Average Error: 7.4 → 7.5
Time: 43.2s
Precision: 64
Internal Precision: 1344
\[\left({\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - {x}^{\left(\frac{1}{n}\right)}\right) - timeout\]
\[\log \left(e^{{\left(1 + x\right)}^{\left(\frac{1}{n}\right)} - {x}^{\left(\frac{1}{n}\right)}}\right) - timeout\]

Error

Bits error versus x

Bits error versus n

Bits error versus timeout

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 7.4

    \[\left({\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - {x}^{\left(\frac{1}{n}\right)}\right) - timeout\]
  2. Using strategy rm
  3. Applied add-log-exp7.6

    \[\leadsto \left({\left(x + 1\right)}^{\left(\frac{1}{n}\right)} - \color{blue}{\log \left(e^{{x}^{\left(\frac{1}{n}\right)}}\right)}\right) - timeout\]
  4. Applied add-log-exp7.6

    \[\leadsto \left(\color{blue}{\log \left(e^{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)}}\right)} - \log \left(e^{{x}^{\left(\frac{1}{n}\right)}}\right)\right) - timeout\]
  5. Applied diff-log7.6

    \[\leadsto \color{blue}{\log \left(\frac{e^{{\left(x + 1\right)}^{\left(\frac{1}{n}\right)}}}{e^{{x}^{\left(\frac{1}{n}\right)}}}\right)} - timeout\]
  6. Applied simplify7.5

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

Runtime

Time bar (total: 43.2s)Debug log

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