Average Error: 0.2 → 0.2
Time: 11.9s
Precision: 64
\[x \ge -0.5 \land x \le 0.5\]
\[\frac{\tan \left(x \cdot 3.141592653589793115997963468544185161591\right) + \tan \left(x \cdot 1.224646799147353304348939673218410462141\right)}{1 - \tan \left(x \cdot 3.141592653589793115997963468544185161591\right) \cdot \tan \left(x \cdot 1.224646799147353304348939673218410462141\right)}\]
\[\frac{\tan \left(x \cdot 3.141592653589793115997963468544185161591\right) + \tan \left(x \cdot 1.224646799147353304348939673218410462141\right)}{1 - \tan \left(x \cdot 3.141592653589793115997963468544185161591\right) \cdot \frac{\sin \left(1.224646799147353304348939673218410462141 \cdot x\right)}{\cos \left(1.224646799147353304348939673218410462141 \cdot x\right)}}\]
\frac{\tan \left(x \cdot 3.141592653589793115997963468544185161591\right) + \tan \left(x \cdot 1.224646799147353304348939673218410462141\right)}{1 - \tan \left(x \cdot 3.141592653589793115997963468544185161591\right) \cdot \tan \left(x \cdot 1.224646799147353304348939673218410462141\right)}
\frac{\tan \left(x \cdot 3.141592653589793115997963468544185161591\right) + \tan \left(x \cdot 1.224646799147353304348939673218410462141\right)}{1 - \tan \left(x \cdot 3.141592653589793115997963468544185161591\right) \cdot \frac{\sin \left(1.224646799147353304348939673218410462141 \cdot x\right)}{\cos \left(1.224646799147353304348939673218410462141 \cdot x\right)}}
double f(double x) {
        double r2307760 = x;
        double r2307761 = 3.141592653589793;
        double r2307762 = r2307760 * r2307761;
        double r2307763 = tan(r2307762);
        double r2307764 = 1.2246467991473533;
        double r2307765 = r2307760 * r2307764;
        double r2307766 = tan(r2307765);
        double r2307767 = r2307763 + r2307766;
        double r2307768 = 1.0;
        double r2307769 = r2307763 * r2307766;
        double r2307770 = r2307768 - r2307769;
        double r2307771 = r2307767 / r2307770;
        return r2307771;
}

double f(double x) {
        double r2307772 = x;
        double r2307773 = 3.141592653589793;
        double r2307774 = r2307772 * r2307773;
        double r2307775 = tan(r2307774);
        double r2307776 = 1.2246467991473533;
        double r2307777 = r2307772 * r2307776;
        double r2307778 = tan(r2307777);
        double r2307779 = r2307775 + r2307778;
        double r2307780 = 1.0;
        double r2307781 = r2307776 * r2307772;
        double r2307782 = sin(r2307781);
        double r2307783 = cos(r2307781);
        double r2307784 = r2307782 / r2307783;
        double r2307785 = r2307775 * r2307784;
        double r2307786 = r2307780 - r2307785;
        double r2307787 = r2307779 / r2307786;
        return r2307787;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.2

    \[\frac{\tan \left(x \cdot 3.141592653589793115997963468544185161591\right) + \tan \left(x \cdot 1.224646799147353304348939673218410462141\right)}{1 - \tan \left(x \cdot 3.141592653589793115997963468544185161591\right) \cdot \tan \left(x \cdot 1.224646799147353304348939673218410462141\right)}\]
  2. Taylor expanded around inf 0.2

    \[\leadsto \frac{\tan \left(x \cdot 3.141592653589793115997963468544185161591\right) + \tan \left(x \cdot 1.224646799147353304348939673218410462141\right)}{1 - \tan \left(x \cdot 3.141592653589793115997963468544185161591\right) \cdot \color{blue}{\frac{\sin \left(1.224646799147353304348939673218410462141 \cdot x\right)}{\cos \left(1.224646799147353304348939673218410462141 \cdot x\right)}}}\]
  3. Final simplification0.2

    \[\leadsto \frac{\tan \left(x \cdot 3.141592653589793115997963468544185161591\right) + \tan \left(x \cdot 1.224646799147353304348939673218410462141\right)}{1 - \tan \left(x \cdot 3.141592653589793115997963468544185161591\right) \cdot \frac{\sin \left(1.224646799147353304348939673218410462141 \cdot x\right)}{\cos \left(1.224646799147353304348939673218410462141 \cdot x\right)}}\]

Reproduce

herbie shell --seed 1 
(FPCore (x)
  :name "(tan(x*3.141592653589793115997963468544185161590576171875)+tan(x*1.22464679914735320717376402945839660462569212467758006379625612680683843791484832763671875))/(1-tan(x*3.141592653589793115997963468544185161590576171875)*tan(x*1.22464679914735320717376402945839660462569212467758006379625612680683843791484832763671875))"
  :precision binary64
  :pre (and (>= x (- 0.5)) (<= x 0.5))
  (/ (+ (tan (* x 3.1415926535897931)) (tan (* x 1.2246467991473533))) (- 1 (* (tan (* x 3.1415926535897931)) (tan (* x 1.2246467991473533))))))