Average Error: 0.3 → 0.3
Time: 12.1s
Precision: binary64
\[e^{-w} \cdot {\ell}^{\left(e^{w}\right)}\]
↓
\[\frac{\frac{{\ell}^{\left(e^{w}\right)}}{\sqrt{e^{w}}}}{\sqrt{e^{w}}}\]
e^{-w} \cdot {\ell}^{\left(e^{w}\right)}
↓
\frac{\frac{{\ell}^{\left(e^{w}\right)}}{\sqrt{e^{w}}}}{\sqrt{e^{w}}}
(FPCore (w l) :precision binary64 (* (exp (- w)) (pow l (exp w))))
↓
(FPCore (w l)
 :precision binary64
 (/ (/ (pow l (exp w)) (sqrt (exp w))) (sqrt (exp w))))
double code(double w, double l) {
	return exp(-w) * pow(l, exp(w));
}
↓
double code(double w, double l) {
	return (pow(l, exp(w)) / sqrt(exp(w))) / sqrt(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. Simplified0.3

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

  4. Applied add-sqr-sqrt_binary640.3

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

  5. Applied associate-/r*_binary640.3

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

  6. Final simplification0.3

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

Reproduce

herbie shell --seed 2020233 
(FPCore (w l)
  :name "exp-w crasher"
  :precision binary64
  (* (exp (- w)) (pow l (exp w))))