Average Error: 37.0 → 37.0
Time: 953.0ms
Precision: binary64
\[\sqrt{\left|\left(\left(1 - x \cdot x\right) - y \cdot y\right) - z \cdot z\right|}\]
↓
\[\sqrt{\left|\left(\left(1 - x \cdot x\right) - y \cdot y\right) - z \cdot z\right|}\]
\sqrt{\left|\left(\left(1 - x \cdot x\right) - y \cdot y\right) - z \cdot z\right|}
↓
\sqrt{\left|\left(\left(1 - x \cdot x\right) - y \cdot y\right) - z \cdot z\right|}
double code(double x, double y, double z) {
	return ((double) sqrt(((double) fabs(((double) (((double) (((double) (1.0 - ((double) (x * x)))) - ((double) (y * y)))) - ((double) (z * z))))))));
}
↓
double code(double x, double y, double z) {
	return ((double) sqrt(((double) fabs(((double) (((double) (((double) (1.0 - ((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 37.0

    \[\sqrt{\left|\left(\left(1 - x \cdot x\right) - y \cdot y\right) - z \cdot z\right|}\]

  2. Final simplification37.0

    \[\leadsto \sqrt{\left|\left(\left(1 - x \cdot x\right) - y \cdot y\right) - z \cdot z\right|}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x y z)
  :name "(sqrt (fabs (- (- (- 1.0 (* x x)) (* y y)) (* z z))))"
  :precision binary64
  (sqrt (fabs (- (- (- 1.0 (* x x)) (* y y)) (* z z)))))