Average Error: 5.3 → 5.3
Time: 978.0ms
Precision: binary64
\[\frac{n - 1}{2} + \frac{x \cdot \left(n \cdot n - 1\right)}{12}\]
↓
\[\frac{n - 1}{2} + \frac{x \cdot \left(n \cdot n - 1\right)}{12}\]
\frac{n - 1}{2} + \frac{x \cdot \left(n \cdot n - 1\right)}{12}
↓
\frac{n - 1}{2} + \frac{x \cdot \left(n \cdot n - 1\right)}{12}
double code(double n, double x) {
	return ((double) (((double) (((double) (n - 1.0)) / 2.0)) + ((double) (((double) (x * ((double) (((double) (n * n)) - 1.0)))) / 12.0))));
}
↓
double code(double n, double x) {
	return ((double) (((double) (((double) (n - 1.0)) / 2.0)) + ((double) (((double) (x * ((double) (((double) (n * n)) - 1.0)))) / 12.0))));
}

Error

Bits error versus n

Bits error versus x

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Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 5.3

    \[\frac{n - 1}{2} + \frac{x \cdot \left(n \cdot n - 1\right)}{12}\]

  2. Final simplification5.3

    \[\leadsto \frac{n - 1}{2} + \frac{x \cdot \left(n \cdot n - 1\right)}{12}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (n x)
  :name "(+ (/ (- n 1) 2) (/ (* x (- (* n n) 1)) 12))"
  :precision binary64
  (+ (/ (- n 1.0) 2.0) (/ (* x (- (* n n) 1.0)) 12.0)))