Average Error: 0.2 → 0.6
Time: 12.5s
Precision: binary64
\[e^{-w} \cdot {\ell}^{\left(e^{w}\right)}\]
↓
\[\frac{{\left(\sqrt{\ell}\right)}^{\left(e^{w}\right)}}{\sqrt[3]{\sqrt{e^{w}}} \cdot \left(\sqrt[3]{e^{w}} \cdot \sqrt[3]{\sqrt{e^{w}}}\right)} \cdot \frac{{\left(\sqrt{\ell}\right)}^{\left(e^{w}\right)}}{\sqrt[3]{e^{w}}}\]
e^{-w} \cdot {\ell}^{\left(e^{w}\right)}
↓
\frac{{\left(\sqrt{\ell}\right)}^{\left(e^{w}\right)}}{\sqrt[3]{\sqrt{e^{w}}} \cdot \left(\sqrt[3]{e^{w}} \cdot \sqrt[3]{\sqrt{e^{w}}}\right)} \cdot \frac{{\left(\sqrt{\ell}\right)}^{\left(e^{w}\right)}}{\sqrt[3]{e^{w}}}
double code(double w, double l) {
	return ((double) (((double) exp(((double) -(w)))) * ((double) pow(l, ((double) exp(w))))));
}
↓
double code(double w, double l) {
	return ((double) ((((double) pow(((double) sqrt(l)), ((double) exp(w)))) / ((double) (((double) cbrt(((double) sqrt(((double) exp(w)))))) * ((double) (((double) cbrt(((double) exp(w)))) * ((double) cbrt(((double) sqrt(((double) exp(w))))))))))) * (((double) pow(((double) sqrt(l)), ((double) exp(w)))) / ((double) cbrt(((double) exp(w)))))));
}

Error

Bits error versus w

Bits error versus l

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.2

    \[e^{-w} \cdot {\ell}^{\left(e^{w}\right)}\]

  2. Simplified0.2

    \[\leadsto \color{blue}{\frac{{\ell}^{\left(e^{w}\right)}}{e^{w}}}\]
  3. Using strategy rm

  4. Applied add-cube-cbrt0.3

    \[\leadsto \frac{{\ell}^{\left(e^{w}\right)}}{\color{blue}{\left(\sqrt[3]{e^{w}} \cdot \sqrt[3]{e^{w}}\right) \cdot \sqrt[3]{e^{w}}}}\]

  5. Applied add-sqr-sqrt0.6

    \[\leadsto \frac{{\color{blue}{\left(\sqrt{\ell} \cdot \sqrt{\ell}\right)}}^{\left(e^{w}\right)}}{\left(\sqrt[3]{e^{w}} \cdot \sqrt[3]{e^{w}}\right) \cdot \sqrt[3]{e^{w}}}\]

  6. Applied unpow-prod-down0.6

    \[\leadsto \frac{\color{blue}{{\left(\sqrt{\ell}\right)}^{\left(e^{w}\right)} \cdot {\left(\sqrt{\ell}\right)}^{\left(e^{w}\right)}}}{\left(\sqrt[3]{e^{w}} \cdot \sqrt[3]{e^{w}}\right) \cdot \sqrt[3]{e^{w}}}\]

  7. Applied times-frac0.6

    \[\leadsto \color{blue}{\frac{{\left(\sqrt{\ell}\right)}^{\left(e^{w}\right)}}{\sqrt[3]{e^{w}} \cdot \sqrt[3]{e^{w}}} \cdot \frac{{\left(\sqrt{\ell}\right)}^{\left(e^{w}\right)}}{\sqrt[3]{e^{w}}}}\]
  8. Using strategy rm

  9. Applied add-sqr-sqrt0.6

    \[\leadsto \frac{{\left(\sqrt{\ell}\right)}^{\left(e^{w}\right)}}{\sqrt[3]{e^{w}} \cdot \sqrt[3]{\color{blue}{\sqrt{e^{w}} \cdot \sqrt{e^{w}}}}} \cdot \frac{{\left(\sqrt{\ell}\right)}^{\left(e^{w}\right)}}{\sqrt[3]{e^{w}}}\]

  10. Applied cbrt-prod0.6

    \[\leadsto \frac{{\left(\sqrt{\ell}\right)}^{\left(e^{w}\right)}}{\sqrt[3]{e^{w}} \cdot \color{blue}{\left(\sqrt[3]{\sqrt{e^{w}}} \cdot \sqrt[3]{\sqrt{e^{w}}}\right)}} \cdot \frac{{\left(\sqrt{\ell}\right)}^{\left(e^{w}\right)}}{\sqrt[3]{e^{w}}}\]

  11. Applied associate-*r*0.6

    \[\leadsto \frac{{\left(\sqrt{\ell}\right)}^{\left(e^{w}\right)}}{\color{blue}{\left(\sqrt[3]{e^{w}} \cdot \sqrt[3]{\sqrt{e^{w}}}\right) \cdot \sqrt[3]{\sqrt{e^{w}}}}} \cdot \frac{{\left(\sqrt{\ell}\right)}^{\left(e^{w}\right)}}{\sqrt[3]{e^{w}}}\]

  12. Final simplification0.6

    \[\leadsto \frac{{\left(\sqrt{\ell}\right)}^{\left(e^{w}\right)}}{\sqrt[3]{\sqrt{e^{w}}} \cdot \left(\sqrt[3]{e^{w}} \cdot \sqrt[3]{\sqrt{e^{w}}}\right)} \cdot \frac{{\left(\sqrt{\ell}\right)}^{\left(e^{w}\right)}}{\sqrt[3]{e^{w}}}\]

Reproduce

herbie shell --seed 2020199 
(FPCore (w l)
  :name "exp-w crasher"
  :precision binary64
  (* (exp (- w)) (pow l (exp w))))