Average Error: 0.2 → 0.2
Time: 6.1s
Precision: binary64
\[\]
↓
\[\]

Error

Bits error versus B

Bits error versus x

Derivation

  1. Initial program 0.2

    \[\]

  2. Taylor expanded around inf 0.2

    \[\leadsto \]

  3. Simplified0.2

    \[\leadsto \]
  4. Using strategy rm

  5. Applied associate-*r/0.2

    \[\leadsto \]

  6. Applied associate-*r/0.2

    \[\leadsto \]

  7. Applied sub-div0.2

    \[\leadsto \]

  8. Simplified0.2

    \[\leadsto \]

  9. Final simplification0.2

    \[\leadsto \]

Reproduce

herbie shell --seed 2020179 
(FPCore (B x)
  :name "VandenBroeck and Keller, Equation (24)"
  :precision binary64
  (+ (neg (* x (/ 1.0 (tan B)))) (/ 1.0 (sin B))))