Average Error: 0.0 → 0.0
Time: 19.4s
Precision: 64
\[e^{-\left(1 - x \cdot x\right)}\]
↓
\[{e}^{\left(-1 + x \cdot x\right)}\]
e^{-\left(1 - x \cdot x\right)}
↓
{e}^{\left(-1 + x \cdot x\right)}
double f(double x) {
        double r1636252 = 1.0;
        double r1636253 = x;
        double r1636254 = r1636253 * r1636253;
        double r1636255 = r1636252 - r1636254;
        double r1636256 = -r1636255;
        double r1636257 = exp(r1636256);
        return r1636257;
}
↓
double f(double x) {
        double r1636258 = exp(1.0);
        double r1636259 = -1.0;
        double r1636260 = x;
        double r1636261 = r1636260 * r1636260;
        double r1636262 = r1636259 + r1636261;
        double r1636263 = pow(r1636258, r1636262);
        return r1636263;
}

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

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

  4. Applied *-un-lft-identity0.0

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

  5. Applied exp-prod0.0

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

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019133 
(FPCore (x)
  :name "exp neg sub"
  (exp (- (- 1 (* x x)))))