Average Error: 17.9 → 0.0
Time: 2.7s
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 r458941 = x;
        double r458942 = y;
        double r458943 = r458941 * r458942;
        double r458944 = r458942 * r458942;
        double r458945 = r458943 + r458944;
        double r458946 = z;
        double r458947 = r458942 * r458946;
        double r458948 = r458945 - r458947;
        double r458949 = r458948 - r458944;
        return r458949;
}
↓
double f(double x, double y, double z) {
        double r458950 = y;
        double r458951 = x;
        double r458952 = z;
        double r458953 = r458951 - r458952;
        double r458954 = 0.0;
        double r458955 = fma(r458950, r458953, r458954);
        return r458955;
}

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 2020001 +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)))