Error

Target

Derivation

1. Split input into 4 regimes

2. if (- b) < -2.6805608240715666e+118

   1. Initial program 48.9

      \[\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]

   2. Taylor expanded around inf 3.4

      \[\leadsto \color{blue}{-1 \cdot \frac{b}{a}}\]

   3. Applied simplify3.4

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

   if -2.6805608240715666e+118 < (- b) < 1.6242126243513356e-246

   1. Initial program 9.8

      \[\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
   2. Using strategy rm

   3. Applied div-inv10.0

      \[\leadsto \color{blue}{\left(\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}\right) \cdot \frac{1}{2 \cdot a}}\]

   if 1.6242126243513356e-246 < (- b) < 4.760127010700881e+19

   1. Initial program 30.5

      \[\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]
   2. Using strategy rm

   3. Applied flip--30.6

      \[\leadsto \frac{\color{blue}{\frac{\left(-b\right) \cdot \left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)} \cdot \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}}}{2 \cdot a}\]

   4. Applied simplify18.1

      \[\leadsto \frac{\frac{\color{blue}{\left(4 \cdot c\right) \cdot a}}{\left(-b\right) + \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}}{2 \cdot a}\]

   5. Applied simplify18.1

      \[\leadsto \frac{\frac{\left(4 \cdot c\right) \cdot a}{\color{blue}{\sqrt{(\left(-4\right) \cdot \left(c \cdot a\right) + \left(b \cdot b\right))_*} - b}}}{2 \cdot a}\]
   6. Using strategy rm

   7. Applied add-sqr-sqrt18.2

      \[\leadsto \frac{\frac{\left(4 \cdot c\right) \cdot a}{\color{blue}{\sqrt{\sqrt{(\left(-4\right) \cdot \left(c \cdot a\right) + \left(b \cdot b\right))_*} - b} \cdot \sqrt{\sqrt{(\left(-4\right) \cdot \left(c \cdot a\right) + \left(b \cdot b\right))_*} - b}}}}{2 \cdot a}\]

   8. Applied times-frac14.5

      \[\leadsto \frac{\color{blue}{\frac{4 \cdot c}{\sqrt{\sqrt{(\left(-4\right) \cdot \left(c \cdot a\right) + \left(b \cdot b\right))_*} - b}} \cdot \frac{a}{\sqrt{\sqrt{(\left(-4\right) \cdot \left(c \cdot a\right) + \left(b \cdot b\right))_*} - b}}}}{2 \cdot a}\]

   9. Applied times-frac9.1

      \[\leadsto \color{blue}{\frac{\frac{4 \cdot c}{\sqrt{\sqrt{(\left(-4\right) \cdot \left(c \cdot a\right) + \left(b \cdot b\right))_*} - b}}}{2} \cdot \frac{\frac{a}{\sqrt{\sqrt{(\left(-4\right) \cdot \left(c \cdot a\right) + \left(b \cdot b\right))_*} - b}}}{a}}\]

   10. Applied simplify9.1

       \[\leadsto \frac{\frac{4 \cdot c}{\sqrt{\sqrt{(\left(-4\right) \cdot \left(c \cdot a\right) + \left(b \cdot b\right))_*} - b}}}{2} \cdot \color{blue}{\frac{1}{\sqrt{\sqrt{(\left(c \cdot a\right) \cdot \left(-4\right) + \left(b \cdot b\right))_*} - b}}}\]

   if 4.760127010700881e+19 < (- b)

   1. Initial program 55.7

      \[\frac{\left(-b\right) - \sqrt{b \cdot b - 4 \cdot \left(a \cdot c\right)}}{2 \cdot a}\]

   2. Taylor expanded around -inf 43.3

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

   3. Applied simplify4.9

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

Runtime

Time bar (total: 1.8m)Debug logProfile

herbie shell --seed '#(1070864556 424010669 783715395 1203517814 4070606583 4107618214)' +o rules:numerics
(FPCore (a b c)
  :name "quadm (p42, negative)"

  :herbie-target
  (if (< b 0) (/ c (* a (/ (+ (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a)))) (/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a)))

  (/ (- (- b) (sqrt (- (* b b) (* 4 (* a c))))) (* 2 a)))