Average Error: 1.7 → 1.7
Time: 23.0s
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 r1031695 = b_2;
        double r1031696 = -r1031695;
        double r1031697 = r1031695 * r1031695;
        double r1031698 = a;
        double r1031699 = c;
        double r1031700 = r1031698 * r1031699;
        double r1031701 = r1031697 - r1031700;
        double r1031702 = sqrt(r1031701);
        double r1031703 = r1031696 - r1031702;
        double r1031704 = r1031703 / r1031698;
        return r1031704;
}
↓
double f(double a, double b_2, double c) {
        double r1031705 = b_2;
        double r1031706 = -r1031705;
        double r1031707 = r1031705 * r1031705;
        double r1031708 = /*Error: no posit support in C */;
        double r1031709 = a;
        double r1031710 = c;
        double r1031711 = /*Error: no posit support in C */;
        double r1031712 = /*Error: no posit support in C */;
        double r1031713 = sqrt(r1031712);
        double r1031714 = r1031706 - r1031713;
        double r1031715 = r1031714 / r1031709;
        return r1031715;
}

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 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))