Average Error: 43.7 → 0.2
Time: 4.6s
Precision: binary64
\[\]
\[\]
↓
\[\]

Error

Bits error versus a

Bits error versus b

Bits error versus c

Derivation

  1. Initial program 43.7

    \[\]
  2. Using strategy rm

  3. Applied flip-+43.7

    \[\leadsto \]

  4. Simplified0.4

    \[\leadsto \]

  5. Simplified0.4

    \[\leadsto \]
  6. Using strategy rm

  7. Applied *-un-lft-identity0.4

    \[\leadsto \]

  8. Applied times-frac0.4

    \[\leadsto \]

  9. Applied times-frac0.4

    \[\leadsto \]

  10. Simplified0.4

    \[\leadsto \]

  11. Simplified0.2

    \[\leadsto \]

  12. Final simplification0.2

    \[\leadsto \]

Reproduce

herbie shell --seed 2020181 
(FPCore (a b c)
  :name "Quadratic roots, medium range"
  :precision binary64
  :pre (and (< 1.1102230246251565e-16 a 9007199254740992.0) (< 1.1102230246251565e-16 b 9007199254740992.0) (< 1.1102230246251565e-16 c 9007199254740992.0))
  (/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a)))