Average Error: 0.0 → 0.0
Time: 10.9s
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 r10590163 = x;
        double r10590164 = y;
        double r10590165 = r10590164 - r10590163;
        double r10590166 = z;
        double r10590167 = r10590165 * r10590166;
        double r10590168 = r10590163 + r10590167;
        return r10590168;
}
↓
double f(double x, double y, double z) {
        double r10590169 = y;
        double r10590170 = x;
        double r10590171 = r10590169 - r10590170;
        double r10590172 = z;
        double r10590173 = fma(r10590171, r10590172, r10590170);
        return r10590173;
}

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 2019163 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, B"
  (+ x (* (- y x) z)))