Average Error: 0.0 → 0.0
Time: 9.2s
Precision: 64
\[\frac{1 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}{2 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}\]
↓
\[\frac{1 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}{2 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}\]
\frac{1 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}{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}}{2 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}
double f(double t) {
        double r54674 = 1.0;
        double r54675 = 2.0;
        double r54676 = t;
        double r54677 = r54675 * r54676;
        double r54678 = r54674 + r54676;
        double r54679 = r54677 / r54678;
        double r54680 = r54679 * r54679;
        double r54681 = r54674 + r54680;
        double r54682 = r54675 + r54680;
        double r54683 = r54681 / r54682;
        return r54683;
}
↓
double f(double t) {
        double r54684 = 1.0;
        double r54685 = 2.0;
        double r54686 = t;
        double r54687 = r54685 * r54686;
        double r54688 = r54684 + r54686;
        double r54689 = r54687 / r54688;
        double r54690 = r54689 * r54689;
        double r54691 = r54684 + r54690;
        double r54692 = r54685 + r54690;
        double r54693 = r54691 / r54692;
        return r54693;
}

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. Final simplification0.0

    \[\leadsto \frac{1 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}{2 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}\]

Reproduce

herbie shell --seed 2020047 
(FPCore (t)
  :name "Kahan p13 Example 1"
  :precision binary64
  (/ (+ 1 (* (/ (* 2 t) (+ 1 t)) (/ (* 2 t) (+ 1 t)))) (+ 2 (* (/ (* 2 t) (+ 1 t)) (/ (* 2 t) (+ 1 t))))))