Average Error: 0.0 → 0.0
Time: 1.8s
Precision: 64
\[x \cdot y + \left(1 - x\right) \cdot z\]
↓
\[\mathsf{fma}\left(x, y, \left(1 - x\right) \cdot z\right)\]
x \cdot y + \left(1 - x\right) \cdot z
↓
\mathsf{fma}\left(x, y, \left(1 - x\right) \cdot z\right)
double f(double x, double y, double z) {
        double r243324 = x;
        double r243325 = y;
        double r243326 = r243324 * r243325;
        double r243327 = 1.0;
        double r243328 = r243327 - r243324;
        double r243329 = z;
        double r243330 = r243328 * r243329;
        double r243331 = r243326 + r243330;
        return r243331;
}
↓
double f(double x, double y, double z) {
        double r243332 = x;
        double r243333 = y;
        double r243334 = 1.0;
        double r243335 = r243334 - r243332;
        double r243336 = z;
        double r243337 = r243335 * r243336;
        double r243338 = fma(r243332, r243333, r243337);
        return r243338;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.0

    \[x \cdot y + \left(1 - x\right) \cdot z\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \left(1 - x\right) \cdot z\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(x, y, \left(1 - x\right) \cdot z\right)\]

Reproduce

herbie shell --seed 2019353 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.Backend.Rasterific:$crender from diagrams-rasterific-1.3.1.3"
  :precision binary64
  (+ (* x y) (* (- 1 x) z)))