Average Error: 1.7 → 1.7
Time: 1.3m
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 r1604182 = b_2;
        double r1604183 = -r1604182;
        double r1604184 = r1604182 * r1604182;
        double r1604185 = a;
        double r1604186 = c;
        double r1604187 = r1604185 * r1604186;
        double r1604188 = r1604184 - r1604187;
        double r1604189 = sqrt(r1604188);
        double r1604190 = r1604183 - r1604189;
        double r1604191 = r1604190 / r1604185;
        return r1604191;
}
↓
double f(double a, double b_2, double c) {
        double r1604192 = b_2;
        double r1604193 = -r1604192;
        double r1604194 = r1604192 * r1604192;
        double r1604195 = /*Error: no posit support in C */;
        double r1604196 = a;
        double r1604197 = c;
        double r1604198 = /*Error: no posit support in C */;
        double r1604199 = /*Error: no posit support in C */;
        double r1604200 = sqrt(r1604199);
        double r1604201 = r1604193 - r1604200;
        double r1604202 = r1604201 / r1604196;
        return r1604202;
}

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 2019152 +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))