Average Error: 0.0 → 0.0
Time: 1.4s
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 r183325 = x;
        double r183326 = y;
        double r183327 = r183326 - r183325;
        double r183328 = z;
        double r183329 = r183327 * r183328;
        double r183330 = r183325 + r183329;
        return r183330;
}
↓
double f(double x, double y, double z) {
        double r183331 = z;
        double r183332 = y;
        double r183333 = x;
        double r183334 = r183332 - r183333;
        double r183335 = fma(r183331, r183334, r183333);
        return r183335;
}

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 2020036 +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)))