Average Error: 1.7 → 1.7
Time: 1.8m
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 r1473060 = b_2;
        double r1473061 = -r1473060;
        double r1473062 = r1473060 * r1473060;
        double r1473063 = a;
        double r1473064 = c;
        double r1473065 = r1473063 * r1473064;
        double r1473066 = r1473062 - r1473065;
        double r1473067 = sqrt(r1473066);
        double r1473068 = r1473061 - r1473067;
        double r1473069 = r1473068 / r1473063;
        return r1473069;
}
↓
double f(double a, double b_2, double c) {
        double r1473070 = b_2;
        double r1473071 = -r1473070;
        double r1473072 = r1473070 * r1473070;
        double r1473073 = /*Error: no posit support in C */;
        double r1473074 = a;
        double r1473075 = c;
        double r1473076 = /*Error: no posit support in C */;
        double r1473077 = /*Error: no posit support in C */;
        double r1473078 = sqrt(r1473077);
        double r1473079 = r1473071 - r1473078;
        double r1473080 = r1473079 / r1473074;
        return r1473080;
}

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 2019151 +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))