Average Error: 29.6 → 0.3
Time: 21.7s
Precision: 64
$\tan x - \tan \left(x + 1\right)$
$\tan x - \frac{\tan x + \tan 1}{1 - \sqrt{\tan 1} \cdot \left(\sqrt{\tan 1} \cdot \tan x\right)}$
\tan x - \tan \left(x + 1\right)
\tan x - \frac{\tan x + \tan 1}{1 - \sqrt{\tan 1} \cdot \left(\sqrt{\tan 1} \cdot \tan x\right)}
double f(double x) {
double r463777 = x;
double r463778 = tan(r463777);
double r463779 = 1.0;
double r463780 = r463777 + r463779;
double r463781 = tan(r463780);
double r463782 = r463778 - r463781;
return r463782;
}


double f(double x) {
double r463783 = x;
double r463784 = tan(r463783);
double r463785 = 1.0;
double r463786 = tan(r463785);
double r463787 = r463784 + r463786;
double r463788 = 1.0;
double r463789 = sqrt(r463786);
double r463790 = r463789 * r463784;
double r463791 = r463789 * r463790;
double r463792 = r463788 - r463791;
double r463793 = r463787 / r463792;
double r463794 = r463784 - r463793;
return r463794;
}



# Try it out

Results

 In Out
Enter valid numbers for all inputs

# Derivation

1. Initial program 29.6

$\tan x - \tan \left(x + 1\right)$
2. Using strategy rm
3. Applied tan-sum0.3

$\leadsto \tan x - \color{blue}{\frac{\tan x + \tan 1}{1 - \tan x \cdot \tan 1}}$
4. Using strategy rm

$\leadsto \tan x - \frac{\tan x + \tan 1}{1 - \tan x \cdot \color{blue}{\left(\sqrt{\tan 1} \cdot \sqrt{\tan 1}\right)}}$
6. Applied associate-*r*0.3

$\leadsto \tan x - \frac{\tan x + \tan 1}{1 - \color{blue}{\left(\tan x \cdot \sqrt{\tan 1}\right) \cdot \sqrt{\tan 1}}}$
7. Final simplification0.3

$\leadsto \tan x - \frac{\tan x + \tan 1}{1 - \sqrt{\tan 1} \cdot \left(\sqrt{\tan 1} \cdot \tan x\right)}$

# Reproduce

herbie shell --seed 1
(FPCore (x)
:name "tan(x)-tan(x+1)"
(- (tan x) (tan (+ x 1.0))))