Cubic critical, medium range

Average Error: 43.7 → 0.2

Time: 4.0s

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 43.7

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2. Using strategy rm

3. Applied flip-+ 43.7

   \[\leadsto \]

4. Simplified 0.5

   \[\leadsto \]

5. Simplified 0.5

   \[\leadsto \]
6. Using strategy rm

7. Applied clear-num 0.6

   \[\leadsto \]

8. Simplified 0.3

   \[\leadsto \]
9. Using strategy rm

10. Applied div-inv 0.4

    \[\leadsto \]

11. Applied add-sqr-sqrt 0.4

    \[\leadsto \]

12. Applied times-frac 0.4

    \[\leadsto \]

13. Simplified 0.4

    \[\leadsto \]

14. Simplified 0.3

    \[\leadsto \]
15. Using strategy rm

16. Applied associate-*l/ 0.2

    \[\leadsto \]

17. Simplified 0.2

    \[\leadsto \]

18. Final simplification 0.2

    \[\leadsto \]

Reproduce

herbie shell --seed 2020179 
(FPCore (a b c)
  :name "Cubic critical, 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) (* (* 3.0 a) c)))) (* 3.0 a)))