Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1, D

Percentage Accurate: 98.0% → 99.6%

Time: 24.6s

Alternatives: 4

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \frac{1}{3} \cdot \cos^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right) \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (* (/ 1.0 3.0) (acos (* (/ (* 3.0 (/ x (* y 27.0))) (* z 2.0)) (sqrt t)))))

C

double code(double x, double y, double z, double t) {
	return (1.0 / 3.0) * acos((((3.0 * (x / (y * 27.0))) / (z * 2.0)) * sqrt(t)));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (1.0d0 / 3.0d0) * acos((((3.0d0 * (x / (y * 27.0d0))) / (z * 2.0d0)) * sqrt(t)))
end function

Java

public static double code(double x, double y, double z, double t) {
	return (1.0 / 3.0) * Math.acos((((3.0 * (x / (y * 27.0))) / (z * 2.0)) * Math.sqrt(t)));
}

Python

def code(x, y, z, t):
	return (1.0 / 3.0) * math.acos((((3.0 * (x / (y * 27.0))) / (z * 2.0)) * math.sqrt(t)))

Julia

function code(x, y, z, t)
	return Float64(Float64(1.0 / 3.0) * acos(Float64(Float64(Float64(3.0 * Float64(x / Float64(y * 27.0))) / Float64(z * 2.0)) * sqrt(t))))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (1.0 / 3.0) * acos((((3.0 * (x / (y * 27.0))) / (z * 2.0)) * sqrt(t)));
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(1.0 / 3.0), $MachinePrecision] * N[ArcCos[N[(N[(N[(3.0 * N[(x / N[(y * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * 2.0), $MachinePrecision]), $MachinePrecision] * N[Sqrt[t], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Initial Program: 98.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{1}{3} \cdot \cos^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right) \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (* (/ 1.0 3.0) (acos (* (/ (* 3.0 (/ x (* y 27.0))) (* z 2.0)) (sqrt t)))))

C

double code(double x, double y, double z, double t) {
	return (1.0 / 3.0) * acos((((3.0 * (x / (y * 27.0))) / (z * 2.0)) * sqrt(t)));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (1.0d0 / 3.0d0) * acos((((3.0d0 * (x / (y * 27.0d0))) / (z * 2.0d0)) * sqrt(t)))
end function

Java

public static double code(double x, double y, double z, double t) {
	return (1.0 / 3.0) * Math.acos((((3.0 * (x / (y * 27.0))) / (z * 2.0)) * Math.sqrt(t)));
}

Python

def code(x, y, z, t):
	return (1.0 / 3.0) * math.acos((((3.0 * (x / (y * 27.0))) / (z * 2.0)) * math.sqrt(t)))

Julia

function code(x, y, z, t)
	return Float64(Float64(1.0 / 3.0) * acos(Float64(Float64(Float64(3.0 * Float64(x / Float64(y * 27.0))) / Float64(z * 2.0)) * sqrt(t))))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (1.0 / 3.0) * acos((((3.0 * (x / (y * 27.0))) / (z * 2.0)) * sqrt(t)));
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(1.0 / 3.0), $MachinePrecision] * N[ArcCos[N[(N[(N[(3.0 * N[(x / N[(y * 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * 2.0), $MachinePrecision]), $MachinePrecision] * N[Sqrt[t], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ {\left(\frac{3}{\cos^{-1} \left(\frac{\frac{\sqrt{t}}{\frac{z}{x}}}{\frac{y}{0.05555555555555555}}\right)}\right)}^{-1} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (pow (/ 3.0 (acos (/ (/ (sqrt t) (/ z x)) (/ y 0.05555555555555555)))) -1.0))

C

double code(double x, double y, double z, double t) {
	return pow((3.0 / acos(((sqrt(t) / (z / x)) / (y / 0.05555555555555555)))), -1.0);
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (3.0d0 / acos(((sqrt(t) / (z / x)) / (y / 0.05555555555555555d0)))) ** (-1.0d0)
end function

Java

public static double code(double x, double y, double z, double t) {
	return Math.pow((3.0 / Math.acos(((Math.sqrt(t) / (z / x)) / (y / 0.05555555555555555)))), -1.0);
}

Python

def code(x, y, z, t):
	return math.pow((3.0 / math.acos(((math.sqrt(t) / (z / x)) / (y / 0.05555555555555555)))), -1.0)

Julia

function code(x, y, z, t)
	return Float64(3.0 / acos(Float64(Float64(sqrt(t) / Float64(z / x)) / Float64(y / 0.05555555555555555)))) ^ -1.0
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (3.0 / acos(((sqrt(t) / (z / x)) / (y / 0.05555555555555555)))) ^ -1.0;
end

Wolfram

code[x_, y_, z_, t_] := N[Power[N[(3.0 / N[ArcCos[N[(N[(N[Sqrt[t], $MachinePrecision] / N[(z / x), $MachinePrecision]), $MachinePrecision] / N[(y / 0.05555555555555555), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], -1.0], $MachinePrecision]

Derivation

1. Initial program 98.5%

   \[\frac{1}{3} \cdot \cos^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right) \]

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: 99.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ {\left(\frac{3}{\cos^{-1} \left(\frac{\sqrt{t}}{\frac{z \cdot y}{x \cdot 0.05555555555555555}}\right)}\right)}^{-1} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (pow (/ 3.0 (acos (/ (sqrt t) (/ (* z y) (* x 0.05555555555555555))))) -1.0))

C

double code(double x, double y, double z, double t) {
	return pow((3.0 / acos((sqrt(t) / ((z * y) / (x * 0.05555555555555555))))), -1.0);
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (3.0d0 / acos((sqrt(t) / ((z * y) / (x * 0.05555555555555555d0))))) ** (-1.0d0)
end function

Java

public static double code(double x, double y, double z, double t) {
	return Math.pow((3.0 / Math.acos((Math.sqrt(t) / ((z * y) / (x * 0.05555555555555555))))), -1.0);
}

Python

def code(x, y, z, t):
	return math.pow((3.0 / math.acos((math.sqrt(t) / ((z * y) / (x * 0.05555555555555555))))), -1.0)

Julia

function code(x, y, z, t)
	return Float64(3.0 / acos(Float64(sqrt(t) / Float64(Float64(z * y) / Float64(x * 0.05555555555555555))))) ^ -1.0
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (3.0 / acos((sqrt(t) / ((z * y) / (x * 0.05555555555555555))))) ^ -1.0;
end

Wolfram

code[x_, y_, z_, t_] := N[Power[N[(3.0 / N[ArcCos[N[(N[Sqrt[t], $MachinePrecision] / N[(N[(z * y), $MachinePrecision] / N[(x * 0.05555555555555555), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], -1.0], $MachinePrecision]

Derivation

1. Initial program 98.5%

   \[\frac{1}{3} \cdot \cos^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right) \]

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

    \[\leadsto expr\]
11. Add Preprocessing

Alternative 3: 98.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 0.3333333333333333 \cdot \cos^{-1} \left(\frac{\frac{\sqrt{t}}{\frac{z}{x}}}{\frac{y}{0.05555555555555555}}\right) \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (*
  0.3333333333333333
  (acos (/ (/ (sqrt t) (/ z x)) (/ y 0.05555555555555555)))))

C

double code(double x, double y, double z, double t) {
	return 0.3333333333333333 * acos(((sqrt(t) / (z / x)) / (y / 0.05555555555555555)));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = 0.3333333333333333d0 * acos(((sqrt(t) / (z / x)) / (y / 0.05555555555555555d0)))
end function

Java

public static double code(double x, double y, double z, double t) {
	return 0.3333333333333333 * Math.acos(((Math.sqrt(t) / (z / x)) / (y / 0.05555555555555555)));
}

Python

def code(x, y, z, t):
	return 0.3333333333333333 * math.acos(((math.sqrt(t) / (z / x)) / (y / 0.05555555555555555)))

Julia

function code(x, y, z, t)
	return Float64(0.3333333333333333 * acos(Float64(Float64(sqrt(t) / Float64(z / x)) / Float64(y / 0.05555555555555555))))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = 0.3333333333333333 * acos(((sqrt(t) / (z / x)) / (y / 0.05555555555555555)));
end

Wolfram

code[x_, y_, z_, t_] := N[(0.3333333333333333 * N[ArcCos[N[(N[(N[Sqrt[t], $MachinePrecision] / N[(z / x), $MachinePrecision]), $MachinePrecision] / N[(y / 0.05555555555555555), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 98.5%

   \[\frac{1}{3} \cdot \cos^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right) \]

3. Simplified 0

   \[\leadsto expr\]
4. Add Preprocessing

6. Applied egg-rr 0

   \[\leadsto expr\]
7. Add Preprocessing

Alternative 4: 98.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 0.3333333333333333 \cdot \cos^{-1} \left(\frac{x \cdot 0.05555555555555555}{y \cdot z} \cdot \sqrt{t}\right) \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (*
  0.3333333333333333
  (acos (* (/ (* x 0.05555555555555555) (* y z)) (sqrt t)))))

C

double code(double x, double y, double z, double t) {
	return 0.3333333333333333 * acos((((x * 0.05555555555555555) / (y * z)) * sqrt(t)));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = 0.3333333333333333d0 * acos((((x * 0.05555555555555555d0) / (y * z)) * sqrt(t)))
end function

Java

public static double code(double x, double y, double z, double t) {
	return 0.3333333333333333 * Math.acos((((x * 0.05555555555555555) / (y * z)) * Math.sqrt(t)));
}

Python

def code(x, y, z, t):
	return 0.3333333333333333 * math.acos((((x * 0.05555555555555555) / (y * z)) * math.sqrt(t)))

Julia

function code(x, y, z, t)
	return Float64(0.3333333333333333 * acos(Float64(Float64(Float64(x * 0.05555555555555555) / Float64(y * z)) * sqrt(t))))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = 0.3333333333333333 * acos((((x * 0.05555555555555555) / (y * z)) * sqrt(t)));
end

Wolfram

code[x_, y_, z_, t_] := N[(0.3333333333333333 * N[ArcCos[N[(N[(N[(x * 0.05555555555555555), $MachinePrecision] / N[(y * z), $MachinePrecision]), $MachinePrecision] * N[Sqrt[t], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 98.5%

   \[\frac{1}{3} \cdot \cos^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right) \]

3. Simplified 0

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

Developer target: 98.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{\cos^{-1} \left(\frac{\frac{x}{27}}{y \cdot z} \cdot \frac{\sqrt{t}}{\frac{2}{3}}\right)}{3} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (/ (acos (* (/ (/ x 27.0) (* y z)) (/ (sqrt t) (/ 2.0 3.0)))) 3.0))

C

double code(double x, double y, double z, double t) {
	return acos((((x / 27.0) / (y * z)) * (sqrt(t) / (2.0 / 3.0)))) / 3.0;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = acos((((x / 27.0d0) / (y * z)) * (sqrt(t) / (2.0d0 / 3.0d0)))) / 3.0d0
end function

Java

public static double code(double x, double y, double z, double t) {
	return Math.acos((((x / 27.0) / (y * z)) * (Math.sqrt(t) / (2.0 / 3.0)))) / 3.0;
}

Python

def code(x, y, z, t):
	return math.acos((((x / 27.0) / (y * z)) * (math.sqrt(t) / (2.0 / 3.0)))) / 3.0

Julia

function code(x, y, z, t)
	return Float64(acos(Float64(Float64(Float64(x / 27.0) / Float64(y * z)) * Float64(sqrt(t) / Float64(2.0 / 3.0)))) / 3.0)
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = acos((((x / 27.0) / (y * z)) * (sqrt(t) / (2.0 / 3.0)))) / 3.0;
end

Wolfram

code[x_, y_, z_, t_] := N[(N[ArcCos[N[(N[(N[(x / 27.0), $MachinePrecision] / N[(y * z), $MachinePrecision]), $MachinePrecision] * N[(N[Sqrt[t], $MachinePrecision] / N[(2.0 / 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / 3.0), $MachinePrecision]

Reproduce

herbie shell --seed 2024110 
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, D"
  :precision binary64

  :alt
  (/ (acos (* (/ (/ x 27.0) (* y z)) (/ (sqrt t) (/ 2.0 3.0)))) 3.0)

  (* (/ 1.0 3.0) (acos (* (/ (* 3.0 (/ x (* y 27.0))) (* z 2.0)) (sqrt t)))))