\[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
Test:
fabs fraction 1
Bits:
128 bits
Bits error versus x
Bits error versus y
Bits error versus z
Time: 5.5 s
Input Error: 0.7
Output Error: 0.7
Log: ⚲
Profile: 🕒
\(\left|\frac{x + 4}{y} - z \cdot \frac{x}{y}\right|\)
  1. Started with
    \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
    0.7
  2. Using strategy rm
    0.7
  3. Applied flip-+ to get
    \[\left|\frac{\color{red}{x + 4}}{y} - \frac{x}{y} \cdot z\right| \leadsto \left|\frac{\color{blue}{\frac{{x}^2 - {4}^2}{x - 4}}}{y} - \frac{x}{y} \cdot z\right|\]
    5.4
  4. Applied associate-/l/ to get
    \[\left|\color{red}{\frac{\frac{{x}^2 - {4}^2}{x - 4}}{y}} - \frac{x}{y} \cdot z\right| \leadsto \left|\color{blue}{\frac{{x}^2 - {4}^2}{y \cdot \left(x - 4\right)}} - \frac{x}{y} \cdot z\right|\]
    6.2
  5. Applied taylor to get
    \[\left|\frac{{x}^2 - {4}^2}{y \cdot \left(x - 4\right)} - \frac{x}{y} \cdot z\right| \leadsto \left|\frac{{x}^2 - {4}^2}{y \cdot x - 4 \cdot y} - \frac{x}{y} \cdot z\right|\]
    6.2
  6. Taylor expanded around 0 to get
    \[\left|\frac{{x}^2 - {4}^2}{\color{red}{y \cdot x - 4 \cdot y}} - \frac{x}{y} \cdot z\right| \leadsto \left|\frac{{x}^2 - {4}^2}{\color{blue}{y \cdot x - 4 \cdot y}} - \frac{x}{y} \cdot z\right|\]
    6.2
  7. Applied simplify to get
    \[\left|\frac{{x}^2 - {4}^2}{y \cdot x - 4 \cdot y} - \frac{x}{y} \cdot z\right| \leadsto \left|\frac{x - 4}{y} \cdot \frac{x + 4}{x - 4} - \frac{x}{\frac{y}{z}}\right|\]
    1.1
  8. Applied final simplification
  9. Applied simplify to get
    \[\color{red}{\left|\frac{x - 4}{y} \cdot \frac{x + 4}{x - 4} - \frac{x}{\frac{y}{z}}\right|} \leadsto \color{blue}{\left|\frac{x + 4}{y} - z \cdot \frac{x}{y}\right|}\]
    0.7
  10. Removed slow pow expressions

Original test:


(lambda ((x default) (y default) (z default))
  #:name "fabs fraction 1"
  (fabs (- (/ (+ x 4) y) (* (/ x y) z))))