Average Error: 17.4 → 0.0
Time: 11.3s
Precision: 64
\[\left(\left(x \cdot y + y \cdot y\right) - y \cdot z\right) - y \cdot y\]
↓
\[y \cdot \left(x - z\right)\]
\left(\left(x \cdot y + y \cdot y\right) - y \cdot z\right) - y \cdot y
↓
y \cdot \left(x - z\right)
double f(double x, double y, double z) {
        double r333904 = x;
        double r333905 = y;
        double r333906 = r333904 * r333905;
        double r333907 = r333905 * r333905;
        double r333908 = r333906 + r333907;
        double r333909 = z;
        double r333910 = r333905 * r333909;
        double r333911 = r333908 - r333910;
        double r333912 = r333911 - r333907;
        return r333912;
}
↓
double f(double x, double y, double z) {
        double r333913 = y;
        double r333914 = x;
        double r333915 = z;
        double r333916 = r333914 - r333915;
        double r333917 = r333913 * r333916;
        return r333917;
}

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

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

  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 2019347 +o rules:numerics
(FPCore (x y z)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, C"
  :precision binary64

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

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