Average Error: 0.1 → 0.1
Time: 15.3s
Precision: 64
\[\frac{841}{108} \cdot x + \frac{4}{29}\]
↓
\[\mathsf{fma}\left(\frac{841}{108}, x, \frac{4}{29}\right)\]
\frac{841}{108} \cdot x + \frac{4}{29}
↓
\mathsf{fma}\left(\frac{841}{108}, x, \frac{4}{29}\right)
double f(double x) {
        double r11202237 = 841.0;
        double r11202238 = 108.0;
        double r11202239 = r11202237 / r11202238;
        double r11202240 = x;
        double r11202241 = r11202239 * r11202240;
        double r11202242 = 4.0;
        double r11202243 = 29.0;
        double r11202244 = r11202242 / r11202243;
        double r11202245 = r11202241 + r11202244;
        return r11202245;
}
↓
double f(double x) {
        double r11202246 = 841.0;
        double r11202247 = 108.0;
        double r11202248 = r11202246 / r11202247;
        double r11202249 = x;
        double r11202250 = 4.0;
        double r11202251 = 29.0;
        double r11202252 = r11202250 / r11202251;
        double r11202253 = fma(r11202248, r11202249, r11202252);
        return r11202253;
}

Error

Bits error versus x

Derivation

  1. Initial program 0.1

    \[\frac{841}{108} \cdot x + \frac{4}{29}\]

  2. Simplified0.1

    \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{841}{108}, x, \frac{4}{29}\right)}\]

  3. Final simplification0.1

    \[\leadsto \mathsf{fma}\left(\frac{841}{108}, x, \frac{4}{29}\right)\]

Reproduce

herbie shell --seed 2019172 +o rules:numerics
(FPCore (x)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, A"
  (+ (* (/ 841.0 108.0) x) (/ 4.0 29.0)))