Average Error: 0.0 → 0.0
Time: 8.8s
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 r134698 = x;
        double r134699 = y;
        double r134700 = r134698 * r134699;
        double r134701 = 1.0;
        double r134702 = r134701 - r134698;
        double r134703 = z;
        double r134704 = r134702 * r134703;
        double r134705 = r134700 + r134704;
        return r134705;
}
↓
double f(double x, double y, double z) {
        double r134706 = x;
        double r134707 = y;
        double r134708 = 1.0;
        double r134709 = r134708 - r134706;
        double r134710 = z;
        double r134711 = r134709 * r134710;
        double r134712 = fma(r134706, r134707, r134711);
        return r134712;
}

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 2019304 +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)))