Average Error: 0.0 → 0.0
Time: 15.8s
Precision: 64
\[e^{-\left(1 - x \cdot x\right)}\]
↓
\[{\left(e^{x}\right)}^{x} \cdot e^{-1}\]
e^{-\left(1 - x \cdot x\right)}
↓
{\left(e^{x}\right)}^{x} \cdot e^{-1}
double f(double x) {
        double r31831 = 1.0;
        double r31832 = x;
        double r31833 = r31832 * r31832;
        double r31834 = r31831 - r31833;
        double r31835 = -r31834;
        double r31836 = exp(r31835);
        return r31836;
}
↓
double f(double x) {
        double r31837 = x;
        double r31838 = exp(r31837);
        double r31839 = pow(r31838, r31837);
        double r31840 = 1.0;
        double r31841 = -r31840;
        double r31842 = exp(r31841);
        double r31843 = r31839 * r31842;
        return r31843;
}

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. Simplified0.0

    \[\leadsto \color{blue}{e^{x \cdot x - 1}}\]
  3. Using strategy rm

  4. Applied sub-neg0.0

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

  5. Applied exp-sum0.0

    \[\leadsto \color{blue}{e^{x \cdot x} \cdot e^{-1}}\]

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019325 
(FPCore (x)
  :name "exp neg sub"
  :precision binary64
  (exp (- (- 1 (* x x)))))