Average Error: 10.2 → 0.0
Time: 1.1s
Precision: binary64
\[\frac{\left(x - y\right) + n \cdot z}{n}\]
↓
\[z + \frac{x - y}{n}\]
\frac{\left(x - y\right) + n \cdot z}{n}
↓
z + \frac{x - y}{n}
double code(double x, double y, double n, double z) {
	return ((double) (((double) (((double) (x - y)) + ((double) (n * z)))) / n));
}
↓
double code(double x, double y, double n, double z) {
	return ((double) (z + ((double) (((double) (x - y)) / n))));
}

Error

Bits error versus x

Bits error versus y

Bits error versus n

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 10.2

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

  2. Simplified0.0

    \[\leadsto \color{blue}{z + \frac{x - y}{n}}\]

  3. Final simplification0.0

    \[\leadsto z + \frac{x - y}{n}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x y n z)
  :name "(/ (+ (- x y) (* n z)) n)"
  :precision binary64
  (/ (+ (- x y) (* n z)) n))