Average Error: 1.7 → 1.7
Time: 24.6s
Precision: 64
\[\frac{\left(\frac{\left(-b_2\right)}{\left(\sqrt{\left(\left(b_2 \cdot b_2\right) - \left(a \cdot c\right)\right)}\right)}\right)}{a}\]
↓
\[\frac{\sqrt{\left(\mathsf{qms}\left(\left(\left(b_2 \cdot b_2\right)\right), c, a\right)\right)} - b_2}{a}\]
\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{\sqrt{\left(\mathsf{qms}\left(\left(\left(b_2 \cdot b_2\right)\right), c, a\right)\right)} - b_2}{a}
double f(double a, double b_2, double c) {
        double r309527 = b_2;
        double r309528 = -r309527;
        double r309529 = r309527 * r309527;
        double r309530 = a;
        double r309531 = c;
        double r309532 = r309530 * r309531;
        double r309533 = r309529 - r309532;
        double r309534 = sqrt(r309533);
        double r309535 = r309528 + r309534;
        double r309536 = r309535 / r309530;
        return r309536;
}
↓
double f(double a, double b_2, double c) {
        double r309537 = b_2;
        double r309538 = r309537 * r309537;
        double r309539 = /*Error: no posit support in C */;
        double r309540 = c;
        double r309541 = a;
        double r309542 = /*Error: no posit support in C */;
        double r309543 = /*Error: no posit support in C */;
        double r309544 = sqrt(r309543);
        double r309545 = r309544 - r309537;
        double r309546 = r309545 / r309541;
        return r309546;
}

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

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

Reproduce

herbie shell --seed 2019153 
(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))