Average Error: 1.7 → 1.7
Time: 22.1s
Precision: 64
\[\frac{\left(\frac{\left(-b_2\right)}{\left(\sqrt{\left(\left(b_2 \cdot b_2\right) - \left(a \cdot c\right)\right)}\right)}\right)}{a}\]
↓
\[\frac{\sqrt{\left(\mathsf{qms}\left(\left(\left(b_2 \cdot b_2\right)\right), c, a\right)\right)} - b_2}{a}\]
\frac{\left(\frac{\left(-b_2\right)}{\left(\sqrt{\left(\left(b_2 \cdot b_2\right) - \left(a \cdot c\right)\right)}\right)}\right)}{a}
↓
\frac{\sqrt{\left(\mathsf{qms}\left(\left(\left(b_2 \cdot b_2\right)\right), c, a\right)\right)} - b_2}{a}
double f(double a, double b_2, double c) {
        double r306875 = b_2;
        double r306876 = -r306875;
        double r306877 = r306875 * r306875;
        double r306878 = a;
        double r306879 = c;
        double r306880 = r306878 * r306879;
        double r306881 = r306877 - r306880;
        double r306882 = sqrt(r306881);
        double r306883 = r306876 + r306882;
        double r306884 = r306883 / r306878;
        return r306884;
}
↓
double f(double a, double b_2, double c) {
        double r306885 = b_2;
        double r306886 = r306885 * r306885;
        double r306887 = /*Error: no posit support in C */;
        double r306888 = c;
        double r306889 = a;
        double r306890 = /*Error: no posit support in C */;
        double r306891 = /*Error: no posit support in C */;
        double r306892 = sqrt(r306891);
        double r306893 = r306892 - r306885;
        double r306894 = r306893 / r306889;
        return r306894;
}

Error

Bits error versus a

Bits error versus b_2

Bits error versus c

Derivation

  1. Initial program 1.7

    \[\frac{\left(\frac{\left(-b_2\right)}{\left(\sqrt{\left(\left(b_2 \cdot b_2\right) - \left(a \cdot c\right)\right)}\right)}\right)}{a}\]

  2. Simplified1.7

    \[\leadsto \color{blue}{\frac{\left(\left(\sqrt{\left(\left(b_2 \cdot b_2\right) - \left(c \cdot a\right)\right)}\right) - b_2\right)}{a}}\]
  3. Using strategy rm

  4. Applied introduce-quire1.7

    \[\leadsto \frac{\left(\left(\sqrt{\left(\color{blue}{\left(\left(\left(b_2 \cdot b_2\right)\right)\right)} - \left(c \cdot a\right)\right)}\right) - b_2\right)}{a}\]

  5. Applied insert-quire-fdp-sub1.7

    \[\leadsto \frac{\left(\left(\sqrt{\color{blue}{\left(\left(\mathsf{qms}\left(\left(\left(b_2 \cdot b_2\right)\right), c, a\right)\right)\right)}}\right) - b_2\right)}{a}\]

  6. Final simplification1.7

    \[\leadsto \frac{\sqrt{\left(\mathsf{qms}\left(\left(\left(b_2 \cdot b_2\right)\right), c, a\right)\right)} - b_2}{a}\]

Reproduce

herbie shell --seed 2019155 
(FPCore (a b_2 c)
  :name "quad2p (problem 3.2.1, positive)"
  (/.p16 (+.p16 (neg.p16 b_2) (sqrt.p16 (-.p16 (*.p16 b_2 b_2) (*.p16 a c)))) a))