Average Error: 0.0 → 0.0
Time: 2.0s
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 r23240 = 1.0;
        double r23241 = x;
        double r23242 = r23241 * r23241;
        double r23243 = r23240 - r23242;
        double r23244 = -r23243;
        double r23245 = exp(r23244);
        return r23245;
}
↓
double f(double x) {
        double r23246 = -1.0;
        double r23247 = exp(r23246);
        double r23248 = 1.0;
        double r23249 = x;
        double r23250 = r23249 * r23249;
        double r23251 = r23248 - r23250;
        double r23252 = pow(r23247, r23251);
        return r23252;
}

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 2020049 
(FPCore (x)
  :name "exp neg sub"
  :precision binary64
  (exp (- (- 1 (* x x)))))