VandenBroeck and Keller, Equation (20)

Average Error: 61.4 → 1.9

Time: 12.9s

Precision: binary64

Math

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↓

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Error

Bits error versus f

Derivation

1. Initial program 61.4

   \[\]
2. Using strategy rm

3. Applied sinh-undef 2.0

   \[\leadsto \]

4. Applied associate-/r* 2.0

   \[\leadsto \]

5. Simplified 2.0

   \[\leadsto \]
6. Using strategy rm

7. Applied add-cube-cbrt 2.1

   \[\leadsto \]

8. Applied log-prod 2.1

   \[\leadsto \]

9. Applied distribute-lft-in 2.1

   \[\leadsto \]

10. Simplified 2.1

    \[\leadsto \]

11. Simplified 2.1

    \[\leadsto \]
12. Using strategy rm

13. Applied pow1/3 1.9

    \[\leadsto \]

14. Final simplification 1.9

    \[\leadsto \]

Reproduce

herbie shell --seed 2020192 
(FPCore (f)
  :name "VandenBroeck and Keller, Equation (20)"
  :precision binary64
  (neg (* (/ 1.0 (/ PI 4.0)) (log (/ (+ (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))) (- (exp (* (/ PI 4.0) f)) (exp (neg (* (/ PI 4.0) f)))))))))