Average Error: 0.0 → 0.0
Time: 16.2s
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 r152435 = x;
        double r152436 = y;
        double r152437 = r152435 * r152436;
        double r152438 = 1.0;
        double r152439 = r152438 - r152435;
        double r152440 = z;
        double r152441 = r152439 * r152440;
        double r152442 = r152437 + r152441;
        return r152442;
}
↓
double f(double x, double y, double z) {
        double r152443 = x;
        double r152444 = y;
        double r152445 = 1.0;
        double r152446 = r152445 - r152443;
        double r152447 = z;
        double r152448 = r152446 * r152447;
        double r152449 = fma(r152443, r152444, r152448);
        return r152449;
}

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 2019199 +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)))