Average Error: 0.6 → 0.0
Time: 27.3s
Precision: 64
Internal Precision: 320
\[e^{1 + x} - e^{x}\]
\[\left(\sqrt{e^{1 + x}} + \sqrt{e^{x}}\right) \cdot \left(\sqrt{e^{1 + x}} - \sqrt{e^{x}}\right)\]

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.6

    \[e^{1 + x} - e^{x}\]
  2. Using strategy rm
  3. Applied add-sqr-sqrt0.7

    \[\leadsto e^{1 + x} - \color{blue}{\sqrt{e^{x}} \cdot \sqrt{e^{x}}}\]
  4. Applied add-sqr-sqrt0.7

    \[\leadsto \color{blue}{\sqrt{e^{1 + x}} \cdot \sqrt{e^{1 + x}}} - \sqrt{e^{x}} \cdot \sqrt{e^{x}}\]
  5. Applied difference-of-squares0.0

    \[\leadsto \color{blue}{\left(\sqrt{e^{1 + x}} + \sqrt{e^{x}}\right) \cdot \left(\sqrt{e^{1 + x}} - \sqrt{e^{x}}\right)}\]

Runtime

Time bar (total: 27.3s)Debug log

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