Average Error: 61.4 → 2.2
Time: 15.0s
Precision: binary64
\[\]
↓
\[\]

Error

Bits error versus f

Derivation

  1. Initial program 61.4

    \[\]

  2. Taylor expanded around 0 2.2

    \[\leadsto \]

  3. Simplified2.3

    \[\leadsto \]
  4. Using strategy rm

  5. Applied add-sqr-sqrt2.5

    \[\leadsto \]

  6. Applied associate-*l*2.2

    \[\leadsto \]

  7. Simplified2.2

    \[\leadsto \]
  8. Using strategy rm

  9. Applied add-cube-cbrt2.2

    \[\leadsto \]

  10. Applied unpow-prod-down2.2

    \[\leadsto \]

  11. Simplified2.2

    \[\leadsto \]
  12. Using strategy rm

  13. Applied add-sqr-sqrt2.2

    \[\leadsto \]

  14. Applied cbrt-prod2.2

    \[\leadsto \]

  15. Applied unpow-prod-down2.2

    \[\leadsto \]

  16. Final simplification2.2

    \[\leadsto \]

Reproduce

herbie shell --seed 2020180 
(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)))))))))