Average Error: 10.1 → 0.7
Time: 50.7s
Precision: 64
Internal Precision: 1344
$\left({x}^{\left(\frac{1}{3}\right)} - {\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right) - timeout$
$\begin{array}{l} \mathbf{if}\;x \le 4270.894638777147:\\ \;\;\;\;\left({x}^{\left(\frac{1}{3}\right)} - {\left(\sqrt{x + 1}\right)}^{\left(\frac{1}{3}\right)} \cdot {\left(\sqrt{x + 1}\right)}^{\left(\frac{1}{3}\right)}\right) - timeout\\ \mathbf{else}:\\ \;\;\;\;\frac{{\left(e^{\frac{1}{3}}\right)}^{\left(\log x\right)}}{x} \cdot \left(\left(\frac{\frac{1}{9}}{x} - \frac{1}{3}\right) - \frac{\frac{\frac{5}{81}}{x}}{x}\right) - timeout\\ \end{array}$

# Try it out

Results

 In Out
Enter valid numbers for all inputs

# Derivation

1. Split input into 2 regimes
2. ## if x < 4270.894638777147

1. Initial program 0.0

$\left({x}^{\left(\frac{1}{3}\right)} - {\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right) - timeout$
2. Using strategy rm

$\leadsto \left({x}^{\left(\frac{1}{3}\right)} - {\color{blue}{\left(\sqrt{x + 1} \cdot \sqrt{x + 1}\right)}}^{\left(\frac{1}{3}\right)}\right) - timeout$
4. Applied unpow-prod-down0.1

$\leadsto \left({x}^{\left(\frac{1}{3}\right)} - \color{blue}{{\left(\sqrt{x + 1}\right)}^{\left(\frac{1}{3}\right)} \cdot {\left(\sqrt{x + 1}\right)}^{\left(\frac{1}{3}\right)}}\right) - timeout$

## if 4270.894638777147 < x

1. Initial program 20.2

$\left({x}^{\left(\frac{1}{3}\right)} - {\left(x + 1\right)}^{\left(\frac{1}{3}\right)}\right) - timeout$
2. Taylor expanded around -inf 62.7

$\leadsto \color{blue}{\left(\frac{1}{9} \cdot \frac{e^{\frac{1}{3} \cdot \left(\log -1 - \log \left(\frac{-1}{x}\right)\right)}}{{x}^{2}} - \left(\frac{5}{81} \cdot \frac{e^{\frac{1}{3} \cdot \left(\log -1 - \log \left(\frac{-1}{x}\right)\right)}}{{x}^{3}} + \frac{1}{3} \cdot \frac{e^{\frac{1}{3} \cdot \left(\log -1 - \log \left(\frac{-1}{x}\right)\right)}}{x}\right)\right)} - timeout$
3. Applied simplify1.4

$\leadsto \color{blue}{\frac{{\left(e^{\frac{1}{3}}\right)}^{\left(\log x\right)}}{x} \cdot \left(\left(\frac{\frac{1}{9}}{x} - \frac{1}{3}\right) - \frac{\frac{\frac{5}{81}}{x}}{x}\right) - timeout}$
3. Recombined 2 regimes into one program.

# Runtime

Time bar (total: 50.7s)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)'
(FPCore (x timeout)
:name "pow(x,1/3)-pow((x+1),1/3) -timeout"
(- (- (pow x (/ 1 3)) (pow (+ x 1) (/ 1 3))) timeout))