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

Average Error: 0.1 → 0

Time: 3.2s

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 r213427 = x;
        double r213428 = 3.0;
        double r213429 = 8.0;
        double r213430 = r213428 / r213429;
        double r213431 = y;
        double r213432 = r213430 * r213431;
        double r213433 = r213427 - r213432;
        return r213433;
}

↓

double f(double x, double y) {
        double r213434 = y;
        double r213435 = -r213434;
        double r213436 = 3.0;
        double r213437 = 8.0;
        double r213438 = r213436 / r213437;
        double r213439 = x;
        double r213440 = fma(r213435, r213438, r213439);
        return r213440;
}

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 2019179 +o rules:numerics
(FPCore (x y)
  :name "Diagrams.Solve.Polynomial:quartForm  from diagrams-solve-0.1, A"
  (- x (* (/ 3.0 8.0) y)))