VandenBroeck and Keller, Equation (23)

Average Error: 13.7 → 10.4

Time: 12.8s

Precision: binary64

Math

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↓

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Error

Bits error versus F

Bits error versus B

Bits error versus x

Derivation

1. Initial program 13.7

   \[\]

2. Simplified 10.5

   \[\leadsto \]
3. Using strategy rm

4. Applied associate-*r/ 10.4

   \[\leadsto \]

5. Final simplification 10.4

   \[\leadsto \]

Reproduce

herbie shell --seed 2020191 
(FPCore (F B x)
  :name "VandenBroeck and Keller, Equation (23)"
  :precision binary64
  (+ (neg (* x (/ 1.0 (tan B)))) (* (/ F (sin B)) (pow (+ (+ (* F F) 2.0) (* 2.0 x)) (neg (/ 1.0 2.0))))))