Average Error: 29.4 → 29.5
Time: 10.4s
Precision: 64
Internal Precision: 576
$\tan \left(\tan^{-1} x - {10}^{\left(-50\right)}\right)$
$\frac{\sin \left(\tan^{-1} x - {10}^{-50}\right)}{\left(\sqrt[3]{\cos \left(\tan^{-1} x - {10}^{-50}\right)} \cdot \sqrt[3]{\cos \left(\tan^{-1} x - {10}^{-50}\right)}\right) \cdot \sqrt[3]{\cos \left(\tan^{-1} x - {10}^{-50}\right)}}$

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# Derivation

1. Initial program 29.4

$\tan \left(\tan^{-1} x - {10}^{\left(-50\right)}\right)$
2. Initial simplification29.4

$\leadsto \tan \left(\tan^{-1} x - {10}^{\left(-50\right)}\right)$
3. Taylor expanded around 0 29.4

$\leadsto \color{blue}{\frac{\sin \left(\tan^{-1} x - {10}^{-50}\right)}{\cos \left(\tan^{-1} x - {10}^{-50}\right)}}$
4. Using strategy rm

$\leadsto \frac{\sin \left(\tan^{-1} x - {10}^{-50}\right)}{\color{blue}{\left(\sqrt[3]{\cos \left(\tan^{-1} x - {10}^{-50}\right)} \cdot \sqrt[3]{\cos \left(\tan^{-1} x - {10}^{-50}\right)}\right) \cdot \sqrt[3]{\cos \left(\tan^{-1} x - {10}^{-50}\right)}}}$
6. Final simplification29.5

$\leadsto \frac{\sin \left(\tan^{-1} x - {10}^{-50}\right)}{\left(\sqrt[3]{\cos \left(\tan^{-1} x - {10}^{-50}\right)} \cdot \sqrt[3]{\cos \left(\tan^{-1} x - {10}^{-50}\right)}\right) \cdot \sqrt[3]{\cos \left(\tan^{-1} x - {10}^{-50}\right)}}$

# Runtime

Time bar (total: 10.4s)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)'
(FPCore (x)
:name "tan(atan(x)-10^-50)"
(tan (- (atan x) (pow 10 (- 50)))))