Average Error: 0.6 → 0.6
Time: 21.9s
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 r5602661 = 1.0;
        double r5602662 = /* ERROR: no posit support in C */;
        double r5602663 = x;
        double r5602664 = sqrt(r5602663);
        double r5602665 = r5602662 / r5602664;
        double r5602666 = r5602663 + r5602662;
        double r5602667 = sqrt(r5602666);
        double r5602668 = r5602662 / r5602667;
        double r5602669 = r5602665 - r5602668;
        return r5602669;
}
↓
double f(double x) {
        double r5602670 = 1.0;
        double r5602671 = x;
        double r5602672 = sqrt(r5602671);
        double r5602673 = r5602670 / r5602672;
        double r5602674 = r5602671 + r5602670;
        double r5602675 = sqrt(r5602674);
        double r5602676 = r5602670 / r5602675;
        double r5602677 = r5602673 - r5602676;
        return r5602677;
}

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 2019158 
(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))))))