Average Error: 0.0 → 0.0
Time: 10.4s
Precision: 64
\[x + \left(y - x\right) \cdot z\]
↓
\[\mathsf{fma}\left(y - x, z, x\right)\]
x + \left(y - x\right) \cdot z
↓
\mathsf{fma}\left(y - x, z, x\right)
double f(double x, double y, double z) {
        double r10382796 = x;
        double r10382797 = y;
        double r10382798 = r10382797 - r10382796;
        double r10382799 = z;
        double r10382800 = r10382798 * r10382799;
        double r10382801 = r10382796 + r10382800;
        return r10382801;
}
↓
double f(double x, double y, double z) {
        double r10382802 = y;
        double r10382803 = x;
        double r10382804 = r10382802 - r10382803;
        double r10382805 = z;
        double r10382806 = fma(r10382804, r10382805, r10382803);
        return r10382806;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019164 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, B"
  (+ x (* (- y x) z)))