Average Error: 0.0 → 0.0
Time: 1.9s
Precision: 64
\[e^{-\left(1 - x \cdot x\right)}\]
↓
\[{e}^{\left(-\left(1 - x \cdot x\right)\right)}\]
e^{-\left(1 - x \cdot x\right)}
↓
{e}^{\left(-\left(1 - x \cdot x\right)\right)}
double f(double x) {
        double r22185 = 1.0;
        double r22186 = x;
        double r22187 = r22186 * r22186;
        double r22188 = r22185 - r22187;
        double r22189 = -r22188;
        double r22190 = exp(r22189);
        return r22190;
}
↓
double f(double x) {
        double r22191 = exp(1.0);
        double r22192 = 1.0;
        double r22193 = x;
        double r22194 = r22193 * r22193;
        double r22195 = r22192 - r22194;
        double r22196 = -r22195;
        double r22197 = pow(r22191, r22196);
        return r22197;
}

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 *-un-lft-identity0.0

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

  4. Applied exp-prod0.0

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

  5. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2020060 
(FPCore (x)
  :name "exp neg sub"
  :precision binary64
  (exp (- (- 1 (* x x)))))