Average Error: 0.3 → 0.3
Time: 7.3s
Precision: binary64
\[\frac{1 - \tan x \cdot \tan x}{1 + \tan x \cdot \tan x}\]
↓
\[\frac{{\tan x}^{2} + -1}{-1 - {\tan x}^{2}}\]
\frac{1 - \tan x \cdot \tan x}{1 + \tan x \cdot \tan x}
↓
\frac{{\tan x}^{2} + -1}{-1 - {\tan x}^{2}}
(FPCore (x)
 :precision binary64
 (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x)))))
↓
(FPCore (x)
 :precision binary64
 (/ (+ (pow (tan x) 2.0) -1.0) (- -1.0 (pow (tan x) 2.0))))
double code(double x) {
	return (1.0 - (tan(x) * tan(x))) / (1.0 + (tan(x) * tan(x)));
}
↓
double code(double x) {
	return (pow(tan(x), 2.0) + -1.0) / (-1.0 - pow(tan(x), 2.0));
}

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 frac-2neg_binary640.3

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

  4. Simplified0.3

    \[\leadsto \frac{\color{blue}{{\tan x}^{2} + -1}}{-\left(1 + \tan x \cdot \tan x\right)}\]

  5. Simplified0.3

    \[\leadsto \frac{{\tan x}^{2} + -1}{\color{blue}{-1 - {\tan x}^{2}}}\]

  6. Final simplification0.3

    \[\leadsto \frac{{\tan x}^{2} + -1}{-1 - {\tan x}^{2}}\]

Reproduce

herbie shell --seed 2020273 
(FPCore (x)
  :name "Trigonometry B"
  :precision binary64
  (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x)))))