Average Error: 0 → 0
Time: 5.5s
Precision: 64
Internal Precision: 384
\[2 \cdot \left(\left(1 \cdot \frac{1}{9} + \frac{1}{9} \cdot \frac{1}{9}\right) + \frac{1}{9} \cdot 1\right)\]
↓
\[\frac{2}{\frac{9}{2}} + \frac{\frac{2}{9}}{9}\]

Error

Target

Original0
Target0
Herbie0
\[\left(\left(\frac{1}{9} \cdot 1\right) \cdot 2 + 2 \cdot \left(\frac{1}{9} \cdot \frac{1}{9}\right)\right) + 2 \cdot \left(1 \cdot \frac{1}{9}\right)\]

Derivation

  1. Initial program 0

    \[2 \cdot \left(\left(1 \cdot \frac{1}{9} + \frac{1}{9} \cdot \frac{1}{9}\right) + \frac{1}{9} \cdot 1\right)\]

  2. Applied simplify0

    \[\leadsto \color{blue}{\left(\frac{2}{9} + \frac{2}{9}\right) + \frac{\frac{2}{9}}{9}}\]

  3. Applied simplify0

    \[\leadsto \color{blue}{\frac{2}{\frac{9}{2}}} + \frac{\frac{2}{9}}{9}\]
  4. Removed slow pow expressions.

Runtime

Time bar (total: 5.5s)Debug logProfile

herbie shell --seed '#(1062930989 876886121 3990119081 3032829768 3060892583 1929069376)' 
(FPCore ()
  :name "Rectangular parallelepiped of dimension a×b×c"

  :herbie-target
  (+ (+ (* (* (/ 1 9) 1) 2) (* 2 (* (/ 1 9) (/ 1 9)))) (* 2 (* 1 (/ 1 9))))

  (* 2 (+ (+ (* 1 (/ 1 9)) (* (/ 1 9) (/ 1 9))) (* (/ 1 9) 1))))