Exception for 2-ancestry mixing, negative discriminant

Specification

Math

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

FPCore

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

C

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

Java

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)));
}

Python

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

Julia

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

MATLAB

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

Wolfram

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]

Reproduce

herbie shell --seed 2025191 
(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

egraph-prove: cannot prove (*.f64 (cos.f64 (fma.f64 #s(literal 1/3 binary64) (acos.f64 (/.f64 (neg.f64 g) h)) (*.f64 (PI.f64) #s(literal 2/3 binary64)))) #s(literal 2 binary64)) is equal to (*.f64 (cos.f64 (fma.f64 #s(literal -1/3 binary64) (acos.f64 (/.f64 (neg.f64 g) h)) #s(literal -2358079250676147/1125899906842624 binary64))) #s(literal 2 binary64)); 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
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