\[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
Test:
fabs fraction 1
Bits:
128 bits
Bits error versus x
Bits error versus y
Bits error versus z
Time: 6.0 s
Input Error: 0.7
Output Error: 1.7
Log: ⚲
Profile: 🕒
\(\left|\frac{\left(x + 4\right) - x \cdot z}{y}\right|\)
  1. Started with
    \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
    0.7
  2. Using strategy rm
    0.7
  3. Applied associate-*l/ to get
    \[\left|\frac{x + 4}{y} - \color{red}{\frac{x}{y} \cdot z}\right| \leadsto \left|\frac{x + 4}{y} - \color{blue}{\frac{x \cdot z}{y}}\right|\]
    1.7
  4. Applied sub-div to get
    \[\left|\color{red}{\frac{x + 4}{y} - \frac{x \cdot z}{y}}\right| \leadsto \left|\color{blue}{\frac{\left(x + 4\right) - x \cdot z}{y}}\right|\]
    1.7
  5. Removed slow pow expressions

Original test:


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