Average Error: 0.3 → 0.4
Time: 14.3s
Precision: 64
\[\frac{1 - \tan x \cdot \tan x}{1 + \tan x \cdot \tan x}\]
↓
\[\frac{1 - \frac{{\left(\sin x\right)}^{2}}{{\left(\cos x\right)}^{2}}}{\frac{{\left(\sin x\right)}^{2}}{{\left(\cos x\right)}^{2}} + 1}\]
\frac{1 - \tan x \cdot \tan x}{1 + \tan x \cdot \tan x}
↓
\frac{1 - \frac{{\left(\sin x\right)}^{2}}{{\left(\cos x\right)}^{2}}}{\frac{{\left(\sin x\right)}^{2}}{{\left(\cos x\right)}^{2}} + 1}
double f(double x) {
        double r19902 = 1.0;
        double r19903 = x;
        double r19904 = tan(r19903);
        double r19905 = r19904 * r19904;
        double r19906 = r19902 - r19905;
        double r19907 = r19902 + r19905;
        double r19908 = r19906 / r19907;
        return r19908;
}
↓
double f(double x) {
        double r19909 = 1.0;
        double r19910 = x;
        double r19911 = sin(r19910);
        double r19912 = 2.0;
        double r19913 = pow(r19911, r19912);
        double r19914 = cos(r19910);
        double r19915 = pow(r19914, r19912);
        double r19916 = r19913 / r19915;
        double r19917 = r19909 - r19916;
        double r19918 = r19916 + r19909;
        double r19919 = r19917 / r19918;
        return r19919;
}

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

    \[\frac{1 - \tan x \cdot \tan x}{1 + \tan x \cdot \tan x}\]

  2. Taylor expanded around inf 0.4

    \[\leadsto \color{blue}{\frac{1 - \frac{{\left(\sin x\right)}^{2}}{{\left(\cos x\right)}^{2}}}{\frac{{\left(\sin x\right)}^{2}}{{\left(\cos x\right)}^{2}} + 1}}\]

  3. Final simplification0.4

    \[\leadsto \frac{1 - \frac{{\left(\sin x\right)}^{2}}{{\left(\cos x\right)}^{2}}}{\frac{{\left(\sin x\right)}^{2}}{{\left(\cos x\right)}^{2}} + 1}\]

Reproduce

herbie shell --seed 2019195 
(FPCore (x)
  :name "Trigonometry B"
  (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x)))))