Average Error: 0.0 → 0.0
Time: 8.6s
Precision: 64
\[x \cdot e^{y \cdot y}\]
↓
\[x \cdot \left(\left({\left(\sqrt{\sqrt{e^{y}}}\right)}^{y} \cdot \sqrt{{\left(\sqrt{e^{y}}\right)}^{y}}\right) \cdot \left({\left(\sqrt{\sqrt{e^{y}}}\right)}^{y} \cdot \sqrt{{\left(\sqrt{e^{y}}\right)}^{y}}\right)\right)\]
x \cdot e^{y \cdot y}
↓
x \cdot \left(\left({\left(\sqrt{\sqrt{e^{y}}}\right)}^{y} \cdot \sqrt{{\left(\sqrt{e^{y}}\right)}^{y}}\right) \cdot \left({\left(\sqrt{\sqrt{e^{y}}}\right)}^{y} \cdot \sqrt{{\left(\sqrt{e^{y}}\right)}^{y}}\right)\right)
double f(double x, double y) {
        double r762543 = x;
        double r762544 = y;
        double r762545 = r762544 * r762544;
        double r762546 = exp(r762545);
        double r762547 = r762543 * r762546;
        return r762547;
}
↓
double f(double x, double y) {
        double r762548 = x;
        double r762549 = y;
        double r762550 = exp(r762549);
        double r762551 = sqrt(r762550);
        double r762552 = sqrt(r762551);
        double r762553 = pow(r762552, r762549);
        double r762554 = pow(r762551, r762549);
        double r762555 = sqrt(r762554);
        double r762556 = r762553 * r762555;
        double r762557 = r762556 * r762556;
        double r762558 = r762548 * r762557;
        return r762558;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.0
Target0.0
Herbie0.0
\[x \cdot {\left(e^{y}\right)}^{y}\]

Derivation

  1. Initial program 0.0

    \[x \cdot e^{y \cdot y}\]
  2. Using strategy rm

  3. Applied add-log-exp0.0

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

  4. Applied exp-to-pow0.0

    \[\leadsto x \cdot \color{blue}{{\left(e^{y}\right)}^{y}}\]
  5. Using strategy rm

  6. Applied add-sqr-sqrt0.0

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

  7. Applied unpow-prod-down0.0

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

  9. Applied add-sqr-sqrt0.0

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

  10. Applied add-sqr-sqrt0.0

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

  11. Applied sqrt-prod0.0

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

  12. Applied unpow-prod-down0.0

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

  13. Applied unswap-sqr0.0

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

  14. Final simplification0.0

    \[\leadsto x \cdot \left(\left({\left(\sqrt{\sqrt{e^{y}}}\right)}^{y} \cdot \sqrt{{\left(\sqrt{e^{y}}\right)}^{y}}\right) \cdot \left({\left(\sqrt{\sqrt{e^{y}}}\right)}^{y} \cdot \sqrt{{\left(\sqrt{e^{y}}\right)}^{y}}\right)\right)\]

Reproduce

herbie shell --seed 2020045 
(FPCore (x y)
  :name "Data.Number.Erf:$dmerfcx from erf-2.0.0.0"
  :precision binary64

  :herbie-target
  (* x (pow (exp y) y))

  (* x (exp (* y y))))