Average Error: 0.0 → 0.0
Time: 30.0s
Precision: 64
\[\frac{1 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}{2 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}\]
↓
\[\frac{1 + \log \left(e^{\frac{t \cdot 2}{1 + t} \cdot \frac{t \cdot 2}{1 + t}}\right)}{2 + \frac{t \cdot 2}{1 + t} \cdot \frac{t \cdot 2}{1 + t}}\]
\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 + \log \left(e^{\frac{t \cdot 2}{1 + t} \cdot \frac{t \cdot 2}{1 + t}}\right)}{2 + \frac{t \cdot 2}{1 + t} \cdot \frac{t \cdot 2}{1 + t}}
double f(double t) {
        double r2755482 = 1.0;
        double r2755483 = 2.0;
        double r2755484 = t;
        double r2755485 = r2755483 * r2755484;
        double r2755486 = r2755482 + r2755484;
        double r2755487 = r2755485 / r2755486;
        double r2755488 = r2755487 * r2755487;
        double r2755489 = r2755482 + r2755488;
        double r2755490 = r2755483 + r2755488;
        double r2755491 = r2755489 / r2755490;
        return r2755491;
}
↓
double f(double t) {
        double r2755492 = 1.0;
        double r2755493 = t;
        double r2755494 = 2.0;
        double r2755495 = r2755493 * r2755494;
        double r2755496 = r2755492 + r2755493;
        double r2755497 = r2755495 / r2755496;
        double r2755498 = r2755497 * r2755497;
        double r2755499 = exp(r2755498);
        double r2755500 = log(r2755499);
        double r2755501 = r2755492 + r2755500;
        double r2755502 = r2755494 + r2755498;
        double r2755503 = r2755501 / r2755502;
        return r2755503;
}

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

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019142 
(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))))))