Average Error: 1.6 → 1.6
Time: 19.4s
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 r793118 = b;
        double r793119 = -r793118;
        double r793120 = r793118 * r793118;
        double r793121 = 4.0;
        double r793122 = /* ERROR: no posit support in C */;
        double r793123 = a;
        double r793124 = c;
        double r793125 = r793123 * r793124;
        double r793126 = r793122 * r793125;
        double r793127 = r793120 - r793126;
        double r793128 = sqrt(r793127);
        double r793129 = r793119 + r793128;
        double r793130 = 2.0;
        double r793131 = /* ERROR: no posit support in C */;
        double r793132 = r793131 * r793123;
        double r793133 = r793129 / r793132;
        return r793133;
}
↓
double f(double a, double b, double c) {
        double r793134 = b;
        double r793135 = r793134 * r793134;
        double r793136 = c;
        double r793137 = a;
        double r793138 = r793136 * r793137;
        double r793139 = 4.0;
        double r793140 = r793138 * r793139;
        double r793141 = r793135 - r793140;
        double r793142 = sqrt(r793141);
        double r793143 = r793142 - r793134;
        double r793144 = 2.0;
        double r793145 = r793143 / r793144;
        double r793146 = r793145 / r793137;
        return r793146;
}

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 2019104 
(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)))