Average Error: 0.0 → 0.0
Time: 8.9s
Precision: 64
\[1 - \frac{1}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}\]
↓
\[1 - \frac{1}{\left(\frac{-2}{1 + t} \cdot \left(-\left(-2 - \frac{-2}{1 + t}\right)\right) + \left(-2 - \frac{-2}{1 + t}\right) \cdot -2\right) - -2}\]
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}{\left(\frac{-2}{1 + t} \cdot \left(-\left(-2 - \frac{-2}{1 + t}\right)\right) + \left(-2 - \frac{-2}{1 + t}\right) \cdot -2\right) - -2}
double f(double t) {
        double r1702199 = 1.0;
        double r1702200 = 2.0;
        double r1702201 = t;
        double r1702202 = r1702200 / r1702201;
        double r1702203 = r1702199 / r1702201;
        double r1702204 = r1702199 + r1702203;
        double r1702205 = r1702202 / r1702204;
        double r1702206 = r1702200 - r1702205;
        double r1702207 = r1702206 * r1702206;
        double r1702208 = r1702200 + r1702207;
        double r1702209 = r1702199 / r1702208;
        double r1702210 = r1702199 - r1702209;
        return r1702210;
}
↓
double f(double t) {
        double r1702211 = 1.0;
        double r1702212 = -2.0;
        double r1702213 = t;
        double r1702214 = r1702211 + r1702213;
        double r1702215 = r1702212 / r1702214;
        double r1702216 = r1702212 - r1702215;
        double r1702217 = -r1702216;
        double r1702218 = r1702215 * r1702217;
        double r1702219 = r1702216 * r1702212;
        double r1702220 = r1702218 + r1702219;
        double r1702221 = r1702220 - r1702212;
        double r1702222 = r1702211 / r1702221;
        double r1702223 = r1702211 - r1702222;
        return r1702223;
}

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

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

  4. Applied sub-neg0.0

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

  5. Applied distribute-lft-in0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019168 
(FPCore (t)
  :name "Kahan p13 Example 3"
  (- 1 (/ 1 (+ 2 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))))))))