Average Error: 0.0 → 0.0
Time: 19.1s
Precision: 64
\[e^{-\left(1 - x \cdot x\right)}\]
↓
\[\frac{{\left(e^{x}\right)}^{x}}{e}\]
e^{-\left(1 - x \cdot x\right)}
↓
\frac{{\left(e^{x}\right)}^{x}}{e}
double f(double x) {
        double r1151852 = 1.0;
        double r1151853 = x;
        double r1151854 = r1151853 * r1151853;
        double r1151855 = r1151852 - r1151854;
        double r1151856 = -r1151855;
        double r1151857 = exp(r1151856);
        return r1151857;
}
↓
double f(double x) {
        double r1151858 = x;
        double r1151859 = exp(r1151858);
        double r1151860 = pow(r1151859, r1151858);
        double r1151861 = exp(1.0);
        double r1151862 = r1151860 / r1151861;
        return r1151862;
}

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

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

  4. Applied exp-prod0.0

    \[\leadsto \frac{\color{blue}{{\left(e^{x}\right)}^{x}}}{e}\]

  5. Final simplification0.0

    \[\leadsto \frac{{\left(e^{x}\right)}^{x}}{e}\]

Reproduce

herbie shell --seed 2019149 
(FPCore (x)
  :name "exp neg sub"
  (exp (- (- 1 (* x x)))))