Average Error: 0.0 → 0.0
Time: 2.9m
Precision: 64
\[\frac{1 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}{2 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}\]
↓
\[\frac{1 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}{\frac{\left(\left(\frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}\right) \cdot \left(\frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}\right)\right) \cdot \left(\frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}\right) + 2 \cdot \left(2 \cdot 2\right)}{2 \cdot 2 + \left(\left(\frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}\right) \cdot \left(\frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}\right) - 2 \cdot \left(\frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}\right)\right)}}\]
\frac{1 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}{2 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}
↓
\frac{1 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}{\frac{\left(\left(\frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}\right) \cdot \left(\frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}\right)\right) \cdot \left(\frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}\right) + 2 \cdot \left(2 \cdot 2\right)}{2 \cdot 2 + \left(\left(\frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}\right) \cdot \left(\frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}\right) - 2 \cdot \left(\frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}\right)\right)}}
double f(double t) {
        double r44185757 = 1.0;
        double r44185758 = 2.0;
        double r44185759 = t;
        double r44185760 = r44185758 * r44185759;
        double r44185761 = r44185757 + r44185759;
        double r44185762 = r44185760 / r44185761;
        double r44185763 = r44185762 * r44185762;
        double r44185764 = r44185757 + r44185763;
        double r44185765 = r44185758 + r44185763;
        double r44185766 = r44185764 / r44185765;
        return r44185766;
}
↓
double f(double t) {
        double r44185767 = 1.0;
        double r44185768 = 2.0;
        double r44185769 = t;
        double r44185770 = r44185768 * r44185769;
        double r44185771 = r44185767 + r44185769;
        double r44185772 = r44185770 / r44185771;
        double r44185773 = r44185772 * r44185772;
        double r44185774 = r44185767 + r44185773;
        double r44185775 = r44185773 * r44185773;
        double r44185776 = r44185775 * r44185773;
        double r44185777 = r44185768 * r44185768;
        double r44185778 = r44185768 * r44185777;
        double r44185779 = r44185776 + r44185778;
        double r44185780 = r44185768 * r44185773;
        double r44185781 = r44185775 - r44185780;
        double r44185782 = r44185777 + r44185781;
        double r44185783 = r44185779 / r44185782;
        double r44185784 = r44185774 / r44185783;
        return r44185784;
}

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

    \[\frac{1 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}{2 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}\]
  2. Using strategy rm

  3. Applied flip3-+0.0

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

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019173 
(FPCore (t)
  :name "Kahan p13 Example 1"
  (/ (+ 1.0 (* (/ (* 2.0 t) (+ 1.0 t)) (/ (* 2.0 t) (+ 1.0 t)))) (+ 2.0 (* (/ (* 2.0 t) (+ 1.0 t)) (/ (* 2.0 t) (+ 1.0 t))))))