Average Error: 0.0 → 0.0
Time: 7.3s
Precision: 64
\[\frac{1 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}{2 + \frac{2 \cdot t}{1 + t} \cdot \frac{2 \cdot t}{1 + t}}\]
↓
\[\frac{1 + \frac{t \cdot 2}{1 + t} \cdot \frac{t \cdot 2}{1 + t}}{2 + \frac{t \cdot 2}{1 + t} \cdot \frac{t \cdot 2}{1 + t}}\]
\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 + \frac{t \cdot 2}{1 + t} \cdot \frac{t \cdot 2}{1 + t}}{2 + \frac{t \cdot 2}{1 + t} \cdot \frac{t \cdot 2}{1 + t}}
double f(double t) {
        double r1822109 = 1.0;
        double r1822110 = 2.0;
        double r1822111 = t;
        double r1822112 = r1822110 * r1822111;
        double r1822113 = r1822109 + r1822111;
        double r1822114 = r1822112 / r1822113;
        double r1822115 = r1822114 * r1822114;
        double r1822116 = r1822109 + r1822115;
        double r1822117 = r1822110 + r1822115;
        double r1822118 = r1822116 / r1822117;
        return r1822118;
}
↓
double f(double t) {
        double r1822119 = 1.0;
        double r1822120 = t;
        double r1822121 = 2.0;
        double r1822122 = r1822120 * r1822121;
        double r1822123 = r1822119 + r1822120;
        double r1822124 = r1822122 / r1822123;
        double r1822125 = r1822124 * r1822124;
        double r1822126 = r1822119 + r1822125;
        double r1822127 = r1822121 + r1822125;
        double r1822128 = r1822126 / r1822127;
        return r1822128;
}

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

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

Reproduce

herbie shell --seed 2019172 
(FPCore (t)
  :name "Kahan p13 Example 1"
  (/ (+ 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))))))