Average Error: 0.1 → 0.1
Time: 1.8s
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 r211213 = 841.0;
        double r211214 = 108.0;
        double r211215 = r211213 / r211214;
        double r211216 = x;
        double r211217 = r211215 * r211216;
        double r211218 = 4.0;
        double r211219 = 29.0;
        double r211220 = r211218 / r211219;
        double r211221 = r211217 + r211220;
        return r211221;
}
↓
double f(double x) {
        double r211222 = 841.0;
        double r211223 = 108.0;
        double r211224 = r211222 / r211223;
        double r211225 = x;
        double r211226 = 4.0;
        double r211227 = 29.0;
        double r211228 = r211226 / r211227;
        double r211229 = fma(r211224, r211225, r211228);
        return r211229;
}

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 2020024 +o rules:numerics
(FPCore (x)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, A"
  :precision binary64
  (+ (* (/ 841 108) x) (/ 4 29)))