Average Error: 0.3 → 0.4
Time: 5.4s
Precision: 64
\[\frac{1 - \tan x \cdot \tan x}{1 + \tan x \cdot \tan x}\]
↓
\[\frac{1 - \tan x \cdot \tan x}{{1}^{3} + {\left(\tan x \cdot \tan x\right)}^{3}} \cdot \left(1 \cdot 1 + \left(\left(\tan x \cdot \tan x\right) \cdot \left(\tan x \cdot \tan x\right) - 1 \cdot \left(\tan x \cdot \tan x\right)\right)\right)\]
\frac{1 - \tan x \cdot \tan x}{1 + \tan x \cdot \tan x}
↓
\frac{1 - \tan x \cdot \tan x}{{1}^{3} + {\left(\tan x \cdot \tan x\right)}^{3}} \cdot \left(1 \cdot 1 + \left(\left(\tan x \cdot \tan x\right) \cdot \left(\tan x \cdot \tan x\right) - 1 \cdot \left(\tan x \cdot \tan x\right)\right)\right)
double f(double x) {
        double r10928 = 1.0;
        double r10929 = x;
        double r10930 = tan(r10929);
        double r10931 = r10930 * r10930;
        double r10932 = r10928 - r10931;
        double r10933 = r10928 + r10931;
        double r10934 = r10932 / r10933;
        return r10934;
}
↓
double f(double x) {
        double r10935 = 1.0;
        double r10936 = x;
        double r10937 = tan(r10936);
        double r10938 = r10937 * r10937;
        double r10939 = r10935 - r10938;
        double r10940 = 3.0;
        double r10941 = pow(r10935, r10940);
        double r10942 = pow(r10938, r10940);
        double r10943 = r10941 + r10942;
        double r10944 = r10939 / r10943;
        double r10945 = r10935 * r10935;
        double r10946 = r10938 * r10938;
        double r10947 = r10935 * r10938;
        double r10948 = r10946 - r10947;
        double r10949 = r10945 + r10948;
        double r10950 = r10944 * r10949;
        return r10950;
}

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 flip3-+0.4

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

  4. Applied associate-/r/0.4

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

  5. Final simplification0.4

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

Reproduce

herbie shell --seed 2019347 
(FPCore (x)
  :name "Trigonometry B"
  :precision binary64
  (/ (- 1 (* (tan x) (tan x))) (+ 1 (* (tan x) (tan x)))))