Average Error: 0.1 → 0.1
Time: 12.1s
Precision: 64
Internal precision: 1408
\[\left(-12 \cdot x1 - 7 \cdot x2\right) + x2 \cdot x2\]
⬇
\[{x2}^2 - \left(12 \cdot x1 + 7 \cdot x2\right)\]

Error

Bits error versus x1

Bits error versus x2

Derivation

  1. Initial program 0.1

    \[\left(-12 \cdot x1 - 7 \cdot x2\right) + x2 \cdot x2\]

  2. Applied simplify 0.1

    \[\leadsto \color{blue}{x1 \cdot -12 - \left(7 - x2\right) \cdot x2}\]

  3. Applied taylor 0.1

    \[\leadsto {x2}^2 - \left(12 \cdot x1 + 7 \cdot x2\right)\]

  4. Taylor expanded around 0 0.1

    \[\leadsto \color{blue}{{x2}^2 - \left(12 \cdot x1 + 7 \cdot x2\right)}\]
  5. Removed slow pow expressions

Runtime

Time bar (total: 12.1s) Debug log

Please include this information when filing a bug report:

herbie shell --seed '#(3052192724 3812927732 3686175817 630908657 2373248591 511094450)'
(FPCore (x1 x2)
  :name "floudas3"
  :pre (and (<= 0 x1 2) (<= 0 x2 3) (>= (+ (* -2 (* (* x1 x1) (* x1 x1))) 2) x2))
  (+ (- (* -12 x1) (* 7 x2)) (* x2 x2)))