Average Error: 0.0 → 0.0
Time: 18.2s
Precision: 64
\[e^{-\left(1 - x \cdot x\right)}\]
↓
\[e^{-1} \cdot e^{x \cdot x}\]
e^{-\left(1 - x \cdot x\right)}
↓
e^{-1} \cdot e^{x \cdot x}
double f(double x) {
        double r1584260 = 1.0;
        double r1584261 = x;
        double r1584262 = r1584261 * r1584261;
        double r1584263 = r1584260 - r1584262;
        double r1584264 = -r1584263;
        double r1584265 = exp(r1584264);
        return r1584265;
}
↓
double f(double x) {
        double r1584266 = 1.0;
        double r1584267 = -r1584266;
        double r1584268 = exp(r1584267);
        double r1584269 = x;
        double r1584270 = r1584269 * r1584269;
        double r1584271 = exp(r1584270);
        double r1584272 = r1584268 * r1584271;
        return r1584272;
}

Error

Bits error versus x

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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. Final simplification0.0

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

Reproduce

herbie shell --seed 2019200 +o rules:numerics
(FPCore (x)
  :name "exp neg sub"
  (exp (- (- 1.0 (* x x)))))