Average Error: 0.3 → 0.4
Time: 20.5s
Precision: 64
\[\frac{1 - \tan x \cdot \tan x}{1 + \tan x \cdot \tan x}\]
↓
\[\frac{1 - \frac{1}{\frac{\cos x}{\tan x \cdot \sin x}}}{1 + \tan x \cdot \tan x}\]
\frac{1 - \tan x \cdot \tan x}{1 + \tan x \cdot \tan x}
↓
\frac{1 - \frac{1}{\frac{\cos x}{\tan x \cdot \sin x}}}{1 + \tan x \cdot \tan x}
double f(double x) {
        double r792353 = 1.0;
        double r792354 = x;
        double r792355 = tan(r792354);
        double r792356 = r792355 * r792355;
        double r792357 = r792353 - r792356;
        double r792358 = r792353 + r792356;
        double r792359 = r792357 / r792358;
        return r792359;
}
↓
double f(double x) {
        double r792360 = 1.0;
        double r792361 = x;
        double r792362 = cos(r792361);
        double r792363 = tan(r792361);
        double r792364 = sin(r792361);
        double r792365 = r792363 * r792364;
        double r792366 = r792362 / r792365;
        double r792367 = r792360 / r792366;
        double r792368 = r792360 - r792367;
        double r792369 = r792363 * r792363;
        double r792370 = r792360 + r792369;
        double r792371 = r792368 / r792370;
        return r792371;
}

Error

Bits error versus x

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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 tan-quot0.4

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

  4. Applied associate-*r/0.4

    \[\leadsto \frac{1 - \color{blue}{\frac{\tan x \cdot \sin x}{\cos x}}}{1 + \tan x \cdot \tan x}\]
  5. Using strategy rm

  6. Applied clear-num0.4

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

  7. Final simplification0.4

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

Reproduce

herbie shell --seed 2019165 
(FPCore (x)
  :name "Trigonometry B"
  (/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x)))))