Average Error: 15.8 → 15.8
Time: 2.3s
Precision: binary64
\[\sqrt{x \cdot y - z \cdot z} - z\]
↓
\[\sqrt{x \cdot y - z \cdot z} - z\]
\sqrt{x \cdot y - z \cdot z} - z
↓
\sqrt{x \cdot y - z \cdot z} - z
double code(double x, double y, double z) {
	return ((double) (((double) sqrt(((double) (((double) (x * y)) - ((double) (z * z)))))) - z));
}
↓
double code(double x, double y, double z) {
	return ((double) (((double) sqrt(((double) (((double) (x * y)) - ((double) (z * 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 15.8

    \[\sqrt{x \cdot y - z \cdot z} - z\]

  2. Final simplification15.8

    \[\leadsto \sqrt{x \cdot y - z \cdot z} - z\]

Reproduce

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