Average Error: 0.0 → 0.0
Time: 994.0ms
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 r186991 = x;
        double r186992 = y;
        double r186993 = r186992 - r186991;
        double r186994 = z;
        double r186995 = r186993 * r186994;
        double r186996 = r186991 + r186995;
        return r186996;
}
↓
double f(double x, double y, double z) {
        double r186997 = z;
        double r186998 = y;
        double r186999 = x;
        double r187000 = r186998 - r186999;
        double r187001 = fma(r186997, r187000, r186999);
        return r187001;
}

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 2020081 +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)))