Average Error: 0.0 → 0.0
Time: 2.5s
Precision: 64
\[e^{-\left(1 - x \cdot x\right)}\]
↓
\[\frac{{\left(e^{x}\right)}^{x}}{e}\]
e^{-\left(1 - x \cdot x\right)}
↓
\frac{{\left(e^{x}\right)}^{x}}{e}
double f(double x) {
        double r1038786 = 1.0;
        double r1038787 = x;
        double r1038788 = r1038787 * r1038787;
        double r1038789 = r1038786 - r1038788;
        double r1038790 = -r1038789;
        double r1038791 = exp(r1038790);
        return r1038791;
}
↓
double f(double x) {
        double r1038792 = x;
        double r1038793 = exp(r1038792);
        double r1038794 = pow(r1038793, r1038792);
        double r1038795 = exp(1.0);
        double r1038796 = r1038794 / r1038795;
        return r1038796;
}

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. Simplified0.0

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

  4. Applied add-log-exp0.0

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

  5. Applied exp-to-pow0.0

    \[\leadsto \frac{\color{blue}{{\left(e^{x}\right)}^{x}}}{e}\]

  6. Final simplification0.0

    \[\leadsto \frac{{\left(e^{x}\right)}^{x}}{e}\]

Reproduce

herbie shell --seed 2019121 
(FPCore (x)
  :name "exp neg sub"
  (exp (- (- 1 (* x x)))))