Average Error: 14.9 → 0.3
Time: 24.9s
Precision: 64
Internal Precision: 1344
$\frac{x}{\tanh x} - 1$
$\begin{array}{l} \mathbf{if}\;\frac{x}{\tanh x} - 1 \le 4.89080122427896 \cdot 10^{-13}:\\ \;\;\;\;\left(\frac{2}{945} \cdot {x}^{6} + \frac{1}{3} \cdot {x}^{2}\right) - \frac{1}{45} \cdot {x}^{4}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(\sqrt[3]{\tanh x} \cdot \sqrt[3]{\tanh x}\right) \cdot \sqrt[3]{\tanh x}} - 1\\ \end{array}$

# Try it out

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# Derivation

1. Split input into 2 regimes
2. ## if (- (/ x (tanh x)) 1) < 4.89080122427896e-13

1. Initial program 30.0

$\frac{x}{\tanh x} - 1$
2. Taylor expanded around 0 0.2

$\leadsto \color{blue}{\left(\frac{2}{945} \cdot {x}^{6} + \frac{1}{3} \cdot {x}^{2}\right) - \frac{1}{45} \cdot {x}^{4}}$

## if 4.89080122427896e-13 < (- (/ x (tanh x)) 1)

1. Initial program 0.4

$\frac{x}{\tanh x} - 1$
2. Using strategy rm
$\leadsto \frac{x}{\color{blue}{\left(\sqrt[3]{\tanh x} \cdot \sqrt[3]{\tanh x}\right) \cdot \sqrt[3]{\tanh x}}} - 1$
herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)'