Average Error: 0.3 → 0.3
Time: 3.9s
Precision: binary64
\[\frac{\sqrt{y - 1} - \sqrt{z}}{\sqrt{z}}\]
↓
\[\frac{\sqrt{y - 1}}{\sqrt{z}} + -1\]
\frac{\sqrt{y - 1} - \sqrt{z}}{\sqrt{z}}
↓
\frac{\sqrt{y - 1}}{\sqrt{z}} + -1
double code(double y, double z) {
	return ((double) (((double) (((double) sqrt(((double) (y - 1.0)))) - ((double) sqrt(z)))) / ((double) sqrt(z))));
}
↓
double code(double y, double z) {
	return ((double) (((double) (((double) sqrt(((double) (y - 1.0)))) / ((double) sqrt(z)))) + -1.0));
}

Error

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 0.3

    \[\frac{\sqrt{y - 1} - \sqrt{z}}{\sqrt{z}}\]

  2. Simplified0.3

    \[\leadsto \color{blue}{\frac{\sqrt{y - 1}}{\sqrt{z}} + -1}\]

  3. Final simplification0.3

    \[\leadsto \frac{\sqrt{y - 1}}{\sqrt{z}} + -1\]

Reproduce

herbie shell --seed 2020152 
(FPCore (y z)
  :name "(/ (- (sqrt (- y 1)) (sqrt z)) (sqrt z))"
  :precision binary64
  (/ (- (sqrt (- y 1.0)) (sqrt z)) (sqrt z)))