Average Error: 12.3 → 0.0
Time: 14.3s
Precision: 64
\[\left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z\]
↓
\[x \cdot y - z \cdot y\]
\left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z
↓
x \cdot y - z \cdot y
double f(double x, double y, double z) {
        double r22037861 = x;
        double r22037862 = y;
        double r22037863 = r22037861 * r22037862;
        double r22037864 = r22037862 * r22037862;
        double r22037865 = r22037863 - r22037864;
        double r22037866 = r22037865 + r22037864;
        double r22037867 = z;
        double r22037868 = r22037862 * r22037867;
        double r22037869 = r22037866 - r22037868;
        return r22037869;
}
↓
double f(double x, double y, double z) {
        double r22037870 = x;
        double r22037871 = y;
        double r22037872 = r22037870 * r22037871;
        double r22037873 = z;
        double r22037874 = r22037873 * r22037871;
        double r22037875 = r22037872 - r22037874;
        return r22037875;
}

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

Original12.3
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 12.3

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

  2. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{x \cdot y} - y \cdot z\]

  3. Final simplification0.0

    \[\leadsto x \cdot y - z \cdot y\]

Reproduce

herbie shell --seed 2019164 +o rules:numerics
(FPCore (x y z)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, D"

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

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