Average Error: 0.0 → 0.0
Time: 15.4s
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 r33731 = 1.0;
        double r33732 = x;
        double r33733 = r33732 * r33732;
        double r33734 = r33731 - r33733;
        double r33735 = -r33734;
        double r33736 = exp(r33735);
        return r33736;
}
↓
double f(double x) {
        double r33737 = 1.0;
        double r33738 = -r33737;
        double r33739 = exp(r33738);
        double r33740 = x;
        double r33741 = exp(r33740);
        double r33742 = pow(r33741, r33740);
        double r33743 = r33739 * r33742;
        return r33743;
}

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