Average Error: 0.0 → 0.0
Time: 6.0s
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 r26650 = 1.0;
        double r26651 = 2.0;
        double r26652 = t;
        double r26653 = r26651 * r26652;
        double r26654 = r26650 + r26652;
        double r26655 = r26653 / r26654;
        double r26656 = r26655 * r26655;
        double r26657 = r26650 + r26656;
        double r26658 = r26651 + r26656;
        double r26659 = r26657 / r26658;
        return r26659;
}
↓
double f(double t) {
        double r26660 = 1.0;
        double r26661 = 2.0;
        double r26662 = t;
        double r26663 = r26661 * r26662;
        double r26664 = r26660 + r26662;
        double r26665 = r26663 / r26664;
        double r26666 = r26665 * r26665;
        double r26667 = r26660 + r26666;
        double r26668 = r26661 + r26666;
        double r26669 = r26667 / r26668;
        return r26669;
}

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 2019235 
(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))))))