Average Error: 25.4 → 25.4
Time: 817.0ms
Precision: binary64
\[\frac{x}{\sqrt{x \cdot x + y \cdot y}}\]
↓
\[\frac{x}{\sqrt{x \cdot x + y \cdot y}}\]
\frac{x}{\sqrt{x \cdot x + y \cdot y}}
↓
\frac{x}{\sqrt{x \cdot x + y \cdot y}}
double code(double x, double y) {
	return ((double) (x / ((double) sqrt(((double) (((double) (x * x)) + ((double) (y * y))))))));
}
↓
double code(double x, double y) {
	return ((double) (x / ((double) sqrt(((double) (((double) (x * x)) + ((double) (y * y))))))));
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 25.4

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

  2. Final simplification25.4

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

Reproduce

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