Average Error: 0.4 → 0.4
Time: 6.4s
Precision: 64
Internal precision: 384
\[\frac{\left(4.0 \cdot x\right) \cdot x}{1 + \frac{x}{1.11} \cdot \frac{x}{1.11}}\]
⬇
\[\frac{4.0 \cdot x}{1} \cdot \frac{x}{1 + {\left(\frac{x}{1.11}\right)}^2}\]

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-identity 0.4

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

  4. Applied times-frac 0.4

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

  5. Applied simplify 0.4

    \[\leadsto \frac{4.0 \cdot x}{1} \cdot \color{blue}{\frac{x}{1 + {\left(\frac{x}{1.11}\right)}^2}}\]
  6. Removed slow pow expressions

Runtime

Time bar (total: 6.4s) Debug log

Please include this information when filing a bug report:

herbie shell --seed '#(3052192724 3812927732 3686175817 630908657 2373248591 511094450)'
(FPCore (x)
  :name "predatorPrey"
  :pre (<= 0.1 x 0.3)
  (/ (* (* 4.0 x) x) (+ 1 (* (/ x 1.11) (/ x 1.11)))))