Average Error: 0.0 → 0.0
Time: 2.3s
Precision: 64
\[x + \left(y - x\right) \cdot z\]
↓
\[\mathsf{fma}\left(z, y - x, x\right)\]
x + \left(y - x\right) \cdot z
↓
\mathsf{fma}\left(z, y - x, x\right)
double f(double x, double y, double z) {
        double r188922 = x;
        double r188923 = y;
        double r188924 = r188923 - r188922;
        double r188925 = z;
        double r188926 = r188924 * r188925;
        double r188927 = r188922 + r188926;
        return r188927;
}
↓
double f(double x, double y, double z) {
        double r188928 = z;
        double r188929 = y;
        double r188930 = x;
        double r188931 = r188929 - r188930;
        double r188932 = fma(r188928, r188931, r188930);
        return r188932;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.0

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

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2020065 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, B"
  :precision binary64
  (+ x (* (- y x) z)))