Error

Derivation

1. Split input into 3 regimes

2. if b/2 < -7.200245550033268e-104

   1. Initial program 51.3

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

   3. Applied flip--51.3

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

   4. Applied simplify25.1

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

   6. Applied div-inv25.2

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

   7. Taylor expanded around -inf 21.4

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

   8. Applied simplify10.5

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

   if -7.200245550033268e-104 < b/2 < 3.409351165504793e+65

   1. Initial program 12.2

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

   3. Applied div-sub12.2

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

   if 3.409351165504793e+65 < b/2

   1. Initial program 38.1

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

   2. Taylor expanded around inf 4.7

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

Runtime

Time bar (total: 46.7s)Debug logProfile

herbie shell --seed '#(1070100504 930361288 1279167582 284574201 1450237281 2578255382)' 
(FPCore (a b/2 c)
  :name "NMSE problem 3.2.1"
  (/ (- (- b/2) (sqrt (- (* b/2 b/2) (* a c)))) a))