Average Error: 1.6 → 1.5
Time: 37.9s
Precision: 64
\[\frac{\left(\frac{\left(-b\right)}{\left(\sqrt{\left(\left(b \cdot b\right) - \left(\left(4\right) \cdot \left(a \cdot c\right)\right)\right)}\right)}\right)}{\left(\left(2\right) \cdot a\right)}\]
↓
\[\frac{\sqrt{\left(\mathsf{qms}\left(\left(\left(b \cdot b\right)\right), c, \left(a \cdot 4\right)\right)\right)} - b}{2 \cdot a}\]
\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{\sqrt{\left(\mathsf{qms}\left(\left(\left(b \cdot b\right)\right), c, \left(a \cdot 4\right)\right)\right)} - b}{2 \cdot a}
double f(double a, double b, double c) {
        double r535564 = b;
        double r535565 = -r535564;
        double r535566 = r535564 * r535564;
        double r535567 = 4.0;
        double r535568 = /* ERROR: no posit support in C */;
        double r535569 = a;
        double r535570 = c;
        double r535571 = r535569 * r535570;
        double r535572 = r535568 * r535571;
        double r535573 = r535566 - r535572;
        double r535574 = sqrt(r535573);
        double r535575 = r535565 + r535574;
        double r535576 = 2.0;
        double r535577 = /* ERROR: no posit support in C */;
        double r535578 = r535577 * r535569;
        double r535579 = r535575 / r535578;
        return r535579;
}
↓
double f(double a, double b, double c) {
        double r535580 = b;
        double r535581 = r535580 * r535580;
        double r535582 = /*Error: no posit support in C */;
        double r535583 = c;
        double r535584 = a;
        double r535585 = 4.0;
        double r535586 = r535584 * r535585;
        double r535587 = /*Error: no posit support in C */;
        double r535588 = /*Error: no posit support in C */;
        double r535589 = sqrt(r535588);
        double r535590 = r535589 - r535580;
        double r535591 = 2.0;
        double r535592 = r535591 * r535584;
        double r535593 = r535590 / r535592;
        return r535593;
}

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-*l*1.6

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

  6. Applied introduce-quire1.6

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

  7. Applied insert-quire-fdp-sub1.5

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

  8. Final simplification1.5

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

Reproduce

herbie shell --seed 2019152 
(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)))