Exception for 2-ancestry mixing, negative discriminant

Specification

\[\begin{array}{l} \\ 2 \cdot \cos \left(\frac{2 \cdot \pi}{3} + \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right) \end{array} \]

(FPCore (g h)
 :precision binary64
 (* 2.0 (cos (+ (/ (* 2.0 PI) 3.0) (/ (acos (/ (- g) h)) 3.0)))))

double code(double g, double h) {
	return 2.0 * cos((((2.0 * ((double) M_PI)) / 3.0) + (acos((-g / h)) / 3.0)));
}

public static double code(double g, double h) {
	return 2.0 * Math.cos((((2.0 * Math.PI) / 3.0) + (Math.acos((-g / h)) / 3.0)));
}

def code(g, h):
	return 2.0 * math.cos((((2.0 * math.pi) / 3.0) + (math.acos((-g / h)) / 3.0)))

function code(g, h)
	return Float64(2.0 * cos(Float64(Float64(Float64(2.0 * pi) / 3.0) + Float64(acos(Float64(Float64(-g) / h)) / 3.0))))
end

function tmp = code(g, h)
	tmp = 2.0 * cos((((2.0 * pi) / 3.0) + (acos((-g / h)) / 3.0)));
end

code[g_, h_] := N[(2.0 * N[Cos[N[(N[(N[(2.0 * Pi), $MachinePrecision] / 3.0), $MachinePrecision] + N[(N[ArcCos[N[((-g) / h), $MachinePrecision]], $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

\begin{array}{l}

\\
2 \cdot \cos \left(\frac{2 \cdot \pi}{3} + \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right)
\end{array}

Reproduce

herbie shell --seed 2025097 
(FPCore (g h)
  :name "2-ancestry mixing, negative discriminant"
  :precision binary64
  (* 2.0 (cos (+ (/ (* 2.0 PI) 3.0) (/ (acos (/ (- g) h)) 3.0)))))

Please file a bug report with this information.

Backtrace

egglog executable not found in PATH		L	C
run-egglog-multi-extractor	/home/nightlies/herbie/optimize-egglog/src/core/egglog-herbie.rkt	132	0
run-rr	/home/nightlies/herbie/optimize-egglog/src/core/patch.rkt	71	0
generate-candidates	/home/nightlies/herbie/optimize-egglog/src/core/patch.rkt	116	0
finish-iter!	/home/nightlies/herbie/optimize-egglog/src/core/mainloop.rkt	226	0
run-improve!	/home/nightlies/herbie/optimize-egglog/src/core/mainloop.rkt	40	0
get-alternatives	/home/nightlies/herbie/optimize-egglog/src/api/sandbox.rkt	61	0
(unnamed)	/home/nightlies/herbie/optimize-egglog/src/api/sandbox.rkt	193	6
(unnamed)	/usr/share/racket/pkgs/profile-lib/main.rkt	40	10
profile-thunk	/usr/share/racket/pkgs/profile-lib/main.rkt	9	0
in-engine	/home/nightlies/herbie/optimize-egglog/src/api/sandbox.rkt	209	2
(unnamed)	/usr/share/racket/collects/racket/engine.rkt	42	24