Exception for Cubic critical

Math

\[\frac{\left(-b\right) + \sqrt{b \cdot b - \left(3 \cdot a\right) \cdot c}}{3 \cdot a} \]

FPCore

(FPCore (a b c)
 :precision binary64
 (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a)))

C

double code(double a, double b, double c) {
	return (-b + sqrt(((b * b) - ((3.0 * a) * c)))) / (3.0 * a);
}

Fortran

real(8) function code(a, b, c)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    code = (-b + sqrt(((b * b) - ((3.0d0 * a) * c)))) / (3.0d0 * a)
end function

Java

public static double code(double a, double b, double c) {
	return (-b + Math.sqrt(((b * b) - ((3.0 * a) * c)))) / (3.0 * a);
}

Python

def code(a, b, c):
	return (-b + math.sqrt(((b * b) - ((3.0 * a) * c)))) / (3.0 * a)

Julia

function code(a, b, c)
	return Float64(Float64(Float64(-b) + sqrt(Float64(Float64(b * b) - Float64(Float64(3.0 * a) * c)))) / Float64(3.0 * a))
end

MATLAB

function tmp = code(a, b, c)
	tmp = (-b + sqrt(((b * b) - ((3.0 * a) * c)))) / (3.0 * a);
end

Wolfram

code[a_, b_, c_] := N[(N[((-b) + N[Sqrt[N[(N[(b * b), $MachinePrecision] - N[(N[(3.0 * a), $MachinePrecision] * c), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / N[(3.0 * a), $MachinePrecision]), $MachinePrecision]

Reproduce

Please include this information when filing a bug report:

herbie shell --seed 2022204 
(FPCore (a b c)
  :name "Cubic critical"
  :precision binary64
  (/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a)))

Backtrace

nan?: contract violation expected: real? given: 0.5000000000000001+0.8660254037844386i		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
taylor-cbrt	/data/pavpan/nightlies/herbie/fix-inf-exact/src/core/taylor.rkt	336	0
hash-ref!	/usr/share/racket/collects/racket/private/more-scheme.rkt	377	2
taylor*	/data/pavpan/nightlies/herbie/fix-inf-exact/src/core/taylor.rkt	98	0
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