Error

Derivation

1. Split input into 4 regimes

2. if b_2 < -1.180819239099574e+88

   1. Initial program 42.4

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

   2. Taylor expanded around -inf 4.2

      \[\leadsto \color{blue}{-2 \cdot \frac{b_2}{a}}\]

   if -1.180819239099574e+88 < b_2 < 1.071999901811407e-120

   1. Initial program 11.2

      \[\frac{\left(-b_2\right) + \sqrt{b_2 \cdot b_2 - a \cdot c}}{a}\]
   2. Using strategy rm

   3. Applied div-inv11.3

      \[\leadsto \color{blue}{\left(\left(-b_2\right) + \sqrt{b_2 \cdot b_2 - a \cdot c}\right) \cdot \frac{1}{a}}\]

   if 1.071999901811407e-120 < b_2 < 2.184756512447019e+51

   1. Initial program 39.6

      \[\frac{\left(-b_2\right) + \sqrt{b_2 \cdot b_2 - a \cdot c}}{a}\]
   2. Using strategy rm

   3. Applied clear-num39.6

      \[\leadsto \color{blue}{\frac{1}{\frac{a}{\left(-b_2\right) + \sqrt{b_2 \cdot b_2 - a \cdot c}}}}\]

   4. Applied simplify39.6

      \[\leadsto \frac{1}{\color{blue}{\frac{a}{\sqrt{b_2 \cdot b_2 - a \cdot c} - b_2}}}\]
   5. Using strategy rm

   6. Applied flip--39.7

      \[\leadsto \frac{1}{\frac{a}{\color{blue}{\frac{\sqrt{b_2 \cdot b_2 - a \cdot c} \cdot \sqrt{b_2 \cdot b_2 - a \cdot c} - b_2 \cdot b_2}{\sqrt{b_2 \cdot b_2 - a \cdot c} + b_2}}}}\]

   7. Applied simplify16.6

      \[\leadsto \frac{1}{\frac{a}{\frac{\color{blue}{\left(-a\right) \cdot c}}{\sqrt{b_2 \cdot b_2 - a \cdot c} + b_2}}}\]

   if 2.184756512447019e+51 < b_2

   1. Initial program 56.4

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

   2. Taylor expanded around inf 15.6

      \[\leadsto \frac{\color{blue}{\frac{-1}{2} \cdot \frac{c \cdot a}{b_2}}}{a}\]

   3. Applied simplify3.8

      \[\leadsto \color{blue}{\frac{-1}{2} \cdot \frac{c}{b_2}}\]
3. Recombined 4 regimes into one program.

Runtime

Time bar (total: 1.1m)Debug logProfile

herbie shell --seed '#(1071948828 1180510430 2986424009 997076509 406109801 420189285)' +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))