Average Error: 0.1 → 0.1
Time: 25.4s
Precision: 64
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)\]
↓
\[1 \cdot \left(a - \frac{1}{3}\right) + \left(1 \cdot \left(a - \frac{1}{3}\right)\right) \cdot \frac{rand}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}}\]
\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)
↓
1 \cdot \left(a - \frac{1}{3}\right) + \left(1 \cdot \left(a - \frac{1}{3}\right)\right) \cdot \frac{rand}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}}
double f(double a, double rand) {
        double r4349253 = a;
        double r4349254 = 1.0;
        double r4349255 = 3.0;
        double r4349256 = r4349254 / r4349255;
        double r4349257 = r4349253 - r4349256;
        double r4349258 = 9.0;
        double r4349259 = r4349258 * r4349257;
        double r4349260 = sqrt(r4349259);
        double r4349261 = r4349254 / r4349260;
        double r4349262 = rand;
        double r4349263 = r4349261 * r4349262;
        double r4349264 = r4349254 + r4349263;
        double r4349265 = r4349257 * r4349264;
        return r4349265;
}
↓
double f(double a, double rand) {
        double r4349266 = 1.0;
        double r4349267 = a;
        double r4349268 = 3.0;
        double r4349269 = r4349266 / r4349268;
        double r4349270 = r4349267 - r4349269;
        double r4349271 = r4349266 * r4349270;
        double r4349272 = rand;
        double r4349273 = 9.0;
        double r4349274 = r4349273 * r4349270;
        double r4349275 = sqrt(r4349274);
        double r4349276 = r4349272 / r4349275;
        double r4349277 = r4349271 * r4349276;
        double r4349278 = r4349271 + r4349277;
        return r4349278;
}

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. Using strategy rm

  3. Applied distribute-lft-in0.1

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

  4. Simplified0.1

    \[\leadsto \left(a - \frac{1}{3}\right) \cdot 1 + \color{blue}{\frac{\left(a - \frac{1}{3}\right) \cdot 1}{\sqrt{\left(a - \frac{1}{3}\right) \cdot 9}} \cdot rand}\]
  5. Using strategy rm

  6. Applied div-inv0.1

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

  7. Applied associate-*l*0.1

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

  8. Simplified0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2019172 
(FPCore (a rand)
  :name "Octave 3.8, oct_fill_randg"
  (* (- a (/ 1.0 3.0)) (+ 1.0 (* (/ 1.0 (sqrt (* 9.0 (- a (/ 1.0 3.0))))) rand))))