Average Error: 61.6 → 2.2
Time: 14.5s
Precision: binary64
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↓
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Error

Bits error versus f

Derivation

  1. Initial program 61.6

    \[\]

  2. Taylor expanded around 0 2.3

    \[\leadsto \]

  3. Simplified2.3

    \[\leadsto \]

  4. Taylor expanded around 0 2.2

    \[\leadsto \]

  5. Simplified2.2

    \[\leadsto \]
  6. Using strategy rm

  7. Applied add-sqr-sqrt2.2

    \[\leadsto \]

  8. Applied pow-unpow2.2

    \[\leadsto \]
  9. Using strategy rm

  10. Applied add-cube-cbrt2.2

    \[\leadsto \]

  11. Applied unpow-prod-down2.2

    \[\leadsto \]

  12. Simplified2.2

    \[\leadsto \]

  13. Final simplification2.2

    \[\leadsto \]

Reproduce

herbie shell --seed 2020181 
(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)))))))))