Average Error: 0.0 → 0.0
Time: 11.7s
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 r9763971 = x;
        double r9763972 = y;
        double r9763973 = r9763971 * r9763972;
        double r9763974 = 1.0;
        double r9763975 = r9763974 - r9763971;
        double r9763976 = z;
        double r9763977 = r9763975 * r9763976;
        double r9763978 = r9763973 + r9763977;
        return r9763978;
}
↓
double f(double x, double y, double z) {
        double r9763979 = 1.0;
        double r9763980 = x;
        double r9763981 = r9763979 - r9763980;
        double r9763982 = z;
        double r9763983 = y;
        double r9763984 = r9763980 * r9763983;
        double r9763985 = fma(r9763981, r9763982, r9763984);
        return r9763985;
}

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 2019163 +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)))