Average Error: 0.0 → 0.0
Time: 6.5s
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 r1121414 = 1.0;
        double r1121415 = 2.0;
        double r1121416 = t;
        double r1121417 = r1121415 * r1121416;
        double r1121418 = r1121414 + r1121416;
        double r1121419 = r1121417 / r1121418;
        double r1121420 = r1121419 * r1121419;
        double r1121421 = r1121414 + r1121420;
        double r1121422 = r1121415 + r1121420;
        double r1121423 = r1121421 / r1121422;
        return r1121423;
}
↓
double f(double t) {
        double r1121424 = 1.0;
        double r1121425 = t;
        double r1121426 = 2.0;
        double r1121427 = r1121425 * r1121426;
        double r1121428 = r1121424 + r1121425;
        double r1121429 = r1121427 / r1121428;
        double r1121430 = r1121429 * r1121429;
        double r1121431 = r1121424 + r1121430;
        double r1121432 = r1121426 + r1121430;
        double r1121433 = r1121431 / r1121432;
        return r1121433;
}

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

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

Reproduce

herbie shell --seed 2019132 +o rules:numerics
(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))))))