Average Error: 1.7 → 1.7
Time: 22.5s
Precision: 64
\[\frac{\left(\frac{\left(-b_2\right)}{\left(\sqrt{\left(\left(b_2 \cdot b_2\right) - \left(a \cdot c\right)\right)}\right)}\right)}{a}\]
↓
\[\frac{\left(\left(\sqrt{\left(\left(\mathsf{qms}\left(\left(\left(b_2 \cdot b_2\right)\right), c, a\right)\right)\right)}\right) - b_2\right)}{a}\]
\frac{\left(\frac{\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(\sqrt{\left(\left(\mathsf{qms}\left(\left(\left(b_2 \cdot b_2\right)\right), c, a\right)\right)\right)}\right) - b_2\right)}{a}
double f(double a, double b_2, double c) {
        double r833703 = b_2;
        double r833704 = -r833703;
        double r833705 = r833703 * r833703;
        double r833706 = a;
        double r833707 = c;
        double r833708 = r833706 * r833707;
        double r833709 = r833705 - r833708;
        double r833710 = sqrt(r833709);
        double r833711 = r833704 + r833710;
        double r833712 = r833711 / r833706;
        return r833712;
}
↓
double f(double a, double b_2, double c) {
        double r833713 = b_2;
        double r833714 = r833713 * r833713;
        double r833715 = /*Error: no posit support in C */;
        double r833716 = c;
        double r833717 = a;
        double r833718 = /*Error: no posit support in C */;
        double r833719 = /*Error: no posit support in C */;
        double r833720 = sqrt(r833719);
        double r833721 = r833720 - r833713;
        double r833722 = r833721 / r833717;
        return r833722;
}

Error

Bits error versus a

Bits error versus b_2

Bits error versus c

Derivation

  1. Initial program 1.7

    \[\frac{\left(\frac{\left(-b_2\right)}{\left(\sqrt{\left(\left(b_2 \cdot b_2\right) - \left(a \cdot c\right)\right)}\right)}\right)}{a}\]

  2. Simplified1.7

    \[\leadsto \color{blue}{\frac{\left(\left(\sqrt{\left(\left(b_2 \cdot b_2\right) - \left(c \cdot a\right)\right)}\right) - b_2\right)}{a}}\]
  3. Using strategy rm

  4. Applied introduce-quire1.7

    \[\leadsto \frac{\left(\left(\sqrt{\left(\color{blue}{\left(\left(\left(b_2 \cdot b_2\right)\right)\right)} - \left(c \cdot a\right)\right)}\right) - b_2\right)}{a}\]

  5. Applied insert-quire-fdp-sub1.7

    \[\leadsto \frac{\left(\left(\sqrt{\color{blue}{\left(\left(\mathsf{qms}\left(\left(\left(b_2 \cdot b_2\right)\right), c, a\right)\right)\right)}}\right) - b_2\right)}{a}\]

  6. Final simplification1.7

    \[\leadsto \frac{\left(\left(\sqrt{\left(\left(\mathsf{qms}\left(\left(\left(b_2 \cdot b_2\right)\right), c, a\right)\right)\right)}\right) - b_2\right)}{a}\]

Reproduce

herbie shell --seed 2019164 
(FPCore (a b_2 c)
  :name "quad2p (problem 3.2.1, positive)"
  (/.p16 (+.p16 (neg.p16 b_2) (sqrt.p16 (-.p16 (*.p16 b_2 b_2) (*.p16 a c)))) a))