Average Error: 29.2 → 28.9
Time: 38.2s
Precision: 64
$\tanh \left(x + 1\right) - \tanh 1$
$\sqrt[3]{\left(\left(\tanh \left(x + 1\right) - \tanh 1\right) \cdot \left(\tanh \left(x + 1\right) - \tanh 1\right)\right) \cdot \left(\tanh \left(x + 1\right) - \tanh 1\right)}$
\tanh \left(x + 1\right) - \tanh 1
\sqrt[3]{\left(\left(\tanh \left(x + 1\right) - \tanh 1\right) \cdot \left(\tanh \left(x + 1\right) - \tanh 1\right)\right) \cdot \left(\tanh \left(x + 1\right) - \tanh 1\right)}
double f(double x) {
double r50808276 = x;
double r50808277 = 1.0;
double r50808278 = r50808276 + r50808277;
double r50808279 = tanh(r50808278);
double r50808280 = tanh(r50808277);
double r50808281 = r50808279 - r50808280;
return r50808281;
}


double f(double x) {
double r50808282 = x;
double r50808283 = 1.0;
double r50808284 = r50808282 + r50808283;
double r50808285 = tanh(r50808284);
double r50808286 = tanh(r50808283);
double r50808287 = r50808285 - r50808286;
double r50808288 = r50808287 * r50808287;
double r50808289 = r50808288 * r50808287;
double r50808290 = cbrt(r50808289);
return r50808290;
}



# Try it out

Results

 In Out
Enter valid numbers for all inputs

# Derivation

1. Initial program 29.2

$\tanh \left(x + 1\right) - \tanh 1$
2. Using strategy rm

$\leadsto \color{blue}{\sqrt[3]{\left(\left(\tanh \left(x + 1\right) - \tanh 1\right) \cdot \left(\tanh \left(x + 1\right) - \tanh 1\right)\right) \cdot \left(\tanh \left(x + 1\right) - \tanh 1\right)}}$
4. Using strategy rm
5. Applied *-un-lft-identity28.9

$\leadsto \sqrt[3]{\color{blue}{\left(1 \cdot \left(\left(\tanh \left(x + 1\right) - \tanh 1\right) \cdot \left(\tanh \left(x + 1\right) - \tanh 1\right)\right)\right)} \cdot \left(\tanh \left(x + 1\right) - \tanh 1\right)}$
6. Final simplification28.9

$\leadsto \sqrt[3]{\left(\left(\tanh \left(x + 1\right) - \tanh 1\right) \cdot \left(\tanh \left(x + 1\right) - \tanh 1\right)\right) \cdot \left(\tanh \left(x + 1\right) - \tanh 1\right)}$

# Reproduce

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