Octave 3.8, oct_fill_randg

Average Error: 0.2 → 0.2

Time: 33.9s

Precision: 64

Math

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

↓

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

C

double f(double a, double rand) {
        double r2951861 = a;
        double r2951862 = 1.0;
        double r2951863 = /* ERROR: no posit support in C */;
        double r2951864 = 3.0;
        double r2951865 = /* ERROR: no posit support in C */;
        double r2951866 = r2951863 / r2951865;
        double r2951867 = r2951861 - r2951866;
        double r2951868 = 1.0;
        double r2951869 = /* ERROR: no posit support in C */;
        double r2951870 = 9.0;
        double r2951871 = /* ERROR: no posit support in C */;
        double r2951872 = r2951871 * r2951867;
        double r2951873 = sqrt(r2951872);
        double r2951874 = r2951869 / r2951873;
        double r2951875 = rand;
        double r2951876 = r2951874 * r2951875;
        double r2951877 = r2951869 + r2951876;
        double r2951878 = r2951867 * r2951877;
        return r2951878;
}

↓

double f(double a, double rand) {
        double r2951879 = a;
        double r2951880 = 1.0;
        double r2951881 = /* ERROR: no posit support in C */;
        double r2951882 = 3.0;
        double r2951883 = /* ERROR: no posit support in C */;
        double r2951884 = r2951881 / r2951883;
        double r2951885 = r2951879 - r2951884;
        double r2951886 = 1.0;
        double r2951887 = /* ERROR: no posit support in C */;
        double r2951888 = rand;
        double r2951889 = r2951888 * r2951887;
        double r2951890 = r2951879 + r2951884;
        double r2951891 = r2951885 / r2951890;
        double r2951892 = r2951884 + r2951879;
        double r2951893 = r2951891 * r2951892;
        double r2951894 = 9.0;
        double r2951895 = /* ERROR: no posit support in C */;
        double r2951896 = r2951893 * r2951895;
        double r2951897 = sqrt(r2951896);
        double r2951898 = r2951889 / r2951897;
        double r2951899 = r2951887 + r2951898;
        double r2951900 = r2951885 * r2951899;
        return r2951900;
}

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 *p16-rgt-identity-expand 0.2

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

4. Applied associate-*l* 0.2

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

5. Simplified 0.2

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

7. Applied p16-flip-- 0.2

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

8. Simplified 0.2

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

10. Applied *p16-rgt-identity-expand 0.2

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

11. Applied p16-times-frac 0.2

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

12. Simplified 0.2

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

13. Final simplification 0.2

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

Reproduce

herbie shell --seed 2019168 
(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))))