Average Error: 0.0 → 0.0
Time: 14.1s
Precision: 64
Internal Precision: 320
\[\left(4 \cdot x + 4 \cdot y\right) + 4 \cdot {\left(x + 1\right)}^{2}\]
\[\left(\left(x + 2\right) \cdot x + \left(y + \left(x + 1\right)\right)\right) \cdot 4\]

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\left(4 \cdot x + 4 \cdot y\right) + 4 \cdot {\left(x + 1\right)}^{2}\]
  2. Taylor expanded around 0 0.0

    \[\leadsto \left(4 \cdot x + 4 \cdot y\right) + 4 \cdot \color{blue}{\left(2 \cdot x + \left(1 + {x}^{2}\right)\right)}\]
  3. Applied simplify0.0

    \[\leadsto \color{blue}{\left(\left(x + 2\right) \cdot x + \left(y + \left(x + 1\right)\right)\right) \cdot 4}\]

Runtime

Time bar (total: 14.1s)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)' 
(FPCore (x y)
  :name "4*x + 4*y + 4(x + 1)^2"
  (+ (+ (* 4 x) (* 4 y)) (* 4 (pow (+ x 1) 2))))