Average Error: 28.9 → 0.3
Time: 4.2s
Precision: binary64
\[\]
\[\]
↓
\[\]

Error

Bits error versus a

Bits error versus b

Bits error versus c

Derivation

  1. Initial program 28.9

    \[\]

  2. Simplified28.9

    \[\leadsto \]
  3. Using strategy rm

  4. Applied flip--28.9

    \[\leadsto \]

  5. Simplified0.6

    \[\leadsto \]

  6. Simplified0.6

    \[\leadsto \]
  7. Using strategy rm

  8. Applied associate-/r*0.6

    \[\leadsto \]

  9. Simplified0.5

    \[\leadsto \]
  10. Using strategy rm

  11. Applied distribute-rgt-neg-out0.5

    \[\leadsto \]

  12. Applied distribute-frac-neg0.5

    \[\leadsto \]

  13. Simplified0.3

    \[\leadsto \]

  14. Final simplification0.3

    \[\leadsto \]

Reproduce

herbie shell --seed 2020192 
(FPCore (a b c)
  :name "Cubic critical, narrow range"
  :precision binary64
  :pre (and (< 1.0536712127723509e-08 a 94906265.62425156) (< 1.0536712127723509e-08 b 94906265.62425156) (< 1.0536712127723509e-08 c 94906265.62425156))
  (/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a)))