Average Error: 37.7 → 37.7
Time: 1.3s
Precision: binary64
\[\sqrt{\left(x \cdot x + y \cdot y\right) - z \cdot z}\]
↓
\[\sqrt{\left(x \cdot x + y \cdot y\right) - z \cdot z}\]
\sqrt{\left(x \cdot x + y \cdot y\right) - z \cdot z}
↓
\sqrt{\left(x \cdot x + y \cdot y\right) - z \cdot z}
double code(double x, double y, double z) {
	return ((double) sqrt(((double) (((double) (((double) (x * x)) + ((double) (y * y)))) - ((double) (z * z))))));
}
↓
double code(double x, double y, double z) {
	return ((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 37.7

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

  2. Final simplification37.7

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

Reproduce

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