Average Error: 0.0 → 0.0
Time: 18.1s
Precision: 64
\[\frac{1 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}{2 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}\]
↓
\[\frac{1 + \frac{t \cdot 2}{1 + t} \cdot \frac{t \cdot 2}{1 + t}}{\log \left(e^{\frac{t \cdot 2}{1 + t} \cdot \frac{t \cdot 2}{1 + t}}\right) + 2}\]
\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}}{\log \left(e^{\frac{t \cdot 2}{1 + t} \cdot \frac{t \cdot 2}{1 + t}}\right) + 2}
double f(double t) {
        double r2909597 = 1.0;
        double r2909598 = 2.0;
        double r2909599 = t;
        double r2909600 = r2909598 * r2909599;
        double r2909601 = r2909597 + r2909599;
        double r2909602 = r2909600 / r2909601;
        double r2909603 = r2909602 * r2909602;
        double r2909604 = r2909597 + r2909603;
        double r2909605 = r2909598 + r2909603;
        double r2909606 = r2909604 / r2909605;
        return r2909606;
}
↓
double f(double t) {
        double r2909607 = 1.0;
        double r2909608 = t;
        double r2909609 = 2.0;
        double r2909610 = r2909608 * r2909609;
        double r2909611 = r2909607 + r2909608;
        double r2909612 = r2909610 / r2909611;
        double r2909613 = r2909612 * r2909612;
        double r2909614 = r2909607 + r2909613;
        double r2909615 = exp(r2909613);
        double r2909616 = log(r2909615);
        double r2909617 = r2909616 + r2909609;
        double r2909618 = r2909614 / r2909617;
        return r2909618;
}

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. Using strategy rm

  3. Applied add-log-exp0.0

    \[\leadsto \frac{1 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}{2 + \color{blue}{\log \left(e^{\frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}\right)}}\]

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019179 +o rules:numerics
(FPCore (t)
  :name "Kahan p13 Example 1"
  (/ (+ 1.0 (* (/ (* 2.0 t) (+ 1.0 t)) (/ (* 2.0 t) (+ 1.0 t)))) (+ 2.0 (* (/ (* 2.0 t) (+ 1.0 t)) (/ (* 2.0 t) (+ 1.0 t))))))