Average Error: 28.8 → 28.8
Time: 31.2s
Precision: 64
Internal Precision: 576
\[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}{3 \cdot a}\]
↓
\[\frac{\sqrt{b \cdot b - \frac{\frac{3}{\frac{-1}{a}}}{\frac{-1}{c}}} - b}{a \cdot 3}\]

Error

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus d

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 28.8

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

  3. Applied add-exp-log28.9

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

  4. Taylor expanded around -inf 63.6

    \[\leadsto \frac{\left(-b\right) + \sqrt{b \cdot b - \color{blue}{e^{\log 3 - \left(\log \left(\frac{-1}{c}\right) + \log \left(\frac{-1}{a}\right)\right)}}}}{3 \cdot a}\]

  5. Applied simplify28.8

    \[\leadsto \color{blue}{\frac{\sqrt{b \cdot b - \frac{\frac{3}{\frac{-1}{a}}}{\frac{-1}{c}}} - b}{a \cdot 3}}\]

Runtime

Time bar (total: 31.2s)Debug logProfile

herbie shell --seed 2018193 
(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)))