Average Error: 28.3 → 0.3
Time: 4.3s
Precision: binary64
\[\]
\[\]
↓
\[\]

Error

Bits error versus a

Bits error versus b

Bits error versus c

Derivation

  1. Initial program 28.3

    \[\]
  2. Using strategy rm

  3. Applied flip-+28.3

    \[\leadsto \]

  4. Simplified0.6

    \[\leadsto \]

  5. Simplified0.6

    \[\leadsto \]
  6. Using strategy rm

  7. Applied *-un-lft-identity0.6

    \[\leadsto \]

  8. Applied times-frac0.6

    \[\leadsto \]

  9. Applied times-frac0.5

    \[\leadsto \]

  10. Simplified0.5

    \[\leadsto \]

  11. Simplified0.3

    \[\leadsto \]
  12. Using strategy rm

  13. Applied flip3--0.3

    \[\leadsto \]

  14. Simplified0.3

    \[\leadsto \]

  15. Simplified0.3

    \[\leadsto \]

  16. Final simplification0.3

    \[\leadsto \]

Reproduce

herbie shell --seed 2020190 
(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)))