Average Error: 0.0 → 0.0
Time: 9.4s
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 r9704499 = x;
        double r9704500 = y;
        double r9704501 = r9704499 * r9704500;
        double r9704502 = 1.0;
        double r9704503 = r9704502 - r9704499;
        double r9704504 = z;
        double r9704505 = r9704503 * r9704504;
        double r9704506 = r9704501 + r9704505;
        return r9704506;
}
↓
double f(double x, double y, double z) {
        double r9704507 = x;
        double r9704508 = y;
        double r9704509 = 1.0;
        double r9704510 = r9704509 - r9704507;
        double r9704511 = z;
        double r9704512 = r9704510 * r9704511;
        double r9704513 = fma(r9704507, r9704508, r9704512);
        return r9704513;
}

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 2019192 +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)))