Average Error: 0.0 → 0.0
Time: 4.2s
Precision: 64
\[\frac{1 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}{2 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}\]
↓
\[\frac{1 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}{2 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}\]
\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{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 f(double t) {
        double r57199 = 1.0;
        double r57200 = 2.0;
        double r57201 = t;
        double r57202 = r57200 * r57201;
        double r57203 = r57199 + r57201;
        double r57204 = r57202 / r57203;
        double r57205 = r57204 * r57204;
        double r57206 = r57199 + r57205;
        double r57207 = r57200 + r57205;
        double r57208 = r57206 / r57207;
        return r57208;
}
↓
double f(double t) {
        double r57209 = 1.0;
        double r57210 = 2.0;
        double r57211 = t;
        double r57212 = r57210 * r57211;
        double r57213 = r57209 + r57211;
        double r57214 = r57212 / r57213;
        double r57215 = r57214 * r57214;
        double r57216 = r57209 + r57215;
        double r57217 = r57210 + r57215;
        double r57218 = r57216 / r57217;
        return r57218;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2020002 +o rules:numerics
(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))))))