Average Error: 0.3 → 0.4
Time: 1.0m
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 r2406170 = 1.0;
        double r2406171 = x;
        double r2406172 = tan(r2406171);
        double r2406173 = r2406172 * r2406172;
        double r2406174 = r2406170 - r2406173;
        double r2406175 = r2406170 + r2406173;
        double r2406176 = r2406174 / r2406175;
        return r2406176;
}
↓
double f(double x) {
        double r2406177 = 1.0;
        double r2406178 = x;
        double r2406179 = tan(r2406178);
        double r2406180 = r2406179 * r2406179;
        double r2406181 = r2406177 - r2406180;
        double r2406182 = r2406180 * r2406180;
        double r2406183 = r2406177 - r2406182;
        double r2406184 = r2406181 / r2406183;
        double r2406185 = r2406184 * r2406181;
        return r2406185;
}

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 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 2019128 
(FPCore (x)
  :name "Trigonometry B"
  (/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x)))))