Average Error: 0.0 → 0.0
Time: 4.8s
Precision: 64
\[x \cdot y + \left(1.0 - x\right) \cdot z\]
↓
\[\mathsf{fma}\left(1.0 - x, z, x \cdot y\right)\]
x \cdot y + \left(1.0 - x\right) \cdot z
↓
\mathsf{fma}\left(1.0 - x, z, x \cdot y\right)
double f(double x, double y, double z) {
        double r10038878 = x;
        double r10038879 = y;
        double r10038880 = r10038878 * r10038879;
        double r10038881 = 1.0;
        double r10038882 = r10038881 - r10038878;
        double r10038883 = z;
        double r10038884 = r10038882 * r10038883;
        double r10038885 = r10038880 + r10038884;
        return r10038885;
}
↓
double f(double x, double y, double z) {
        double r10038886 = 1.0;
        double r10038887 = x;
        double r10038888 = r10038886 - r10038887;
        double r10038889 = z;
        double r10038890 = y;
        double r10038891 = r10038887 * r10038890;
        double r10038892 = fma(r10038888, r10038889, r10038891);
        return r10038892;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.0

    \[x \cdot y + \left(1.0 - x\right) \cdot z\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(1.0 - x, z, y \cdot x\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(1.0 - x, z, x \cdot y\right)\]

Reproduce

herbie shell --seed 2019162 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.Backend.Rasterific:$crender from diagrams-rasterific-1.3.1.3"
  (+ (* x y) (* (- 1.0 x) z)))