Average Error: 0.0 → 0.0
Time: 6.1s
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 r211782 = x;
        double r211783 = y;
        double r211784 = r211782 * r211783;
        double r211785 = 1.0;
        double r211786 = r211785 - r211782;
        double r211787 = z;
        double r211788 = r211786 * r211787;
        double r211789 = r211784 + r211788;
        return r211789;
}
↓
double f(double x, double y, double z) {
        double r211790 = x;
        double r211791 = y;
        double r211792 = 1.0;
        double r211793 = r211792 - r211790;
        double r211794 = z;
        double r211795 = r211793 * r211794;
        double r211796 = fma(r211790, r211791, r211795);
        return r211796;
}

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 2020045 +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)))