Average Error: 0.1 → 0.1
Time: 9.2s
Precision: 64
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)\]
↓
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)\]
\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)
↓
\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)
double f(double a, double rand) {
        double r141305 = a;
        double r141306 = 1.0;
        double r141307 = 3.0;
        double r141308 = r141306 / r141307;
        double r141309 = r141305 - r141308;
        double r141310 = 9.0;
        double r141311 = r141310 * r141309;
        double r141312 = sqrt(r141311);
        double r141313 = r141306 / r141312;
        double r141314 = rand;
        double r141315 = r141313 * r141314;
        double r141316 = r141306 + r141315;
        double r141317 = r141309 * r141316;
        return r141317;
}
↓
double f(double a, double rand) {
        double r141318 = a;
        double r141319 = 1.0;
        double r141320 = 3.0;
        double r141321 = r141319 / r141320;
        double r141322 = r141318 - r141321;
        double r141323 = 9.0;
        double r141324 = r141323 * r141322;
        double r141325 = sqrt(r141324);
        double r141326 = r141319 / r141325;
        double r141327 = rand;
        double r141328 = r141326 * r141327;
        double r141329 = r141319 + r141328;
        double r141330 = r141322 * r141329;
        return r141330;
}

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

    \[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)\]

  2. Final simplification0.1

    \[\leadsto \left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)\]

Reproduce

herbie shell --seed 2020065 
(FPCore (a rand)
  :name "Octave 3.8, oct_fill_randg"
  :precision binary64
  (* (- a (/ 1 3)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1 3))))) rand))))