Average Error: 1.7 → 1.7
Time: 1.9m
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 r2391024 = b_2;
        double r2391025 = -r2391024;
        double r2391026 = r2391024 * r2391024;
        double r2391027 = a;
        double r2391028 = c;
        double r2391029 = r2391027 * r2391028;
        double r2391030 = r2391026 - r2391029;
        double r2391031 = sqrt(r2391030);
        double r2391032 = r2391025 - r2391031;
        double r2391033 = r2391032 / r2391027;
        return r2391033;
}
↓
double f(double a, double b_2, double c) {
        double r2391034 = b_2;
        double r2391035 = -r2391034;
        double r2391036 = r2391034 * r2391034;
        double r2391037 = /*Error: no posit support in C */;
        double r2391038 = a;
        double r2391039 = c;
        double r2391040 = /*Error: no posit support in C */;
        double r2391041 = /*Error: no posit support in C */;
        double r2391042 = sqrt(r2391041);
        double r2391043 = r2391035 - r2391042;
        double r2391044 = r2391043 / r2391038;
        return r2391044;
}

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 2019149 +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))