Average Error: 0.0 → 0.0
Time: 16.2s
Precision: 64
\[e^{-\left(1 - x \cdot x\right)}\]
↓
\[e^{-1} \cdot {\left(e^{x}\right)}^{x}\]
e^{-\left(1 - x \cdot x\right)}
↓
e^{-1} \cdot {\left(e^{x}\right)}^{x}
double f(double x) {
        double r47688 = 1.0;
        double r47689 = x;
        double r47690 = r47689 * r47689;
        double r47691 = r47688 - r47690;
        double r47692 = -r47691;
        double r47693 = exp(r47692);
        return r47693;
}
↓
double f(double x) {
        double r47694 = 1.0;
        double r47695 = -r47694;
        double r47696 = exp(r47695);
        double r47697 = x;
        double r47698 = exp(r47697);
        double r47699 = pow(r47698, r47697);
        double r47700 = r47696 * r47699;
        return r47700;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[e^{-\left(1 - x \cdot x\right)}\]
  2. Using strategy rm

  3. Applied sub-neg0.0

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

  4. Applied distribute-neg-in0.0

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

  5. Applied exp-sum0.0

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

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019195 
(FPCore (x)
  :name "exp neg sub"
  (exp (- (- 1.0 (* x x)))))