Average Error: 0.2 → 0.2
Time: 57.2s
Precision: 64
\[\left(a - \left(\frac{\left(1.0\right)}{\left(3.0\right)}\right)\right) \cdot \left(\frac{\left(1\right)}{\left(\left(\frac{\left(1\right)}{\left(\sqrt{\left(\left(9\right) \cdot \left(a - \left(\frac{\left(1.0\right)}{\left(3.0\right)}\right)\right)\right)}\right)}\right) \cdot rand\right)}\right)\]
↓
\[\left(a - \frac{1.0}{3.0}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1.0}{3.0}\right)}} \cdot rand\right)\]
\left(a - \left(\frac{\left(1.0\right)}{\left(3.0\right)}\right)\right) \cdot \left(\frac{\left(1\right)}{\left(\left(\frac{\left(1\right)}{\left(\sqrt{\left(\left(9\right) \cdot \left(a - \left(\frac{\left(1.0\right)}{\left(3.0\right)}\right)\right)\right)}\right)}\right) \cdot rand\right)}\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)
double f(double a, double rand) {
        double r4617350 = a;
        double r4617351 = 1.0;
        double r4617352 = /* ERROR: no posit support in C */;
        double r4617353 = 3.0;
        double r4617354 = /* ERROR: no posit support in C */;
        double r4617355 = r4617352 / r4617354;
        double r4617356 = r4617350 - r4617355;
        double r4617357 = 1.0;
        double r4617358 = /* ERROR: no posit support in C */;
        double r4617359 = 9.0;
        double r4617360 = /* ERROR: no posit support in C */;
        double r4617361 = r4617360 * r4617356;
        double r4617362 = sqrt(r4617361);
        double r4617363 = r4617358 / r4617362;
        double r4617364 = rand;
        double r4617365 = r4617363 * r4617364;
        double r4617366 = r4617358 + r4617365;
        double r4617367 = r4617356 * r4617366;
        return r4617367;
}
↓
double f(double a, double rand) {
        double r4617368 = a;
        double r4617369 = 1.0;
        double r4617370 = 3.0;
        double r4617371 = r4617369 / r4617370;
        double r4617372 = r4617368 - r4617371;
        double r4617373 = 1.0;
        double r4617374 = 9.0;
        double r4617375 = r4617374 * r4617372;
        double r4617376 = sqrt(r4617375);
        double r4617377 = r4617373 / r4617376;
        double r4617378 = rand;
        double r4617379 = r4617377 * r4617378;
        double r4617380 = r4617373 + r4617379;
        double r4617381 = r4617372 * r4617380;
        return r4617381;
}

Error

Bits error versus a

Bits error versus rand

Derivation

  1. Initial program 0.2

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

  2. Final simplification0.2

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

Reproduce

herbie shell --seed 2019135 
(FPCore (a rand)
  :name "Octave 3.8, oct_fill_randg"
  (*.p16 (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0))) (+.p16 (real->posit16 1) (*.p16 (/.p16 (real->posit16 1) (sqrt.p16 (*.p16 (real->posit16 9) (-.p16 a (/.p16 (real->posit16 1.0) (real->posit16 3.0)))))) rand))))