Average Error: 0.0 → 0.0
Time: 18.1s
Precision: 64
\[e^{-\left(1 - x \cdot x\right)}\]
↓
\[{\left(e^{-1}\right)}^{\left(1 - x \cdot x\right)}\]
e^{-\left(1 - x \cdot x\right)}
↓
{\left(e^{-1}\right)}^{\left(1 - x \cdot x\right)}
double f(double x) {
        double r29976 = 1.0;
        double r29977 = x;
        double r29978 = r29977 * r29977;
        double r29979 = r29976 - r29978;
        double r29980 = -r29979;
        double r29981 = exp(r29980);
        return r29981;
}
↓
double f(double x) {
        double r29982 = -1.0;
        double r29983 = exp(r29982);
        double r29984 = 1.0;
        double r29985 = x;
        double r29986 = r29985 * r29985;
        double r29987 = r29984 - r29986;
        double r29988 = pow(r29983, r29987);
        return r29988;
}

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 neg-mul-10.0

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

  4. Applied exp-prod0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019323 
(FPCore (x)
  :name "exp neg sub"
  :precision binary64
  (exp (- (- 1 (* x x)))))