Average Error: 0.1 → 0.1
Time: 8.4s
Precision: 64
Internal Precision: 576
\[\left(\left(aA1 \cdot k\right) \cdot k + aA2 \cdot k\right) + aA3\]
\[k \cdot \left(aA2 + k \cdot aA1\right) + aA3\]

Error

Bits error versus aA1

Bits error versus k

Bits error versus aA2

Bits error versus aA3

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[\left(\left(aA1 \cdot k\right) \cdot k + aA2 \cdot k\right) + aA3\]
  2. Taylor expanded around -inf 4.2

    \[\leadsto \color{blue}{\left(aA2 \cdot k + aA1 \cdot {k}^{2}\right)} + aA3\]
  3. Simplified0.1

    \[\leadsto \color{blue}{k \cdot \left(aA2 + aA1 \cdot k\right)} + aA3\]
  4. Final simplification0.1

    \[\leadsto k \cdot \left(aA2 + k \cdot aA1\right) + aA3\]

Runtime

Time bar (total: 8.4s)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)' 
(FPCore (aA1 k aA2 aA3)
  :name "aA1*k*k + aA2*k + aA3"
  (+ (+ (* (* aA1 k) k) (* aA2 k)) aA3))