Average Error: 0.3 → 0.4
Time: 23.0s
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 r429664 = 1.0;
        double r429665 = x;
        double r429666 = tan(r429665);
        double r429667 = r429666 * r429666;
        double r429668 = r429664 - r429667;
        double r429669 = r429664 + r429667;
        double r429670 = r429668 / r429669;
        return r429670;
}
↓
double f(double x) {
        double r429671 = 1.0;
        double r429672 = x;
        double r429673 = tan(r429672);
        double r429674 = r429673 * r429673;
        double r429675 = r429671 - r429674;
        double r429676 = r429674 * r429674;
        double r429677 = r429671 - r429676;
        double r429678 = r429675 / r429677;
        double r429679 = r429678 * r429675;
        return r429679;
}

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 2019139 
(FPCore (x)
  :name "Trigonometry B"
  (/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x)))))