Numeric error propagation

Numeric error propagation is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

If f, a, and b are values with uncertainties σ_f, σ_a, and σ_b. and c is a constant; then if f is derived from a, b, and c in the following ways, then σ_f can be calculated as follows:

Addition/Subtraction

• If f = a ± c, or f = c ± a then σ_f = σ_a
• If f = a ± b then σ_f² = σ_a² + σ_b²

Multiplication/Division

• If f = ca or f = ac then σ_f = cσ_a
• If f = ab or f = a / b then σ_f² = f²( (σ_a / a)² + (σ_b / b)²)

Exponentiation

• If f = a^c then σ_f = fc(σ_a / a)

Task details

1. Add an uncertain number type to your language that can support addition, subtraction, multiplication, division, and exponentiation between numbers with an associated error term together with 'normal' floating point numbers without an associated error term.
   Implement enough functionality to perform the following calculations.
2. Given coordinates and their errors:

x1 = 100 ± 1.1

x2 = 200 ± 2.2

y1 = 50 ± 1.2

y2 = 100 ± 2.3

1. if point p1 is located (x1, y1) and p2 is at (x2, y2); calculate the distance between the two points using the formula
   d = √((x1 - x2)² + (y1 - y2)²)
2. Print and display both d and its error.

References

• A Guide to Error Propagation B. Keeney, 2005.
• Propagation of uncertainty Wikipedia.