Diagrams.Solve.Polynomial:quartForm from diagrams-solve-0.1, A

Average Error: 0.1 → 0

Time: 2.2s

Precision: 64

Math

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

↓

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

C

double f(double x, double y) {
        double r214042 = x;
        double r214043 = 3.0;
        double r214044 = 8.0;
        double r214045 = r214043 / r214044;
        double r214046 = y;
        double r214047 = r214045 * r214046;
        double r214048 = r214042 - r214047;
        return r214048;
}

↓

double f(double x, double y) {
        double r214049 = y;
        double r214050 = -r214049;
        double r214051 = 3.0;
        double r214052 = 8.0;
        double r214053 = r214051 / r214052;
        double r214054 = x;
        double r214055 = fma(r214050, r214053, r214054);
        return r214055;
}

Error

Bits error versus x

Bits error versus y

Derivation

1. Initial program 0.1

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

2. Simplified 0

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

3. Final simplification 0

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

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore (x y)
  :name "Diagrams.Solve.Polynomial:quartForm  from diagrams-solve-0.1, A"
  (- x (* (/ 3.0 8.0) y)))