Average Error: 12.4 → 0.0
Time: 9.4s
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 r649888 = x;
        double r649889 = y;
        double r649890 = r649888 * r649889;
        double r649891 = r649889 * r649889;
        double r649892 = r649890 - r649891;
        double r649893 = r649892 + r649891;
        double r649894 = z;
        double r649895 = r649889 * r649894;
        double r649896 = r649893 - r649895;
        return r649896;
}
↓
double f(double x, double y, double z) {
        double r649897 = x;
        double r649898 = z;
        double r649899 = r649897 - r649898;
        double r649900 = y;
        double r649901 = r649899 * r649900;
        return r649901;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

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Results

Enter valid numbers for all inputs

Target

Original12.4
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 12.4

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

  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 2020047 
(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)))