Average Error: 0.1 → 0.1
Time: 4.3s
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 r248681 = 841.0;
        double r248682 = 108.0;
        double r248683 = r248681 / r248682;
        double r248684 = x;
        double r248685 = r248683 * r248684;
        double r248686 = 4.0;
        double r248687 = 29.0;
        double r248688 = r248686 / r248687;
        double r248689 = r248685 + r248688;
        return r248689;
}
↓
double f(double x) {
        double r248690 = 841.0;
        double r248691 = 108.0;
        double r248692 = r248690 / r248691;
        double r248693 = x;
        double r248694 = 4.0;
        double r248695 = 29.0;
        double r248696 = r248694 / r248695;
        double r248697 = fma(r248692, r248693, r248696);
        return r248697;
}

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 2020020 +o rules:numerics
(FPCore (x)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, A"
  :precision binary64
  (+ (* (/ 841 108) x) (/ 4 29)))