Average Error: 0.0 → 0.0
Time: 5.6s
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 r137360 = x;
        double r137361 = y;
        double r137362 = r137360 * r137361;
        double r137363 = 1.0;
        double r137364 = r137363 - r137360;
        double r137365 = z;
        double r137366 = r137364 * r137365;
        double r137367 = r137362 + r137366;
        return r137367;
}
↓
double f(double x, double y, double z) {
        double r137368 = x;
        double r137369 = y;
        double r137370 = 1.0;
        double r137371 = r137370 - r137368;
        double r137372 = z;
        double r137373 = r137371 * r137372;
        double r137374 = fma(r137368, r137369, r137373);
        return r137374;
}

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 2019350 +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)))