Average Error: 1.7 → 1.7
Time: 23.7s
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 r349129 = b_2;
        double r349130 = -r349129;
        double r349131 = r349129 * r349129;
        double r349132 = a;
        double r349133 = c;
        double r349134 = r349132 * r349133;
        double r349135 = r349131 - r349134;
        double r349136 = sqrt(r349135);
        double r349137 = r349130 - r349136;
        double r349138 = r349137 / r349132;
        return r349138;
}
↓
double f(double a, double b_2, double c) {
        double r349139 = b_2;
        double r349140 = -r349139;
        double r349141 = r349139 * r349139;
        double r349142 = /*Error: no posit support in C */;
        double r349143 = a;
        double r349144 = c;
        double r349145 = /*Error: no posit support in C */;
        double r349146 = /*Error: no posit support in C */;
        double r349147 = sqrt(r349146);
        double r349148 = r349140 - r349147;
        double r349149 = r349148 / r349143;
        return r349149;
}

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 2019154 
(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))