Average Error: 1.5 → 1.5
Time: 31.3s
Precision: 64
Internal Precision: 128
\[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
↓
\[\left|\left(4 + x\right) \cdot \frac{1}{y} - \frac{x}{y} \cdot z\right|\]

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 1.5

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

  3. Applied div-inv1.5

    \[\leadsto \left|\color{blue}{\left(x + 4\right) \cdot \frac{1}{y}} - \frac{x}{y} \cdot z\right|\]

  4. Final simplification1.5

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

Reproduce

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