Average Error: 18.3 → 18.4
Time: 29.8s
Precision: 64
Internal Precision: 320
\[\frac{2 \cdot aA2 - \left(\left(2 \cdot aA0\right) \cdot k\right) \cdot k}{\left(\left(aA0 \cdot k\right) \cdot k + aA1 \cdot k\right) + aA2}\]
\[\left(2 \cdot aA2 - \left(\left(aA0 \cdot 2\right) \cdot k\right) \cdot k\right) \cdot \frac{1}{\left(k \cdot aA1 + \left(k \cdot aA0\right) \cdot k\right) + aA2}\]

Error

Bits error versus aA2

Bits error versus aA0

Bits error versus k

Bits error versus aA1

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 18.3

    \[\frac{2 \cdot aA2 - \left(\left(2 \cdot aA0\right) \cdot k\right) \cdot k}{\left(\left(aA0 \cdot k\right) \cdot k + aA1 \cdot k\right) + aA2}\]
  2. Using strategy rm
  3. Applied div-inv18.4

    \[\leadsto \color{blue}{\left(2 \cdot aA2 - \left(\left(2 \cdot aA0\right) \cdot k\right) \cdot k\right) \cdot \frac{1}{\left(\left(aA0 \cdot k\right) \cdot k + aA1 \cdot k\right) + aA2}}\]
  4. Final simplification18.4

    \[\leadsto \left(2 \cdot aA2 - \left(\left(aA0 \cdot 2\right) \cdot k\right) \cdot k\right) \cdot \frac{1}{\left(k \cdot aA1 + \left(k \cdot aA0\right) \cdot k\right) + aA2}\]

Runtime

Time bar (total: 29.8s)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)' 
(FPCore (aA2 aA0 k aA1)
  :name "(2*aA2 - 2*aA0*k*k)/(aA0*k*k + aA1*k + aA2)"
  (/ (- (* 2 aA2) (* (* (* 2 aA0) k) k)) (+ (+ (* (* aA0 k) k) (* aA1 k)) aA2)))