Average Error: 0.0 → 0.0
Time: 13.0s
Precision: 64
\[e^{-\left(1 - x \cdot x\right)}\]
↓
\[{\left(e^{x}\right)}^{x} \cdot e^{-1}\]
e^{-\left(1 - x \cdot x\right)}
↓
{\left(e^{x}\right)}^{x} \cdot e^{-1}
double f(double x) {
        double r1734895 = 1.0;
        double r1734896 = x;
        double r1734897 = r1734896 * r1734896;
        double r1734898 = r1734895 - r1734897;
        double r1734899 = -r1734898;
        double r1734900 = exp(r1734899);
        return r1734900;
}
↓
double f(double x) {
        double r1734901 = x;
        double r1734902 = exp(r1734901);
        double r1734903 = pow(r1734902, r1734901);
        double r1734904 = 1.0;
        double r1734905 = -r1734904;
        double r1734906 = exp(r1734905);
        double r1734907 = r1734903 * r1734906;
        return r1734907;
}

Error

Bits error versus x

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Your Program's Arguments

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. Using strategy rm

  4. Applied exp-diff0.0

    \[\leadsto \color{blue}{\frac{e^{x \cdot x}}{e^{1}}}\]
  5. Using strategy rm

  6. Applied add-log-exp0.0

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

  7. Applied exp-to-pow0.0

    \[\leadsto \frac{\color{blue}{{\left(e^{x}\right)}^{x}}}{e^{1}}\]
  8. Using strategy rm

  9. Applied div-inv0.0

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

  10. Simplified0.0

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

  11. Final simplification0.0

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

Reproduce

herbie shell --seed 2019179 
(FPCore (x)
  :name "exp neg sub"
  (exp (- (- 1.0 (* x x)))))