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Derivation

1. Split input into 2 regimes

2. if x < -2.1690543199597533e+36 or 3.2828098054217477e-87 < x

   1. Initial program 0.4

      \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]

   2. Initial simplification0.4

      \[\leadsto \left|\frac{4 + x}{y} - \frac{x}{\frac{y}{z}}\right|\]

   if -2.1690543199597533e+36 < x < 3.2828098054217477e-87

   1. Initial program 2.0

      \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
   2. Using strategy rm

   3. Applied associate-*l/0.1

      \[\leadsto \left|\frac{x + 4}{y} - \color{blue}{\frac{x \cdot z}{y}}\right|\]

   4. Applied sub-div0.1

      \[\leadsto \left|\color{blue}{\frac{\left(x + 4\right) - x \cdot z}{y}}\right|\]
3. Recombined 2 regimes into one program.

4. Final simplification0.2

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -2.1690543199597533 \cdot 10^{+36} \lor \neg \left(x \le 3.2828098054217477 \cdot 10^{-87}\right):\\ \;\;\;\;\left|\frac{4 + x}{y} - \frac{x}{\frac{y}{z}}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{\left(4 + x\right) - z \cdot x}{y}\right|\\ \end{array}\]

Reproduce

herbie shell --seed 2018362 
(FPCore (x y z)
  :name "fabs fraction 1"
  (fabs (- (/ (+ x 4) y) (* (/ x y) z))))

Details

Time bar (total: 11.0s)Debug log