Average Error: 0.1 → 0.1
Time: 3.5s
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 r324374 = 841.0;
        double r324375 = 108.0;
        double r324376 = r324374 / r324375;
        double r324377 = x;
        double r324378 = r324376 * r324377;
        double r324379 = 4.0;
        double r324380 = 29.0;
        double r324381 = r324379 / r324380;
        double r324382 = r324378 + r324381;
        return r324382;
}
↓
double f(double x) {
        double r324383 = 841.0;
        double r324384 = 108.0;
        double r324385 = r324383 / r324384;
        double r324386 = x;
        double r324387 = 4.0;
        double r324388 = 29.0;
        double r324389 = r324387 / r324388;
        double r324390 = fma(r324385, r324386, r324389);
        return r324390;
}

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 2020062 +o rules:numerics
(FPCore (x)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, A"
  :precision binary64
  (+ (* (/ 841 108) x) (/ 4 29)))