Average Error: 0.6 → 0.6
Time: 58.8s
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 r7964005 = 1.0;
        double r7964006 = /* ERROR: no posit support in C */;
        double r7964007 = x;
        double r7964008 = sqrt(r7964007);
        double r7964009 = r7964006 / r7964008;
        double r7964010 = r7964007 + r7964006;
        double r7964011 = sqrt(r7964010);
        double r7964012 = r7964006 / r7964011;
        double r7964013 = r7964009 - r7964012;
        return r7964013;
}
↓
double f(double x) {
        double r7964014 = 1.0;
        double r7964015 = x;
        double r7964016 = sqrt(r7964015);
        double r7964017 = r7964014 / r7964016;
        double r7964018 = r7964015 + r7964014;
        double r7964019 = sqrt(r7964018);
        double r7964020 = r7964014 / r7964019;
        double r7964021 = r7964017 - r7964020;
        return r7964021;
}

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 2019134 
(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))))))