Average Error: 0.0 → 0.0
Time: 9.1s
Precision: 64
\[\frac{1 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}\]
↓
\[\frac{1 + \left(\frac{-2}{1 + t} - -2\right) \cdot \left(\frac{-2}{1 + t} - -2\right)}{\left(\frac{-2}{1 + t} - -2\right) \cdot \left(\frac{-2}{1 + t} - -2\right) - -2}\]
\frac{1 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}
↓
\frac{1 + \left(\frac{-2}{1 + t} - -2\right) \cdot \left(\frac{-2}{1 + t} - -2\right)}{\left(\frac{-2}{1 + t} - -2\right) \cdot \left(\frac{-2}{1 + t} - -2\right) - -2}
double f(double t) {
        double r1043959 = 1.0;
        double r1043960 = 2.0;
        double r1043961 = t;
        double r1043962 = r1043960 / r1043961;
        double r1043963 = r1043959 / r1043961;
        double r1043964 = r1043959 + r1043963;
        double r1043965 = r1043962 / r1043964;
        double r1043966 = r1043960 - r1043965;
        double r1043967 = r1043966 * r1043966;
        double r1043968 = r1043959 + r1043967;
        double r1043969 = r1043960 + r1043967;
        double r1043970 = r1043968 / r1043969;
        return r1043970;
}
↓
double f(double t) {
        double r1043971 = 1.0;
        double r1043972 = -2.0;
        double r1043973 = t;
        double r1043974 = r1043971 + r1043973;
        double r1043975 = r1043972 / r1043974;
        double r1043976 = r1043975 - r1043972;
        double r1043977 = r1043976 * r1043976;
        double r1043978 = r1043971 + r1043977;
        double r1043979 = r1043977 - r1043972;
        double r1043980 = r1043978 / r1043979;
        return r1043980;
}

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

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

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019135 
(FPCore (t)
  :name "Kahan p13 Example 2"
  (/ (+ 1 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))))) (+ 2 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (- 2 (/ (/ 2 t) (+ 1 (/ 1 t))))))))