Average Error: 0.3 → 0.4
Time: 18.2s
Precision: 64
\[\frac{1 - \tan x \cdot \tan x}{1 + \tan x \cdot \tan x}\]
↓
\[\frac{1 - \tan x \cdot \tan x}{1 - \left(\tan x \cdot \tan x\right) \cdot \left(\tan x \cdot \tan x\right)} \cdot \left(1 - \tan x \cdot \tan x\right)\]
\frac{1 - \tan x \cdot \tan x}{1 + \tan x \cdot \tan x}
↓
\frac{1 - \tan x \cdot \tan x}{1 - \left(\tan x \cdot \tan x\right) \cdot \left(\tan x \cdot \tan x\right)} \cdot \left(1 - \tan x \cdot \tan x\right)
double f(double x) {
        double r276810 = 1.0;
        double r276811 = x;
        double r276812 = tan(r276811);
        double r276813 = r276812 * r276812;
        double r276814 = r276810 - r276813;
        double r276815 = r276810 + r276813;
        double r276816 = r276814 / r276815;
        return r276816;
}
↓
double f(double x) {
        double r276817 = 1.0;
        double r276818 = x;
        double r276819 = tan(r276818);
        double r276820 = r276819 * r276819;
        double r276821 = r276817 - r276820;
        double r276822 = r276820 * r276820;
        double r276823 = r276817 - r276822;
        double r276824 = r276821 / r276823;
        double r276825 = r276824 * r276821;
        return r276825;
}

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 flip-+0.4

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

  4. Applied associate-/r/0.4

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

  5. Simplified0.4

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

  6. Final simplification0.4

    \[\leadsto \frac{1 - \tan x \cdot \tan x}{1 - \left(\tan x \cdot \tan x\right) \cdot \left(\tan x \cdot \tan x\right)} \cdot \left(1 - \tan x \cdot \tan x\right)\]

Reproduce

herbie shell --seed 2019128 +o rules:numerics
(FPCore (x)
  :name "Trigonometry B"
  (/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x)))))