Average Error: 12.6 → 0.0
Time: 16.9s
Precision: 64
\[\left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z\]
↓
\[\left(x - z\right) \cdot y\]
\left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z
↓
\left(x - z\right) \cdot y
double f(double x, double y, double z) {
        double r382929 = x;
        double r382930 = y;
        double r382931 = r382929 * r382930;
        double r382932 = r382930 * r382930;
        double r382933 = r382931 - r382932;
        double r382934 = r382933 + r382932;
        double r382935 = z;
        double r382936 = r382930 * r382935;
        double r382937 = r382934 - r382936;
        return r382937;
}
↓
double f(double x, double y, double z) {
        double r382938 = x;
        double r382939 = z;
        double r382940 = r382938 - r382939;
        double r382941 = y;
        double r382942 = r382940 * r382941;
        return r382942;
}

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

Target

Original12.6
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 12.6

    \[\left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\left(x - z\right) \cdot y}\]

  3. Final simplification0.0

    \[\leadsto \left(x - z\right) \cdot y\]

Reproduce

herbie shell --seed 2019304 
(FPCore (x y z)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, D"
  :precision binary64

  :herbie-target
  (* (- x z) y)

  (- (+ (- (* x y) (* y y)) (* y y)) (* y z)))