Average Error: 0.0 → 0.0
Time: 9.3s
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 r167547 = x;
        double r167548 = y;
        double r167549 = r167547 * r167548;
        double r167550 = 1.0;
        double r167551 = r167550 - r167547;
        double r167552 = z;
        double r167553 = r167551 * r167552;
        double r167554 = r167549 + r167553;
        return r167554;
}
↓
double f(double x, double y, double z) {
        double r167555 = x;
        double r167556 = y;
        double r167557 = 1.0;
        double r167558 = r167557 - r167555;
        double r167559 = z;
        double r167560 = r167558 * r167559;
        double r167561 = fma(r167555, r167556, r167560);
        return r167561;
}

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 2019179 +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)))