Example - 1

Muller's Recurrence is a series that is supposed to converge to the number 5. When running this series with the following code, different implementations of real numbers fail at specific iterations:

108.0 - ((815.0 - 1500.0 / z) / y);


x.push(rec_float(x[number - 1], x[number - 2]));
let mut x: Vec<f64> = vec![4.0, 4.25];(2..turns + 1).for_each(|number| {});x[turns]
fn rec_float(y: f64, z: f64) -> f64 {}fn float_calc(turns: usize) -> f64 {}

The chart below shows values for different data structures in the rust language when Muller's recurrence is executed to 80 iterations. The data structure f64 is a 64 bit float. The data structures IF are fixed representations 128 bits in length that use the first number as the size of the integer and the second size as the size of the fraction (e.g. I16F112 uses 16 bits for the integer and 112 bits for the fraction). The data structure of Ratio comes in three different implementations: i32 uses a ratio of 32 bit signed integers, i64 uses a ratio of 64 bit signed integers and BigInt uses a ratio of signed integer with up to 2^32 digits of base 256. Notice how even with 112 bits of fractions or ratios of 64bit unsigned integers, this math still does not converge to an expected value of 5.

- ((BigRational::from_integer(BigInt::from(815))- BigRational::from_integer(BigInt::from(1500)) / z)/ y)BigRational::from_integer(BigInt::from(108))


x.push(rec_big(x[number - 1].clone(), x[number - 2].clone()));
let mut x: Vec<BigRational> = vec![BigRational::from_float(4.0).unwrap(), BigRational::from_float(4.25).unwrap(),];(2..turns + 1).for_each(|number| {});x[turns].clone()
Use num_rational::BigRational;fn rec_big(y: BigRational, z: BigRational) -> BigRational{}fn big_calc(turns: usize) -> BigRational {}

Example - 2

On February 25, 1991, during the eve of the of an Iraqi invasion of Saudi Arabia, a Scud missile fired from Iraqi positions hit a US Army barracks in Dhahran, Saudi Arabia. It miscalculated time and killed 28 people [REF-1190].

Example - 3

Sleipner A, an offshore drilling platform in the North Sea, was incorrectly constructed with an underestimate of 50% of strength in a critical cluster of buoyancy cells needed for construction. This led to a leak in buoyancy cells during lowering, causing a seismic event of 3.0 on the Richter Scale and about $700M loss [REF-1281].