2-ancestry mixing, negative discriminant

Average Error: 1.0 → 1.0

Time: 6.0s

Precision: binary64

Cost: 26368

Math

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

↓

\[2 \cdot \cos \left({\left(\frac{1.5}{\pi}\right)}^{-1} + \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right) \]

FPCore

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

↓

(FPCore (g h)
 :precision binary64
 (* 2.0 (cos (+ (pow (/ 1.5 PI) -1.0) (/ (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)));
}

↓

double code(double g, double h) {
	return 2.0 * cos((pow((1.5 / ((double) M_PI)), -1.0) + (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)));
}

↓

public static double code(double g, double h) {
	return 2.0 * Math.cos((Math.pow((1.5 / Math.PI), -1.0) + (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)))

↓

def code(g, h):
	return 2.0 * math.cos((math.pow((1.5 / math.pi), -1.0) + (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

↓

function code(g, h)
	return Float64(2.0 * cos(Float64((Float64(1.5 / pi) ^ -1.0) + 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

↓

function tmp = code(g, h)
	tmp = 2.0 * cos((((1.5 / pi) ^ -1.0) + (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]

↓

code[g_, h_] := N[(2.0 * N[Cos[N[(N[Power[N[(1.5 / Pi), $MachinePrecision], -1.0], $MachinePrecision] + N[(N[ArcCos[N[((-g) / h), $MachinePrecision]], $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 1.0

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

2. Applied egg-rr 1.0

   \[\leadsto 2 \cdot \cos \left(\color{blue}{{\left(\frac{1.5}{\pi}\right)}^{-1}} + \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right) \]

3. Final simplification 1.0

   \[\leadsto 2 \cdot \cos \left({\left(\frac{1.5}{\pi}\right)}^{-1} + \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right) \]

Alternatives

Alternative 1
Error	1.0
Cost	19904

\[2 \cdot \cos \left(\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3} + \pi \cdot 0.6666666666666666\right) \]

Alternative 2
Error	2.1
Cost	19840

\[2 \cdot \cos \left(\pi \cdot 0.6666666666666666 + \cos^{-1} \left(\frac{g}{h}\right) \cdot 0.3333333333333333\right) \]

Reproduce

herbie shell --seed 2022291 
(FPCore (g h)
  :name "2-ancestry mixing, negative discriminant"
  :precision binary64
  (* 2.0 (cos (+ (/ (* 2.0 PI) 3.0) (/ (acos (/ (- g) h)) 3.0)))))