Average Error: 0.3 → 0.3
Time: 18.9s
Precision: binary64
\[e^{-w} \cdot {\ell}^{\left(e^{w}\right)}\]
↓
\[\sqrt{e^{-w}} \cdot \left(\sqrt{e^{-w}} \cdot {\ell}^{\left(e^{w}\right)}\right)\]
e^{-w} \cdot {\ell}^{\left(e^{w}\right)}
↓
\sqrt{e^{-w}} \cdot \left(\sqrt{e^{-w}} \cdot {\ell}^{\left(e^{w}\right)}\right)
(FPCore (w l) :precision binary64 (* (exp (- w)) (pow l (exp w))))
↓
(FPCore (w l)
 :precision binary64
 (* (sqrt (exp (- w))) (* (sqrt (exp (- w))) (pow l (exp w)))))
double code(double w, double l) {
	return exp(-w) * pow(l, exp(w));
}
↓
double code(double w, double l) {
	return sqrt(exp(-w)) * (sqrt(exp(-w)) * pow(l, 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 0.3

    \[e^{-w} \cdot {\ell}^{\left(e^{w}\right)}\]
  2. Using strategy rm

  3. Applied add-sqr-sqrt_binary64_7820.3

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

  4. Applied associate-*l*_binary64_7010.3

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

  5. Simplified0.3

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

  6. Final simplification0.3

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

Reproduce

herbie shell --seed 2021094 
(FPCore (w l)
  :name "exp-w crasher"
  :precision binary64
  (* (exp (- w)) (pow l (exp w))))