Average Error: 0.0 → 0.5
Time: 3.9s
Precision: 64
\[\frac{1 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}{2 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}\]
↓
\[\sqrt{\frac{1 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}{2 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}} \cdot \sqrt{\frac{1 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}{2 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}}\]
\frac{1 + \frac{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}}
↓
\sqrt{\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}}} \cdot \sqrt{\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}}}
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) sqrt(((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) sqrt(((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))))))))))))));
}

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-sqr-sqrt0.5

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

  4. Final simplification0.5

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

Reproduce

herbie shell --seed 2020120 
(FPCore (t)
  :name "Kahan p13 Example 1"
  :precision binary64
  (/ (+ 1 (* (/ (* 2 t) (+ 1 t)) (/ (* 2 t) (+ 1 t)))) (+ 2 (* (/ (* 2 t) (+ 1 t)) (/ (* 2 t) (+ 1 t))))))