Average Error: 0.1 → 0.1
Time: 21.2s
Precision: 64
\[\left(a - \frac{1.0}{3.0}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1.0}{3.0}\right)}} \cdot rand\right)\]
↓
\[\left(a - \frac{1.0}{3.0}\right) \cdot \frac{rand}{\sqrt{9 \cdot \left(a - \frac{1.0}{3.0}\right)}} + \left(a - \frac{1.0}{3.0}\right)\]
\left(a - \frac{1.0}{3.0}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1.0}{3.0}\right)}} \cdot rand\right)
↓
\left(a - \frac{1.0}{3.0}\right) \cdot \frac{rand}{\sqrt{9 \cdot \left(a - \frac{1.0}{3.0}\right)}} + \left(a - \frac{1.0}{3.0}\right)
double f(double a, double rand) {
        double r2424269 = a;
        double r2424270 = 1.0;
        double r2424271 = 3.0;
        double r2424272 = r2424270 / r2424271;
        double r2424273 = r2424269 - r2424272;
        double r2424274 = 1.0;
        double r2424275 = 9.0;
        double r2424276 = r2424275 * r2424273;
        double r2424277 = sqrt(r2424276);
        double r2424278 = r2424274 / r2424277;
        double r2424279 = rand;
        double r2424280 = r2424278 * r2424279;
        double r2424281 = r2424274 + r2424280;
        double r2424282 = r2424273 * r2424281;
        return r2424282;
}
↓
double f(double a, double rand) {
        double r2424283 = a;
        double r2424284 = 1.0;
        double r2424285 = 3.0;
        double r2424286 = r2424284 / r2424285;
        double r2424287 = r2424283 - r2424286;
        double r2424288 = rand;
        double r2424289 = 9.0;
        double r2424290 = r2424289 * r2424287;
        double r2424291 = sqrt(r2424290);
        double r2424292 = r2424288 / r2424291;
        double r2424293 = r2424287 * r2424292;
        double r2424294 = r2424293 + r2424287;
        return r2424294;
}

Error

Bits error versus a

Bits error versus rand

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[\left(a - \frac{1.0}{3.0}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1.0}{3.0}\right)}} \cdot rand\right)\]

  2. Simplified0.1

    \[\leadsto \color{blue}{\left(a - \frac{1.0}{3.0}\right) \cdot \frac{rand}{\sqrt{9 \cdot \left(a - \frac{1.0}{3.0}\right)}} + \left(a - \frac{1.0}{3.0}\right)}\]

  3. Final simplification0.1

    \[\leadsto \left(a - \frac{1.0}{3.0}\right) \cdot \frac{rand}{\sqrt{9 \cdot \left(a - \frac{1.0}{3.0}\right)}} + \left(a - \frac{1.0}{3.0}\right)\]

Reproduce

herbie shell --seed 2019129 
(FPCore (a rand)
  :name "Octave 3.8, oct_fill_randg"
  (* (- a (/ 1.0 3.0)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand))))