Average Error: 0.7 → 0.7
Time: 17.1s
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 r1727162 = beta;
        double r1727163 = alpha;
        double r1727164 = r1727162 - r1727163;
        double r1727165 = r1727163 + r1727162;
        double r1727166 = 2.0;
        double r1727167 = r1727165 + r1727166;
        double r1727168 = r1727164 / r1727167;
        double r1727169 = 1.0;
        double r1727170 = r1727168 + r1727169;
        double r1727171 = r1727170 / r1727166;
        return r1727171;
}
↓
double f(double alpha, double beta) {
        double r1727172 = beta;
        double r1727173 = alpha;
        double r1727174 = r1727172 - r1727173;
        double r1727175 = r1727173 + r1727172;
        double r1727176 = 2.0;
        double r1727177 = r1727175 + r1727176;
        double r1727178 = r1727174 / r1727177;
        double r1727179 = 1.0;
        double r1727180 = r1727178 + r1727179;
        double r1727181 = r1727180 / r1727176;
        return r1727181;
}


\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 +o rules:numerics
(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)))