Average Error: 0.0 → 0.0
Time: 10.1s
Precision: 64
\[e^{-\left(1 - x \cdot x\right)}\]
↓
\[\frac{{\left(e^{x}\right)}^{\left(x - \sqrt{1}\right)} \cdot {\left(e^{\sqrt{1}}\right)}^{x}}{{\left(e^{\sqrt{1}}\right)}^{\left(\sqrt{1}\right)}}\]
e^{-\left(1 - x \cdot x\right)}
↓
\frac{{\left(e^{x}\right)}^{\left(x - \sqrt{1}\right)} \cdot {\left(e^{\sqrt{1}}\right)}^{x}}{{\left(e^{\sqrt{1}}\right)}^{\left(\sqrt{1}\right)}}
double f(double x) {
        double r34890 = 1.0;
        double r34891 = x;
        double r34892 = r34891 * r34891;
        double r34893 = r34890 - r34892;
        double r34894 = -r34893;
        double r34895 = exp(r34894);
        return r34895;
}
↓
double f(double x) {
        double r34896 = x;
        double r34897 = exp(r34896);
        double r34898 = 1.0;
        double r34899 = sqrt(r34898);
        double r34900 = r34896 - r34899;
        double r34901 = pow(r34897, r34900);
        double r34902 = exp(r34899);
        double r34903 = pow(r34902, r34896);
        double r34904 = r34901 * r34903;
        double r34905 = pow(r34902, r34899);
        double r34906 = r34904 / r34905;
        return r34906;
}

Error

Bits error versus x

Try it out

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 exp-sum0.0

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

  9. Applied unpow-prod-down0.0

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

  11. Applied pow-sub0.0

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

  12. Applied associate-*r/0.0

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

  13. Final simplification0.0

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

Reproduce

herbie shell --seed 2020045 
(FPCore (x)
  :name "exp neg sub"
  :precision binary64
  (exp (- (- 1 (* x x)))))