Average Error: 58.3 → 0.7
Time: 11.1s
Precision: 64
Internal Precision: 1344
\[e^{X} - e^{X \cdot X}\]
\[X - \left(\frac{1}{2} - \frac{1}{6} \cdot X\right) \cdot \left(X \cdot X\right)\]

Error

Bits error versus X

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 58.3

    \[e^{X} - e^{X \cdot X}\]
  2. Initial simplification58.3

    \[\leadsto e^{X} - e^{X \cdot X}\]
  3. Taylor expanded around 0 0.7

    \[\leadsto \color{blue}{\left(X + \frac{1}{6} \cdot {X}^{3}\right) - \frac{1}{2} \cdot {X}^{2}}\]
  4. Simplified0.7

    \[\leadsto \color{blue}{X - \left(X \cdot X\right) \cdot \left(\frac{1}{2} - X \cdot \frac{1}{6}\right)}\]
  5. Final simplification0.7

    \[\leadsto X - \left(\frac{1}{2} - \frac{1}{6} \cdot X\right) \cdot \left(X \cdot X\right)\]

Runtime

Time bar (total: 11.1s)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)' 
(FPCore (X)
  :name "exp(X) - exp(X * X)"
  (- (exp X) (exp (* X X))))