Average Error: 0.0 → 0.0
Time: 1.3s
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 r205444 = x;
        double r205445 = y;
        double r205446 = r205444 * r205445;
        double r205447 = 1.0;
        double r205448 = r205447 - r205444;
        double r205449 = z;
        double r205450 = r205448 * r205449;
        double r205451 = r205446 + r205450;
        return r205451;
}
↓
double f(double x, double y, double z) {
        double r205452 = x;
        double r205453 = y;
        double r205454 = 1.0;
        double r205455 = r205454 - r205452;
        double r205456 = z;
        double r205457 = r205455 * r205456;
        double r205458 = fma(r205452, r205453, r205457);
        return r205458;
}

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 2020033 +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)))