Average Error: 0.4 → 0.4
Time: 5.5s
Precision: 64
Internal Precision: 320
\[\frac{e^{x}}{1 + e^{x}}\]
\[e^{x - \log \left(1 + e^{x}\right)}\]

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.4

    \[\frac{e^{x}}{1 + e^{x}}\]
  2. Using strategy rm
  3. Applied add-exp-log0.4

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

    \[\leadsto \color{blue}{e^{x - \log \left(1 + e^{x}\right)}}\]
  5. Final simplification0.4

    \[\leadsto e^{x - \log \left(1 + e^{x}\right)}\]

Runtime

Time bar (total: 5.5s)Debug log

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