Average Error: 0.1 → 0.1
Time: 33.8s
Precision: 64
\[\frac{1 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}{2 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}\]
↓
\[\frac{1 + \frac{t \cdot 2}{1 + t} \cdot \frac{t \cdot 2}{1 + t}}{2 + \frac{t \cdot 2}{1 + t} \cdot \frac{t \cdot 2}{1 + t}}\]
\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{t \cdot 2}{1 + t} \cdot \frac{t \cdot 2}{1 + t}}{2 + \frac{t \cdot 2}{1 + t} \cdot \frac{t \cdot 2}{1 + t}}
double f(double t) {
        double r7587786 = 1.0;
        double r7587787 = 2.0;
        double r7587788 = t;
        double r7587789 = r7587787 * r7587788;
        double r7587790 = r7587786 + r7587788;
        double r7587791 = r7587789 / r7587790;
        double r7587792 = r7587791 * r7587791;
        double r7587793 = r7587786 + r7587792;
        double r7587794 = r7587787 + r7587792;
        double r7587795 = r7587793 / r7587794;
        return r7587795;
}
↓
double f(double t) {
        double r7587796 = 1.0;
        double r7587797 = t;
        double r7587798 = 2.0;
        double r7587799 = r7587797 * r7587798;
        double r7587800 = r7587796 + r7587797;
        double r7587801 = r7587799 / r7587800;
        double r7587802 = r7587801 * r7587801;
        double r7587803 = r7587796 + r7587802;
        double r7587804 = r7587798 + r7587802;
        double r7587805 = r7587803 / r7587804;
        return r7587805;
}

Error

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

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

  2. Final simplification0.1

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

Reproduce

herbie shell --seed 2019107 
(FPCore (t)
  :name "Kahan p13 Example 1"
  (/ (+ 1 (* (/ (* 2 t) (+ 1 t)) (/ (* 2 t) (+ 1 t)))) (+ 2 (* (/ (* 2 t) (+ 1 t)) (/ (* 2 t) (+ 1 t))))))