Average Error: 0.3 → 0.4
Time: 19.5s
Precision: 64
\[\frac{1 - \tan x \cdot \tan x}{1 + \tan x \cdot \tan x}\]
↓
\[\left(1 + \left(\left(\tan x \cdot \tan x\right) \cdot \left(\tan x \cdot \tan x\right) - \tan x \cdot \tan x\right)\right) \cdot \frac{1 - \tan x \cdot \tan x}{1 + \left(\tan x \cdot \tan x\right) \cdot \left(\left(\tan x \cdot \tan x\right) \cdot \left(\tan x \cdot \tan x\right)\right)}\]
\frac{1 - \tan x \cdot \tan x}{1 + \tan x \cdot \tan x}
↓
\left(1 + \left(\left(\tan x \cdot \tan x\right) \cdot \left(\tan x \cdot \tan x\right) - \tan x \cdot \tan x\right)\right) \cdot \frac{1 - \tan x \cdot \tan x}{1 + \left(\tan x \cdot \tan x\right) \cdot \left(\left(\tan x \cdot \tan x\right) \cdot \left(\tan x \cdot \tan x\right)\right)}
double f(double x) {
        double r840662 = 1.0;
        double r840663 = x;
        double r840664 = tan(r840663);
        double r840665 = r840664 * r840664;
        double r840666 = r840662 - r840665;
        double r840667 = r840662 + r840665;
        double r840668 = r840666 / r840667;
        return r840668;
}
↓
double f(double x) {
        double r840669 = 1.0;
        double r840670 = x;
        double r840671 = tan(r840670);
        double r840672 = r840671 * r840671;
        double r840673 = r840672 * r840672;
        double r840674 = r840673 - r840672;
        double r840675 = r840669 + r840674;
        double r840676 = r840669 - r840672;
        double r840677 = r840672 * r840673;
        double r840678 = r840669 + r840677;
        double r840679 = r840676 / r840678;
        double r840680 = r840675 * r840679;
        return r840680;
}

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 flip3-+0.4

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

  4. Applied associate-/r/0.4

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

  5. Simplified0.4

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

  6. Final simplification0.4

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

Reproduce

herbie shell --seed 2019158 
(FPCore (x)
  :name "Trigonometry B"
  (/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x)))))