Average Error: 0.0 → 0.0
Time: 7.6s
Precision: binary64
\[\frac{1 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}{2 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}\]
↓
\[\frac{\frac{\frac{1 \cdot 1}{1} - \frac{{\left(\frac{2 \cdot t}{1 + t}\right)}^{4}}{1}}{1 - \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}}{2 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}\]
\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{\frac{\frac{1 \cdot 1}{1} - \frac{{\left(\frac{2 \cdot t}{1 + t}\right)}^{4}}{1}}{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 code(double t) {
	return ((double) (((double) (1.0 + ((double) (((double) (((double) (2.0 * t)) / ((double) (1.0 + t)))) * ((double) (((double) (2.0 * t)) / ((double) (1.0 + t)))))))) / ((double) (2.0 + ((double) (((double) (((double) (2.0 * t)) / ((double) (1.0 + t)))) * ((double) (((double) (2.0 * t)) / ((double) (1.0 + t))))))))));
}
↓
double code(double t) {
	return ((double) (((double) (((double) (((double) (((double) (1.0 * 1.0)) / 1.0)) - ((double) (((double) pow(((double) (((double) (2.0 * t)) / ((double) (1.0 + t)))), 4.0)) / 1.0)))) / ((double) (1.0 - ((double) (((double) (((double) (2.0 * t)) / ((double) (1.0 + t)))) * ((double) (((double) (2.0 * t)) / ((double) (1.0 + t)))))))))) / ((double) (2.0 + ((double) (((double) (((double) (2.0 * t)) / ((double) (1.0 + t)))) * ((double) (((double) (2.0 * t)) / ((double) (1.0 + t))))))))));
}

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 flip-+0.0

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

  4. Simplified0.0

    \[\leadsto \frac{\frac{\color{blue}{\frac{1 \cdot 1}{1} - \frac{{\left(\frac{2 \cdot t}{1 + t}\right)}^{4}}{1}}}{1 - \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}}{2 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}\]

  5. Final simplification0.0

    \[\leadsto \frac{\frac{\frac{1 \cdot 1}{1} - \frac{{\left(\frac{2 \cdot t}{1 + t}\right)}^{4}}{1}}{1 - \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}}{2 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}\]

Reproduce

herbie shell --seed 2020157 
(FPCore (t)
  :name "Kahan p13 Example 1"
  :precision binary64
  (/ (+ 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))))))