Octave 3.8, oct_fill_randg

Average Error: 0.2 → 0.2

Time: 45.0s

Precision: 64

Math

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

↓

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

C

double f(double a, double rand) {
        double r3434409 = a;
        double r3434410 = 1.0;
        double r3434411 = /* ERROR: no posit support in C */;
        double r3434412 = 3.0;
        double r3434413 = /* ERROR: no posit support in C */;
        double r3434414 = r3434411 / r3434413;
        double r3434415 = r3434409 - r3434414;
        double r3434416 = 1.0;
        double r3434417 = /* ERROR: no posit support in C */;
        double r3434418 = 9.0;
        double r3434419 = /* ERROR: no posit support in C */;
        double r3434420 = r3434419 * r3434415;
        double r3434421 = sqrt(r3434420);
        double r3434422 = r3434417 / r3434421;
        double r3434423 = rand;
        double r3434424 = r3434422 * r3434423;
        double r3434425 = r3434417 + r3434424;
        double r3434426 = r3434415 * r3434425;
        return r3434426;
}

↓

double f(double a, double rand) {
        double r3434427 = 1.0;
        double r3434428 = /* ERROR: no posit support in C */;
        double r3434429 = a;
        double r3434430 = 1.0;
        double r3434431 = /* ERROR: no posit support in C */;
        double r3434432 = 3.0;
        double r3434433 = /* ERROR: no posit support in C */;
        double r3434434 = r3434431 / r3434433;
        double r3434435 = r3434429 - r3434434;
        double r3434436 = r3434428 * r3434435;
        double r3434437 = rand;
        double r3434438 = r3434428 * r3434437;
        double r3434439 = r3434438 * r3434435;
        double r3434440 = 9.0;
        double r3434441 = /* ERROR: no posit support in C */;
        double r3434442 = r3434441 * r3434435;
        double r3434443 = sqrt(r3434442);
        double r3434444 = r3434439 / r3434443;
        double r3434445 = /*Error: no posit support in C */;
        double r3434446 = /*Error: no posit support in C */;
        double r3434447 = r3434436 + r3434446;
        return r3434447;
}

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. Using strategy rm

3. Applied distribute-rgt-in 0.2

   \[\leadsto \color{blue}{\frac{\left(\left(1\right) \cdot \left(a - \left(\frac{\left(1.0\right)}{\left(3.0\right)}\right)\right)\right)}{\left(\left(\left(\frac{\left(1\right)}{\left(\sqrt{\left(\left(9\right) \cdot \left(a - \left(\frac{\left(1.0\right)}{\left(3.0\right)}\right)\right)\right)}\right)}\right) \cdot rand\right) \cdot \left(a - \left(\frac{\left(1.0\right)}{\left(3.0\right)}\right)\right)\right)}}\]
4. Using strategy rm

5. Applied sub-neg 0.2

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

6. Applied distribute-rgt-in 0.2

   \[\leadsto \frac{\left(\left(1\right) \cdot \left(a - \left(\frac{\left(1.0\right)}{\left(3.0\right)}\right)\right)\right)}{\left(\left(\left(\frac{\left(1\right)}{\left(\sqrt{\color{blue}{\left(\frac{\left(a \cdot \left(9\right)\right)}{\left(\left(-\left(\frac{\left(1.0\right)}{\left(3.0\right)}\right)\right) \cdot \left(9\right)\right)}\right)}}\right)}\right) \cdot rand\right) \cdot \left(a - \left(\frac{\left(1.0\right)}{\left(3.0\right)}\right)\right)\right)}\]
7. Using strategy rm

8. Applied introduce-quire 0.2

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

9. Simplified 0.2

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

10. Final simplification 0.2

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

Reproduce

herbie shell --seed 2019164 +o rules:numerics
(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))))