Average Error: 0.0 → 0.0
Time: 38.9s
Precision: 64
Internal Precision: 576
$\left(\left(\sqrt{x + 1} - \sqrt{x}\right) - \log x\right) + \frac{\sinh x}{\cos x}$
$\log \left(\frac{\frac{e^{\sqrt{x + 1}}}{e^{\sqrt{x}}}}{x}\right) + \frac{\sinh x}{\cos x}$

# Try it out

Results

 In Out
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# Derivation

1. Initial program 0.0

$\left(\left(\sqrt{x + 1} - \sqrt{x}\right) - \log x\right) + \frac{\sinh x}{\cos x}$
2. Using strategy rm

$\leadsto \left(\left(\sqrt{x + 1} - \color{blue}{\log \left(e^{\sqrt{x}}\right)}\right) - \log x\right) + \frac{\sinh x}{\cos x}$

$\leadsto \left(\left(\color{blue}{\log \left(e^{\sqrt{x + 1}}\right)} - \log \left(e^{\sqrt{x}}\right)\right) - \log x\right) + \frac{\sinh x}{\cos x}$
5. Applied diff-log0.0

$\leadsto \left(\color{blue}{\log \left(\frac{e^{\sqrt{x + 1}}}{e^{\sqrt{x}}}\right)} - \log x\right) + \frac{\sinh x}{\cos x}$
6. Applied diff-log0.0

$\leadsto \color{blue}{\log \left(\frac{\frac{e^{\sqrt{x + 1}}}{e^{\sqrt{x}}}}{x}\right)} + \frac{\sinh x}{\cos x}$

# Runtime

Time bar (total: 38.9s)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)'
(FPCore (x)
:name "sqrt(x+1) - sqrt(x) - log(x) + sinh(x) / cos(x)"
(+ (- (- (sqrt (+ x 1)) (sqrt x)) (log x)) (/ (sinh x) (cos x))))