Average Error: 1.7 → 1.7
Time: 23.5s
Precision: 64
\[\frac{\left(\left(-b_2\right) - \left(\sqrt{\left(\left(b_2 \cdot b_2\right) - \left(a \cdot c\right)\right)}\right)\right)}{a}\]
↓
\[\frac{\left(\left(-b_2\right) - \left(\sqrt{\left(\left(\mathsf{qms}\left(\left(\left(b_2 \cdot b_2\right)\right), a, c\right)\right)\right)}\right)\right)}{a}\]
\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 r1015018 = b_2;
        double r1015019 = -r1015018;
        double r1015020 = r1015018 * r1015018;
        double r1015021 = a;
        double r1015022 = c;
        double r1015023 = r1015021 * r1015022;
        double r1015024 = r1015020 - r1015023;
        double r1015025 = sqrt(r1015024);
        double r1015026 = r1015019 - r1015025;
        double r1015027 = r1015026 / r1015021;
        return r1015027;
}
↓
double f(double a, double b_2, double c) {
        double r1015028 = b_2;
        double r1015029 = -r1015028;
        double r1015030 = r1015028 * r1015028;
        double r1015031 = /*Error: no posit support in C */;
        double r1015032 = a;
        double r1015033 = c;
        double r1015034 = /*Error: no posit support in C */;
        double r1015035 = /*Error: no posit support in C */;
        double r1015036 = sqrt(r1015035);
        double r1015037 = r1015029 - r1015036;
        double r1015038 = r1015037 / r1015032;
        return r1015038;
}

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 2019168 
(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))