Average Error: 0.0 → 0.0
Time: 32.8s
Precision: 64
\[e^{-\left(1 - x \cdot x\right)}\]
↓
\[{\left(e^{x}\right)}^{x} \cdot e^{-1}\]
e^{-\left(1 - x \cdot x\right)}
↓
{\left(e^{x}\right)}^{x} \cdot e^{-1}
double f(double x) {
        double r54287 = 1.0;
        double r54288 = x;
        double r54289 = r54288 * r54288;
        double r54290 = r54287 - r54289;
        double r54291 = -r54290;
        double r54292 = exp(r54291);
        return r54292;
}
↓
double f(double x) {
        double r54293 = x;
        double r54294 = exp(r54293);
        double r54295 = pow(r54294, r54293);
        double r54296 = 1.0;
        double r54297 = -r54296;
        double r54298 = exp(r54297);
        double r54299 = r54295 * r54298;
        return r54299;
}

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

    \[\leadsto \color{blue}{e^{x \cdot x - 1}}\]
  3. Using strategy rm

  4. Applied sub-neg0.0

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

  5. Applied exp-sum0.0

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

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

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