Average Error: 1.7 → 1.7
Time: 22.5s
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 r1321506 = b_2;
        double r1321507 = -r1321506;
        double r1321508 = r1321506 * r1321506;
        double r1321509 = a;
        double r1321510 = c;
        double r1321511 = r1321509 * r1321510;
        double r1321512 = r1321508 - r1321511;
        double r1321513 = sqrt(r1321512);
        double r1321514 = r1321507 - r1321513;
        double r1321515 = r1321514 / r1321509;
        return r1321515;
}
↓
double f(double a, double b_2, double c) {
        double r1321516 = b_2;
        double r1321517 = -r1321516;
        double r1321518 = r1321516 * r1321516;
        double r1321519 = /*Error: no posit support in C */;
        double r1321520 = a;
        double r1321521 = c;
        double r1321522 = /*Error: no posit support in C */;
        double r1321523 = /*Error: no posit support in C */;
        double r1321524 = sqrt(r1321523);
        double r1321525 = r1321517 - r1321524;
        double r1321526 = r1321525 / r1321520;
        return r1321526;
}

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 2019158 
(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))