Average Error: 52.7 → 0.1
Time: 4.3s
Precision: binary64
\[\]
\[\]
↓
\[\]

Error

Bits error versus a

Bits error versus b

Bits error versus c

Derivation

  1. Initial program 52.7

    \[\]
  2. Using strategy rm

  3. Applied flip-+52.7

    \[\leadsto \]

  4. Simplified0.5

    \[\leadsto \]

  5. Simplified0.5

    \[\leadsto \]
  6. Using strategy rm

  7. Applied *-un-lft-identity0.5

    \[\leadsto \]

  8. Applied times-frac0.5

    \[\leadsto \]

  9. Applied times-frac0.4

    \[\leadsto \]

  10. Simplified0.4

    \[\leadsto \]

  11. Simplified0.1

    \[\leadsto \]

  12. Final simplification0.1

    \[\leadsto \]

Reproduce

herbie shell --seed 2020181 
(FPCore (a b c)
  :name "Cubic critical, wide range"
  :precision binary64
  :pre (and (< 4.930380657631324e-32 a 2.028240960365167e+31) (< 4.930380657631324e-32 b 2.028240960365167e+31) (< 4.930380657631324e-32 c 2.028240960365167e+31))
  (/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a)))