Average Error: 0.0 → 0.0
Time: 14.4s
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 r31905 = 1.0;
        double r31906 = x;
        double r31907 = r31906 * r31906;
        double r31908 = r31905 - r31907;
        double r31909 = -r31908;
        double r31910 = exp(r31909);
        return r31910;
}
↓
double f(double x) {
        double r31911 = 1.0;
        double r31912 = -r31911;
        double r31913 = exp(r31912);
        double r31914 = x;
        double r31915 = exp(r31914);
        double r31916 = pow(r31915, r31914);
        double r31917 = r31913 * r31916;
        return r31917;
}

Error

Bits error versus x

Try it out

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