Average Error: 27.0 → 23.4
Time: 1.9s
Precision: binary64
\[\left(\left(\frac{x \cdot \left(n - 3\right)}{n} + \frac{y \cdot \left(n - 2\right)}{n}\right) + \frac{z \cdot \left(n - 1\right)}{n}\right) + \frac{w \cdot n}{n}\]
↓
\[\left(w + \left(\frac{y \cdot \left(n - 2\right)}{n} + \frac{z \cdot \left(n - 1\right)}{n}\right)\right) + \frac{x \cdot \left(n - 3\right)}{n}\]
\left(\left(\frac{x \cdot \left(n - 3\right)}{n} + \frac{y \cdot \left(n - 2\right)}{n}\right) + \frac{z \cdot \left(n - 1\right)}{n}\right) + \frac{w \cdot n}{n}
↓
\left(w + \left(\frac{y \cdot \left(n - 2\right)}{n} + \frac{z \cdot \left(n - 1\right)}{n}\right)\right) + \frac{x \cdot \left(n - 3\right)}{n}
double code(double x, double n, double y, double z, double w) {
	return ((double) (((double) (((double) (((double) (((double) (x * ((double) (n - 3.0)))) / n)) + ((double) (((double) (y * ((double) (n - 2.0)))) / n)))) + ((double) (((double) (z * ((double) (n - 1.0)))) / n)))) + ((double) (((double) (w * n)) / n))));
}
↓
double code(double x, double n, double y, double z, double w) {
	return ((double) (((double) (w + ((double) (((double) (((double) (y * ((double) (n - 2.0)))) / n)) + ((double) (((double) (z * ((double) (n - 1.0)))) / n)))))) + ((double) (((double) (x * ((double) (n - 3.0)))) / n))));
}

Error

Bits error versus x

Bits error versus n

Bits error versus y

Bits error versus z

Bits error versus w

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 27.0

    \[\left(\left(\frac{x \cdot \left(n - 3\right)}{n} + \frac{y \cdot \left(n - 2\right)}{n}\right) + \frac{z \cdot \left(n - 1\right)}{n}\right) + \frac{w \cdot n}{n}\]

  2. Simplified23.4

    \[\leadsto \color{blue}{\left(w + \left(\frac{y \cdot \left(n - 2\right)}{n} + \frac{z \cdot \left(n - 1\right)}{n}\right)\right) + \frac{x \cdot \left(n - 3\right)}{n}}\]

  3. Final simplification23.4

    \[\leadsto \left(w + \left(\frac{y \cdot \left(n - 2\right)}{n} + \frac{z \cdot \left(n - 1\right)}{n}\right)\right) + \frac{x \cdot \left(n - 3\right)}{n}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x n y z w)
  :name "(+ (+ (+ (/ (* x (- n 3)) n) (/ (* y (- n 2)) n)) (/ (* z (- n 1)) n)) (/ (* w n) n))"
  :precision binary64
  (+ (+ (+ (/ (* x (- n 3.0)) n) (/ (* y (- n 2.0)) n)) (/ (* z (- n 1.0)) n)) (/ (* w n) n)))