Average Error: 16.7 → 12.6
Time: 1.3m
Precision: 64
Internal Precision: 2944
\[\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right)\]
↓
\[\ell \cdot \pi - \frac{\frac{\tan \left(\ell \cdot \pi\right)}{F}}{F}\]

Error

Bits error versus F

Bits error versus l

Derivation

  1. Initial program 16.7

    \[\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right)\]

  2. Applied simplify16.4

    \[\leadsto \color{blue}{\ell \cdot \pi - \frac{\tan \left(\ell \cdot \pi\right)}{F \cdot F}}\]
  3. Using strategy rm

  4. Applied associate-/r*12.6

    \[\leadsto \ell \cdot \pi - \color{blue}{\frac{\frac{\tan \left(\ell \cdot \pi\right)}{F}}{F}}\]

Runtime

Time bar (total: 1.3m)Debug logProfile

herbie shell --seed '#(1070578969 3140398606 632207097 462683394 1189254563 964980650)' 
(FPCore (F l)
  :name "VandenBroeck and Keller, Equation (6)"
  (- (* PI l) (* (/ 1 (* F F)) (tan (* PI l)))))