Average Error: 17.5 → 0.0
Time: 13.0s
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 r381880 = x;
        double r381881 = y;
        double r381882 = r381880 * r381881;
        double r381883 = z;
        double r381884 = r381881 * r381883;
        double r381885 = r381882 - r381884;
        double r381886 = r381881 * r381881;
        double r381887 = r381885 - r381886;
        double r381888 = r381887 + r381886;
        return r381888;
}
↓
double f(double x, double y, double z) {
        double r381889 = y;
        double r381890 = x;
        double r381891 = z;
        double r381892 = r381890 - r381891;
        double r381893 = r381889 * r381892;
        return r381893;
}

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

Original17.5
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 17.5

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

  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 2019209 +o rules:numerics
(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)))