Average Error: 0.0 → 0.0
Time: 14.9s
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 r212856 = x;
        double r212857 = y;
        double r212858 = r212856 * r212857;
        double r212859 = 1.0;
        double r212860 = r212859 - r212856;
        double r212861 = z;
        double r212862 = r212860 * r212861;
        double r212863 = r212858 + r212862;
        return r212863;
}
↓
double f(double x, double y, double z) {
        double r212864 = x;
        double r212865 = y;
        double r212866 = 1.0;
        double r212867 = r212866 - r212864;
        double r212868 = z;
        double r212869 = r212867 * r212868;
        double r212870 = fma(r212864, r212865, r212869);
        return r212870;
}

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 2019208 +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)))