Average Error: 0.1 → 0.2
Time: 24.6s
Precision: 64
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)\]
↓
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \left(\frac{\sqrt{1}}{\sqrt{9}} \cdot \frac{\sqrt{1}}{\sqrt{a - \frac{1}{3}}}\right) \cdot rand\right)\]
\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 + \left(\frac{\sqrt{1}}{\sqrt{9}} \cdot \frac{\sqrt{1}}{\sqrt{a - \frac{1}{3}}}\right) \cdot rand\right)
double f(double a, double rand) {
        double r80278 = a;
        double r80279 = 1.0;
        double r80280 = 3.0;
        double r80281 = r80279 / r80280;
        double r80282 = r80278 - r80281;
        double r80283 = 9.0;
        double r80284 = r80283 * r80282;
        double r80285 = sqrt(r80284);
        double r80286 = r80279 / r80285;
        double r80287 = rand;
        double r80288 = r80286 * r80287;
        double r80289 = r80279 + r80288;
        double r80290 = r80282 * r80289;
        return r80290;
}
↓
double f(double a, double rand) {
        double r80291 = a;
        double r80292 = 1.0;
        double r80293 = 3.0;
        double r80294 = r80292 / r80293;
        double r80295 = r80291 - r80294;
        double r80296 = sqrt(r80292);
        double r80297 = 9.0;
        double r80298 = sqrt(r80297);
        double r80299 = r80296 / r80298;
        double r80300 = sqrt(r80295);
        double r80301 = r80296 / r80300;
        double r80302 = r80299 * r80301;
        double r80303 = rand;
        double r80304 = r80302 * r80303;
        double r80305 = r80292 + r80304;
        double r80306 = r80295 * r80305;
        return r80306;
}

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. Using strategy rm

  5. Applied sqrt-prod0.1

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

  6. Applied add-sqr-sqrt0.1

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

  7. Applied times-frac0.2

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

  8. Final simplification0.2

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

Reproduce

herbie shell --seed 2019291 
(FPCore (a rand)
  :name "Octave 3.8, oct_fill_randg"
  :precision binary64
  (* (- a (/ 1 3)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1 3))))) rand))))