Average Error: 17.8 → 0.0
Time: 2.2s
Precision: 64
\[\left(\left(x \cdot y + y \cdot y\right) - y \cdot z\right) - y \cdot y\]
↓
\[\mathsf{fma}\left(y, x - z, 0\right)\]
\left(\left(x \cdot y + y \cdot y\right) - y \cdot z\right) - y \cdot y
↓
\mathsf{fma}\left(y, x - z, 0\right)
double f(double x, double y, double z) {
        double r488868 = x;
        double r488869 = y;
        double r488870 = r488868 * r488869;
        double r488871 = r488869 * r488869;
        double r488872 = r488870 + r488871;
        double r488873 = z;
        double r488874 = r488869 * r488873;
        double r488875 = r488872 - r488874;
        double r488876 = r488875 - r488871;
        return r488876;
}
↓
double f(double x, double y, double z) {
        double r488877 = y;
        double r488878 = x;
        double r488879 = z;
        double r488880 = r488878 - r488879;
        double r488881 = 0.0;
        double r488882 = fma(r488877, r488880, r488881);
        return r488882;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original17.8
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 17.8

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

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(y, x - z, 0\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(y, x - z, 0\right)\]

Reproduce

herbie shell --seed 2020018 +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)))