Average Error: 0.1 → 0
Time: 2.9s
Precision: 64
\[x - \frac{3}{8} \cdot y\]
↓
\[\mathsf{fma}\left(-y, \frac{3}{8}, x\right)\]
x - \frac{3}{8} \cdot y
↓
\mathsf{fma}\left(-y, \frac{3}{8}, x\right)
double f(double x, double y) {
        double r143328 = x;
        double r143329 = 3.0;
        double r143330 = 8.0;
        double r143331 = r143329 / r143330;
        double r143332 = y;
        double r143333 = r143331 * r143332;
        double r143334 = r143328 - r143333;
        return r143334;
}
↓
double f(double x, double y) {
        double r143335 = y;
        double r143336 = -r143335;
        double r143337 = 3.0;
        double r143338 = 8.0;
        double r143339 = r143337 / r143338;
        double r143340 = x;
        double r143341 = fma(r143336, r143339, r143340);
        return r143341;
}

Error

Bits error versus x

Bits error versus y

Derivation

  1. Initial program 0.1

    \[x - \frac{3}{8} \cdot y\]

  2. Simplified0

    \[\leadsto \color{blue}{\mathsf{fma}\left(-y, \frac{3}{8}, x\right)}\]

  3. Final simplification0

    \[\leadsto \mathsf{fma}\left(-y, \frac{3}{8}, x\right)\]

Reproduce

herbie shell --seed 2019194 +o rules:numerics
(FPCore (x y)
  :name "Diagrams.Solve.Polynomial:quartForm  from diagrams-solve-0.1, A"
  (- x (* (/ 3.0 8.0) y)))