Average Error: 0.0 → 0.0
Time: 9.8s
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 r133440 = x;
        double r133441 = y;
        double r133442 = r133440 * r133441;
        double r133443 = 1.0;
        double r133444 = r133443 - r133440;
        double r133445 = z;
        double r133446 = r133444 * r133445;
        double r133447 = r133442 + r133446;
        return r133447;
}
↓
double f(double x, double y, double z) {
        double r133448 = x;
        double r133449 = y;
        double r133450 = 1.0;
        double r133451 = r133450 - r133448;
        double r133452 = z;
        double r133453 = r133451 * r133452;
        double r133454 = fma(r133448, r133449, r133453);
        return r133454;
}

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 2019323 +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)))