Average Error: 58.3 → 0.7
Time: 14.4s
Precision: 64
Internal Precision: 1344
\[e^{x} - e^{{x}^{2}}\]
\[\left(x \cdot \frac{1}{6} - \frac{1}{2}\right) \cdot \left(x \cdot x\right) + x\]

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

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

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

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

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

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

Runtime

Time bar (total: 14.4s)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)' 
(FPCore (x)
  :name "exp(x)-exp(x^2)"
  (- (exp x) (exp (pow x 2))))