Derivation

Split input into 3 regimes
if x < -1.8773929785352215e+142
1. Initial program 0.1
  \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
2. Using strategy rm
3. Applied sub-neg0.1
  \[\leadsto \left|\color{blue}{\frac{x + 4}{y} + \left(-\frac{x}{y} \cdot z\right)}\right|\]
if -1.8773929785352215e+142 < x < 4.431127015599397e-157
1. Initial program 1.9
  \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
2. Using strategy rm
3. Applied associate-*l/0.8
  \[\leadsto \left|\frac{x + 4}{y} - \color{blue}{\frac{x \cdot z}{y}}\right|\]
4. Applied sub-div0.8
  \[\leadsto \left|\color{blue}{\frac{\left(x + 4\right) - x \cdot z}{y}}\right|\]
if 4.431127015599397e-157 < x
1. Initial program 1.1
  \[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
2. Initial simplification1.5
  \[\leadsto \left|\frac{4 + x}{y} - \frac{x}{\frac{y}{z}}\right|\]
Recombined 3 regimes into one program.
Final simplification1.0
\[\leadsto \begin{array}{l} \mathbf{if}\;x \le -1.8773929785352215 \cdot 10^{+142}:\\ \;\;\;\;\left|\frac{x}{y} \cdot \left(-z\right) + \frac{4 + x}{y}\right|\\ \mathbf{elif}\;x \le 4.431127015599397 \cdot 10^{-157}:\\ \;\;\;\;\left|\frac{\left(4 + x\right) - x \cdot z}{y}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\frac{4 + x}{y} - \frac{x}{\frac{y}{z}}\right|\\ \end{array}\]

Runtime

herbie shell --seed 2018255 
(FPCore (x y z)
  :name "fabs fraction 1"
  (fabs (- (/ (+ x 4) y) (* (/ x y) z))))

In
Out