Average Error: 0.0 → 0.0
Time: 9.3s
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 r8355056 = x;
        double r8355057 = y;
        double r8355058 = r8355057 - r8355056;
        double r8355059 = z;
        double r8355060 = r8355058 * r8355059;
        double r8355061 = r8355056 + r8355060;
        return r8355061;
}
↓
double f(double x, double y, double z) {
        double r8355062 = y;
        double r8355063 = x;
        double r8355064 = r8355062 - r8355063;
        double r8355065 = z;
        double r8355066 = fma(r8355064, r8355065, r8355063);
        return r8355066;
}

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 2019169 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, B"
  (+ x (* (- y x) z)))