(/ (+ (+ (* (- k) k) k) (* 2 n)) (* 2 k))

Average Error: 18.4 → 0.0

Time: 856.0ms

Precision: binary64

Math

\[\frac{\left(\left(-k\right) \cdot k + k\right) + 2 \cdot n}{2 \cdot k}\]

↓

\[\frac{\left(1 - k\right) + \frac{2 \cdot n}{k}}{2}\]

Error

Bits error versus k

Bits error versus n

Derivation

1. Initial program 18.4

   \[\frac{\left(\left(-k\right) \cdot k + k\right) + 2 \cdot n}{2 \cdot k}\]

2. Simplified 0.0

   \[\leadsto \color{blue}{\frac{\left(1 - k\right) + \frac{2 \cdot n}{k}}{2}}\]

3. Final simplification 0.0

   \[\leadsto \frac{\left(1 - k\right) + \frac{2 \cdot n}{k}}{2}\]

Reproduce

herbie shell --seed 2020152 
(FPCore (k n)
  :name "(/ (+ (+ (* (- k) k) k) (* 2 n)) (* 2 k))"
  :precision binary64
  (/ (+ (+ (* (neg k) k) k) (* 2.0 n)) (* 2.0 k)))