Average Error: 1.7 → 1.7
Time: 23.3s
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 r1113506 = b_2;
        double r1113507 = -r1113506;
        double r1113508 = r1113506 * r1113506;
        double r1113509 = a;
        double r1113510 = c;
        double r1113511 = r1113509 * r1113510;
        double r1113512 = r1113508 - r1113511;
        double r1113513 = sqrt(r1113512);
        double r1113514 = r1113507 - r1113513;
        double r1113515 = r1113514 / r1113509;
        return r1113515;
}
↓
double f(double a, double b_2, double c) {
        double r1113516 = b_2;
        double r1113517 = -r1113516;
        double r1113518 = r1113516 * r1113516;
        double r1113519 = /*Error: no posit support in C */;
        double r1113520 = a;
        double r1113521 = c;
        double r1113522 = /*Error: no posit support in C */;
        double r1113523 = /*Error: no posit support in C */;
        double r1113524 = sqrt(r1113523);
        double r1113525 = r1113517 - r1113524;
        double r1113526 = r1113525 / r1113520;
        return r1113526;
}

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 2019164 
(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))