Average Error: 0.6 → 0.6
Time: 22.3s
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 r7016701 = 1.0;
        double r7016702 = /* ERROR: no posit support in C */;
        double r7016703 = x;
        double r7016704 = sqrt(r7016703);
        double r7016705 = r7016702 / r7016704;
        double r7016706 = r7016703 + r7016702;
        double r7016707 = sqrt(r7016706);
        double r7016708 = r7016702 / r7016707;
        double r7016709 = r7016705 - r7016708;
        return r7016709;
}
↓
double f(double x) {
        double r7016710 = 1.0;
        double r7016711 = x;
        double r7016712 = sqrt(r7016711);
        double r7016713 = r7016710 / r7016712;
        double r7016714 = r7016711 + r7016710;
        double r7016715 = sqrt(r7016714);
        double r7016716 = r7016710 / r7016715;
        double r7016717 = r7016713 - r7016716;
        return r7016717;
}

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 +o rules:numerics
(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))))))