Average Error: 1.5 → 1.5
Time: 23.6s
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 r1588701 = b;
        double r1588702 = -r1588701;
        double r1588703 = r1588701 * r1588701;
        double r1588704 = 4.0;
        double r1588705 = /* ERROR: no posit support in C */;
        double r1588706 = a;
        double r1588707 = c;
        double r1588708 = r1588706 * r1588707;
        double r1588709 = r1588705 * r1588708;
        double r1588710 = r1588703 - r1588709;
        double r1588711 = sqrt(r1588710);
        double r1588712 = r1588702 + r1588711;
        double r1588713 = 2.0;
        double r1588714 = /* ERROR: no posit support in C */;
        double r1588715 = r1588714 * r1588706;
        double r1588716 = r1588712 / r1588715;
        return r1588716;
}
↓
double f(double a, double b, double c) {
        double r1588717 = b;
        double r1588718 = r1588717 * r1588717;
        double r1588719 = c;
        double r1588720 = a;
        double r1588721 = r1588719 * r1588720;
        double r1588722 = 4.0;
        double r1588723 = r1588721 * r1588722;
        double r1588724 = r1588718 - r1588723;
        double r1588725 = sqrt(r1588724);
        double r1588726 = r1588725 - r1588717;
        double r1588727 = 2.0;
        double r1588728 = r1588726 / r1588727;
        double r1588729 = r1588728 / r1588720;
        return r1588729;
}

Error

Bits error versus a

Bits error versus b

Bits error versus c

Derivation

  1. Initial program 1.5

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

  2. Simplified1.5

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

  4. Applied associate-/r*1.5

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

  5. Final simplification1.5

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

Reproduce

herbie shell --seed 2019130 
(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)))