Here’s Lexus’ dad joke, a creamsicle-on-wheels that they hope you’ll try instead of a top-flight German sports sedan and say, “Orange I glad I did? I yam.” And not to worry – if you’d rather have a colour other than the retina-searing Solar Flare, the GS F comes in six boring colours and three exciting ones. I’d go for the lovely, although stupidly named, Ultrasonic Blue Mica 2.0.

However, even in Oh Hello Officer Orange, it’s hard not to like this car. Yes, the Lexus design language is a bit shouty, especially when grafted onto the incongruously soft RX crossover, but here at least the GS F has some cojones to back up its big-mouthed bragging. What’s more, your modern Audi now looks like a basking shark crossed with the speaker tower at an AC/DC concert; BMWs all have their once-delicate kidney grilles flared out like the nostrils of a moose on bath salts; and the gawping lower air intakes of a Mercedes-AMG product look like a Wallace and Gromit character thinking about something terrifying. Everybody’s crazy – why not Lexus too?

So, perhaps some allowance can be made for the Dukes of Aichi Prefecture’s visual yee-haw, with its swooshy LED mascara, stabby 19” forged alloys and spindle grille the size of a Cylon baleen whale. The basic GS sedan is aggressive enough, and this one gets even more hunched out, its fenders flaring and the hood bulging with the powerplant barely wedged underneath. Out back, there’s a carbon-fibre upper lip and offset quad tailpipes that pay homage to the original IS-F’s lunacy.

Pop that bonnet, as an Elizabethan rapper might say, and the GS F displays further visual wonderment. You can see the engine! It’s right there! Almost everybody else will let you have a carefully crafted plastic engine cover, perhaps with the signature of der Handwerker who built the beast underneath, but Lexus actually lets you have a gander at a blue-shaded intake manifold.

This is F-performance’s current crown jewel, a 5.0L V8 making 467 hp at 7,100 rpm and 389 lb-ft at 4,800 rpm. Direct injection, dual variable-valve timing control, 12.3:1 compression, 7,300 rpm redline – it’s all here, and it’s all wonderful.

But what’s the Japanese for uh-oh? Last time I checked, both the BMW M5 and the Mercedes-AMG E63 were cranking out nearly 600hp from large-displacement V8s. That’s quite the power gap compared to the top-dog Lexus: has Lexus brought a Mustang to a rocket fight?

Both AMG and M are more expensive machines, and quite a bit heavier. The GS F is no lightweight, tipping the scales at a solid 1,830kg, but it’s not actually that much heavier than the RC-F coupe. When compared the Germans’ big guns, it’s nearly 10% lighter. It’s also less of a heavy hit to your wallet, creeping just in a shade under a hundred grand.

I know, I know. What a deal – trading in my 1997 V6 Camry tomorrow. But still, in the rarefied air of the max-performance luxury sedan, the GS F offers an interesting alternative to M-sport versions of the 550i and the S6, without the nagging feeling you get from BMW and Audi that there’s a plateau above you that you couldn’t quite reach. The GS F is the fastest Lexus four-door, but it’s a little more attainable than the competition. And things get more interesting when you stop playing the cerebral numbers game and get to the heart of this thing.