Average Error: 0.0 → 0.0
Time: 22.6s
Precision: 64
\[e^{-\left(1 - x \cdot x\right)}\]
↓
\[{\left(e^{2 \cdot \left(x + \sqrt{1}\right)}\right)}^{\left(\frac{x - \sqrt{1}}{2}\right)}\]
e^{-\left(1 - x \cdot x\right)}
↓
{\left(e^{2 \cdot \left(x + \sqrt{1}\right)}\right)}^{\left(\frac{x - \sqrt{1}}{2}\right)}
double f(double x) {
        double r43656 = 1.0;
        double r43657 = x;
        double r43658 = r43657 * r43657;
        double r43659 = r43656 - r43658;
        double r43660 = -r43659;
        double r43661 = exp(r43660);
        return r43661;
}
↓
double f(double x) {
        double r43662 = 2.0;
        double r43663 = x;
        double r43664 = 1.0;
        double r43665 = sqrt(r43664);
        double r43666 = r43663 + r43665;
        double r43667 = r43662 * r43666;
        double r43668 = exp(r43667);
        double r43669 = r43663 - r43665;
        double r43670 = r43669 / r43662;
        double r43671 = pow(r43668, r43670);
        return r43671;
}

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 add-sqr-sqrt0.0

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

  5. Applied difference-of-squares0.0

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

  6. Applied exp-prod0.0

    \[\leadsto \color{blue}{{\left(e^{x + \sqrt{1}}\right)}^{\left(x - \sqrt{1}\right)}}\]
  7. Using strategy rm

  8. Applied add-sqr-sqrt0.0

    \[\leadsto \color{blue}{\sqrt{{\left(e^{x + \sqrt{1}}\right)}^{\left(x - \sqrt{1}\right)}} \cdot \sqrt{{\left(e^{x + \sqrt{1}}\right)}^{\left(x - \sqrt{1}\right)}}}\]
  9. Using strategy rm

  10. Applied sqrt-pow10.0

    \[\leadsto \sqrt{{\left(e^{x + \sqrt{1}}\right)}^{\left(x - \sqrt{1}\right)}} \cdot \color{blue}{{\left(e^{x + \sqrt{1}}\right)}^{\left(\frac{x - \sqrt{1}}{2}\right)}}\]

  11. Applied sqrt-pow10.0

    \[\leadsto \color{blue}{{\left(e^{x + \sqrt{1}}\right)}^{\left(\frac{x - \sqrt{1}}{2}\right)}} \cdot {\left(e^{x + \sqrt{1}}\right)}^{\left(\frac{x - \sqrt{1}}{2}\right)}\]

  12. Applied pow-prod-down0.0

    \[\leadsto \color{blue}{{\left(e^{x + \sqrt{1}} \cdot e^{x + \sqrt{1}}\right)}^{\left(\frac{x - \sqrt{1}}{2}\right)}}\]

  13. Simplified0.0

    \[\leadsto {\color{blue}{\left(e^{2 \cdot \left(x + \sqrt{1}\right)}\right)}}^{\left(\frac{x - \sqrt{1}}{2}\right)}\]

  14. Final simplification0.0

    \[\leadsto {\left(e^{2 \cdot \left(x + \sqrt{1}\right)}\right)}^{\left(\frac{x - \sqrt{1}}{2}\right)}\]

Reproduce

herbie shell --seed 2019199 +o rules:numerics
(FPCore (x)
  :name "exp neg sub"
  (exp (- (- 1.0 (* x x)))))