sqrtOpt

An optimizer for my own square root formula

$$\sqrt(x) \approx \frac{x + (H(x) + \frac{x}{20 + \frac{x}{n}})^{2}}{2(H(x)+\frac{x}{20+\frac{x}{n}})}$$

• Where H is the Harmonic number of x
• Smaller numbers tend to be more accurate with a higher n
• Larger numbers tend to be more accurate with a smaller n
• I have calculated that for numbers 1-1000, 43.993 works generally OK
• 41.905 works well for smaller numbers (1-100)
• desmos

To try yourself, in main

• Change lower for the lowest number to optimize for
• Change upper for the highest number to be optimizing for