Average Error: 17.9 → 0.0
Time: 2.1s
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 r624047 = x;
        double r624048 = y;
        double r624049 = r624047 * r624048;
        double r624050 = r624048 * r624048;
        double r624051 = r624049 + r624050;
        double r624052 = z;
        double r624053 = r624048 * r624052;
        double r624054 = r624051 - r624053;
        double r624055 = r624054 - r624050;
        return r624055;
}
↓
double f(double x, double y, double z) {
        double r624056 = y;
        double r624057 = x;
        double r624058 = z;
        double r624059 = r624057 - r624058;
        double r624060 = 0.0;
        double r624061 = fma(r624056, r624059, r624060);
        return r624061;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original17.9
Target0.0
Herbie0.0
\[\left(x - z\right) \cdot y\]

Derivation

  1. Initial program 17.9

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

  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 2019354 +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)))