Average Error: 0.1 → 0.1
Time: 25.0s
Precision: 64
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)\]
↓
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1 \cdot rand}{\sqrt{9} \cdot \sqrt{a - \frac{1}{3}}}\right)\]
\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)
↓
\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1 \cdot rand}{\sqrt{9} \cdot \sqrt{a - \frac{1}{3}}}\right)
double f(double a, double rand) {
        double r88249 = a;
        double r88250 = 1.0;
        double r88251 = 3.0;
        double r88252 = r88250 / r88251;
        double r88253 = r88249 - r88252;
        double r88254 = 9.0;
        double r88255 = r88254 * r88253;
        double r88256 = sqrt(r88255);
        double r88257 = r88250 / r88256;
        double r88258 = rand;
        double r88259 = r88257 * r88258;
        double r88260 = r88250 + r88259;
        double r88261 = r88253 * r88260;
        return r88261;
}
↓
double f(double a, double rand) {
        double r88262 = a;
        double r88263 = 1.0;
        double r88264 = 3.0;
        double r88265 = r88263 / r88264;
        double r88266 = r88262 - r88265;
        double r88267 = rand;
        double r88268 = r88263 * r88267;
        double r88269 = 9.0;
        double r88270 = sqrt(r88269);
        double r88271 = sqrt(r88266);
        double r88272 = r88270 * r88271;
        double r88273 = r88268 / r88272;
        double r88274 = r88263 + r88273;
        double r88275 = r88266 * r88274;
        return r88275;
}

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 sqrt-prod0.2

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

  4. Applied add-sqr-sqrt0.2

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

  5. Applied times-frac0.2

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

  6. Applied associate-*l*0.2

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

  8. Applied associate-*l/0.2

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

  9. Applied frac-times0.1

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

  10. Simplified0.1

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

  11. Final simplification0.1

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

Reproduce

herbie shell --seed 2019195 
(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))))