Average Error: 0.0 → 0.0
Time: 3.7s
Precision: 64
\[1 - \frac{1}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}\]
↓
\[1 - \frac{1}{2 + \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}\]
1 - \frac{1}{2 + \left(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(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right) \cdot \left(2 - \frac{\frac{2}{t}}{1 + \frac{1}{t}}\right)}
double f(double t) {
        double r39150 = 1.0;
        double r39151 = 2.0;
        double r39152 = t;
        double r39153 = r39151 / r39152;
        double r39154 = r39150 / r39152;
        double r39155 = r39150 + r39154;
        double r39156 = r39153 / r39155;
        double r39157 = r39151 - r39156;
        double r39158 = r39157 * r39157;
        double r39159 = r39151 + r39158;
        double r39160 = r39150 / r39159;
        double r39161 = r39150 - r39160;
        return r39161;
}
↓
double f(double t) {
        double r39162 = 1.0;
        double r39163 = 2.0;
        double r39164 = t;
        double r39165 = r39163 / r39164;
        double r39166 = r39162 / r39164;
        double r39167 = r39162 + r39166;
        double r39168 = r39165 / r39167;
        double r39169 = r39163 - r39168;
        double r39170 = r39169 * r39169;
        double r39171 = r39163 + r39170;
        double r39172 = r39162 / r39171;
        double r39173 = r39162 - r39172;
        return r39173;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2020035 +o rules:numerics
(FPCore (t)
  :name "Kahan p13 Example 3"
  :precision binary64
  (- 1 (/ 1 (+ 2 (* (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))) (- 2 (/ (/ 2 t) (+ 1 (/ 1 t)))))))))