Average Error: 0.0 → 0.0
Time: 9.4s
Precision: 64
\[e^{-\left(1 - x \cdot x\right)}\]
↓
\[e^{x \cdot x - 1}\]
e^{-\left(1 - x \cdot x\right)}
↓
e^{x \cdot x - 1}
double f(double x) {
        double r786972 = 1.0;
        double r786973 = x;
        double r786974 = r786973 * r786973;
        double r786975 = r786972 - r786974;
        double r786976 = -r786975;
        double r786977 = exp(r786976);
        return r786977;
}
↓
double f(double x) {
        double r786978 = x;
        double r786979 = r786978 * r786978;
        double r786980 = 1.0;
        double r786981 = r786979 - r786980;
        double r786982 = exp(r786981);
        return r786982;
}

Error

Bits error versus x

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Results

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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. Final simplification0.0

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

Reproduce

herbie shell --seed 2019172 +o rules:numerics
(FPCore (x)
  :name "exp neg sub"
  (exp (- (- 1.0 (* x x)))))