Average Error: 0.3 → 0.4
Time: 38.6s
Precision: 64
\[\frac{1 - \tan x \cdot \tan x}{1 + \tan x \cdot \tan x}\]
↓
\[\frac{1 - \tan x \cdot \tan x}{\sqrt[3]{\left(\tan x \cdot \left(\tan x \cdot \tan x\right)\right) \cdot \left(\tan x \cdot \left(\tan x \cdot \tan x\right)\right)} + 1}\]
\frac{1 - \tan x \cdot \tan x}{1 + \tan x \cdot \tan x}
↓
\frac{1 - \tan x \cdot \tan x}{\sqrt[3]{\left(\tan x \cdot \left(\tan x \cdot \tan x\right)\right) \cdot \left(\tan x \cdot \left(\tan x \cdot \tan x\right)\right)} + 1}
double f(double x) {
        double r654250 = 1.0;
        double r654251 = x;
        double r654252 = tan(r654251);
        double r654253 = r654252 * r654252;
        double r654254 = r654250 - r654253;
        double r654255 = r654250 + r654253;
        double r654256 = r654254 / r654255;
        return r654256;
}
↓
double f(double x) {
        double r654257 = 1.0;
        double r654258 = x;
        double r654259 = tan(r654258);
        double r654260 = r654259 * r654259;
        double r654261 = r654257 - r654260;
        double r654262 = r654259 * r654260;
        double r654263 = r654262 * r654262;
        double r654264 = cbrt(r654263);
        double r654265 = r654264 + r654257;
        double r654266 = r654261 / r654265;
        return r654266;
}

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 add-cbrt-cube0.4

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

  4. Applied add-cbrt-cube0.5

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

  5. Applied cbrt-unprod0.4

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

  6. Final simplification0.4

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

Reproduce

herbie shell --seed 2019200 
(FPCore (x)
  :name "Trigonometry B"
  (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x)))))