\[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
Test:
fabs fraction 1
Bits:
128 bits
Bits error versus x
Bits error versus y
Bits error versus z
Time: 8.9 s
Input Error: 1.5
Output Error: 0.3
Log: ⚲
Profile: 🕒
\(\begin{cases} \left|\frac{x + 4}{y} - x \cdot \frac{z}{y}\right| & \text{when } x \le -1.8761786892897277 \cdot 10^{+22} \\ \left|\frac{\left(x + 4\right) - x \cdot z}{y}\right| & \text{when } x \le 4.935713117721222 \cdot 10^{-100} \\ \left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right| & \text{otherwise} \end{cases}\)

    if x < -1.8761786892897277e+22

    1. Started with
      \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
      0.1
    2. Using strategy rm
      0.1
    3. Applied div-inv to get
      \[\left|\frac{x + 4}{y} - \color{red}{\frac{x}{y}} \cdot z\right| \leadsto \left|\frac{x + 4}{y} - \color{blue}{\left(x \cdot \frac{1}{y}\right)} \cdot z\right|\]
      0.2
    4. Applied associate-*l* to get
      \[\left|\frac{x + 4}{y} - \color{red}{\left(x \cdot \frac{1}{y}\right) \cdot z}\right| \leadsto \left|\frac{x + 4}{y} - \color{blue}{x \cdot \left(\frac{1}{y} \cdot z\right)}\right|\]
      0.2
    5. Applied simplify to get
      \[\left|\frac{x + 4}{y} - x \cdot \color{red}{\left(\frac{1}{y} \cdot z\right)}\right| \leadsto \left|\frac{x + 4}{y} - x \cdot \color{blue}{\frac{z}{y}}\right|\]
      0.1

    if -1.8761786892897277e+22 < x < 4.935713117721222e-100

    1. Started with
      \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
      2.4
    2. Using strategy rm
      2.4
    3. Applied associate-*l/ to get
      \[\left|\frac{x + 4}{y} - \color{red}{\frac{x}{y} \cdot z}\right| \leadsto \left|\frac{x + 4}{y} - \color{blue}{\frac{x \cdot z}{y}}\right|\]
      0.1
    4. Applied sub-div to get
      \[\left|\color{red}{\frac{x + 4}{y} - \frac{x \cdot z}{y}}\right| \leadsto \left|\color{blue}{\frac{\left(x + 4\right) - x \cdot z}{y}}\right|\]
      0.1

    if 4.935713117721222e-100 < x

    1. Started with
      \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
      0.8
  1. Removed slow pow expressions

Original test:


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