\[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
Test:
fabs fraction 1
Bits:
128 bits
Bits error versus x
Bits error versus y
Bits error versus z
Time: 6.4 s
Input Error: 0.8
Output Error: 0.8
Log: ⚲
Profile: 🕒
\(\left|\left(\frac{x}{y} + \frac{4}{y}\right) - \frac{\frac{x}{y}}{\frac{1}{z}}\right|\)
  1. Started with
    \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
    0.8
  2. Applied taylor to get
    \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right| \leadsto \left|\left(\frac{x}{y} + 4 \cdot \frac{1}{y}\right) - \frac{x \cdot z}{y}\right|\]
    1.7
  3. Taylor expanded around 0 to get
    \[\left|\color{red}{\left(\frac{x}{y} + 4 \cdot \frac{1}{y}\right) - \frac{x \cdot z}{y}}\right| \leadsto \left|\color{blue}{\left(\frac{x}{y} + 4 \cdot \frac{1}{y}\right) - \frac{x \cdot z}{y}}\right|\]
    1.7
  4. Applied simplify to get
    \[\color{red}{\left|\left(\frac{x}{y} + 4 \cdot \frac{1}{y}\right) - \frac{x \cdot z}{y}\right|} \leadsto \color{blue}{\left|\left(\frac{x}{y} + \frac{4}{y}\right) - \frac{x}{\frac{y}{z}}\right|}\]
    1.1
  5. Using strategy rm
    1.1
  6. Applied div-inv to get
    \[\left|\left(\frac{x}{y} + \frac{4}{y}\right) - \frac{x}{\color{red}{\frac{y}{z}}}\right| \leadsto \left|\left(\frac{x}{y} + \frac{4}{y}\right) - \frac{x}{\color{blue}{y \cdot \frac{1}{z}}}\right|\]
    1.1
  7. Applied associate-/r* to get
    \[\left|\left(\frac{x}{y} + \frac{4}{y}\right) - \color{red}{\frac{x}{y \cdot \frac{1}{z}}}\right| \leadsto \left|\left(\frac{x}{y} + \frac{4}{y}\right) - \color{blue}{\frac{\frac{x}{y}}{\frac{1}{z}}}\right|\]
    0.8

Original test:


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