Average Error: 0.1 → 0.1
Time: 11.0s
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 r7919304 = 841.0;
        double r7919305 = 108.0;
        double r7919306 = r7919304 / r7919305;
        double r7919307 = x;
        double r7919308 = r7919306 * r7919307;
        double r7919309 = 4.0;
        double r7919310 = 29.0;
        double r7919311 = r7919309 / r7919310;
        double r7919312 = r7919308 + r7919311;
        return r7919312;
}
↓
double f(double x) {
        double r7919313 = 841.0;
        double r7919314 = 108.0;
        double r7919315 = r7919313 / r7919314;
        double r7919316 = x;
        double r7919317 = 4.0;
        double r7919318 = 29.0;
        double r7919319 = r7919317 / r7919318;
        double r7919320 = fma(r7919315, r7919316, r7919319);
        return r7919320;
}

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 2019162 +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)))