Average Error: 0.0 → 0.0
Time: 14.6s
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 r9745738 = x;
        double r9745739 = y;
        double r9745740 = r9745739 - r9745738;
        double r9745741 = z;
        double r9745742 = r9745740 * r9745741;
        double r9745743 = r9745738 + r9745742;
        return r9745743;
}
↓
double f(double x, double y, double z) {
        double r9745744 = y;
        double r9745745 = x;
        double r9745746 = r9745744 - r9745745;
        double r9745747 = z;
        double r9745748 = fma(r9745746, r9745747, r9745745);
        return r9745748;
}

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)))