Average Error: 0.0 → 0.0
Time: 1.8s
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 r199448 = x;
        double r199449 = y;
        double r199450 = r199448 * r199449;
        double r199451 = 1.0;
        double r199452 = r199451 - r199448;
        double r199453 = z;
        double r199454 = r199452 * r199453;
        double r199455 = r199450 + r199454;
        return r199455;
}
↓
double f(double x, double y, double z) {
        double r199456 = x;
        double r199457 = y;
        double r199458 = 1.0;
        double r199459 = r199458 - r199456;
        double r199460 = z;
        double r199461 = r199459 * r199460;
        double r199462 = fma(r199456, r199457, r199461);
        return r199462;
}

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 2019353 +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)))