Average Error: 0.1 → 0.1
Time: 13.0s
Precision: 64
Internal precision: 384
\[\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot x2\right) \cdot x3 + \left(3 \cdot x3\right) \cdot x3\right) - \left(\left(x2 \cdot x1\right) \cdot x2\right) \cdot x3\right) + \left(3 \cdot x3\right) \cdot x3\right) - x2\]
\[\left(6 \cdot {x3}^2 - x2\right) - \left(x2 \cdot x3\right) \cdot \left(x1 \cdot \left(x2 - 2\right)\right)\]

Error

Bits error versus x1

Bits error versus x2

Bits error versus x3

Derivation

  1. Initial program 0.1

    \[\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot x2\right) \cdot x3 + \left(3 \cdot x3\right) \cdot x3\right) - \left(\left(x2 \cdot x1\right) \cdot x2\right) \cdot x3\right) + \left(3 \cdot x3\right) \cdot x3\right) - x2\]
  2. Applied simplify 0.1

    \[\leadsto \color{blue}{\left(\left(x3 \cdot 3\right) \cdot \left(x3 + x3\right) - x2\right) - \left(x2 \cdot x3\right) \cdot \left(x1 \cdot \left(x2 - 2\right)\right)}\]
  3. Applied taylor 0.1

    \[\leadsto \left(6 \cdot {x3}^2 - x2\right) - \left(x2 \cdot x3\right) \cdot \left(x1 \cdot \left(x2 - 2\right)\right)\]
  4. Taylor expanded around 0 0.1

    \[\leadsto \left(\color{blue}{6 \cdot {x3}^2} - x2\right) - \left(x2 \cdot x3\right) \cdot \left(x1 \cdot \left(x2 - 2\right)\right)\]
  5. Removed slow pow expressions

Runtime

Time bar (total: 13.0s) Debug log

Please include this information when filing a bug report:

herbie shell --seed '#(3052192724 3812927732 3686175817 630908657 2373248591 511094450)'
(FPCore (x1 x2 x3)
  :name "rigidBody2"
  :pre (and (<= -15 x1 15) (<= -15 x2 15) (<= -15 x3 15))
  (- (+ (- (+ (* (* (* 2 x1) x2) x3) (* (* 3 x3) x3)) (* (* (* x2 x1) x2) x3)) (* (* 3 x3) x3)) x2))