Average Error: 0.0 → 0.0
Time: 1.4s
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 r175561 = x;
        double r175562 = y;
        double r175563 = r175561 * r175562;
        double r175564 = 1.0;
        double r175565 = r175564 - r175561;
        double r175566 = z;
        double r175567 = r175565 * r175566;
        double r175568 = r175563 + r175567;
        return r175568;
}
↓
double f(double x, double y, double z) {
        double r175569 = x;
        double r175570 = y;
        double r175571 = 1.0;
        double r175572 = r175571 - r175569;
        double r175573 = z;
        double r175574 = r175572 * r175573;
        double r175575 = fma(r175569, r175570, r175574);
        return r175575;
}

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 2020027 +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)))