Average Error: 0.0 → 0.0
Time: 4.9s
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 r192971 = x;
        double r192972 = y;
        double r192973 = r192971 * r192972;
        double r192974 = 1.0;
        double r192975 = r192974 - r192971;
        double r192976 = z;
        double r192977 = r192975 * r192976;
        double r192978 = r192973 + r192977;
        return r192978;
}
↓
double f(double x, double y, double z) {
        double r192979 = x;
        double r192980 = y;
        double r192981 = 1.0;
        double r192982 = r192981 - r192979;
        double r192983 = z;
        double r192984 = r192982 * r192983;
        double r192985 = fma(r192979, r192980, r192984);
        return r192985;
}

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 2020047 +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)))