Average Error: 0.7 → 0.8
Time: 1.9m
Precision: 64
\[\alpha \gt \left(-1\right) \land \beta \gt \left(-1\right)\]
\[\frac{\left(\frac{\left(\frac{\left(\beta - \alpha\right)}{\left(\frac{\left(\frac{\alpha}{\beta}\right)}{\left(2.0\right)}\right)}\right)}{\left(1.0\right)}\right)}{\left(2.0\right)}\]
↓
\[\frac{\left(\frac{\left(\frac{\left(1.0\right)}{\left(\frac{\left(\frac{\alpha}{\left(\frac{\beta}{\left(2.0\right)}\right)}\right)}{\left(\beta - \alpha\right)}\right)}\right)}{\left(1.0\right)}\right)}{\left(2.0\right)}\]
\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)}
↓
\frac{\left(\frac{\left(\frac{\left(1.0\right)}{\left(\frac{\left(\frac{\alpha}{\left(\frac{\beta}{\left(2.0\right)}\right)}\right)}{\left(\beta - \alpha\right)}\right)}\right)}{\left(1.0\right)}\right)}{\left(2.0\right)}
double f(double alpha, double beta) {
        double r3424636 = beta;
        double r3424637 = alpha;
        double r3424638 = r3424636 - r3424637;
        double r3424639 = r3424637 + r3424636;
        double r3424640 = 2.0;
        double r3424641 = /* ERROR: no posit support in C */;
        double r3424642 = r3424639 + r3424641;
        double r3424643 = r3424638 / r3424642;
        double r3424644 = 1.0;
        double r3424645 = /* ERROR: no posit support in C */;
        double r3424646 = r3424643 + r3424645;
        double r3424647 = r3424646 / r3424641;
        return r3424647;
}
↓
double f(double alpha, double beta) {
        double r3424648 = 1.0;
        double r3424649 = /* ERROR: no posit support in C */;
        double r3424650 = alpha;
        double r3424651 = beta;
        double r3424652 = 2.0;
        double r3424653 = /* ERROR: no posit support in C */;
        double r3424654 = r3424651 + r3424653;
        double r3424655 = r3424650 + r3424654;
        double r3424656 = r3424651 - r3424650;
        double r3424657 = r3424655 / r3424656;
        double r3424658 = r3424649 / r3424657;
        double r3424659 = r3424658 + r3424649;
        double r3424660 = r3424659 / r3424653;
        return r3424660;
}

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. Using strategy rm

  3. Applied associate-+l+0.7

    \[\leadsto \frac{\left(\frac{\left(\frac{\left(\beta - \alpha\right)}{\color{blue}{\left(\frac{\alpha}{\left(\frac{\beta}{\left(2.0\right)}\right)}\right)}}\right)}{\left(1.0\right)}\right)}{\left(2.0\right)}\]
  4. Using strategy rm

  5. Applied p16-*-un-lft-identity0.7

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

  6. Applied associate-/l*0.8

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

  7. Final simplification0.8

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

Reproduce

herbie shell --seed 2019164 
(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)))