Average Error: 0.0 → 0.0
Time: 10.6s
Precision: 64
\[e^{-\left(1 - x \cdot x\right)}\]
↓
\[\frac{{\left(e^{-\sqrt{1}}\right)}^{\left(\sqrt{1}\right)} \cdot {\left(e^{-x}\right)}^{\left(\sqrt{1} - x\right)}}{{\left(e^{-\sqrt{1}}\right)}^{x}}\]
e^{-\left(1 - x \cdot x\right)}
↓
\frac{{\left(e^{-\sqrt{1}}\right)}^{\left(\sqrt{1}\right)} \cdot {\left(e^{-x}\right)}^{\left(\sqrt{1} - x\right)}}{{\left(e^{-\sqrt{1}}\right)}^{x}}
double f(double x) {
        double r44202 = 1.0;
        double r44203 = x;
        double r44204 = r44203 * r44203;
        double r44205 = r44202 - r44204;
        double r44206 = -r44205;
        double r44207 = exp(r44206);
        return r44207;
}
↓
double f(double x) {
        double r44208 = 1.0;
        double r44209 = sqrt(r44208);
        double r44210 = -r44209;
        double r44211 = exp(r44210);
        double r44212 = pow(r44211, r44209);
        double r44213 = x;
        double r44214 = -r44213;
        double r44215 = exp(r44214);
        double r44216 = r44209 - r44213;
        double r44217 = pow(r44215, r44216);
        double r44218 = r44212 * r44217;
        double r44219 = pow(r44211, r44213);
        double r44220 = r44218 / r44219;
        return r44220;
}

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. Using strategy rm

  3. Applied add-sqr-sqrt0.0

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

  4. Applied difference-of-squares0.0

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

  5. Applied distribute-lft-neg-in0.0

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

  6. Applied exp-prod0.0

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

  8. Applied distribute-neg-in0.0

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

  9. Applied exp-sum0.0

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

  10. Applied unpow-prod-down0.0

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

  12. Applied pow-sub0.0

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

  13. Applied associate-*l/0.0

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

  14. Final simplification0.0

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

Reproduce

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