Average Error: 18.2 → 0.0
Time: 12.7s
Precision: 64
\[\left(\left(x \cdot y + y \cdot y\right) - y \cdot z\right) - y \cdot y\]
↓
\[y \cdot \left(-z\right) + x \cdot y\]
\left(\left(x \cdot y + y \cdot y\right) - y \cdot z\right) - y \cdot y
↓
y \cdot \left(-z\right) + x \cdot y
double f(double x, double y, double z) {
        double r19695896 = x;
        double r19695897 = y;
        double r19695898 = r19695896 * r19695897;
        double r19695899 = r19695897 * r19695897;
        double r19695900 = r19695898 + r19695899;
        double r19695901 = z;
        double r19695902 = r19695897 * r19695901;
        double r19695903 = r19695900 - r19695902;
        double r19695904 = r19695903 - r19695899;
        return r19695904;
}
↓
double f(double x, double y, double z) {
        double r19695905 = y;
        double r19695906 = z;
        double r19695907 = -r19695906;
        double r19695908 = r19695905 * r19695907;
        double r19695909 = x;
        double r19695910 = r19695909 * r19695905;
        double r19695911 = r19695908 + r19695910;
        return r19695911;
}

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

Original18.2
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 18.2

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

  2. Simplified0.0

    \[\leadsto \color{blue}{y \cdot \left(x - z\right)}\]
  3. Using strategy rm

  4. Applied sub-neg0.0

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

  5. Applied distribute-rgt-in0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019179 +o rules:numerics
(FPCore (x y z)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, C"

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

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