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Derivation

1. Initial program 52.5

   \[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}{3 \cdot a}\]
2. Using strategy rm

3. Applied add-exp-log52.5

   \[\leadsto \frac{\left(-b\right) + \sqrt{b \cdot b - \color{blue}{e^{\log \left(\left(3 \cdot a\right) \cdot c\right)}}}}{3 \cdot a}\]
4. Using strategy rm

5. Applied add-cube-cbrt52.5

   \[\leadsto \frac{\left(-b\right) + \sqrt{b \cdot b - \color{blue}{\left(\sqrt[3]{e^{\log \left(\left(3 \cdot a\right) \cdot c\right)}} \cdot \sqrt[3]{e^{\log \left(\left(3 \cdot a\right) \cdot c\right)}}\right) \cdot \sqrt[3]{e^{\log \left(\left(3 \cdot a\right) \cdot c\right)}}}}}{3 \cdot a}\]

6. Applied simplify52.5

   \[\leadsto \frac{\left(-b\right) + \sqrt{b \cdot b - \color{blue}{\left(\sqrt[3]{a \cdot \left(3 \cdot c\right)} \cdot \sqrt[3]{a \cdot \left(3 \cdot c\right)}\right)} \cdot \sqrt[3]{e^{\log \left(\left(3 \cdot a\right) \cdot c\right)}}}}{3 \cdot a}\]

7. Applied simplify52.5

   \[\leadsto \frac{\left(-b\right) + \sqrt{b \cdot b - \left(\sqrt[3]{a \cdot \left(3 \cdot c\right)} \cdot \sqrt[3]{a \cdot \left(3 \cdot c\right)}\right) \cdot \color{blue}{\sqrt[3]{\left(a \cdot c\right) \cdot 3}}}}{3 \cdot a}\]

Runtime

Time bar (total: 20.2s)Debug logProfile

herbie shell --seed '#(1072936661 1621281212 3440817831 3219514234 460296804 1258167384)' 
(FPCore (a b c d)
  :name "Cubic critical, wide range"
  :pre (and (< 4.930380657631324e-32 a 2.028240960365167e+31) (< 4.930380657631324e-32 b 2.028240960365167e+31) (< 4.930380657631324e-32 c 2.028240960365167e+31))
  (/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a)))