Average Error: 0.0 → 0.0
Time: 8.3s
Precision: 64
\[1 - \frac{1}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}\]
↓
\[1 - \frac{1}{\left(-2 - \frac{-2}{1 + t}\right) \cdot \left(-2 - \frac{-2}{1 + t}\right) - -2}\]
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(-2 - \frac{-2}{1 + t}\right) \cdot \left(-2 - \frac{-2}{1 + t}\right) - -2}
double f(double t) {
        double r1618083 = 1.0;
        double r1618084 = 2.0;
        double r1618085 = t;
        double r1618086 = r1618084 / r1618085;
        double r1618087 = r1618083 / r1618085;
        double r1618088 = r1618083 + r1618087;
        double r1618089 = r1618086 / r1618088;
        double r1618090 = r1618084 - r1618089;
        double r1618091 = r1618090 * r1618090;
        double r1618092 = r1618084 + r1618091;
        double r1618093 = r1618083 / r1618092;
        double r1618094 = r1618083 - r1618093;
        return r1618094;
}
↓
double f(double t) {
        double r1618095 = 1.0;
        double r1618096 = -2.0;
        double r1618097 = t;
        double r1618098 = r1618095 + r1618097;
        double r1618099 = r1618096 / r1618098;
        double r1618100 = r1618096 - r1618099;
        double r1618101 = r1618100 * r1618100;
        double r1618102 = r1618101 - r1618096;
        double r1618103 = r1618095 / r1618102;
        double r1618104 = r1618095 - r1618103;
        return r1618104;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2019158 
(FPCore (t)
  :name "Kahan p13 Example 3"
  (- 1 (/ 1 (+ 2 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))))))))