Average Error: 5.6 → 4.8
Time: 13.5s
Precision: 64
Internal Precision: 1344
\[{\left(1 + x\right)}^{y}\]
\[\begin{array}{l} \mathbf{if}\;y \le 1.18920312127323 \cdot 10^{+190}:\\ \;\;\;\;{\left(x + 1\right)}^{y}\\ \mathbf{else}:\\ \;\;\;\;{x}^{y}\\ \end{array}\]

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 2 regimes
  2. if y < 1.18920312127323e+190

    1. Initial program 4.1

      \[{\left(1 + x\right)}^{y}\]

    if 1.18920312127323e+190 < y

    1. Initial program 41.3

      \[{\left(1 + x\right)}^{y}\]
    2. Taylor expanded around inf 62.7

      \[\leadsto \color{blue}{e^{-1 \cdot \left(\log \left(\frac{1}{x}\right) \cdot y\right)}}\]
    3. Simplified21.5

      \[\leadsto \color{blue}{{x}^{y}}\]
  3. Recombined 2 regimes into one program.
  4. Final simplification4.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le 1.18920312127323 \cdot 10^{+190}:\\ \;\;\;\;{\left(x + 1\right)}^{y}\\ \mathbf{else}:\\ \;\;\;\;{x}^{y}\\ \end{array}\]

Runtime

Time bar (total: 13.5s)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)' 
(FPCore (x y)
  :name "(1+x)^y"
  (pow (+ 1 x) y))