Average Error: 0.0 → 0.0
Time: 8.8s
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 r7276059 = x;
        double r7276060 = y;
        double r7276061 = r7276059 * r7276060;
        double r7276062 = 1.0;
        double r7276063 = r7276062 - r7276059;
        double r7276064 = z;
        double r7276065 = r7276063 * r7276064;
        double r7276066 = r7276061 + r7276065;
        return r7276066;
}
↓
double f(double x, double y, double z) {
        double r7276067 = x;
        double r7276068 = y;
        double r7276069 = 1.0;
        double r7276070 = r7276069 - r7276067;
        double r7276071 = z;
        double r7276072 = r7276070 * r7276071;
        double r7276073 = fma(r7276067, r7276068, r7276072);
        return r7276073;
}

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

    \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, z \cdot \left(1 - x\right)\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(x, y, \left(1 - x\right) \cdot z\right)\]

Reproduce

herbie shell --seed 2019171 +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)))