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

# Try it out

Results

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# 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)'