Average Error: 0.3 → 0.4
Time: 21.2s
Precision: 64
\[\frac{1 - \tan x \cdot \tan x}{1 + \tan x \cdot \tan x}\]
↓
\[\frac{\frac{1 - \tan x}{\frac{1 - \tan x}{1 - \tan x \cdot \tan x}}}{1 + \tan x \cdot \tan x}\]
\frac{1 - \tan x \cdot \tan x}{1 + \tan x \cdot \tan x}
↓
\frac{\frac{1 - \tan x}{\frac{1 - \tan x}{1 - \tan x \cdot \tan x}}}{1 + \tan x \cdot \tan x}
double f(double x) {
        double r789223 = 1.0;
        double r789224 = x;
        double r789225 = tan(r789224);
        double r789226 = r789225 * r789225;
        double r789227 = r789223 - r789226;
        double r789228 = r789223 + r789226;
        double r789229 = r789227 / r789228;
        return r789229;
}
↓
double f(double x) {
        double r789230 = 1.0;
        double r789231 = x;
        double r789232 = tan(r789231);
        double r789233 = r789230 - r789232;
        double r789234 = r789232 * r789232;
        double r789235 = r789230 - r789234;
        double r789236 = r789233 / r789235;
        double r789237 = r789233 / r789236;
        double r789238 = r789230 + r789234;
        double r789239 = r789237 / r789238;
        return r789239;
}

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 *-un-lft-identity0.3

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

  4. Applied difference-of-squares0.4

    \[\leadsto \frac{\color{blue}{\left(1 + \tan x\right) \cdot \left(1 - \tan x\right)}}{1 + \tan x \cdot \tan x}\]
  5. Using strategy rm

  6. Applied flip-+0.3

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

  7. Applied associate-*l/0.4

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

  8. Simplified0.4

    \[\leadsto \frac{\frac{\color{blue}{\left(1 - \tan x \cdot \tan x\right) \cdot \left(1 - \tan x\right)}}{1 - \tan x}}{1 + \tan x \cdot \tan x}\]
  9. Using strategy rm

  10. Applied *-commutative0.4

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

  11. Applied associate-/l*0.4

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

  12. Final simplification0.4

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

Reproduce

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