Average Error: 0.1 → 0
Time: 3.3s
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 r142981 = x;
        double r142982 = 3.0;
        double r142983 = 8.0;
        double r142984 = r142982 / r142983;
        double r142985 = y;
        double r142986 = r142984 * r142985;
        double r142987 = r142981 - r142986;
        return r142987;
}
↓
double f(double x, double y) {
        double r142988 = y;
        double r142989 = -r142988;
        double r142990 = 3.0;
        double r142991 = 8.0;
        double r142992 = r142990 / r142991;
        double r142993 = x;
        double r142994 = fma(r142989, r142992, r142993);
        return r142994;
}

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 2019196 +o rules:numerics
(FPCore (x y)
  :name "Diagrams.Solve.Polynomial:quartForm  from diagrams-solve-0.1, A"
  (- x (* (/ 3.0 8.0) y)))