Error

Derivation

1. Split input into 3 regimes

2. if b/2 < -3.6739491154146663e+114

   1. Initial program 49.1

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

   2. Taylor expanded around -inf 3.2

      \[\leadsto \color{blue}{-2 \cdot \frac{b/2}{a}}\]

   if -3.6739491154146663e+114 < b/2 < 2.046828728801563e-87

   1. Initial program 12.0

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

   3. Applied clear-num12.1

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

   if 2.046828728801563e-87 < b/2

   1. Initial program 52.2

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

   3. Applied flip-+52.3

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

   4. Applied simplify24.9

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

   5. Taylor expanded around inf 20.2

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

   6. Applied simplify9.2

      \[\leadsto \color{blue}{\frac{c}{(\left(\frac{1}{2} \cdot a\right) \cdot \left(\frac{c}{b/2}\right) + \left(-b/2\right))_* - b/2}}\]
3. Recombined 3 regimes into one program.

Runtime

Time bar (total: 47.0s)Debug logProfile

herbie shell --seed '#(1070100504 930361288 1279167582 284574201 1450237281 2578255382)' +o rules:numerics
(FPCore (a b/2 c)
  :name "quad2p (problem 3.2.1, positive)"
  (/ (+ (- b/2) (sqrt (- (* b/2 b/2) (* a c)))) a))