3. *-commutative83.3%

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

      4. associate-/r*83.2%

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

      5. metadata-eval83.2%

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

      6. associate-*l*99.3%

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

   6. Applied egg-rr99.3%

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

   if -1.75 < x < 1.71999999999999997

   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. *-commutative99.4%

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

      3. associate-/r*99.8%

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

   3. Simplified99.8%

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

   4. Taylor expanded in x around 0 99.1%

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

      1. *-commutative99.1%

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

   6. Simplified99.1%

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

   7. 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 simplification99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.75 \lor \neg \left(x \leq 1.72\right):\\ \;\;\;\;\left(x + -4\right) \cdot \left(x \cdot \frac{0.3333333333333333}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \end{array} \]

1. Split input into 2 regimes

2. if x < -1.75 or 1.71999999999999997 < x

   1. Initial program 83.8%

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

   2. Taylor expanded in x around inf 83.3%

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

      1. +-commutative83.3%

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

      2. unpow283.3%

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

      3. distribute-rgt-out83.3%

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

   4. Simplified83.3%

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

      1. div-inv83.3%

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

      2. *-commutative83.3%

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

      3. *-commutative83.3%

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

      4. associate-/r*83.2%

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

      5. metadata-eval83.2%

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

      6. associate-*l*99.3%

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

   6. Applied egg-rr99.3%

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

   if -1.75 < x < 1.71999999999999997

   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. *-commutative99.4%

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

      3. associate-/r*99.8%

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

   3. Simplified99.8%

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

   4. Taylor expanded in x around 0 99.1%

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

      1. *-commutative99.1%

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

   6. Simplified99.1%

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

4. Final simplification99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.75 \lor \neg \left(x \leq 1.72\right):\\ \;\;\;\;\left(x + -4\right) \cdot \left(x \cdot \frac{0.3333333333333333}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{y} + \frac{x}{y} \cdot -1.3333333333333333\\ \end{array} \]

1. Split input into 2 regimes

2. if x < -3.7999999999999998 or 3 < x

   1. Initial program 83.8%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   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. *-commutative99.7%

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

      3. associate-/r*99.7%

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

   3. Simplified99.7%

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

   4. Taylor expanded in x around inf 82.3%

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

      1. unpow282.3%

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

   6. Simplified82.3%

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

   if -3.7999999999999998 < x < 3

   1. Initial program 99.6%

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

      1. associate-/l*99.9%

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

      2. *-commutative99.9%

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

   3. Simplified99.9%

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

   4. Taylor expanded in x around 0 98.0%

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

4. Final simplification90.5%

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

1. Split input into 2 regimes

2. if x < -3.7999999999999998 or 3 < x

   1. Initial program 83.8%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   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. *-commutative99.7%

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

      3. associate-/r*99.7%

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

   3. Simplified99.7%

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

      1. clear-num99.6%

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

      2. un-div-inv99.7%

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

      3. associate-/r/99.7%

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

   5. Applied egg-rr99.7%

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

   6. Taylor expanded in x around inf 82.3%

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

      1. unpow282.3%

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

      2. associate-*r/82.2%

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

      3. associate-*l/82.2%

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

      4. *-commutative82.2%

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

      5. associate-*r*98.3%

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

   8. Simplified98.3%

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

   if -3.7999999999999998 < x < 3

   1. Initial program 99.6%

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

      1. associate-/l*99.9%

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

      2. *-commutative99.9%

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

   3. Simplified99.9%

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

   4. Taylor expanded in x around 0 98.0%

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

4. Final simplification98.1%

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

1. Split input into 2 regimes

2. if x < -4.5999999999999996 or 3 < x

   1. Initial program 83.8%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   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. *-commutative99.7%

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

      3. associate-/r*99.7%

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

   3. Simplified99.7%

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

      1. clear-num99.6%

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

      2. un-div-inv99.7%

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

      3. associate-/r/99.7%

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

   5. Applied egg-rr99.7%

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

   6. Taylor expanded in x around inf 82.3%

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

      1. unpow282.3%

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

      2. associate-*r/82.2%

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

      3. associate-*l/82.2%

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

      4. *-commutative82.2%

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

      5. associate-*r*98.3%

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

   8. Simplified98.3%

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

   if -4.5999999999999996 < 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/99.4%

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

      2. *-commutative99.4%

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

      3. associate-/r*99.8%

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

   3. Simplified99.8%

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

   4. Taylor expanded in x around 0 99.1%

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

      1. *-commutative99.1%

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

   6. Simplified99.1%

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

   7. 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 simplification98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.6 \lor \neg \left(x \leq 3\right):\\ \;\;\;\;x \cdot \left(x \cdot \frac{0.3333333333333333}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \end{array} \]

1. Split input into 3 regimes

2. if x < -4.5999999999999996

   1. Initial program 81.8%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   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. *-commutative99.7%

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

      3. associate-/r*99.7%

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

   3. Simplified99.7%

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

   4. Taylor expanded in x around inf 79.8%

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

      1. associate-*r/79.7%

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

      2. unpow279.7%

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

   6. Simplified79.7%

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

      1. associate-/l*79.7%

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

      2. associate-/r/79.8%

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

   8. Applied egg-rr79.8%

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

      1. associate-*l/79.7%

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

      2. associate-*r*79.9%

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

      3. metadata-eval79.9%

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

      4. associate-/r/79.9%

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

      5. clear-num80.0%

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

      6. associate-/r/80.0%

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

      7. associate-/l/97.9%

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

      8. associate-/r*98.0%

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

   10. Applied egg-rr98.0%

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

   if -4.5999999999999996 < 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/99.4%

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

      2. *-commutative99.4%

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

      3. associate-/r*99.8%

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

   3. Simplified99.8%

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

   4. Taylor expanded in x around 0 99.1%

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

      1. *-commutative99.1%

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

   6. Simplified99.1%

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

   7. Taylor expanded in y around 0 99.1%

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

   if 3 < x

   1. Initial program 86.2%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   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. *-commutative99.7%

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

      3. associate-/r*99.7%

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

   3. Simplified99.7%

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

      1. clear-num99.6%

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

      2. un-div-inv99.6%

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

      3. associate-/r/99.7%

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

   5. Applied egg-rr99.7%

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

   6. Taylor expanded in x around inf 85.2%

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

      1. unpow285.2%

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

      2. associate-*r/85.2%

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

      3. associate-*l/85.2%

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

      4. *-commutative85.2%

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

      5. associate-*r*98.7%

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

   8. Simplified98.7%

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

4. Final simplification98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.6:\\ \;\;\;\;\frac{\frac{x}{y}}{\frac{3}{x}}\\ \mathbf{elif}\;x \leq 3:\\ \;\;\;\;\frac{1 + x \cdot -1.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(x \cdot \frac{0.3333333333333333}{y}\right)\\ \end{array} \]

1. Initial program 92.1%

   \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
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. *-commutative99.6%

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

   3. associate-/r*99.7%

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

3. Simplified99.7%

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

4. Final simplification99.7%

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

1. Split input into 2 regimes

2. if x < -0.75

   1. Initial program 81.8%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   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. *-commutative99.7%

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

      3. associate-/r*99.7%

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

   3. Simplified99.7%

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

   4. Taylor expanded in x around 0 31.6%

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

      1. *-commutative31.6%

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

   6. Simplified31.6%

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

   7. Taylor expanded in y around 0 31.6%

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

   8. Taylor expanded in x around inf 31.6%

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

   if -0.75 < x

   1. Initial program 95.7%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   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. *-commutative99.5%

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

      3. associate-/r*99.8%

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

   3. Simplified99.8%

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

   4. Taylor expanded in x around 0 70.6%

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

4. Final simplification60.4%

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

1. Split input into 2 regimes

2. if x < -1

   1. Initial program 81.8%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   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. *-commutative99.7%

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

      3. associate-/r*99.7%

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

   3. Simplified99.7%

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

   4. Taylor expanded in x around inf 98.1%

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

   5. Taylor expanded in x around 0 31.6%

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

      1. neg-mul-131.6%

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

      2. distribute-neg-frac31.6%

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

   7. Simplified31.6%

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

   if -1 < x

   1. Initial program 95.7%

      \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
   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. *-commutative99.5%

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

      3. associate-/r*99.8%

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

   3. Simplified99.8%

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

   4. Taylor expanded in x around 0 70.6%

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

4. Final simplification60.4%

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

1. Initial program 92.1%

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

   1. associate-/l*99.8%

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

   2. *-commutative99.8%

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

3. Simplified99.8%

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

4. Taylor expanded in x around 0 59.7%

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

5. Final simplification59.7%

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

1. Initial program 92.1%

   \[\frac{\left(1 - x\right) \cdot \left(3 - x\right)}{y \cdot 3} \]
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. *-commutative99.6%

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

   3. associate-/r*99.7%

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

3. Simplified99.7%

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

4. Taylor expanded in x around 0 53.4%

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

5. Final simplification53.4%

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

herbie shell --seed 2023167 
(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)))