Quadratic roots, narrow range

Average Error: 28.7 → 0.3

Time: 4.2s

Precision: binary64

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Math

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↓

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Error

Bits error versus a

Bits error versus b

Bits error versus c

Derivation

1. Initial program 28.7

   \[\]
2. Using strategy rm

3. Applied flip-+ 28.7

   \[\leadsto \]

4. Simplified 0.4

   \[\leadsto \]

5. Simplified 0.4

   \[\leadsto \]
6. Using strategy rm

7. Applied *-un-lft-identity 0.4

   \[\leadsto \]

8. Applied times-frac 0.4

   \[\leadsto \]

9. Applied times-frac 0.4

   \[\leadsto \]

10. Simplified 0.4

    \[\leadsto \]

11. Simplified 0.3

    \[\leadsto \]
12. Using strategy rm

13. Applied add-cbrt-cube 0.3

    \[\leadsto \]

14. Simplified 0.3

    \[\leadsto \]

15. Final simplification 0.3

    \[\leadsto \]

Reproduce

herbie shell --seed 2020181 
(FPCore (a b c)
  :name "Quadratic roots, 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) (* (* 4.0 a) c)))) (* 2.0 a)))