Average Error: 1.6 → 1.6
Time: 27.9s
Precision: 64
\[\frac{\left(\frac{\left(-b\right)}{\left(\sqrt{\left(\left(b \cdot b\right) - \left(\left(4\right) \cdot \left(a \cdot c\right)\right)\right)}\right)}\right)}{\left(\left(2\right) \cdot a\right)}\]
↓
\[\frac{\frac{\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4} - b}{2}}{a}\]
\frac{\left(\frac{\left(-b\right)}{\left(\sqrt{\left(\left(b \cdot b\right) - \left(\left(4\right) \cdot \left(a \cdot c\right)\right)\right)}\right)}\right)}{\left(\left(2\right) \cdot a\right)}
↓
\frac{\frac{\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4} - b}{2}}{a}
double f(double a, double b, double c) {
        double r1741589 = b;
        double r1741590 = -r1741589;
        double r1741591 = r1741589 * r1741589;
        double r1741592 = 4.0;
        double r1741593 = /* ERROR: no posit support in C */;
        double r1741594 = a;
        double r1741595 = c;
        double r1741596 = r1741594 * r1741595;
        double r1741597 = r1741593 * r1741596;
        double r1741598 = r1741591 - r1741597;
        double r1741599 = sqrt(r1741598);
        double r1741600 = r1741590 + r1741599;
        double r1741601 = 2.0;
        double r1741602 = /* ERROR: no posit support in C */;
        double r1741603 = r1741602 * r1741594;
        double r1741604 = r1741600 / r1741603;
        return r1741604;
}
↓
double f(double a, double b, double c) {
        double r1741605 = b;
        double r1741606 = r1741605 * r1741605;
        double r1741607 = c;
        double r1741608 = a;
        double r1741609 = r1741607 * r1741608;
        double r1741610 = 4.0;
        double r1741611 = r1741609 * r1741610;
        double r1741612 = r1741606 - r1741611;
        double r1741613 = sqrt(r1741612);
        double r1741614 = r1741613 - r1741605;
        double r1741615 = 2.0;
        double r1741616 = r1741614 / r1741615;
        double r1741617 = r1741616 / r1741608;
        return r1741617;
}

Error

Bits error versus a

Bits error versus b

Bits error versus c

Derivation

  1. Initial program 1.6

    \[\frac{\left(\frac{\left(-b\right)}{\left(\sqrt{\left(\left(b \cdot b\right) - \left(\left(4\right) \cdot \left(a \cdot c\right)\right)\right)}\right)}\right)}{\left(\left(2\right) \cdot a\right)}\]

  2. Simplified1.6

    \[\leadsto \color{blue}{\frac{\left(\left(\sqrt{\left(\left(b \cdot b\right) - \left(\left(c \cdot a\right) \cdot \left(4\right)\right)\right)}\right) - b\right)}{\left(\left(2\right) \cdot a\right)}}\]
  3. Using strategy rm

  4. Applied associate-/r*1.6

    \[\leadsto \color{blue}{\frac{\left(\frac{\left(\left(\sqrt{\left(\left(b \cdot b\right) - \left(\left(c \cdot a\right) \cdot \left(4\right)\right)\right)}\right) - b\right)}{\left(2\right)}\right)}{a}}\]

  5. Final simplification1.6

    \[\leadsto \frac{\frac{\sqrt{b \cdot b - \left(c \cdot a\right) \cdot 4} - b}{2}}{a}\]

Reproduce

herbie shell --seed 2019135 
(FPCore (a b c)
  :name "quadp (p42, positive)"
  (/.p16 (+.p16 (neg.p16 b) (sqrt.p16 (-.p16 (*.p16 b b) (*.p16 (real->posit16 4) (*.p16 a c))))) (*.p16 (real->posit16 2) a)))