Average Error: 1.7 → 1.7
Time: 1.6m
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 r1777068 = b_2;
        double r1777069 = -r1777068;
        double r1777070 = r1777068 * r1777068;
        double r1777071 = a;
        double r1777072 = c;
        double r1777073 = r1777071 * r1777072;
        double r1777074 = r1777070 - r1777073;
        double r1777075 = sqrt(r1777074);
        double r1777076 = r1777069 - r1777075;
        double r1777077 = r1777076 / r1777071;
        return r1777077;
}
↓
double f(double a, double b_2, double c) {
        double r1777078 = b_2;
        double r1777079 = -r1777078;
        double r1777080 = r1777078 * r1777078;
        double r1777081 = /*Error: no posit support in C */;
        double r1777082 = a;
        double r1777083 = c;
        double r1777084 = /*Error: no posit support in C */;
        double r1777085 = /*Error: no posit support in C */;
        double r1777086 = sqrt(r1777085);
        double r1777087 = r1777079 - r1777086;
        double r1777088 = r1777087 / r1777082;
        return r1777088;
}

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 2019142 +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))