Average Error: 0.0 → 0.0
Time: 8.7s
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 r174728 = x;
        double r174729 = y;
        double r174730 = r174728 * r174729;
        double r174731 = 1.0;
        double r174732 = r174731 - r174728;
        double r174733 = z;
        double r174734 = r174732 * r174733;
        double r174735 = r174730 + r174734;
        return r174735;
}
↓
double f(double x, double y, double z) {
        double r174736 = x;
        double r174737 = y;
        double r174738 = 1.0;
        double r174739 = r174738 - r174736;
        double r174740 = z;
        double r174741 = r174739 * r174740;
        double r174742 = fma(r174736, r174737, r174741);
        return r174742;
}

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 2019303 +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)))