Average Error: 35.9 → 7.4
Time: 57.3s
Precision: 64
Internal precision: 3200
\[\frac{\left(-b/2\right) - \sqrt{b/2 \cdot b/2 - a \cdot c}}{a}\]
⬇
\[\begin{array}{l} \mathbf{if}\;b/2 \le -1.9038547349802057 \cdot 10^{-44}:\\ \;\;\;\;\frac{c}{\left(\frac{1}{2} \cdot c\right) \cdot \frac{a}{b/2} - \left(b/2 - \left(-b/2\right)\right)}\\ \mathbf{if}\;b/2 \le 4.585114762073355 \cdot 10^{+93}:\\ \;\;\;\;\left(\left(-b/2\right) - \sqrt{b/2 \cdot b/2 - a \cdot c}\right) \cdot \frac{1}{a}\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \frac{b/2}{a}\\ \end{array}\]

Error

Bits error versus a

Bits error versus b/2

Bits error versus c

Derivation

  1. Split input into 3 regimes.

  2. if b/2 < -1.9038547349802057e-44

    1. Initial program 58.3

      \[\frac{\left(-b/2\right) - \sqrt{b/2 \cdot b/2 - a \cdot c}}{a}\]
    2. Using strategy rm

    3. Applied flip-- 58.4

      \[\leadsto \frac{\color{blue}{\frac{\left(-b/2\right) \cdot \left(-b/2\right) - \sqrt{b/2 \cdot b/2 - a \cdot c} \cdot \sqrt{b/2 \cdot b/2 - a \cdot c}}{\left(-b/2\right) + \sqrt{b/2 \cdot b/2 - a \cdot c}}}}{a}\]

    4. Applied simplify 33.6

      \[\leadsto \frac{\frac{\color{blue}{c \cdot a}}{\left(-b/2\right) + \sqrt{b/2 \cdot b/2 - a \cdot c}}}{a}\]

    5. Taylor expanded around -inf 15.5

      \[\leadsto \frac{\frac{c \cdot a}{\left(-b/2\right) + \color{blue}{\left(\frac{1}{2} \cdot \frac{c \cdot a}{b/2} - b/2\right)}}}{a}\]

    6. Applied simplify 3.1

      \[\leadsto \color{blue}{\frac{c}{\left(\frac{1}{2} \cdot c\right) \cdot \frac{a}{b/2} - \left(b/2 - \left(-b/2\right)\right)}}\]

    if -1.9038547349802057e-44 < b/2 < 4.585114762073355e+93

    1. Initial program 13.6

      \[\frac{\left(-b/2\right) - \sqrt{b/2 \cdot b/2 - a \cdot c}}{a}\]
    2. Using strategy rm

    3. Applied div-inv 13.7

      \[\leadsto \color{blue}{\left(\left(-b/2\right) - \sqrt{b/2 \cdot b/2 - a \cdot c}\right) \cdot \frac{1}{a}}\]

    if 4.585114762073355e+93 < b/2

    1. Initial program 44.8

      \[\frac{\left(-b/2\right) - \sqrt{b/2 \cdot b/2 - a \cdot c}}{a}\]

    2. Taylor expanded around inf 0

      \[\leadsto \color{blue}{-2 \cdot \frac{b/2}{a}}\]
  3. Recombined 3 regimes into one program.
  4. Removed slow pow expressions

Runtime

Time bar (total: 57.3s) Debug log

Please include this information when filing a bug report:

herbie shell --seed '#(2329929097 3210370195 3111198779 2406363002 3511342718 2136436390)'
(FPCore (a b/2 c)
  :name "quad2m (problem 3.2.1, negative)"
  (/ (- (- b/2) (sqrt (- (* b/2 b/2) (* a c)))) a))