Average Error: 0.3 → 0.4
Time: 42.0s
Precision: 64
\[\frac{1.0 - \tan x \cdot \tan x}{1.0 + \tan x \cdot \tan x}\]
↓
\[\frac{1.0 - \frac{1}{\frac{\cos x}{\sin x \cdot \tan x}}}{1.0 + \tan x \cdot \tan x}\]
\frac{1.0 - \tan x \cdot \tan x}{1.0 + \tan x \cdot \tan x}
↓
\frac{1.0 - \frac{1}{\frac{\cos x}{\sin x \cdot \tan x}}}{1.0 + \tan x \cdot \tan x}
double f(double x) {
        double r796883 = 1.0;
        double r796884 = x;
        double r796885 = tan(r796884);
        double r796886 = r796885 * r796885;
        double r796887 = r796883 - r796886;
        double r796888 = r796883 + r796886;
        double r796889 = r796887 / r796888;
        return r796889;
}
↓
double f(double x) {
        double r796890 = 1.0;
        double r796891 = 1.0;
        double r796892 = x;
        double r796893 = cos(r796892);
        double r796894 = sin(r796892);
        double r796895 = tan(r796892);
        double r796896 = r796894 * r796895;
        double r796897 = r796893 / r796896;
        double r796898 = r796891 / r796897;
        double r796899 = r796890 - r796898;
        double r796900 = r796895 * r796895;
        double r796901 = r796890 + r796900;
        double r796902 = r796899 / r796901;
        return r796902;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.3

    \[\frac{1.0 - \tan x \cdot \tan x}{1.0 + \tan x \cdot \tan x}\]
  2. Using strategy rm

  3. Applied tan-quot0.4

    \[\leadsto \frac{1.0 - \color{blue}{\frac{\sin x}{\cos x}} \cdot \tan x}{1.0 + \tan x \cdot \tan x}\]

  4. Applied associate-*l/0.4

    \[\leadsto \frac{1.0 - \color{blue}{\frac{\sin x \cdot \tan x}{\cos x}}}{1.0 + \tan x \cdot \tan x}\]
  5. Using strategy rm

  6. Applied clear-num0.4

    \[\leadsto \frac{1.0 - \color{blue}{\frac{1}{\frac{\cos x}{\sin x \cdot \tan x}}}}{1.0 + \tan x \cdot \tan x}\]

  7. Final simplification0.4

    \[\leadsto \frac{1.0 - \frac{1}{\frac{\cos x}{\sin x \cdot \tan x}}}{1.0 + \tan x \cdot \tan x}\]

Reproduce

herbie shell --seed 2019165 
(FPCore (x)
  :name "Trigonometry B"
  (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x)))))