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

↓

\[\left|(\left(4 + x\right) \cdot \left(\frac{1}{y}\right) + \left(\left(-\frac{x}{y}\right) \cdot z\right))_*\right|\]

Error

Derivation

Initial program 1.5
\[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
Using strategy rm
Applied div-inv1.5
\[\leadsto \left|\color{blue}{\left(x + 4\right) \cdot \frac{1}{y}} - \frac{x}{y} \cdot z\right|\]
Applied fma-neg1.5
\[\leadsto \left|\color{blue}{(\left(x + 4\right) \cdot \left(\frac{1}{y}\right) + \left(-\frac{x}{y} \cdot z\right))_*}\right|\]
Final simplification1.5
\[\leadsto \left|(\left(4 + x\right) \cdot \left(\frac{1}{y}\right) + \left(\left(-\frac{x}{y}\right) \cdot z\right))_*\right|\]

herbie shell --seed 2019091 +o rules:numerics
(FPCore (x y z)
  :name "fabs fraction 1"
  (fabs (- (/ (+ x 4) y) (* (/ x y) z))))