Average Error: 0.6 → 0.6
Time: 16.8s
Precision: 64
\[\left(\frac{\left(1\right)}{\left(\sqrt{x}\right)}\right) - \left(\frac{\left(1\right)}{\left(\sqrt{\left(\frac{x}{\left(1\right)}\right)}\right)}\right)\]
↓
\[\frac{1}{\sqrt{x}} - \frac{1}{\sqrt{x + 1}}\]
\left(\frac{\left(1\right)}{\left(\sqrt{x}\right)}\right) - \left(\frac{\left(1\right)}{\left(\sqrt{\left(\frac{x}{\left(1\right)}\right)}\right)}\right)
↓
\frac{1}{\sqrt{x}} - \frac{1}{\sqrt{x + 1}}
double f(double x) {
        double r1693543 = 1.0;
        double r1693544 = /* ERROR: no posit support in C */;
        double r1693545 = x;
        double r1693546 = sqrt(r1693545);
        double r1693547 = r1693544 / r1693546;
        double r1693548 = r1693545 + r1693544;
        double r1693549 = sqrt(r1693548);
        double r1693550 = r1693544 / r1693549;
        double r1693551 = r1693547 - r1693550;
        return r1693551;
}
↓
double f(double x) {
        double r1693552 = 1.0;
        double r1693553 = x;
        double r1693554 = sqrt(r1693553);
        double r1693555 = r1693552 / r1693554;
        double r1693556 = r1693553 + r1693552;
        double r1693557 = sqrt(r1693556);
        double r1693558 = r1693552 / r1693557;
        double r1693559 = r1693555 - r1693558;
        return r1693559;
}

Error

Bits error versus x

Derivation

  1. Initial program 0.6

    \[\left(\frac{\left(1\right)}{\left(\sqrt{x}\right)}\right) - \left(\frac{\left(1\right)}{\left(\sqrt{\left(\frac{x}{\left(1\right)}\right)}\right)}\right)\]

  2. Final simplification0.6

    \[\leadsto \frac{1}{\sqrt{x}} - \frac{1}{\sqrt{x + 1}}\]

Reproduce

herbie shell --seed 2019156 
(FPCore (x)
  :name "2isqrt (example 3.6)"
  (-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))))