Average Error: 1.7 → 1.7
Time: 23.9s
Precision: 64
\[\frac{\left(\left(-b_2\right) - \left(\sqrt{\left(\left(b_2 \cdot b_2\right) - \left(a \cdot c\right)\right)}\right)\right)}{a}\]
↓
\[\left(\left(\frac{\left(-b_2\right) - \sqrt{\left(\mathsf{qms}\left(\left(\left(b_2 \cdot b_2\right)\right), a, c\right)\right)}}{a}\right)\right)\]
\frac{\left(\left(-b_2\right) - \left(\sqrt{\left(\left(b_2 \cdot b_2\right) - \left(a \cdot c\right)\right)}\right)\right)}{a}
↓
\left(\left(\frac{\left(-b_2\right) - \sqrt{\left(\mathsf{qms}\left(\left(\left(b_2 \cdot b_2\right)\right), a, c\right)\right)}}{a}\right)\right)
double f(double a, double b_2, double c) {
        double r324285 = b_2;
        double r324286 = -r324285;
        double r324287 = r324285 * r324285;
        double r324288 = a;
        double r324289 = c;
        double r324290 = r324288 * r324289;
        double r324291 = r324287 - r324290;
        double r324292 = sqrt(r324291);
        double r324293 = r324286 - r324292;
        double r324294 = r324293 / r324288;
        return r324294;
}
↓
double f(double a, double b_2, double c) {
        double r324295 = b_2;
        double r324296 = -r324295;
        double r324297 = r324295 * r324295;
        double r324298 = /*Error: no posit support in C */;
        double r324299 = a;
        double r324300 = c;
        double r324301 = /*Error: no posit support in C */;
        double r324302 = /*Error: no posit support in C */;
        double r324303 = sqrt(r324302);
        double r324304 = r324296 - r324303;
        double r324305 = r324304 / r324299;
        double r324306 = /*Error: no posit support in C */;
        double r324307 = /*Error: no posit support in C */;
        return r324307;
}

Error

Bits error versus a

Bits error versus b_2

Bits error versus c

Derivation

  1. Initial program 1.7

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

  3. Applied introduce-quire1.7

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

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

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

  6. Applied introduce-quire1.7

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

  7. Final simplification1.7

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

Reproduce

herbie shell --seed 2019155 
(FPCore (a b_2 c)
  :name "quad2m (problem 3.2.1, negative)"
  (/.p16 (-.p16 (neg.p16 b_2) (sqrt.p16 (-.p16 (*.p16 b_2 b_2) (*.p16 a c)))) a))