Average Error: 1.5 → 1.5
Time: 17.2s
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 r649189 = b;
        double r649190 = -r649189;
        double r649191 = r649189 * r649189;
        double r649192 = 4.0;
        double r649193 = /* ERROR: no posit support in C */;
        double r649194 = a;
        double r649195 = c;
        double r649196 = r649194 * r649195;
        double r649197 = r649193 * r649196;
        double r649198 = r649191 - r649197;
        double r649199 = sqrt(r649198);
        double r649200 = r649190 + r649199;
        double r649201 = 2.0;
        double r649202 = /* ERROR: no posit support in C */;
        double r649203 = r649202 * r649194;
        double r649204 = r649200 / r649203;
        return r649204;
}
↓
double f(double a, double b, double c) {
        double r649205 = b;
        double r649206 = r649205 * r649205;
        double r649207 = c;
        double r649208 = a;
        double r649209 = r649207 * r649208;
        double r649210 = 4.0;
        double r649211 = r649209 * r649210;
        double r649212 = r649206 - r649211;
        double r649213 = sqrt(r649212);
        double r649214 = r649213 - r649205;
        double r649215 = 2.0;
        double r649216 = r649214 / r649215;
        double r649217 = r649216 / r649208;
        return r649217;
}

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 2019119 
(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)))