Average Error: 0.3 → 0.4
Time: 4.5s
Precision: binary64
\[\frac{1 - \tan x \cdot \tan x}{1 + \tan x \cdot \tan x}\]
↓
\[\log \left(e^{\frac{1 - {\tan x}^{2}}{1 + {\tan x}^{2}}}\right)\]
\frac{1 - \tan x \cdot \tan x}{1 + \tan x \cdot \tan x}
↓
\log \left(e^{\frac{1 - {\tan x}^{2}}{1 + {\tan x}^{2}}}\right)
(FPCore (x)
 :precision binary64
 (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x)))))
↓
(FPCore (x)
 :precision binary64
 (log (exp (/ (- 1.0 (pow (tan x) 2.0)) (+ 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 log(exp((1.0 - pow(tan(x), 2.0)) / (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 add-log-exp_binary640.4

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

  4. Simplified0.4

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

  5. Final simplification0.4

    \[\leadsto \log \left(e^{\frac{1 - {\tan x}^{2}}{1 + {\tan x}^{2}}}\right)\]

Reproduce

herbie shell --seed 2020231 
(FPCore (x)
  :name "Trigonometry B"
  :precision binary64
  (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x)))))