Average Error: 0.0 → 0.0
Time: 22.9s
Precision: 64
\[1 - \frac{1}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}\]
↓
\[1 - \frac{1}{2 + \left(\left(-\left(2 - \frac{2}{1 \cdot t + 1}\right)\right) \cdot \frac{2}{1 \cdot t + 1} + \left(2 - \frac{2}{1 \cdot t + 1}\right) \cdot 2\right)}\]
1 - \frac{1}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}
↓
1 - \frac{1}{2 + \left(\left(-\left(2 - \frac{2}{1 \cdot t + 1}\right)\right) \cdot \frac{2}{1 \cdot t + 1} + \left(2 - \frac{2}{1 \cdot t + 1}\right) \cdot 2\right)}
double f(double t) {
        double r2219713 = 1.0;
        double r2219714 = 2.0;
        double r2219715 = t;
        double r2219716 = r2219714 / r2219715;
        double r2219717 = r2219713 / r2219715;
        double r2219718 = r2219713 + r2219717;
        double r2219719 = r2219716 / r2219718;
        double r2219720 = r2219714 - r2219719;
        double r2219721 = r2219720 * r2219720;
        double r2219722 = r2219714 + r2219721;
        double r2219723 = r2219713 / r2219722;
        double r2219724 = r2219713 - r2219723;
        return r2219724;
}
↓
double f(double t) {
        double r2219725 = 1.0;
        double r2219726 = 2.0;
        double r2219727 = t;
        double r2219728 = r2219725 * r2219727;
        double r2219729 = r2219728 + r2219725;
        double r2219730 = r2219726 / r2219729;
        double r2219731 = r2219726 - r2219730;
        double r2219732 = -r2219731;
        double r2219733 = r2219732 * r2219730;
        double r2219734 = r2219731 * r2219726;
        double r2219735 = r2219733 + r2219734;
        double r2219736 = r2219726 + r2219735;
        double r2219737 = r2219725 / r2219736;
        double r2219738 = r2219725 - r2219737;
        return r2219738;
}

Error

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[1 - \frac{1}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}\]

  2. Simplified0.0

    \[\leadsto \color{blue}{1 - \frac{1}{2 + \left(2 - \frac{2}{1 + 1 \cdot t}\right) \cdot \left(2 - \frac{2}{1 + 1 \cdot t}\right)}}\]
  3. Using strategy rm

  4. Applied sub-neg0.0

    \[\leadsto 1 - \frac{1}{2 + \left(2 - \frac{2}{1 + 1 \cdot t}\right) \cdot \color{blue}{\left(2 + \left(-\frac{2}{1 + 1 \cdot t}\right)\right)}}\]

  5. Applied distribute-lft-in0.0

    \[\leadsto 1 - \frac{1}{2 + \color{blue}{\left(\left(2 - \frac{2}{1 + 1 \cdot t}\right) \cdot 2 + \left(2 - \frac{2}{1 + 1 \cdot t}\right) \cdot \left(-\frac{2}{1 + 1 \cdot t}\right)\right)}}\]

  6. Final simplification0.0

    \[\leadsto 1 - \frac{1}{2 + \left(\left(-\left(2 - \frac{2}{1 \cdot t + 1}\right)\right) \cdot \frac{2}{1 \cdot t + 1} + \left(2 - \frac{2}{1 \cdot t + 1}\right) \cdot 2\right)}\]

Reproduce

herbie shell --seed 2019168 
(FPCore (t)
  :name "Kahan p13 Example 3"
  (- 1.0 (/ 1.0 (+ 2.0 (* (- 2.0 (/ (/ 2.0 t) (+ 1.0 (/ 1.0 t)))) (- 2.0 (/ (/ 2.0 t) (+ 1.0 (/ 1.0 t)))))))))