Average Error: 28.7 → 28.7
Time: 58.0s
Precision: 64
Internal Precision: 576
\[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}{3 \cdot a}\]
↓
\[\frac{\left(-b\right) + \sqrt{b \cdot b - \sqrt[3]{{\left(\left(a \cdot 3\right) \cdot c\right)}^{3}}}}{3 \cdot a}\]

Error

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus d

Try it out

  1. Inputs

  2. Original Output:

    Herbie Output:

Derivation

  1. Initial program 28.7

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

  3. Applied add-cbrt-cube28.7

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

  4. Applied simplify28.7

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

Runtime

Time bar (total: 58.0s)Debug logProfile

herbie shell --seed '#(1072361757 3390613284 2339397988 1175251238 145061547 3101881848)' 
(FPCore (a b c d)
  :name "Cubic critical, narrow range"
  :pre (and (< 1.0536712127723509e-08 a 94906265.62425156) (< 1.0536712127723509e-08 b 94906265.62425156) (< 1.0536712127723509e-08 c 94906265.62425156))
  (/ (+ (- b) (sqrt (- (* b b) (* (* 3 a) c)))) (* 3 a)))