Exception for 2-ancestry mixing, positive discriminant

Specification

\[\begin{array}{l} t_0 := \frac{1}{2 \cdot a}\\ t_1 := \sqrt{g \cdot g - h \cdot h}\\ \sqrt[3]{t\_0 \cdot \left(\left(-g\right) + t\_1\right)} + \sqrt[3]{t\_0 \cdot \left(\left(-g\right) - t\_1\right)} \end{array} \]

(FPCore (g h a)
 :precision binary64
 (let* ((t_0 (/ 1.0 (* 2.0 a))) (t_1 (sqrt (- (* g g) (* h h)))))
   (+ (cbrt (* t_0 (+ (- g) t_1))) (cbrt (* t_0 (- (- g) t_1))))))

double code(double g, double h, double a) {
	double t_0 = 1.0 / (2.0 * a);
	double t_1 = sqrt(((g * g) - (h * h)));
	return cbrt((t_0 * (-g + t_1))) + cbrt((t_0 * (-g - t_1)));
}

public static double code(double g, double h, double a) {
	double t_0 = 1.0 / (2.0 * a);
	double t_1 = Math.sqrt(((g * g) - (h * h)));
	return Math.cbrt((t_0 * (-g + t_1))) + Math.cbrt((t_0 * (-g - t_1)));
}

function code(g, h, a)
	t_0 = Float64(1.0 / Float64(2.0 * a))
	t_1 = sqrt(Float64(Float64(g * g) - Float64(h * h)))
	return Float64(cbrt(Float64(t_0 * Float64(Float64(-g) + t_1))) + cbrt(Float64(t_0 * Float64(Float64(-g) - t_1))))
end

code[g_, h_, a_] := Block[{t$95$0 = N[(1.0 / N[(2.0 * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[Sqrt[N[(N[(g * g), $MachinePrecision] - N[(h * h), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, N[(N[Power[N[(t$95$0 * N[((-g) + t$95$1), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision] + N[Power[N[(t$95$0 * N[((-g) - t$95$1), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision]]]

\begin{array}{l}
t_0 := \frac{1}{2 \cdot a}\\
t_1 := \sqrt{g \cdot g - h \cdot h}\\
\sqrt[3]{t\_0 \cdot \left(\left(-g\right) + t\_1\right)} + \sqrt[3]{t\_0 \cdot \left(\left(-g\right) - t\_1\right)}
\end{array}

Reproduce

herbie shell --seed 2025191 
(FPCore (g h a)
  :name "2-ancestry mixing, positive discriminant"
  :precision binary64
  (+ (cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h)))))) (cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))))

Please file a bug report with this information.

Backtrace

egraph-prove: cannot prove (+.f64 (cbrt.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) a)) (.f64 (-.f64 #s(literal 1 binary64) (/.f64 g (sqrt.f64 (.f64 (-.f64 g h) (+.f64 h g))))) (sqrt.f64 (.f64 (-.f64 g h) (+.f64 h g)))))) (cbrt.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) a)) (-.f64 (neg.f64 g) (sqrt.f64 (-.f64 (.f64 g g) (.f64 h h))))))) is equal to (.f64 (/.f64 #s(literal -1 binary64) (cbrt.f64 a)) (cbrt.f64 g)); not equal		L	C
add-derivations-to	/home/nightlies/herbie/batch-reconstruct-alt/src/core/derivations.rkt	16	0
hash-ref!	/usr/share/racket/collects/racket/private/more-scheme.rkt	377	2
loop	.../private/map.rkt	40	19
alt-map	/home/nightlies/herbie/batch-reconstruct-alt/src/utils/alternative.rkt	20	0
add-derivations	/home/nightlies/herbie/batch-reconstruct-alt/src/core/derivations.rkt	30	0
extract!	/home/nightlies/herbie/batch-reconstruct-alt/src/core/mainloop.rkt	70	0
run-improve!	/home/nightlies/herbie/batch-reconstruct-alt/src/core/mainloop.rkt	42	0
get-alternatives	/home/nightlies/herbie/batch-reconstruct-alt/src/api/sandbox.rkt	61	0
(unnamed)	/home/nightlies/herbie/batch-reconstruct-alt/src/api/sandbox.rkt	181	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/batch-reconstruct-alt/src/api/sandbox.rkt	197	2
(unnamed)	/usr/share/racket/collects/racket/engine.rkt	42	24