Average Error: 0.1 → 0.1
Time: 16.3s
Precision: 64
\[\frac{841.0}{108.0} \cdot x + \frac{4.0}{29.0}\]
↓
\[\mathsf{fma}\left(\frac{841.0}{108.0}, x, \frac{4.0}{29.0}\right)\]
\frac{841.0}{108.0} \cdot x + \frac{4.0}{29.0}
↓
\mathsf{fma}\left(\frac{841.0}{108.0}, x, \frac{4.0}{29.0}\right)
double f(double x) {
        double r14345839 = 841.0;
        double r14345840 = 108.0;
        double r14345841 = r14345839 / r14345840;
        double r14345842 = x;
        double r14345843 = r14345841 * r14345842;
        double r14345844 = 4.0;
        double r14345845 = 29.0;
        double r14345846 = r14345844 / r14345845;
        double r14345847 = r14345843 + r14345846;
        return r14345847;
}
↓
double f(double x) {
        double r14345848 = 841.0;
        double r14345849 = 108.0;
        double r14345850 = r14345848 / r14345849;
        double r14345851 = x;
        double r14345852 = 4.0;
        double r14345853 = 29.0;
        double r14345854 = r14345852 / r14345853;
        double r14345855 = fma(r14345850, r14345851, r14345854);
        return r14345855;
}

Error

Bits error versus x

Derivation

  1. Initial program 0.1

    \[\frac{841.0}{108.0} \cdot x + \frac{4.0}{29.0}\]

  2. Simplified0.1

    \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{841.0}{108.0}, x, \frac{4.0}{29.0}\right)}\]

  3. Final simplification0.1

    \[\leadsto \mathsf{fma}\left(\frac{841.0}{108.0}, x, \frac{4.0}{29.0}\right)\]

Reproduce

herbie shell --seed 2019158 +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)))