Average Error: 0.3 → 0.3
Time: 18.2s
Precision: binary64
\[e^{-w} \cdot {\ell}^{\left(e^{w}\right)} \]
↓
\[-\frac{{\ell}^{\left(e^{w}\right)}}{-e^{w}} \]
e^{-w} \cdot {\ell}^{\left(e^{w}\right)}
↓
-\frac{{\ell}^{\left(e^{w}\right)}}{-e^{w}}

(FPCore (w l) :precision binary64 (* (exp (- w)) (pow l (exp w))))
↓
(FPCore (w l) :precision binary64 (- (/ (pow l (exp w)) (- (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)) / -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. Applied frac-2neg_binary640.3

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

  4. Applied distribute-frac-neg_binary640.3

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

  5. Final simplification0.3

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

Reproduce

herbie shell --seed 2021215 
(FPCore (w l)
  :name "exp-w crasher"
  :precision binary64
  (* (exp (- w)) (pow l (exp w))))