Error

Derivation

1. Split input into 3 regimes

2. if b < -1.4403352106256782e+109

   1. Initial program 45.5

      \[\begin{array}{l} \mathbf{if}\;b \ge 0:\\ \;\;\;\;\frac{2 \cdot c}{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\\ \end{array}\]

   2. Taylor expanded around -inf 9.2

      \[\leadsto \begin{array}{l} \mathbf{if}\;b \ge 0:\\ \;\;\;\;\frac{2 \cdot c}{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-b\right) + \left(2 \cdot \frac{c \cdot a}{b} - b\right)}{2 \cdot a}\\ \end{array}\]

   3. Applied simplify3.7

      \[\leadsto \color{blue}{\begin{array}{l} \mathbf{if}\;b \ge 0:\\ \;\;\;\;\frac{c + c}{\left(-b\right) - \sqrt{b \cdot b - \left(a \cdot c\right) \cdot 4}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{c}{b}}{1} - \frac{b - \left(-b\right)}{a + a}\\ \end{array}}\]

   4. Applied simplify3.7

      \[\leadsto \begin{array}{l} \mathbf{if}\;b \ge 0:\\ \;\;\;\;\frac{c + c}{\left(-b\right) - \sqrt{b \cdot b - \left(a \cdot c\right) \cdot 4}}\\ \mathbf{else}:\\ \;\;\;\;\frac{c}{b} - \frac{b - \left(-b\right)}{a + a}\\ \end{array}\]

   if -1.4403352106256782e+109 < b < 1.9633433623178084e+123

   1. Initial program 9.0

      \[\begin{array}{l} \mathbf{if}\;b \ge 0:\\ \;\;\;\;\frac{2 \cdot c}{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\\ \end{array}\]
   2. Using strategy rm

   3. Applied add-sqr-sqrt9.0

      \[\leadsto \begin{array}{l} \mathbf{if}\;b \ge 0:\\ \;\;\;\;\frac{2 \cdot c}{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-b\right) + \sqrt{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c} \cdot \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}}{2 \cdot a}\\ \end{array}\]

   4. Applied sqrt-prod9.1

      \[\leadsto \begin{array}{l} \mathbf{if}\;b \ge 0:\\ \;\;\;\;\frac{2 \cdot c}{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-b\right) + \sqrt{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}} \cdot \sqrt{\sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}}{2 \cdot a}\\ \end{array}\]

   if 1.9633433623178084e+123 < b

   1. Initial program 32.6

      \[\begin{array}{l} \mathbf{if}\;b \ge 0:\\ \;\;\;\;\frac{2 \cdot c}{\left(-b\right) - \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\\ \end{array}\]

   2. Taylor expanded around inf 6.1

      \[\leadsto \begin{array}{l} \mathbf{if}\;b \ge 0:\\ \;\;\;\;\frac{2 \cdot c}{\color{blue}{2 \cdot \frac{c \cdot a}{b} - 2 \cdot b}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{2 \cdot a}\\ \end{array}\]

   3. Applied simplify1.7

      \[\leadsto \color{blue}{\begin{array}{l} \mathbf{if}\;b \ge 0:\\ \;\;\;\;\frac{c}{c \cdot \frac{a}{b} - b}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{a + a}\\ \end{array}}\]
   4. Using strategy rm

   5. Applied add-cube-cbrt1.7

      \[\leadsto \begin{array}{l} \mathbf{if}\;b \ge 0:\\ \;\;\;\;\frac{c}{\color{blue}{\left(\sqrt[3]{c \cdot \frac{a}{b}} \cdot \sqrt[3]{c \cdot \frac{a}{b}}\right) \cdot \sqrt[3]{c \cdot \frac{a}{b}}} - b}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{a + a}\\ \end{array}\]
   6. Using strategy rm

   7. Applied add-cube-cbrt1.7

      \[\leadsto \begin{array}{l} \mathbf{if}\;b \ge 0:\\ \;\;\;\;\frac{c}{\left(\sqrt[3]{c \cdot \frac{a}{b}} \cdot \sqrt[3]{c \cdot \frac{a}{b}}\right) \cdot \color{blue}{\left(\left(\sqrt[3]{\sqrt[3]{c \cdot \frac{a}{b}}} \cdot \sqrt[3]{\sqrt[3]{c \cdot \frac{a}{b}}}\right) \cdot \sqrt[3]{\sqrt[3]{c \cdot \frac{a}{b}}}\right)} - b}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-b\right) + \sqrt{b \cdot b - \left(4 \cdot a\right) \cdot c}}{a + a}\\ \end{array}\]
3. Recombined 3 regimes into one program.
4. Removed slow pow expressions.

Runtime

Time bar (total: 1.2m)Debug logProfile

herbie shell --seed '#(1063282112 2455465480 4141627379 3773598652 1647277307 776739644)' 
(FPCore (a b c)
  :name "jeff quadratic root 2"
  (if (>= b 0) (/ (* 2 c) (- (- b) (sqrt (- (* b b) (* (* 4 a) c))))) (/ (+ (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (* 2 a))))