Average Error: 0.4 → 0.4
Time: 1.1m
Precision: 64
Internal Precision: 384
\[\frac{\left(4.0 \cdot x\right) \cdot x}{1 + \frac{x}{1.11} \cdot \frac{x}{1.11}}\]
↓
\[\frac{4.0 \cdot x}{1} \cdot \frac{x}{1 + \frac{x}{1.11} \cdot \frac{x}{1.11}}\]

Error

Bits error versus x

Derivation

  1. Initial program 0.4

    \[\frac{\left(4.0 \cdot x\right) \cdot x}{1 + \frac{x}{1.11} \cdot \frac{x}{1.11}}\]
  2. Using strategy rm

  3. Applied *-un-lft-identity0.4

    \[\leadsto \frac{\left(4.0 \cdot x\right) \cdot x}{\color{blue}{1 \cdot \left(1 + \frac{x}{1.11} \cdot \frac{x}{1.11}\right)}}\]

  4. Applied times-frac0.4

    \[\leadsto \color{blue}{\frac{4.0 \cdot x}{1} \cdot \frac{x}{1 + \frac{x}{1.11} \cdot \frac{x}{1.11}}}\]

Runtime

Time bar (total: 1.1m)Debug log

herbie shell --seed '#(1743936871 1855164119 3668777427 1254258049 132811564 1366975197)' 
(FPCore (x)
  :name "predatorPrey"
  :pre (<= 0.1 x 0.3)
  (/ (* (* 4.0 x) x) (+ 1 (* (/ x 1.11) (/ x 1.11)))))