Average Error: 0.3 → 0.4
Time: 21.9s
Precision: 64
\[\frac{1 - \tan x \cdot \tan x}{1 + \tan x \cdot \tan x}\]
↓
\[\left(\left(\sqrt{1} - \tan x\right) \cdot \left(\tan x + \sqrt{1}\right)\right) \cdot \frac{1}{1 + \tan x \cdot \tan x}\]
\frac{1 - \tan x \cdot \tan x}{1 + \tan x \cdot \tan x}
↓
\left(\left(\sqrt{1} - \tan x\right) \cdot \left(\tan x + \sqrt{1}\right)\right) \cdot \frac{1}{1 + \tan x \cdot \tan x}
double f(double x) {
        double r969087 = 1.0;
        double r969088 = x;
        double r969089 = tan(r969088);
        double r969090 = r969089 * r969089;
        double r969091 = r969087 - r969090;
        double r969092 = r969087 + r969090;
        double r969093 = r969091 / r969092;
        return r969093;
}
↓
double f(double x) {
        double r969094 = 1.0;
        double r969095 = sqrt(r969094);
        double r969096 = x;
        double r969097 = tan(r969096);
        double r969098 = r969095 - r969097;
        double r969099 = r969097 + r969095;
        double r969100 = r969098 * r969099;
        double r969101 = 1.0;
        double r969102 = r969097 * r969097;
        double r969103 = r969094 + r969102;
        double r969104 = r969101 / r969103;
        double r969105 = r969100 * r969104;
        return r969105;
}

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 add-sqr-sqrt0.3

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

  4. Applied difference-of-squares0.4

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

  5. Applied associate-/l*0.4

    \[\leadsto \color{blue}{\frac{\sqrt{1} + \tan x}{\frac{1 + \tan x \cdot \tan x}{\sqrt{1} - \tan x}}}\]
  6. Using strategy rm

  7. Applied div-inv0.4

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

  8. Applied *-un-lft-identity0.4

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

  9. Applied times-frac0.4

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

  10. Simplified0.4

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

  11. Final simplification0.4

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

Reproduce

herbie shell --seed 2019169 
(FPCore (x)
  :name "Trigonometry B"
  (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x)))))