Average Error: 0.0 → 0.0
Time: 1.6s
Precision: 64
\[e^{-\left(1 - x \cdot x\right)}\]
↓
\[e^{-1} \cdot e^{{x}^{2}}\]
e^{-\left(1 - x \cdot x\right)}
↓
e^{-1} \cdot e^{{x}^{2}}
double f(double x) {
        double r19861 = 1.0;
        double r19862 = x;
        double r19863 = r19862 * r19862;
        double r19864 = r19861 - r19863;
        double r19865 = -r19864;
        double r19866 = exp(r19865);
        return r19866;
}
↓
double f(double x) {
        double r19867 = 1.0;
        double r19868 = -r19867;
        double r19869 = exp(r19868);
        double r19870 = x;
        double r19871 = 2.0;
        double r19872 = pow(r19870, r19871);
        double r19873 = exp(r19872);
        double r19874 = r19869 * r19873;
        return r19874;
}

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

    \[\leadsto e^{-1} \cdot \color{blue}{e^{{x}^{2}}}\]

  7. Final simplification0.0

    \[\leadsto e^{-1} \cdot e^{{x}^{2}}\]

Reproduce

herbie shell --seed 2020003 +o rules:numerics
(FPCore (x)
  :name "exp neg sub"
  :precision binary64
  (exp (- (- 1 (* x x)))))