Average Error: 13.1 → 0.0
Time: 25.2s
Precision: 64
\[\left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z\]
↓
\[\mathsf{fma}\left(y, x, y \cdot \left(-z\right)\right)\]
\left(\left(x \cdot y - y \cdot y\right) + y \cdot y\right) - y \cdot z
↓
\mathsf{fma}\left(y, x, y \cdot \left(-z\right)\right)
double f(double x, double y, double z) {
        double r380142 = x;
        double r380143 = y;
        double r380144 = r380142 * r380143;
        double r380145 = r380143 * r380143;
        double r380146 = r380144 - r380145;
        double r380147 = r380146 + r380145;
        double r380148 = z;
        double r380149 = r380143 * r380148;
        double r380150 = r380147 - r380149;
        return r380150;
}
↓
double f(double x, double y, double z) {
        double r380151 = y;
        double r380152 = x;
        double r380153 = z;
        double r380154 = -r380153;
        double r380155 = r380151 * r380154;
        double r380156 = fma(r380151, r380152, r380155);
        return r380156;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original13.1
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 13.1

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

  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-lft-in0.0

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

  7. Applied fma-def0.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2019305 +o rules:numerics
(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)))