Average Error: 0.1 → 0.1
Time: 18.5s
Precision: 64
Internal Precision: 320
\[\left(\left(6 \cdot {10}^{200}\right) \cdot {x}^{2} + \left(5 \cdot {10}^{200}\right) \cdot x\right) + \left(-4\right) \cdot {10}^{200}\]
\[x \cdot \left(500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 + x \cdot 600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\right) - 400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\]

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[\left(\left(6 \cdot {10}^{200}\right) \cdot {x}^{2} + \left(5 \cdot {10}^{200}\right) \cdot x\right) + \left(-4\right) \cdot {10}^{200}\]
  2. Initial simplification0.1

    \[\leadsto {10}^{200} \cdot \left(\left(x \cdot 5 - 4\right) + \left(x \cdot x\right) \cdot 6\right)\]
  3. Taylor expanded around inf 0.1

    \[\leadsto \color{blue}{\left(500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 \cdot x + 600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 \cdot {x}^{2}\right) - 400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}\]
  4. Taylor expanded around -inf 63.2

    \[\leadsto \color{blue}{\left(500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 \cdot x + 600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 \cdot e^{2 \cdot \left(\log -1 - \log \left(\frac{-1}{x}\right)\right)}\right)} - 400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\]
  5. Simplified0.1

    \[\leadsto \color{blue}{x \cdot \left(500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 + 600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 \cdot x\right)} - 400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\]
  6. Final simplification0.1

    \[\leadsto x \cdot \left(500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 + x \cdot 600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\right) - 400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\]

Runtime

Time bar (total: 18.5s)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)' 
(FPCore (x)
  :name "(6*10^200)x^2+(5*10^200)x+(-4*10^200)"
  (+ (+ (* (* 6 (pow 10 200)) (pow x 2)) (* (* 5 (pow 10 200)) x)) (* (- 4) (pow 10 200))))