Average Error: 0.0 → 0.0
Time: 1.1s
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 r307678 = x;
        double r307679 = y;
        double r307680 = r307678 * r307679;
        double r307681 = 1.0;
        double r307682 = r307681 - r307678;
        double r307683 = z;
        double r307684 = r307682 * r307683;
        double r307685 = r307680 + r307684;
        return r307685;
}
↓
double f(double x, double y, double z) {
        double r307686 = x;
        double r307687 = y;
        double r307688 = 1.0;
        double r307689 = r307688 - r307686;
        double r307690 = z;
        double r307691 = r307689 * r307690;
        double r307692 = fma(r307686, r307687, r307691);
        return r307692;
}

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 2020081 +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)))