Average Error: 0.3 → 1.0
Time: 4.4s
Precision: binary64
\[\frac{1 - \tan x \cdot \tan x}{1 + \tan x \cdot \tan x}\]
↓
\[\frac{1}{\frac{1 + {\tan x}^{2}}{1 - \log \left(e^{{\tan x}^{2}}\right)}}\]
\frac{1 - \tan x \cdot \tan x}{1 + \tan x \cdot \tan x}
↓
\frac{1}{\frac{1 + {\tan x}^{2}}{1 - \log \left(e^{{\tan x}^{2}}\right)}}
(FPCore (x)
 :precision binary64
 (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x)))))
↓
(FPCore (x)
 :precision binary64
 (/ 1.0 (/ (+ 1.0 (pow (tan x) 2.0)) (- 1.0 (log (exp (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 1.0 / ((1.0 + pow(tan(x), 2.0)) / (1.0 - log(exp(pow(tan(x), 2.0)))));
}

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 clear-num_binary640.4

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

  4. Simplified0.4

    \[\leadsto \frac{1}{\color{blue}{\frac{1 + {\tan x}^{2}}{1 - {\tan x}^{2}}}}\]
  5. Using strategy rm

  6. Applied add-log-exp_binary641.0

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

  7. Final simplification1.0

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

Reproduce

herbie shell --seed 2020219 
(FPCore (x)
  :name "Trigonometry B"
  :precision binary64
  (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x)))))