Exception for 2-ancestry mixing, positive discriminant

Math

\[\sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right)} + \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)} \]

FPCore

(FPCore (g h a)
 :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))))))))

C

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

Java

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

Julia

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

Wolfram

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

Reproduce

Please include this information when filing a bug report:

herbie shell --seed 2022204 
(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))))))))

Backtrace

nan?: contract violation expected: real? given: 0.39685026299205+0.6873648184993013i		L	C
simplify-node*	/data/pavpan/nightlies/herbie/fix-inf-exact/src/core/reduce.rkt	61	0
hash-ref!	/usr/share/racket/collects/racket/private/more-scheme.rkt	377	2
hash-ref!	/usr/share/racket/collects/racket/private/more-scheme.rkt	377	2
approximate	/data/pavpan/nightlies/herbie/fix-inf-exact/src/core/taylor.rkt	7	0
taylor-expr	/data/pavpan/nightlies/herbie/fix-inf-exact/src/patch.rkt	78	0
taylor-alt	/data/pavpan/nightlies/herbie/fix-inf-exact/src/patch.rkt	85	0
gen-series!	/data/pavpan/nightlies/herbie/fix-inf-exact/src/patch.rkt	101	0
patch-table-run	/data/pavpan/nightlies/herbie/fix-inf-exact/src/patch.rkt	310	0
(unnamed)	/usr/share/racket/collects/racket/contract/private/arrow-val-first.rkt	486	18
run-iter!	/data/pavpan/nightlies/herbie/fix-inf-exact/src/mainloop.rkt	242	0
mutate!	/data/pavpan/nightlies/herbie/fix-inf-exact/src/mainloop.rkt	348	0
run-improve!	/data/pavpan/nightlies/herbie/fix-inf-exact/src/mainloop.rkt	296	0
(unnamed)	/data/pavpan/nightlies/herbie/fix-inf-exact/src/sandbox.rkt	55	6
(unnamed)	/usr/share/racket/pkgs/profile-lib/main.rkt	40	10
profile-thunk	/usr/share/racket/pkgs/profile-lib/main.rkt	9	0
(unnamed)	/usr/share/racket/collects/racket/engine.rkt	42	24