Average Error: 0.7 → 0.7
Time: 19.0s
Precision: 64
\[\frac{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2.0} + 1.0}{2.0}\]
↓
\[\frac{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2.0} + 1.0}{2.0}\]
double f(double alpha, double beta) {
        double r1182788 = beta;
        double r1182789 = alpha;
        double r1182790 = r1182788 - r1182789;
        double r1182791 = r1182789 + r1182788;
        double r1182792 = 2.0;
        double r1182793 = r1182791 + r1182792;
        double r1182794 = r1182790 / r1182793;
        double r1182795 = 1.0;
        double r1182796 = r1182794 + r1182795;
        double r1182797 = r1182796 / r1182792;
        return r1182797;
}
↓
double f(double alpha, double beta) {
        double r1182798 = beta;
        double r1182799 = alpha;
        double r1182800 = r1182798 - r1182799;
        double r1182801 = r1182799 + r1182798;
        double r1182802 = 2.0;
        double r1182803 = r1182801 + r1182802;
        double r1182804 = r1182800 / r1182803;
        double r1182805 = 1.0;
        double r1182806 = r1182804 + r1182805;
        double r1182807 = r1182806 / r1182802;
        return r1182807;
}


\frac{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2.0} + 1.0}{2.0}
↓
\frac{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2.0} + 1.0}{2.0}

Error

Bits error versus alpha

Bits error versus beta

Derivation

  1. Initial program 0.7

    \[\frac{\left(\frac{\left(\frac{\left(\beta - \alpha\right)}{\left(\frac{\left(\frac{\alpha}{\beta}\right)}{\left(2.0\right)}\right)}\right)}{\left(1.0\right)}\right)}{\left(2.0\right)}\]

  2. Final simplification0.7

    \[\leadsto \frac{\frac{\beta - \alpha}{\left(\alpha + \beta\right) + 2.0} + 1.0}{2.0}\]

Reproduce

herbie shell --seed 2019101 
(FPCore (alpha beta)
  :name "Octave 3.8, jcobi/1"
  :pre (and (>.p16 alpha (real->posit16 -1)) (>.p16 beta (real->posit16 -1)))
  (/.p16 (+.p16 (/.p16 (-.p16 beta alpha) (+.p16 (+.p16 alpha beta) (real->posit16 2.0))) (real->posit16 1.0)) (real->posit16 2.0)))