VandenBroeck and Keller, Equation (20)

Average Error: 61.4 → 1.8

Time: 17.1s

Precision: binary64

Math

\[\]

↓

\[\]

Error

Bits error versus f

Derivation

1. Initial program 61.4

   \[\]
2. Using strategy rm

3. Applied sinh-undef 1.8

   \[\leadsto \]

4. Applied add-cube-cbrt 1.9

   \[\leadsto \]

5. Applied times-frac 1.9

   \[\leadsto \]

6. Applied log-prod 2.0

   \[\leadsto \]

7. Applied distribute-lft-in 1.8

   \[\leadsto \]

8. Simplified 1.8

   \[\leadsto \]

9. Simplified 1.8

   \[\leadsto \]

10. Final simplification 1.8

    \[\leadsto \]

Reproduce

herbie shell --seed 2020191 
(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)))))))))