Average Error: 25.9 → 0
Time: 20.0s
Precision: 64
Internal Precision: 3392
\[\left(earth_radius_km \cdot earth_radius_km + \left(earth_radius_km + satellite_height_km\right) \cdot \left(earth_radius_km + satellite_height_km\right)\right) - \left(2 \cdot earth_radius_km\right) \cdot \left(earth_radius_km + satellite_height_km\right)\]
\[{satellite_height_km}^{2}\]

Error

Bits error versus earth_radius_km

Bits error versus satellite_height_km

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 25.9

    \[\left(earth_radius_km \cdot earth_radius_km + \left(earth_radius_km + satellite_height_km\right) \cdot \left(earth_radius_km + satellite_height_km\right)\right) - \left(2 \cdot earth_radius_km\right) \cdot \left(earth_radius_km + satellite_height_km\right)\]
  2. Applied simplify25.8

    \[\leadsto \color{blue}{\left(earth_radius_km + satellite_height_km\right) \cdot \left(\left(earth_radius_km + satellite_height_km\right) - earth_radius_km \cdot 2\right) + earth_radius_km \cdot earth_radius_km}\]
  3. Taylor expanded around 0 0

    \[\leadsto \color{blue}{{satellite_height_km}^{2}}\]

Runtime

Time bar (total: 20.0s)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)' 
(FPCore (earth_radius_km satellite_height_km)
  :name "earth_radius_km * earth_radius_km +              (earth_radius_km + satellite_height_km) *              (earth_radius_km + satellite_height_km) - 2 * earth_radius_km *              (earth_radius_km + satellite_height_km) "
  (- (+ (* earth_radius_km earth_radius_km) (* (+ earth_radius_km satellite_height_km) (+ earth_radius_km satellite_height_km))) (* (* 2 earth_radius_km) (+ earth_radius_km satellite_height_km))))