Average Error: 0.0 → 0.0
Time: 838.0ms
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 r206603 = x;
        double r206604 = y;
        double r206605 = r206604 - r206603;
        double r206606 = z;
        double r206607 = r206605 * r206606;
        double r206608 = r206603 + r206607;
        return r206608;
}
↓
double f(double x, double y, double z) {
        double r206609 = z;
        double r206610 = y;
        double r206611 = x;
        double r206612 = r206610 - r206611;
        double r206613 = fma(r206609, r206612, r206611);
        return r206613;
}

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 2020021 +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)))