Average Error: 31.1 → 31.1
Time: 1.5s
Precision: binary64
\[x - y \cdot \frac{x \cdot y}{y \cdot y + z \cdot z}\]
↓
\[x - y \cdot \frac{x \cdot y}{y \cdot y + z \cdot z}\]
x - y \cdot \frac{x \cdot y}{y \cdot y + z \cdot z}
↓
x - y \cdot \frac{x \cdot y}{y \cdot y + z \cdot z}
double code(double x, double y, double z) {
	return ((double) (x - ((double) (y * ((double) (((double) (x * y)) / ((double) (((double) (y * y)) + ((double) (z * z))))))))));
}
↓
double code(double x, double y, double z) {
	return ((double) (x - ((double) (y * ((double) (((double) (x * y)) / ((double) (((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 31.1

    \[x - y \cdot \frac{x \cdot y}{y \cdot y + z \cdot z}\]

  2. Final simplification31.1

    \[\leadsto x - y \cdot \frac{x \cdot y}{y \cdot y + z \cdot z}\]

Reproduce

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