Average Error: 1.7 → 1.7
Time: 22.3s
Precision: 64
\[\frac{\left(\left(-b_2\right) - \left(\sqrt{\left(\left(b_2 \cdot b_2\right) - \left(a \cdot c\right)\right)}\right)\right)}{a}\]
↓
\[\frac{\left(\left(-b_2\right) - \left(\sqrt{\left(\left(\mathsf{qms}\left(\left(\left(b_2 \cdot b_2\right)\right), a, c\right)\right)\right)}\right)\right)}{a}\]
\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(\left(-b_2\right) - \left(\sqrt{\left(\left(\mathsf{qms}\left(\left(\left(b_2 \cdot b_2\right)\right), a, c\right)\right)\right)}\right)\right)}{a}
double f(double a, double b_2, double c) {
        double r1134706 = b_2;
        double r1134707 = -r1134706;
        double r1134708 = r1134706 * r1134706;
        double r1134709 = a;
        double r1134710 = c;
        double r1134711 = r1134709 * r1134710;
        double r1134712 = r1134708 - r1134711;
        double r1134713 = sqrt(r1134712);
        double r1134714 = r1134707 - r1134713;
        double r1134715 = r1134714 / r1134709;
        return r1134715;
}
↓
double f(double a, double b_2, double c) {
        double r1134716 = b_2;
        double r1134717 = -r1134716;
        double r1134718 = r1134716 * r1134716;
        double r1134719 = /*Error: no posit support in C */;
        double r1134720 = a;
        double r1134721 = c;
        double r1134722 = /*Error: no posit support in C */;
        double r1134723 = /*Error: no posit support in C */;
        double r1134724 = sqrt(r1134723);
        double r1134725 = r1134717 - r1134724;
        double r1134726 = r1134725 / r1134720;
        return r1134726;
}

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

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

Reproduce

herbie shell --seed 2019163 +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))