Average Error: 17.4 → 0.0
Time: 1.7s
Precision: 64
\[\left(\left(x \cdot y - y \cdot z\right) - y \cdot y\right) + y \cdot y\]
↓
\[y \cdot \left(x - z\right)\]
\left(\left(x \cdot y - y \cdot z\right) - y \cdot y\right) + y \cdot y
↓
y \cdot \left(x - z\right)
double f(double x, double y, double z) {
        double r496843 = x;
        double r496844 = y;
        double r496845 = r496843 * r496844;
        double r496846 = z;
        double r496847 = r496844 * r496846;
        double r496848 = r496845 - r496847;
        double r496849 = r496844 * r496844;
        double r496850 = r496848 - r496849;
        double r496851 = r496850 + r496849;
        return r496851;
}
↓
double f(double x, double y, double z) {
        double r496852 = y;
        double r496853 = x;
        double r496854 = z;
        double r496855 = r496853 - r496854;
        double r496856 = r496852 * r496855;
        return r496856;
}

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

Original17.4
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 17.4

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

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2020081 
(FPCore (x y z)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, B"
  :precision binary64

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

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