Average Error: 20.1 → 20.1
Time: 793.0ms
Precision: binary64
\[\frac{x}{\sqrt{x \cdot x + z}}\]
↓
\[\frac{x}{\sqrt{x \cdot x + z}}\]
\frac{x}{\sqrt{x \cdot x + z}}
↓
\frac{x}{\sqrt{x \cdot x + z}}
double code(double x, double z) {
	return ((double) (x / ((double) sqrt(((double) (((double) (x * x)) + z))))));
}
↓
double code(double x, double z) {
	return ((double) (x / ((double) sqrt(((double) (((double) (x * x)) + z))))));
}

Error

Bits error versus x

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 20.1

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

  2. Final simplification20.1

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

Reproduce

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