Average Error: 1.7 → 1.7
Time: 21.9s
Precision: 64
\[\frac{\left(\left(-b_2\right) - \left(\sqrt{\left(\left(b_2 \cdot b_2\right) - \left(a \cdot c\right)\right)}\right)\right)}{a}\]
↓
\[\frac{\left(-b_2\right) - \sqrt{\left(\mathsf{qms}\left(\left(\left(b_2 \cdot b_2\right)\right), a, c\right)\right)}}{a}\]
\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}
↓
\frac{\left(-b_2\right) - \sqrt{\left(\mathsf{qms}\left(\left(\left(b_2 \cdot b_2\right)\right), a, c\right)\right)}}{a}
double f(double a, double b_2, double c) {
        double r1341218 = b_2;
        double r1341219 = -r1341218;
        double r1341220 = r1341218 * r1341218;
        double r1341221 = a;
        double r1341222 = c;
        double r1341223 = r1341221 * r1341222;
        double r1341224 = r1341220 - r1341223;
        double r1341225 = sqrt(r1341224);
        double r1341226 = r1341219 - r1341225;
        double r1341227 = r1341226 / r1341221;
        return r1341227;
}
↓
double f(double a, double b_2, double c) {
        double r1341228 = b_2;
        double r1341229 = -r1341228;
        double r1341230 = r1341228 * r1341228;
        double r1341231 = /*Error: no posit support in C */;
        double r1341232 = a;
        double r1341233 = c;
        double r1341234 = /*Error: no posit support in C */;
        double r1341235 = /*Error: no posit support in C */;
        double r1341236 = sqrt(r1341235);
        double r1341237 = r1341229 - r1341236;
        double r1341238 = r1341237 / r1341232;
        return r1341238;
}

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. Final simplification1.7

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

Reproduce

herbie shell --seed 2019158 +o rules:numerics
(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))