Average Error: 0.3 → 0.4
Time: 4.2s
Precision: 64
\[\frac{1 - \tan x \cdot \tan x}{1 + \tan x \cdot \tan x}\]
↓
\[\frac{{\left(1 - \sqrt[3]{{\left(\tan x\right)}^{6}}\right)}^{1}}{1 + \sqrt[3]{{\left(\tan x\right)}^{6}}}\]
\frac{1 - \tan x \cdot \tan x}{1 + \tan x \cdot \tan x}
↓
\frac{{\left(1 - \sqrt[3]{{\left(\tan x\right)}^{6}}\right)}^{1}}{1 + \sqrt[3]{{\left(\tan x\right)}^{6}}}
double f(double x) {
        double r10216 = 1.0;
        double r10217 = x;
        double r10218 = tan(r10217);
        double r10219 = r10218 * r10218;
        double r10220 = r10216 - r10219;
        double r10221 = r10216 + r10219;
        double r10222 = r10220 / r10221;
        return r10222;
}
↓
double f(double x) {
        double r10223 = 1.0;
        double r10224 = x;
        double r10225 = tan(r10224);
        double r10226 = 6.0;
        double r10227 = pow(r10225, r10226);
        double r10228 = cbrt(r10227);
        double r10229 = r10223 - r10228;
        double r10230 = 1.0;
        double r10231 = pow(r10229, r10230);
        double r10232 = r10223 + r10228;
        double r10233 = r10231 / r10232;
        return r10233;
}

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. Using strategy rm

  3. Applied pow10.3

    \[\leadsto \frac{\color{blue}{{\left(1 - \tan x \cdot \tan x\right)}^{1}}}{1 + \tan x \cdot \tan x}\]
  4. Using strategy rm

  5. Applied add-cbrt-cube0.5

    \[\leadsto \frac{{\left(1 - \tan x \cdot \color{blue}{\sqrt[3]{\left(\tan x \cdot \tan x\right) \cdot \tan x}}\right)}^{1}}{1 + \tan x \cdot \tan x}\]

  6. Applied add-cbrt-cube0.6

    \[\leadsto \frac{{\left(1 - \color{blue}{\sqrt[3]{\left(\tan x \cdot \tan x\right) \cdot \tan x}} \cdot \sqrt[3]{\left(\tan x \cdot \tan x\right) \cdot \tan x}\right)}^{1}}{1 + \tan x \cdot \tan x}\]

  7. Applied cbrt-unprod0.5

    \[\leadsto \frac{{\left(1 - \color{blue}{\sqrt[3]{\left(\left(\tan x \cdot \tan x\right) \cdot \tan x\right) \cdot \left(\left(\tan x \cdot \tan x\right) \cdot \tan x\right)}}\right)}^{1}}{1 + \tan x \cdot \tan x}\]

  8. Simplified0.5

    \[\leadsto \frac{{\left(1 - \sqrt[3]{\color{blue}{{\left(\tan x\right)}^{6}}}\right)}^{1}}{1 + \tan x \cdot \tan x}\]
  9. Using strategy rm

  10. Applied add-cbrt-cube0.5

    \[\leadsto \frac{{\left(1 - \sqrt[3]{{\left(\tan x\right)}^{6}}\right)}^{1}}{1 + \tan x \cdot \color{blue}{\sqrt[3]{\left(\tan x \cdot \tan x\right) \cdot \tan x}}}\]

  11. Applied add-cbrt-cube0.5

    \[\leadsto \frac{{\left(1 - \sqrt[3]{{\left(\tan x\right)}^{6}}\right)}^{1}}{1 + \color{blue}{\sqrt[3]{\left(\tan x \cdot \tan x\right) \cdot \tan x}} \cdot \sqrt[3]{\left(\tan x \cdot \tan x\right) \cdot \tan x}}\]

  12. Applied cbrt-unprod0.4

    \[\leadsto \frac{{\left(1 - \sqrt[3]{{\left(\tan x\right)}^{6}}\right)}^{1}}{1 + \color{blue}{\sqrt[3]{\left(\left(\tan x \cdot \tan x\right) \cdot \tan x\right) \cdot \left(\left(\tan x \cdot \tan x\right) \cdot \tan x\right)}}}\]

  13. Simplified0.4

    \[\leadsto \frac{{\left(1 - \sqrt[3]{{\left(\tan x\right)}^{6}}\right)}^{1}}{1 + \sqrt[3]{\color{blue}{{\left(\tan x\right)}^{6}}}}\]

  14. Final simplification0.4

    \[\leadsto \frac{{\left(1 - \sqrt[3]{{\left(\tan x\right)}^{6}}\right)}^{1}}{1 + \sqrt[3]{{\left(\tan x\right)}^{6}}}\]

Reproduce

herbie shell --seed 2020065 
(FPCore (x)
  :name "Trigonometry B"
  :precision binary64
  (/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x)))))