Average Error: 1.7 → 1.7
Time: 28.8s
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 r343941 = b_2;
        double r343942 = -r343941;
        double r343943 = r343941 * r343941;
        double r343944 = a;
        double r343945 = c;
        double r343946 = r343944 * r343945;
        double r343947 = r343943 - r343946;
        double r343948 = sqrt(r343947);
        double r343949 = r343942 - r343948;
        double r343950 = r343949 / r343944;
        return r343950;
}
↓
double f(double a, double b_2, double c) {
        double r343951 = b_2;
        double r343952 = -r343951;
        double r343953 = r343951 * r343951;
        double r343954 = /*Error: no posit support in C */;
        double r343955 = a;
        double r343956 = c;
        double r343957 = /*Error: no posit support in C */;
        double r343958 = /*Error: no posit support in C */;
        double r343959 = sqrt(r343958);
        double r343960 = r343952 - r343959;
        double r343961 = r343960 / r343955;
        return r343961;
}

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 2019152 
(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))