Average Error: 0.0 → 0.0
Time: 3.3s
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 r185471 = x;
        double r185472 = y;
        double r185473 = r185471 * r185472;
        double r185474 = 1.0;
        double r185475 = r185474 - r185471;
        double r185476 = z;
        double r185477 = r185475 * r185476;
        double r185478 = r185473 + r185477;
        return r185478;
}
↓
double f(double x, double y, double z) {
        double r185479 = x;
        double r185480 = y;
        double r185481 = 1.0;
        double r185482 = r185481 - r185479;
        double r185483 = z;
        double r185484 = r185482 * r185483;
        double r185485 = fma(r185479, r185480, r185484);
        return r185485;
}

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 2020036 +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)))