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

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

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
  3. Applied add-log-exp0.0

    \[\leadsto \left(\left(\sqrt{x + 1} - \color{blue}{\log \left(e^{\sqrt{x}}\right)}\right) - \log x\right) + \frac{\sinh x}{\cos x}\]
  4. Applied add-log-exp0.0

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