Average Error: 11.3 → 11.3
Time: 1.2s
Precision: binary64
\[\frac{1}{\left(\left(\left(\left(\left(2 \cdot x\right) \cdot y + \left(2 \cdot x\right) \cdot z\right) + \left(2 \cdot y\right) \cdot z\right) - x \cdot x\right) - y \cdot y\right) - z \cdot z}\]
↓
\[\frac{1}{\left(\left(\left(\left(\left(2 \cdot x\right) \cdot y + \left(2 \cdot x\right) \cdot z\right) + \left(2 \cdot y\right) \cdot z\right) - x \cdot x\right) - y \cdot y\right) - z \cdot z}\]
\frac{1}{\left(\left(\left(\left(\left(2 \cdot x\right) \cdot y + \left(2 \cdot x\right) \cdot z\right) + \left(2 \cdot y\right) \cdot z\right) - x \cdot x\right) - y \cdot y\right) - z \cdot z}
↓
\frac{1}{\left(\left(\left(\left(\left(2 \cdot x\right) \cdot y + \left(2 \cdot x\right) \cdot z\right) + \left(2 \cdot y\right) \cdot z\right) - x \cdot x\right) - y \cdot y\right) - z \cdot z}
double code(double x, double y, double z) {
	return ((double) (1.0 / ((double) (((double) (((double) (((double) (((double) (((double) (((double) (2.0 * x)) * y)) + ((double) (((double) (2.0 * x)) * z)))) + ((double) (((double) (2.0 * y)) * z)))) - ((double) (x * x)))) - ((double) (y * y)))) - ((double) (z * z))))));
}
↓
double code(double x, double y, double z) {
	return ((double) (1.0 / ((double) (((double) (((double) (((double) (((double) (((double) (((double) (2.0 * x)) * y)) + ((double) (((double) (2.0 * x)) * z)))) + ((double) (((double) (2.0 * y)) * z)))) - ((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 11.3

    \[\frac{1}{\left(\left(\left(\left(\left(2 \cdot x\right) \cdot y + \left(2 \cdot x\right) \cdot z\right) + \left(2 \cdot y\right) \cdot z\right) - x \cdot x\right) - y \cdot y\right) - z \cdot z}\]

  2. Final simplification11.3

    \[\leadsto \frac{1}{\left(\left(\left(\left(\left(2 \cdot x\right) \cdot y + \left(2 \cdot x\right) \cdot z\right) + \left(2 \cdot y\right) \cdot z\right) - x \cdot x\right) - y \cdot y\right) - z \cdot z}\]

Reproduce

herbie shell --seed 2020152 
(FPCore (x y z)
  :name "(/ 1 (- (- (- (+ (+ (* (* 2 x) y) (* (* 2 x) z)) (* (* 2 y) z)) (* x x)) (* y y)) (* z z)))"
  :precision binary64
  (/ 1.0 (- (- (- (+ (+ (* (* 2.0 x) y) (* (* 2.0 x) z)) (* (* 2.0 y) z)) (* x x)) (* y y)) (* z z))))