Average Error: 0.3 → 0.3
Time: 22.8s
Precision: binary64
\[e^{-w} \cdot {\ell}^{\left(e^{w}\right)} \]
↓
\[\begin{array}{l} t_0 := \sqrt[3]{e^{w}}\\ t_1 := \sqrt[3]{t_0 \cdot t_0}\\ t_2 := \sqrt[3]{\frac{1}{t_1 \cdot \left(t_1 \cdot t_1\right)}}\\ \left(t_2 \cdot \left(t_2 \cdot t_2\right)\right) \cdot \left(\sqrt[3]{e^{-w}} \cdot {\ell}^{\left(e^{w}\right)}\right) \end{array} \]
e^{-w} \cdot {\ell}^{\left(e^{w}\right)}
↓
\begin{array}{l}
t_0 := \sqrt[3]{e^{w}}\\
t_1 := \sqrt[3]{t_0 \cdot t_0}\\
t_2 := \sqrt[3]{\frac{1}{t_1 \cdot \left(t_1 \cdot t_1\right)}}\\
\left(t_2 \cdot \left(t_2 \cdot t_2\right)\right) \cdot \left(\sqrt[3]{e^{-w}} \cdot {\ell}^{\left(e^{w}\right)}\right)
\end{array}

(FPCore (w l) :precision binary64 (* (exp (- w)) (pow l (exp w))))
↓
(FPCore (w l)
 :precision binary64
 (let* ((t_0 (cbrt (exp w)))
        (t_1 (cbrt (* t_0 t_0)))
        (t_2 (cbrt (/ 1.0 (* t_1 (* t_1 t_1))))))
   (* (* t_2 (* t_2 t_2)) (* (cbrt (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) {
	double t_0 = cbrt(exp(w));
	double t_1 = cbrt(t_0 * t_0);
	double t_2 = cbrt(1.0 / (t_1 * (t_1 * t_1)));
	return (t_2 * (t_2 * t_2)) * (cbrt(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. Applied add-cube-cbrt_binary640.3

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

  3. Applied associate-*l*_binary640.3

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

  4. Applied add-cube-cbrt_binary640.3

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

  5. Applied exp-neg_binary640.3

    \[\leadsto \left(\left(\sqrt[3]{\sqrt[3]{e^{-w}} \cdot \sqrt[3]{e^{-w}}} \cdot \sqrt[3]{\sqrt[3]{e^{-w}} \cdot \sqrt[3]{e^{-w}}}\right) \cdot \sqrt[3]{\sqrt[3]{e^{-w}} \cdot \sqrt[3]{\color{blue}{\frac{1}{e^{w}}}}}\right) \cdot \left(\sqrt[3]{e^{-w}} \cdot {\ell}^{\left(e^{w}\right)}\right) \]

  6. Applied cbrt-div_binary640.3

    \[\leadsto \left(\left(\sqrt[3]{\sqrt[3]{e^{-w}} \cdot \sqrt[3]{e^{-w}}} \cdot \sqrt[3]{\sqrt[3]{e^{-w}} \cdot \sqrt[3]{e^{-w}}}\right) \cdot \sqrt[3]{\sqrt[3]{e^{-w}} \cdot \color{blue}{\frac{\sqrt[3]{1}}{\sqrt[3]{e^{w}}}}}\right) \cdot \left(\sqrt[3]{e^{-w}} \cdot {\ell}^{\left(e^{w}\right)}\right) \]

  7. Applied exp-neg_binary640.3

    \[\leadsto \left(\left(\sqrt[3]{\sqrt[3]{e^{-w}} \cdot \sqrt[3]{e^{-w}}} \cdot \sqrt[3]{\sqrt[3]{e^{-w}} \cdot \sqrt[3]{e^{-w}}}\right) \cdot \sqrt[3]{\sqrt[3]{\color{blue}{\frac{1}{e^{w}}}} \cdot \frac{\sqrt[3]{1}}{\sqrt[3]{e^{w}}}}\right) \cdot \left(\sqrt[3]{e^{-w}} \cdot {\ell}^{\left(e^{w}\right)}\right) \]

  8. Applied cbrt-div_binary640.3

    \[\leadsto \left(\left(\sqrt[3]{\sqrt[3]{e^{-w}} \cdot \sqrt[3]{e^{-w}}} \cdot \sqrt[3]{\sqrt[3]{e^{-w}} \cdot \sqrt[3]{e^{-w}}}\right) \cdot \sqrt[3]{\color{blue}{\frac{\sqrt[3]{1}}{\sqrt[3]{e^{w}}}} \cdot \frac{\sqrt[3]{1}}{\sqrt[3]{e^{w}}}}\right) \cdot \left(\sqrt[3]{e^{-w}} \cdot {\ell}^{\left(e^{w}\right)}\right) \]

  9. Applied frac-times_binary640.3

    \[\leadsto \left(\left(\sqrt[3]{\sqrt[3]{e^{-w}} \cdot \sqrt[3]{e^{-w}}} \cdot \sqrt[3]{\sqrt[3]{e^{-w}} \cdot \sqrt[3]{e^{-w}}}\right) \cdot \sqrt[3]{\color{blue}{\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\sqrt[3]{e^{w}} \cdot \sqrt[3]{e^{w}}}}}\right) \cdot \left(\sqrt[3]{e^{-w}} \cdot {\ell}^{\left(e^{w}\right)}\right) \]

  10. Applied cbrt-div_binary640.3

    \[\leadsto \left(\left(\sqrt[3]{\sqrt[3]{e^{-w}} \cdot \sqrt[3]{e^{-w}}} \cdot \sqrt[3]{\sqrt[3]{e^{-w}} \cdot \sqrt[3]{e^{-w}}}\right) \cdot \color{blue}{\frac{\sqrt[3]{\sqrt[3]{1} \cdot \sqrt[3]{1}}}{\sqrt[3]{\sqrt[3]{e^{w}} \cdot \sqrt[3]{e^{w}}}}}\right) \cdot \left(\sqrt[3]{e^{-w}} \cdot {\ell}^{\left(e^{w}\right)}\right) \]

  11. Applied exp-neg_binary640.3

    \[\leadsto \left(\left(\sqrt[3]{\sqrt[3]{e^{-w}} \cdot \sqrt[3]{e^{-w}}} \cdot \sqrt[3]{\sqrt[3]{e^{-w}} \cdot \sqrt[3]{\color{blue}{\frac{1}{e^{w}}}}}\right) \cdot \frac{\sqrt[3]{\sqrt[3]{1} \cdot \sqrt[3]{1}}}{\sqrt[3]{\sqrt[3]{e^{w}} \cdot \sqrt[3]{e^{w}}}}\right) \cdot \left(\sqrt[3]{e^{-w}} \cdot {\ell}^{\left(e^{w}\right)}\right) \]

  12. Applied cbrt-div_binary640.3

    \[\leadsto \left(\left(\sqrt[3]{\sqrt[3]{e^{-w}} \cdot \sqrt[3]{e^{-w}}} \cdot \sqrt[3]{\sqrt[3]{e^{-w}} \cdot \color{blue}{\frac{\sqrt[3]{1}}{\sqrt[3]{e^{w}}}}}\right) \cdot \frac{\sqrt[3]{\sqrt[3]{1} \cdot \sqrt[3]{1}}}{\sqrt[3]{\sqrt[3]{e^{w}} \cdot \sqrt[3]{e^{w}}}}\right) \cdot \left(\sqrt[3]{e^{-w}} \cdot {\ell}^{\left(e^{w}\right)}\right) \]

  13. Applied exp-neg_binary640.3

    \[\leadsto \left(\left(\sqrt[3]{\sqrt[3]{e^{-w}} \cdot \sqrt[3]{e^{-w}}} \cdot \sqrt[3]{\sqrt[3]{\color{blue}{\frac{1}{e^{w}}}} \cdot \frac{\sqrt[3]{1}}{\sqrt[3]{e^{w}}}}\right) \cdot \frac{\sqrt[3]{\sqrt[3]{1} \cdot \sqrt[3]{1}}}{\sqrt[3]{\sqrt[3]{e^{w}} \cdot \sqrt[3]{e^{w}}}}\right) \cdot \left(\sqrt[3]{e^{-w}} \cdot {\ell}^{\left(e^{w}\right)}\right) \]

  14. Applied cbrt-div_binary640.3

    \[\leadsto \left(\left(\sqrt[3]{\sqrt[3]{e^{-w}} \cdot \sqrt[3]{e^{-w}}} \cdot \sqrt[3]{\color{blue}{\frac{\sqrt[3]{1}}{\sqrt[3]{e^{w}}}} \cdot \frac{\sqrt[3]{1}}{\sqrt[3]{e^{w}}}}\right) \cdot \frac{\sqrt[3]{\sqrt[3]{1} \cdot \sqrt[3]{1}}}{\sqrt[3]{\sqrt[3]{e^{w}} \cdot \sqrt[3]{e^{w}}}}\right) \cdot \left(\sqrt[3]{e^{-w}} \cdot {\ell}^{\left(e^{w}\right)}\right) \]

  15. Applied frac-times_binary640.3

    \[\leadsto \left(\left(\sqrt[3]{\sqrt[3]{e^{-w}} \cdot \sqrt[3]{e^{-w}}} \cdot \sqrt[3]{\color{blue}{\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\sqrt[3]{e^{w}} \cdot \sqrt[3]{e^{w}}}}}\right) \cdot \frac{\sqrt[3]{\sqrt[3]{1} \cdot \sqrt[3]{1}}}{\sqrt[3]{\sqrt[3]{e^{w}} \cdot \sqrt[3]{e^{w}}}}\right) \cdot \left(\sqrt[3]{e^{-w}} \cdot {\ell}^{\left(e^{w}\right)}\right) \]

  16. Applied cbrt-div_binary640.3

    \[\leadsto \left(\left(\sqrt[3]{\sqrt[3]{e^{-w}} \cdot \sqrt[3]{e^{-w}}} \cdot \color{blue}{\frac{\sqrt[3]{\sqrt[3]{1} \cdot \sqrt[3]{1}}}{\sqrt[3]{\sqrt[3]{e^{w}} \cdot \sqrt[3]{e^{w}}}}}\right) \cdot \frac{\sqrt[3]{\sqrt[3]{1} \cdot \sqrt[3]{1}}}{\sqrt[3]{\sqrt[3]{e^{w}} \cdot \sqrt[3]{e^{w}}}}\right) \cdot \left(\sqrt[3]{e^{-w}} \cdot {\ell}^{\left(e^{w}\right)}\right) \]

  17. Applied exp-neg_binary640.3

    \[\leadsto \left(\left(\sqrt[3]{\sqrt[3]{e^{-w}} \cdot \sqrt[3]{\color{blue}{\frac{1}{e^{w}}}}} \cdot \frac{\sqrt[3]{\sqrt[3]{1} \cdot \sqrt[3]{1}}}{\sqrt[3]{\sqrt[3]{e^{w}} \cdot \sqrt[3]{e^{w}}}}\right) \cdot \frac{\sqrt[3]{\sqrt[3]{1} \cdot \sqrt[3]{1}}}{\sqrt[3]{\sqrt[3]{e^{w}} \cdot \sqrt[3]{e^{w}}}}\right) \cdot \left(\sqrt[3]{e^{-w}} \cdot {\ell}^{\left(e^{w}\right)}\right) \]

  18. Applied cbrt-div_binary640.3

    \[\leadsto \left(\left(\sqrt[3]{\sqrt[3]{e^{-w}} \cdot \color{blue}{\frac{\sqrt[3]{1}}{\sqrt[3]{e^{w}}}}} \cdot \frac{\sqrt[3]{\sqrt[3]{1} \cdot \sqrt[3]{1}}}{\sqrt[3]{\sqrt[3]{e^{w}} \cdot \sqrt[3]{e^{w}}}}\right) \cdot \frac{\sqrt[3]{\sqrt[3]{1} \cdot \sqrt[3]{1}}}{\sqrt[3]{\sqrt[3]{e^{w}} \cdot \sqrt[3]{e^{w}}}}\right) \cdot \left(\sqrt[3]{e^{-w}} \cdot {\ell}^{\left(e^{w}\right)}\right) \]

  19. Applied exp-neg_binary640.3

    \[\leadsto \left(\left(\sqrt[3]{\sqrt[3]{\color{blue}{\frac{1}{e^{w}}}} \cdot \frac{\sqrt[3]{1}}{\sqrt[3]{e^{w}}}} \cdot \frac{\sqrt[3]{\sqrt[3]{1} \cdot \sqrt[3]{1}}}{\sqrt[3]{\sqrt[3]{e^{w}} \cdot \sqrt[3]{e^{w}}}}\right) \cdot \frac{\sqrt[3]{\sqrt[3]{1} \cdot \sqrt[3]{1}}}{\sqrt[3]{\sqrt[3]{e^{w}} \cdot \sqrt[3]{e^{w}}}}\right) \cdot \left(\sqrt[3]{e^{-w}} \cdot {\ell}^{\left(e^{w}\right)}\right) \]

  20. Applied cbrt-div_binary640.3

    \[\leadsto \left(\left(\sqrt[3]{\color{blue}{\frac{\sqrt[3]{1}}{\sqrt[3]{e^{w}}}} \cdot \frac{\sqrt[3]{1}}{\sqrt[3]{e^{w}}}} \cdot \frac{\sqrt[3]{\sqrt[3]{1} \cdot \sqrt[3]{1}}}{\sqrt[3]{\sqrt[3]{e^{w}} \cdot \sqrt[3]{e^{w}}}}\right) \cdot \frac{\sqrt[3]{\sqrt[3]{1} \cdot \sqrt[3]{1}}}{\sqrt[3]{\sqrt[3]{e^{w}} \cdot \sqrt[3]{e^{w}}}}\right) \cdot \left(\sqrt[3]{e^{-w}} \cdot {\ell}^{\left(e^{w}\right)}\right) \]

  21. Applied frac-times_binary640.3

    \[\leadsto \left(\left(\sqrt[3]{\color{blue}{\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\sqrt[3]{e^{w}} \cdot \sqrt[3]{e^{w}}}}} \cdot \frac{\sqrt[3]{\sqrt[3]{1} \cdot \sqrt[3]{1}}}{\sqrt[3]{\sqrt[3]{e^{w}} \cdot \sqrt[3]{e^{w}}}}\right) \cdot \frac{\sqrt[3]{\sqrt[3]{1} \cdot \sqrt[3]{1}}}{\sqrt[3]{\sqrt[3]{e^{w}} \cdot \sqrt[3]{e^{w}}}}\right) \cdot \left(\sqrt[3]{e^{-w}} \cdot {\ell}^{\left(e^{w}\right)}\right) \]

  22. Applied cbrt-div_binary640.3

    \[\leadsto \left(\left(\color{blue}{\frac{\sqrt[3]{\sqrt[3]{1} \cdot \sqrt[3]{1}}}{\sqrt[3]{\sqrt[3]{e^{w}} \cdot \sqrt[3]{e^{w}}}}} \cdot \frac{\sqrt[3]{\sqrt[3]{1} \cdot \sqrt[3]{1}}}{\sqrt[3]{\sqrt[3]{e^{w}} \cdot \sqrt[3]{e^{w}}}}\right) \cdot \frac{\sqrt[3]{\sqrt[3]{1} \cdot \sqrt[3]{1}}}{\sqrt[3]{\sqrt[3]{e^{w}} \cdot \sqrt[3]{e^{w}}}}\right) \cdot \left(\sqrt[3]{e^{-w}} \cdot {\ell}^{\left(e^{w}\right)}\right) \]

  23. Applied frac-times_binary640.3

    \[\leadsto \left(\color{blue}{\frac{\sqrt[3]{\sqrt[3]{1} \cdot \sqrt[3]{1}} \cdot \sqrt[3]{\sqrt[3]{1} \cdot \sqrt[3]{1}}}{\sqrt[3]{\sqrt[3]{e^{w}} \cdot \sqrt[3]{e^{w}}} \cdot \sqrt[3]{\sqrt[3]{e^{w}} \cdot \sqrt[3]{e^{w}}}}} \cdot \frac{\sqrt[3]{\sqrt[3]{1} \cdot \sqrt[3]{1}}}{\sqrt[3]{\sqrt[3]{e^{w}} \cdot \sqrt[3]{e^{w}}}}\right) \cdot \left(\sqrt[3]{e^{-w}} \cdot {\ell}^{\left(e^{w}\right)}\right) \]

  24. Applied frac-times_binary640.3

    \[\leadsto \color{blue}{\frac{\left(\sqrt[3]{\sqrt[3]{1} \cdot \sqrt[3]{1}} \cdot \sqrt[3]{\sqrt[3]{1} \cdot \sqrt[3]{1}}\right) \cdot \sqrt[3]{\sqrt[3]{1} \cdot \sqrt[3]{1}}}{\left(\sqrt[3]{\sqrt[3]{e^{w}} \cdot \sqrt[3]{e^{w}}} \cdot \sqrt[3]{\sqrt[3]{e^{w}} \cdot \sqrt[3]{e^{w}}}\right) \cdot \sqrt[3]{\sqrt[3]{e^{w}} \cdot \sqrt[3]{e^{w}}}}} \cdot \left(\sqrt[3]{e^{-w}} \cdot {\ell}^{\left(e^{w}\right)}\right) \]

  25. Applied add-cube-cbrt_binary640.3

    \[\leadsto \color{blue}{\left(\left(\sqrt[3]{\frac{\left(\sqrt[3]{\sqrt[3]{1} \cdot \sqrt[3]{1}} \cdot \sqrt[3]{\sqrt[3]{1} \cdot \sqrt[3]{1}}\right) \cdot \sqrt[3]{\sqrt[3]{1} \cdot \sqrt[3]{1}}}{\left(\sqrt[3]{\sqrt[3]{e^{w}} \cdot \sqrt[3]{e^{w}}} \cdot \sqrt[3]{\sqrt[3]{e^{w}} \cdot \sqrt[3]{e^{w}}}\right) \cdot \sqrt[3]{\sqrt[3]{e^{w}} \cdot \sqrt[3]{e^{w}}}}} \cdot \sqrt[3]{\frac{\left(\sqrt[3]{\sqrt[3]{1} \cdot \sqrt[3]{1}} \cdot \sqrt[3]{\sqrt[3]{1} \cdot \sqrt[3]{1}}\right) \cdot \sqrt[3]{\sqrt[3]{1} \cdot \sqrt[3]{1}}}{\left(\sqrt[3]{\sqrt[3]{e^{w}} \cdot \sqrt[3]{e^{w}}} \cdot \sqrt[3]{\sqrt[3]{e^{w}} \cdot \sqrt[3]{e^{w}}}\right) \cdot \sqrt[3]{\sqrt[3]{e^{w}} \cdot \sqrt[3]{e^{w}}}}}\right) \cdot \sqrt[3]{\frac{\left(\sqrt[3]{\sqrt[3]{1} \cdot \sqrt[3]{1}} \cdot \sqrt[3]{\sqrt[3]{1} \cdot \sqrt[3]{1}}\right) \cdot \sqrt[3]{\sqrt[3]{1} \cdot \sqrt[3]{1}}}{\left(\sqrt[3]{\sqrt[3]{e^{w}} \cdot \sqrt[3]{e^{w}}} \cdot \sqrt[3]{\sqrt[3]{e^{w}} \cdot \sqrt[3]{e^{w}}}\right) \cdot \sqrt[3]{\sqrt[3]{e^{w}} \cdot \sqrt[3]{e^{w}}}}}\right)} \cdot \left(\sqrt[3]{e^{-w}} \cdot {\ell}^{\left(e^{w}\right)}\right) \]

  26. Final simplification0.3

    \[\leadsto \left(\sqrt[3]{\frac{1}{\sqrt[3]{\sqrt[3]{e^{w}} \cdot \sqrt[3]{e^{w}}} \cdot \left(\sqrt[3]{\sqrt[3]{e^{w}} \cdot \sqrt[3]{e^{w}}} \cdot \sqrt[3]{\sqrt[3]{e^{w}} \cdot \sqrt[3]{e^{w}}}\right)}} \cdot \left(\sqrt[3]{\frac{1}{\sqrt[3]{\sqrt[3]{e^{w}} \cdot \sqrt[3]{e^{w}}} \cdot \left(\sqrt[3]{\sqrt[3]{e^{w}} \cdot \sqrt[3]{e^{w}}} \cdot \sqrt[3]{\sqrt[3]{e^{w}} \cdot \sqrt[3]{e^{w}}}\right)}} \cdot \sqrt[3]{\frac{1}{\sqrt[3]{\sqrt[3]{e^{w}} \cdot \sqrt[3]{e^{w}}} \cdot \left(\sqrt[3]{\sqrt[3]{e^{w}} \cdot \sqrt[3]{e^{w}}} \cdot \sqrt[3]{\sqrt[3]{e^{w}} \cdot \sqrt[3]{e^{w}}}\right)}}\right)\right) \cdot \left(\sqrt[3]{e^{-w}} \cdot {\ell}^{\left(e^{w}\right)}\right) \]

Reproduce

herbie shell --seed 2021275 
(FPCore (w l)
  :name "exp-w crasher"
  :precision binary64
  (* (exp (- w)) (pow l (exp w))))