Average Error: 24.9 → 24.9
Time: 696.0ms
Precision: binary64
\[\frac{z}{\sqrt{x \cdot x + z \cdot z}}\]
↓
\[\frac{z}{\sqrt{x \cdot x + z \cdot z}}\]
\frac{z}{\sqrt{x \cdot x + z \cdot z}}
↓
\frac{z}{\sqrt{x \cdot x + z \cdot z}}
double code(double z, double x) {
	return ((double) (z / ((double) sqrt(((double) (((double) (x * x)) + ((double) (z * z))))))));
}
↓
double code(double z, double x) {
	return ((double) (z / ((double) sqrt(((double) (((double) (x * x)) + ((double) (z * z))))))));
}

Error

Bits error versus z

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 24.9

    \[\frac{z}{\sqrt{x \cdot x + z \cdot z}}\]

  2. Final simplification24.9

    \[\leadsto \frac{z}{\sqrt{x \cdot x + z \cdot z}}\]

Reproduce

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