Average Error: 26.9 → 26.9
Time: 940.0ms
Precision: binary64
\[\frac{x}{\sqrt{\left(x \cdot x + y \cdot y\right) + z \cdot z}}\]
↓
\[\frac{x}{\sqrt{\left(x \cdot x + y \cdot y\right) + z \cdot z}}\]
\frac{x}{\sqrt{\left(x \cdot x + y \cdot y\right) + z \cdot z}}
↓
\frac{x}{\sqrt{\left(x \cdot x + y \cdot y\right) + z \cdot z}}
double code(double x, double y, double z) {
	return ((double) (x / ((double) sqrt(((double) (((double) (((double) (x * x)) + ((double) (y * y)))) + ((double) (z * z))))))));
}
↓
double code(double x, double y, double z) {
	return ((double) (x / ((double) sqrt(((double) (((double) (((double) (x * x)) + ((double) (y * y)))) + ((double) (z * z))))))));
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 26.9

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

  2. Final simplification26.9

    \[\leadsto \frac{x}{\sqrt{\left(x \cdot x + y \cdot y\right) + z \cdot z}}\]

Reproduce

herbie shell --seed 2020152 
(FPCore (x y z)
  :name "(/ x (sqrt (+ (+ (* x x) (* y y)) (* z z))))"
  :precision binary64
  (/ x (sqrt (+ (+ (* x x) (* y y)) (* z z)))))