Average Error: 0.2 → 0.2
Time: 16.1s
Precision: binary64
\[e^{-w} \cdot {\ell}^{\left(e^{w}\right)}\]
↓
\[\frac{1}{\sqrt{e^{w}}} \cdot \frac{{\ell}^{\left(e^{w}\right)}}{\sqrt{e^{w}}}\]
e^{-w} \cdot {\ell}^{\left(e^{w}\right)}
↓
\frac{1}{\sqrt{e^{w}}} \cdot \frac{{\ell}^{\left(e^{w}\right)}}{\sqrt{e^{w}}}
(FPCore (w l) :precision binary64 (* (exp (- w)) (pow l (exp w))))
↓
(FPCore (w l)
 :precision binary64
 (* (/ 1.0 (sqrt (exp w))) (/ (pow l (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 (1.0 / sqrt(exp(w))) * (pow(l, 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 0.2

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

  2. Simplified0.2

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

  4. Applied add-sqr-sqrt_binary64_7890.2

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

  5. Applied *-un-lft-identity_binary64_7670.2

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

  6. Applied unpow-prod-down_binary64_8460.2

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

  7. Applied times-frac_binary64_7730.2

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

  8. Simplified0.2

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

  9. Final simplification0.2

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

Reproduce

herbie shell --seed 2020281 
(FPCore (w l)
  :name "exp-w crasher"
  :precision binary64
  (* (exp (- w)) (pow l (exp w))))