Average Error: 0.0 → 0.0
Time: 5.6s
Precision: 64
\[x \cdot y + \left(1.0 - x\right) \cdot z\]
↓
\[\mathsf{fma}\left(1.0 - x, z, x \cdot y\right)\]
x \cdot y + \left(1.0 - x\right) \cdot z
↓
\mathsf{fma}\left(1.0 - x, z, x \cdot y\right)
double f(double x, double y, double z) {
        double r4276402 = x;
        double r4276403 = y;
        double r4276404 = r4276402 * r4276403;
        double r4276405 = 1.0;
        double r4276406 = r4276405 - r4276402;
        double r4276407 = z;
        double r4276408 = r4276406 * r4276407;
        double r4276409 = r4276404 + r4276408;
        return r4276409;
}
↓
double f(double x, double y, double z) {
        double r4276410 = 1.0;
        double r4276411 = x;
        double r4276412 = r4276410 - r4276411;
        double r4276413 = z;
        double r4276414 = y;
        double r4276415 = r4276411 * r4276414;
        double r4276416 = fma(r4276412, r4276413, r4276415);
        return r4276416;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.0

    \[x \cdot y + \left(1.0 - x\right) \cdot z\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(1.0 - x, z, y \cdot x\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(1.0 - x, z, x \cdot y\right)\]

Reproduce

herbie shell --seed 2019156 +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)))