Average Error: 55.7 → 47.1
Time: 17.4s
Precision: 64
Internal Precision: 128
\[\frac{\left(-b_2\right) + \sqrt{b_2 \cdot b_2 - a \cdot c}}{a}\]
↓
\[0\]

Error

Bits error versus a

Bits error versus b_2

Bits error versus c

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Results

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Derivation

  1. Initial program 55.7

    \[\frac{\left(-b_2\right) + \sqrt{b_2 \cdot b_2 - a \cdot c}}{a}\]

  2. Initial simplification55.7

    \[\leadsto \frac{\sqrt{b_2 \cdot b_2 - a \cdot c} - b_2}{a}\]

  3. Taylor expanded around inf 47.1

    \[\leadsto \color{blue}{0}\]

  4. Final simplification47.1

    \[\leadsto 0\]

Runtime

Time bar (total: 17.4s)Debug logProfile

herbie shell --seed 2018255 
(FPCore (a b_2 c)
  :name "quad2p (problem 3.2.1, positive)"
  (/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a))