Average Error: 1.5 → 1.5
Time: 29.0s
Precision: 64
Internal Precision: 576
\[\left|\frac{x + 4}{y} - \frac{x}{y} \cdot z\right|\]
↓
\[\left|\frac{x}{y} \cdot \left(-z\right) + \left(\frac{4}{y} + \frac{x}{y}\right)\right|\]

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. Taylor expanded around 0 3.1

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

  3. Applied simplify1.5

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

Runtime

Time bar (total: 29.0s)Debug logProfile

herbie shell --seed '#(1072107073 2127697367 3936270018 2300570620 2134894798 4023771849)' 
(FPCore (x y z)
  :name "fabs fraction 1"
  (fabs (- (/ (+ x 4) y) (* (/ x y) z))))