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 r248176 = x;
        double r248177 = y;
        double r248178 = r248176 * r248177;
        double r248179 = 1.0;
        double r248180 = r248179 - r248176;
        double r248181 = z;
        double r248182 = r248180 * r248181;
        double r248183 = r248178 + r248182;
        return r248183;
}
↓
double f(double x, double y, double z) {
        double r248184 = x;
        double r248185 = y;
        double r248186 = 1.0;
        double r248187 = r248186 - r248184;
        double r248188 = z;
        double r248189 = r248187 * r248188;
        double r248190 = fma(r248184, r248185, r248189);
        return r248190;
}

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 2020046 +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)))