Average Error: 27.0 → 27.0
Time: 1.6s
Precision: binary64
\[\frac{\left(\left(x \cdot \left(n - 3\right) + y \cdot \left(n - 2\right)\right) + z \cdot \left(n - 1\right)\right) + w \cdot n}{n}\]
↓
\[\frac{\left(\left(x \cdot \left(n - 3\right) + y \cdot \left(n - 2\right)\right) + z \cdot \left(n - 1\right)\right) + w \cdot n}{n}\]
\frac{\left(\left(x \cdot \left(n - 3\right) + y \cdot \left(n - 2\right)\right) + z \cdot \left(n - 1\right)\right) + w \cdot n}{n}
↓
\frac{\left(\left(x \cdot \left(n - 3\right) + y \cdot \left(n - 2\right)\right) + z \cdot \left(n - 1\right)\right) + w \cdot n}{n}
double code(double x, double n, double y, double z, double w) {
	return ((double) (((double) (((double) (((double) (((double) (x * ((double) (n - 3.0)))) + ((double) (y * ((double) (n - 2.0)))))) + ((double) (z * ((double) (n - 1.0)))))) + ((double) (w * n)))) / n));
}
↓
double code(double x, double n, double y, double z, double w) {
	return ((double) (((double) (((double) (((double) (((double) (x * ((double) (n - 3.0)))) + ((double) (y * ((double) (n - 2.0)))))) + ((double) (z * ((double) (n - 1.0)))))) + ((double) (w * n)))) / 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

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

  2. Final simplification27.0

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

Reproduce

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