Average Error: 0.0 → 0.0
Time: 4.2m
Precision: 64
\[\frac{1 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}{2 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}\]
↓
\[\frac{1 + e^{\log \left(\frac{t \cdot 2}{1 + t} \cdot \frac{t \cdot 2}{1 + t}\right)}}{2 + \frac{t \cdot 2}{1 + t} \cdot \frac{t \cdot 2}{1 + t}}\]
\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 + e^{\log \left(\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 r31073179 = 1.0;
        double r31073180 = 2.0;
        double r31073181 = t;
        double r31073182 = r31073180 * r31073181;
        double r31073183 = r31073179 + r31073181;
        double r31073184 = r31073182 / r31073183;
        double r31073185 = r31073184 * r31073184;
        double r31073186 = r31073179 + r31073185;
        double r31073187 = r31073180 + r31073185;
        double r31073188 = r31073186 / r31073187;
        return r31073188;
}
↓
double f(double t) {
        double r31073189 = 1.0;
        double r31073190 = t;
        double r31073191 = 2.0;
        double r31073192 = r31073190 * r31073191;
        double r31073193 = r31073189 + r31073190;
        double r31073194 = r31073192 / r31073193;
        double r31073195 = r31073194 * r31073194;
        double r31073196 = log(r31073195);
        double r31073197 = exp(r31073196);
        double r31073198 = r31073189 + r31073197;
        double r31073199 = r31073191 + r31073195;
        double r31073200 = r31073198 / r31073199;
        return r31073200;
}

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-exp-log0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019120 
(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))))))