Average Error: 23.0 → 23.0
Time: 1.1s
Precision: binary64
\[\frac{\frac{x}{\sqrt{x \cdot x + z \cdot z}} \cdot y}{\sqrt{\left(x \cdot x + y \cdot y\right) + z \cdot z}}\]
↓
\[\frac{\frac{x}{\sqrt{x \cdot x + z \cdot z}} \cdot y}{\sqrt{\left(x \cdot x + y \cdot y\right) + z \cdot z}}\]
\frac{\frac{x}{\sqrt{x \cdot x + z \cdot z}} \cdot y}{\sqrt{\left(x \cdot x + y \cdot y\right) + z \cdot z}}
↓
\frac{\frac{x}{\sqrt{x \cdot x + z \cdot z}} \cdot y}{\sqrt{\left(x \cdot x + y \cdot y\right) + z \cdot z}}
double code(double x, double z, double y) {
	return ((double) (((double) (((double) (x / ((double) sqrt(((double) (((double) (x * x)) + ((double) (z * z)))))))) * y)) / ((double) sqrt(((double) (((double) (((double) (x * x)) + ((double) (y * y)))) + ((double) (z * z))))))));
}
↓
double code(double x, double z, double y) {
	return ((double) (((double) (((double) (x / ((double) sqrt(((double) (((double) (x * x)) + ((double) (z * z)))))))) * y)) / ((double) sqrt(((double) (((double) (((double) (x * x)) + ((double) (y * y)))) + ((double) (z * z))))))));
}

Error

Bits error versus x

Bits error versus z

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 23.0

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

  2. Final simplification23.0

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

Reproduce

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