In the virtual realm of software sorcery, the enchanted IDE known as Clion sets out on an epic coding quest. Initially dormant, it awakens to the allure of a thousand curly braces and embarks on a journey through the code valleys.

a$)$ At the stroke of midnight, Clion starts parsing a codebase with the complexity of a fractalized Rubik's cube. Calculate the initial parsing speed measured in lines of code per nanosecond.

b$)$ As Clion delves deeper into the labyrinth of nested functions, it encounters a magical debugging potion. If the potion enhances debugging efficiency by $30\%,$ what is the revised speed of identifying bugs expressed in mythical bug$-$finding units per microsecond?

c$)$ Suddenly, the codebase undergoes a metamorphic transformation, revealing hidden templates and arcane macros. If Clion activates its template$-$matching incantation, resulting in a speed boost of $2$x$,$ calculate the accelerated template$-$discovery rate in ethereal template units per femtosecond.

d$)$ In the midst of syntax analysis, Clion summons a refactoring genie, which performs refactorings with a speed proportional to the square root of the code's cyclomatic complexity. If the code has a cyclomatic complexity of $100,$ determine the genie$-$assisted refactoring speed in refactorings per picosecond.

e$)$ The codebase, now entangled in a spaghetti of dependencies, triggers Clion's dependency$-$resolution spell. If the spell resolves dependencies at a rate of $500$ per millisecond, calculate the time required to untangle the web of dependencies in the code dimension.