Average Error: 0.3 → 1.2
Time: 5.6s
Precision: binary64
\[\frac{1 - \tan x \cdot \tan x}{1 + \tan x \cdot \tan x}\]
↓
\[\left(\sqrt{1} + \tan x\right) \cdot \frac{\sqrt{1} - \tan x}{1 + \log \left(e^{\tan x \cdot \tan x}\right)}\]
\frac{1 - \tan x \cdot \tan x}{1 + \tan x \cdot \tan x}
↓
\left(\sqrt{1} + \tan x\right) \cdot \frac{\sqrt{1} - \tan x}{1 + \log \left(e^{\tan x \cdot \tan x}\right)}
double code(double x) {
	return ((double) (((double) (1.0 - ((double) (((double) tan(x)) * ((double) tan(x)))))) / ((double) (1.0 + ((double) (((double) tan(x)) * ((double) tan(x))))))));
}
↓
double code(double x) {
	return ((double) (((double) (((double) sqrt(1.0)) + ((double) tan(x)))) * ((double) (((double) (((double) sqrt(1.0)) - ((double) tan(x)))) / ((double) (1.0 + ((double) log(((double) exp(((double) (((double) tan(x)) * ((double) tan(x))))))))))))));
}

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 *-un-lft-identity0.3

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

  4. Applied add-sqr-sqrt0.3

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

  5. Applied difference-of-squares0.4

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

  6. Applied times-frac0.4

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

  7. Simplified0.4

    \[\leadsto \color{blue}{\left(\sqrt{1} + \tan x\right)} \cdot \frac{\sqrt{1} - \tan x}{1 + \tan x \cdot \tan x}\]
  8. Using strategy rm

  9. Applied add-log-exp1.2

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

  10. Final simplification1.2

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

Reproduce

herbie shell --seed 2020174 
(FPCore (x)
  :name "Trigonometry B"
  :precision binary64
  (/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x)))))