Average Error: 0.0 → 0.0
Time: 773.0ms
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 r160811 = x;
        double r160812 = y;
        double r160813 = r160812 - r160811;
        double r160814 = z;
        double r160815 = r160813 * r160814;
        double r160816 = r160811 + r160815;
        return r160816;
}
↓
double f(double x, double y, double z) {
        double r160817 = z;
        double r160818 = y;
        double r160819 = x;
        double r160820 = r160818 - r160819;
        double r160821 = fma(r160817, r160820, r160819);
        return r160821;
}

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 2020002 +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)))