2-ancestry mixing, negative discriminant

Percentage Accurate: 98.5% → 99.9%

Time: 56.0s

Alternatives: 4

Speedup: 1.0×

Specification

Math

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

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]

Initial Program: 98.5% accurate, 1.0× speedup

Math

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

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]

Alternative 1: 99.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \cos^{-1} \left(0 - \frac{g}{h}\right)\\ t_1 := \frac{t\_0}{-3}\\ t_2 := \pi \cdot 0.6666666666666666 + t\_1\\ \left(\frac{2}{\cos \left(\frac{\frac{{t\_0}^{2}}{9} + 0.4444444444444444 \cdot \left(\pi \cdot \pi\right)}{t\_2}\right)} \cdot \cos \left(\pi \cdot 0.6666666666666666 - t\_1\right)\right) \cdot \cos \left(\frac{{\left(\frac{t\_0}{3}\right)}^{2} + \pi \cdot \left(\pi \cdot 0.4444444444444444\right)}{t\_2}\right) \end{array} \end{array} \]

FPCore

(FPCore (g h)
 :precision binary64
 (let* ((t_0 (acos (- 0.0 (/ g h))))
        (t_1 (/ t_0 -3.0))
        (t_2 (+ (* PI 0.6666666666666666) t_1)))
   (*
    (*
     (/
      2.0
      (cos (/ (+ (/ (pow t_0 2.0) 9.0) (* 0.4444444444444444 (* PI PI))) t_2)))
     (cos (- (* PI 0.6666666666666666) t_1)))
    (cos (/ (+ (pow (/ t_0 3.0) 2.0) (* PI (* PI 0.4444444444444444))) t_2)))))

C

double code(double g, double h) {
	double t_0 = acos((0.0 - (g / h)));
	double t_1 = t_0 / -3.0;
	double t_2 = (((double) M_PI) * 0.6666666666666666) + t_1;
	return ((2.0 / cos((((pow(t_0, 2.0) / 9.0) + (0.4444444444444444 * (((double) M_PI) * ((double) M_PI)))) / t_2))) * cos(((((double) M_PI) * 0.6666666666666666) - t_1))) * cos(((pow((t_0 / 3.0), 2.0) + (((double) M_PI) * (((double) M_PI) * 0.4444444444444444))) / t_2));
}

Java

public static double code(double g, double h) {
	double t_0 = Math.acos((0.0 - (g / h)));
	double t_1 = t_0 / -3.0;
	double t_2 = (Math.PI * 0.6666666666666666) + t_1;
	return ((2.0 / Math.cos((((Math.pow(t_0, 2.0) / 9.0) + (0.4444444444444444 * (Math.PI * Math.PI))) / t_2))) * Math.cos(((Math.PI * 0.6666666666666666) - t_1))) * Math.cos(((Math.pow((t_0 / 3.0), 2.0) + (Math.PI * (Math.PI * 0.4444444444444444))) / t_2));
}

Python

def code(g, h):
	t_0 = math.acos((0.0 - (g / h)))
	t_1 = t_0 / -3.0
	t_2 = (math.pi * 0.6666666666666666) + t_1
	return ((2.0 / math.cos((((math.pow(t_0, 2.0) / 9.0) + (0.4444444444444444 * (math.pi * math.pi))) / t_2))) * math.cos(((math.pi * 0.6666666666666666) - t_1))) * math.cos(((math.pow((t_0 / 3.0), 2.0) + (math.pi * (math.pi * 0.4444444444444444))) / t_2))

Julia

function code(g, h)
	t_0 = acos(Float64(0.0 - Float64(g / h)))
	t_1 = Float64(t_0 / -3.0)
	t_2 = Float64(Float64(pi * 0.6666666666666666) + t_1)
	return Float64(Float64(Float64(2.0 / cos(Float64(Float64(Float64((t_0 ^ 2.0) / 9.0) + Float64(0.4444444444444444 * Float64(pi * pi))) / t_2))) * cos(Float64(Float64(pi * 0.6666666666666666) - t_1))) * cos(Float64(Float64((Float64(t_0 / 3.0) ^ 2.0) + Float64(pi * Float64(pi * 0.4444444444444444))) / t_2)))
end

MATLAB

function tmp = code(g, h)
	t_0 = acos((0.0 - (g / h)));
	t_1 = t_0 / -3.0;
	t_2 = (pi * 0.6666666666666666) + t_1;
	tmp = ((2.0 / cos(((((t_0 ^ 2.0) / 9.0) + (0.4444444444444444 * (pi * pi))) / t_2))) * cos(((pi * 0.6666666666666666) - t_1))) * cos(((((t_0 / 3.0) ^ 2.0) + (pi * (pi * 0.4444444444444444))) / t_2));
end

Wolfram

code[g_, h_] := Block[{t$95$0 = N[ArcCos[N[(0.0 - N[(g / h), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 / -3.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(Pi * 0.6666666666666666), $MachinePrecision] + t$95$1), $MachinePrecision]}, N[(N[(N[(2.0 / N[Cos[N[(N[(N[(N[Power[t$95$0, 2.0], $MachinePrecision] / 9.0), $MachinePrecision] + N[(0.4444444444444444 * N[(Pi * Pi), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[Cos[N[(N[(Pi * 0.6666666666666666), $MachinePrecision] - t$95$1), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[Cos[N[(N[(N[Power[N[(t$95$0 / 3.0), $MachinePrecision], 2.0], $MachinePrecision] + N[(Pi * N[(Pi * 0.4444444444444444), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$2), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Initial program 98.4%

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

3. Simplified 0

   \[\leadsto expr\]
4. Add Preprocessing

6. Applied egg-rr 0

   \[\leadsto expr\]

8. Applied egg-rr 0

   \[\leadsto expr\]

10. Applied egg-rr 0

    \[\leadsto expr\]

12. Applied egg-rr 0

    \[\leadsto expr\]
13. Add Preprocessing

Alternative 2: 98.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ 2 \cdot \cos \left(\mathsf{fma}\left(\sqrt[3]{\pi \cdot \left(\pi \cdot \pi\right)}, 0.6666666666666666, \frac{\cos^{-1} \left(0 - \frac{g}{h}\right)}{3}\right)\right) \end{array} \]

FPCore

(FPCore (g h)
 :precision binary64
 (*
  2.0
  (cos
   (fma
    (cbrt (* PI (* PI PI)))
    0.6666666666666666
    (/ (acos (- 0.0 (/ g h))) 3.0)))))

C

double code(double g, double h) {
	return 2.0 * cos(fma(cbrt((((double) M_PI) * (((double) M_PI) * ((double) M_PI)))), 0.6666666666666666, (acos((0.0 - (g / h))) / 3.0)));
}

Julia

function code(g, h)
	return Float64(2.0 * cos(fma(cbrt(Float64(pi * Float64(pi * pi))), 0.6666666666666666, Float64(acos(Float64(0.0 - Float64(g / h))) / 3.0))))
end

Wolfram

code[g_, h_] := N[(2.0 * N[Cos[N[(N[Power[N[(Pi * N[(Pi * Pi), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision] * 0.6666666666666666 + N[(N[ArcCos[N[(0.0 - N[(g / h), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 98.4%

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

3. Simplified 0

   \[\leadsto expr\]
4. Add Preprocessing

6. Applied egg-rr 0

   \[\leadsto expr\]

8. Applied egg-rr 0

   \[\leadsto expr\]
9. Add Preprocessing

Alternative 3: 98.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ 2 \cdot \cos \left(\mathsf{fma}\left(\pi, 0.6666666666666666, \frac{\cos^{-1} \left(0 - \frac{g}{h}\right)}{3}\right)\right) \end{array} \]

FPCore

(FPCore (g h)
 :precision binary64
 (* 2.0 (cos (fma PI 0.6666666666666666 (/ (acos (- 0.0 (/ g h))) 3.0)))))

C

double code(double g, double h) {
	return 2.0 * cos(fma(((double) M_PI), 0.6666666666666666, (acos((0.0 - (g / h))) / 3.0)));
}

Julia

function code(g, h)
	return Float64(2.0 * cos(fma(pi, 0.6666666666666666, Float64(acos(Float64(0.0 - Float64(g / h))) / 3.0))))
end

Wolfram

code[g_, h_] := N[(2.0 * N[Cos[N[(Pi * 0.6666666666666666 + N[(N[ArcCos[N[(0.0 - N[(g / h), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 98.4%

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

3. Simplified 0

   \[\leadsto expr\]
4. Add Preprocessing

6. Applied egg-rr 0

   \[\leadsto expr\]
7. Add Preprocessing

Alternative 4: 98.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 2 \cdot \cos \left(\pi \cdot 0.6666666666666666 + \frac{\cos^{-1} \left(\frac{g}{0 - h}\right)}{3}\right) \end{array} \]

FPCore

(FPCore (g h)
 :precision binary64
 (* 2.0 (cos (+ (* PI 0.6666666666666666) (/ (acos (/ g (- 0.0 h))) 3.0)))))

C

double code(double g, double h) {
	return 2.0 * cos(((((double) M_PI) * 0.6666666666666666) + (acos((g / (0.0 - h))) / 3.0)));
}

Java

public static double code(double g, double h) {
	return 2.0 * Math.cos(((Math.PI * 0.6666666666666666) + (Math.acos((g / (0.0 - h))) / 3.0)));
}

Python

def code(g, h):
	return 2.0 * math.cos(((math.pi * 0.6666666666666666) + (math.acos((g / (0.0 - h))) / 3.0)))

Julia

function code(g, h)
	return Float64(2.0 * cos(Float64(Float64(pi * 0.6666666666666666) + Float64(acos(Float64(g / Float64(0.0 - h))) / 3.0))))
end

MATLAB

function tmp = code(g, h)
	tmp = 2.0 * cos(((pi * 0.6666666666666666) + (acos((g / (0.0 - h))) / 3.0)));
end

Wolfram

code[g_, h_] := N[(2.0 * N[Cos[N[(N[(Pi * 0.6666666666666666), $MachinePrecision] + N[(N[ArcCos[N[(g / N[(0.0 - h), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 98.4%

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

3. Simplified 0

   \[\leadsto expr\]
4. Add Preprocessing
5. Add Preprocessing

Reproduce

herbie shell --seed 2024110 
(FPCore (g h)
  :name "2-ancestry mixing, negative discriminant"
  :precision binary64
  (* 2.0 (cos (+ (/ (* 2.0 PI) 3.0) (/ (acos (/ (- g) h)) 3.0)))))