Average Error: 0.5 → 0.5
Time: 1.0m
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 r8968162 = 1.0;
        double r8968163 = /* ERROR: no posit support in C */;
        double r8968164 = x;
        double r8968165 = sqrt(r8968164);
        double r8968166 = r8968163 / r8968165;
        double r8968167 = r8968164 + r8968163;
        double r8968168 = sqrt(r8968167);
        double r8968169 = r8968163 / r8968168;
        double r8968170 = r8968166 - r8968169;
        return r8968170;
}
↓
double f(double x) {
        double r8968171 = 1.0;
        double r8968172 = x;
        double r8968173 = sqrt(r8968172);
        double r8968174 = r8968171 / r8968173;
        double r8968175 = r8968172 + r8968171;
        double r8968176 = sqrt(r8968175);
        double r8968177 = r8968171 / r8968176;
        double r8968178 = r8968174 - r8968177;
        return r8968178;
}

Error

Bits error versus x

Derivation

  1. Initial program 0.5

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

  2. Final simplification0.5

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

Reproduce

herbie shell --seed 2019133 
(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))))))