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

Percentage Accurate: 98.1% → 98.6%

Time: 27.8s

Alternatives: 4

Speedup: 1.2×

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: 98.1% 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: 98.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\\ \mathbf{if}\;t\_1 \leq 5 \cdot 10^{-177}:\\ \;\;\;\;{\left(\frac{3}{\cos^{-1} \left(\frac{\sqrt{t} \cdot \left(x \cdot 0.05555555555555555\right)}{y \cdot z}\right)}\right)}^{-1}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \cos^{-1} t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ (* 3.0 (/ x (* y 27.0))) (* z 2.0)) (sqrt t))))
   (if (<= t_1 5e-177)
     (pow
      (/ 3.0 (acos (/ (* (sqrt t) (* x 0.05555555555555555)) (* y z))))
      -1.0)
     (* 0.3333333333333333 (acos t_1)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = ((3.0 * (x / (y * 27.0))) / (z * 2.0)) * sqrt(t);
	double tmp;
	if (t_1 <= 5e-177) {
		tmp = pow((3.0 / acos(((sqrt(t) * (x * 0.05555555555555555)) / (y * z)))), -1.0);
	} else {
		tmp = 0.3333333333333333 * acos(t_1);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((3.0d0 * (x / (y * 27.0d0))) / (z * 2.0d0)) * sqrt(t)
    if (t_1 <= 5d-177) then
        tmp = (3.0d0 / acos(((sqrt(t) * (x * 0.05555555555555555d0)) / (y * z)))) ** (-1.0d0)
    else
        tmp = 0.3333333333333333d0 * acos(t_1)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = ((3.0 * (x / (y * 27.0))) / (z * 2.0)) * Math.sqrt(t);
	double tmp;
	if (t_1 <= 5e-177) {
		tmp = Math.pow((3.0 / Math.acos(((Math.sqrt(t) * (x * 0.05555555555555555)) / (y * z)))), -1.0);
	} else {
		tmp = 0.3333333333333333 * Math.acos(t_1);
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = ((3.0 * (x / (y * 27.0))) / (z * 2.0)) * math.sqrt(t)
	tmp = 0
	if t_1 <= 5e-177:
		tmp = math.pow((3.0 / math.acos(((math.sqrt(t) * (x * 0.05555555555555555)) / (y * z)))), -1.0)
	else:
		tmp = 0.3333333333333333 * math.acos(t_1)
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(3.0 * Float64(x / Float64(y * 27.0))) / Float64(z * 2.0)) * sqrt(t))
	tmp = 0.0
	if (t_1 <= 5e-177)
		tmp = Float64(3.0 / acos(Float64(Float64(sqrt(t) * Float64(x * 0.05555555555555555)) / Float64(y * z)))) ^ -1.0;
	else
		tmp = Float64(0.3333333333333333 * acos(t_1));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = ((3.0 * (x / (y * 27.0))) / (z * 2.0)) * sqrt(t);
	tmp = 0.0;
	if (t_1 <= 5e-177)
		tmp = (3.0 / acos(((sqrt(t) * (x * 0.05555555555555555)) / (y * z)))) ^ -1.0;
	else
		tmp = 0.3333333333333333 * acos(t_1);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = 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]}, If[LessEqual[t$95$1, 5e-177], N[Power[N[(3.0 / N[ArcCos[N[(N[(N[Sqrt[t], $MachinePrecision] * N[(x * 0.05555555555555555), $MachinePrecision]), $MachinePrecision] / N[(y * z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], -1.0], $MachinePrecision], N[(0.3333333333333333 * N[ArcCos[t$95$1], $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (/.f64 (*.f64 #s(literal 3 binary64) (/.f64 x (*.f64 y #s(literal 27 binary64)))) (*.f64 z #s(literal 2 binary64))) (sqrt.f64 t)) < 5e-177

   1. Initial program 97.0%

      \[\frac{1}{3} \cdot \cos^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right) \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. metadata-eval 97.0

         \[\leadsto \color{blue}{0.3333333333333333} \cdot \cos^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right) \]

   4. Applied rewrites 97.0%

      \[\leadsto \color{blue}{0.3333333333333333} \cdot \cos^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right) \]

   6. Applied rewrites 98.0%

      \[\leadsto 0.3333333333333333 \cdot \color{blue}{\frac{1}{\frac{1}{\cos^{-1} \left(\frac{0.05555555555555555 \cdot \left(x \cdot \sqrt{t}\right)}{y \cdot z}\right)}}} \]
   7. Step-by-step derivation

      1. lift-/.f64 N/A

         \[\leadsto \frac{1}{3} \cdot \frac{1}{\color{blue}{\frac{1}{\cos^{-1} \left(\frac{\frac{1}{18} \cdot \left(x \cdot \sqrt{t}\right)}{y \cdot z}\right)}}} \]

      2. inv-pow N/A

         \[\leadsto \frac{1}{3} \cdot \frac{1}{\color{blue}{{\cos^{-1} \left(\frac{\frac{1}{18} \cdot \left(x \cdot \sqrt{t}\right)}{y \cdot z}\right)}^{-1}}} \]

      3. metadata-eval N/A

         \[\leadsto \frac{1}{3} \cdot \frac{1}{{\cos^{-1} \left(\frac{\frac{1}{18} \cdot \left(x \cdot \sqrt{t}\right)}{y \cdot z}\right)}^{\color{blue}{\left(2 - 3\right)}}} \]

      4. pow-div N/A

         \[\leadsto \frac{1}{3} \cdot \frac{1}{\color{blue}{\frac{{\cos^{-1} \left(\frac{\frac{1}{18} \cdot \left(x \cdot \sqrt{t}\right)}{y \cdot z}\right)}^{2}}{{\cos^{-1} \left(\frac{\frac{1}{18} \cdot \left(x \cdot \sqrt{t}\right)}{y \cdot z}\right)}^{3}}}} \]

      5. lift-pow.f64 N/A

         \[\leadsto \frac{1}{3} \cdot \frac{1}{\frac{\color{blue}{{\cos^{-1} \left(\frac{\frac{1}{18} \cdot \left(x \cdot \sqrt{t}\right)}{y \cdot z}\right)}^{2}}}{{\cos^{-1} \left(\frac{\frac{1}{18} \cdot \left(x \cdot \sqrt{t}\right)}{y \cdot z}\right)}^{3}}} \]

      6. +-rgt-identity N/A

         \[\leadsto \frac{1}{3} \cdot \frac{1}{\frac{\color{blue}{{\cos^{-1} \left(\frac{\frac{1}{18} \cdot \left(x \cdot \sqrt{t}\right)}{y \cdot z}\right)}^{2} + 0}}{{\cos^{-1} \left(\frac{\frac{1}{18} \cdot \left(x \cdot \sqrt{t}\right)}{y \cdot z}\right)}^{3}}} \]

      7. metadata-eval N/A

         \[\leadsto \frac{1}{3} \cdot \frac{1}{\frac{{\cos^{-1} \left(\frac{\frac{1}{18} \cdot \left(x \cdot \sqrt{t}\right)}{y \cdot z}\right)}^{2} + \color{blue}{\left(\mathsf{neg}\left(0\right)\right)}}{{\cos^{-1} \left(\frac{\frac{1}{18} \cdot \left(x \cdot \sqrt{t}\right)}{y \cdot z}\right)}^{3}}} \]

      8. mul0-lft N/A

         \[\leadsto \frac{1}{3} \cdot \frac{1}{\frac{{\cos^{-1} \left(\frac{\frac{1}{18} \cdot \left(x \cdot \sqrt{t}\right)}{y \cdot z}\right)}^{2} + \left(\mathsf{neg}\left(\color{blue}{0 \cdot \cos^{-1} \left(\frac{\frac{1}{18} \cdot \left(x \cdot \sqrt{t}\right)}{y \cdot z}\right)}\right)\right)}{{\cos^{-1} \left(\frac{\frac{1}{18} \cdot \left(x \cdot \sqrt{t}\right)}{y \cdot z}\right)}^{3}}} \]

      9. lift-*.f64 N/A

         \[\leadsto \frac{1}{3} \cdot \frac{1}{\frac{{\cos^{-1} \left(\frac{\frac{1}{18} \cdot \left(x \cdot \sqrt{t}\right)}{y \cdot z}\right)}^{2} + \left(\mathsf{neg}\left(\color{blue}{0 \cdot \cos^{-1} \left(\frac{\frac{1}{18} \cdot \left(x \cdot \sqrt{t}\right)}{y \cdot z}\right)}\right)\right)}{{\cos^{-1} \left(\frac{\frac{1}{18} \cdot \left(x \cdot \sqrt{t}\right)}{y \cdot z}\right)}^{3}}} \]

      10. sub-neg N/A

          \[\leadsto \frac{1}{3} \cdot \frac{1}{\frac{\color{blue}{{\cos^{-1} \left(\frac{\frac{1}{18} \cdot \left(x \cdot \sqrt{t}\right)}{y \cdot z}\right)}^{2} - 0 \cdot \cos^{-1} \left(\frac{\frac{1}{18} \cdot \left(x \cdot \sqrt{t}\right)}{y \cdot z}\right)}}{{\cos^{-1} \left(\frac{\frac{1}{18} \cdot \left(x \cdot \sqrt{t}\right)}{y \cdot z}\right)}^{3}}} \]

      11. lift--.f64 N/A

          \[\leadsto \frac{1}{3} \cdot \frac{1}{\frac{\color{blue}{{\cos^{-1} \left(\frac{\frac{1}{18} \cdot \left(x \cdot \sqrt{t}\right)}{y \cdot z}\right)}^{2} - 0 \cdot \cos^{-1} \left(\frac{\frac{1}{18} \cdot \left(x \cdot \sqrt{t}\right)}{y \cdot z}\right)}}{{\cos^{-1} \left(\frac{\frac{1}{18} \cdot \left(x \cdot \sqrt{t}\right)}{y \cdot z}\right)}^{3}}} \]

      12. sqr-pow N/A

          \[\leadsto \frac{1}{3} \cdot \frac{1}{\frac{{\cos^{-1} \left(\frac{\frac{1}{18} \cdot \left(x \cdot \sqrt{t}\right)}{y \cdot z}\right)}^{2} - 0 \cdot \cos^{-1} \left(\frac{\frac{1}{18} \cdot \left(x \cdot \sqrt{t}\right)}{y \cdot z}\right)}{\color{blue}{{\cos^{-1} \left(\frac{\frac{1}{18} \cdot \left(x \cdot \sqrt{t}\right)}{y \cdot z}\right)}^{\left(\frac{3}{2}\right)} \cdot {\cos^{-1} \left(\frac{\frac{1}{18} \cdot \left(x \cdot \sqrt{t}\right)}{y \cdot z}\right)}^{\left(\frac{3}{2}\right)}}}} \]

   8. Applied rewrites 99.5%

      \[\leadsto 0.3333333333333333 \cdot \frac{1}{\color{blue}{\frac{\sqrt{\cos^{-1} \left(\frac{x \cdot \left(0.05555555555555555 \cdot \sqrt{t}\right)}{z \cdot y}\right)}}{{\cos^{-1} \left(\frac{x \cdot \left(0.05555555555555555 \cdot \sqrt{t}\right)}{z \cdot y}\right)}^{1.5}}}} \]
   9. Step-by-step derivation

      1. lift-*.f64 N/A

         \[\leadsto \color{blue}{\frac{1}{3} \cdot \frac{1}{\frac{\sqrt{\cos^{-1} \left(\frac{x \cdot \left(\frac{1}{18} \cdot \sqrt{t}\right)}{z \cdot y}\right)}}{{\cos^{-1} \left(\frac{x \cdot \left(\frac{1}{18} \cdot \sqrt{t}\right)}{z \cdot y}\right)}^{\frac{3}{2}}}}} \]

      2. lift-/.f64 N/A

         \[\leadsto \frac{1}{3} \cdot \color{blue}{\frac{1}{\frac{\sqrt{\cos^{-1} \left(\frac{x \cdot \left(\frac{1}{18} \cdot \sqrt{t}\right)}{z \cdot y}\right)}}{{\cos^{-1} \left(\frac{x \cdot \left(\frac{1}{18} \cdot \sqrt{t}\right)}{z \cdot y}\right)}^{\frac{3}{2}}}}} \]

      3. un-div-inv N/A

         \[\leadsto \color{blue}{\frac{\frac{1}{3}}{\frac{\sqrt{\cos^{-1} \left(\frac{x \cdot \left(\frac{1}{18} \cdot \sqrt{t}\right)}{z \cdot y}\right)}}{{\cos^{-1} \left(\frac{x \cdot \left(\frac{1}{18} \cdot \sqrt{t}\right)}{z \cdot y}\right)}^{\frac{3}{2}}}}} \]

      4. lift-/.f64 N/A

         \[\leadsto \frac{\frac{1}{3}}{\color{blue}{\frac{\sqrt{\cos^{-1} \left(\frac{x \cdot \left(\frac{1}{18} \cdot \sqrt{t}\right)}{z \cdot y}\right)}}{{\cos^{-1} \left(\frac{x \cdot \left(\frac{1}{18} \cdot \sqrt{t}\right)}{z \cdot y}\right)}^{\frac{3}{2}}}}} \]

      5. lift-sqrt.f64 N/A

         \[\leadsto \frac{\frac{1}{3}}{\frac{\color{blue}{\sqrt{\cos^{-1} \left(\frac{x \cdot \left(\frac{1}{18} \cdot \sqrt{t}\right)}{z \cdot y}\right)}}}{{\cos^{-1} \left(\frac{x \cdot \left(\frac{1}{18} \cdot \sqrt{t}\right)}{z \cdot y}\right)}^{\frac{3}{2}}}} \]

      6. pow1/2 N/A

         \[\leadsto \frac{\frac{1}{3}}{\frac{\color{blue}{{\cos^{-1} \left(\frac{x \cdot \left(\frac{1}{18} \cdot \sqrt{t}\right)}{z \cdot y}\right)}^{\frac{1}{2}}}}{{\cos^{-1} \left(\frac{x \cdot \left(\frac{1}{18} \cdot \sqrt{t}\right)}{z \cdot y}\right)}^{\frac{3}{2}}}} \]

      7. lift-pow.f64 N/A

         \[\leadsto \frac{\frac{1}{3}}{\frac{{\cos^{-1} \left(\frac{x \cdot \left(\frac{1}{18} \cdot \sqrt{t}\right)}{z \cdot y}\right)}^{\frac{1}{2}}}{\color{blue}{{\cos^{-1} \left(\frac{x \cdot \left(\frac{1}{18} \cdot \sqrt{t}\right)}{z \cdot y}\right)}^{\frac{3}{2}}}}} \]

      8. pow-div N/A

         \[\leadsto \frac{\frac{1}{3}}{\color{blue}{{\cos^{-1} \left(\frac{x \cdot \left(\frac{1}{18} \cdot \sqrt{t}\right)}{z \cdot y}\right)}^{\left(\frac{1}{2} - \frac{3}{2}\right)}}} \]

   10. Applied rewrites 99.5%

       \[\leadsto \color{blue}{{\left(\frac{3}{\cos^{-1} \left(\frac{\sqrt{t} \cdot \left(x \cdot 0.05555555555555555\right)}{z \cdot y}\right)}\right)}^{-1}} \]

   if 5e-177 < (*.f64 (/.f64 (*.f64 #s(literal 3 binary64) (/.f64 x (*.f64 y #s(literal 27 binary64)))) (*.f64 z #s(literal 2 binary64))) (sqrt.f64 t))

   1. Initial program 96.5%

      \[\frac{1}{3} \cdot \cos^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right) \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. lift-/.f64 N/A

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

      2. metadata-eval 96.5

         \[\leadsto \color{blue}{0.3333333333333333} \cdot \cos^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right) \]

   4. Applied rewrites 96.5%

      \[\leadsto \color{blue}{0.3333333333333333} \cdot \cos^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t} \leq 5 \cdot 10^{-177}:\\ \;\;\;\;{\left(\frac{3}{\cos^{-1} \left(\frac{\sqrt{t} \cdot \left(x \cdot 0.05555555555555555\right)}{y \cdot z}\right)}\right)}^{-1}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \cos^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 98.0% accurate, 1.1× speedup

Math

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

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (*
  0.3333333333333333
  (acos (* (sqrt t) (/ (/ (* x 0.05555555555555555) z) y)))))

C

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

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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) * (((x * 0.05555555555555555d0) / z) / y)))
end function

Java

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

Python

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

Julia

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

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp = code(x, y, z, t)
	tmp = 0.3333333333333333 * acos((sqrt(t) * (((x * 0.05555555555555555) / z) / y)));
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := N[(0.3333333333333333 * N[ArcCos[N[(N[Sqrt[t], $MachinePrecision] * N[(N[(N[(x * 0.05555555555555555), $MachinePrecision] / z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 96.9%

   \[\frac{1}{3} \cdot \cos^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right) \]
2. Add Preprocessing
3. Step-by-step derivation

   1. lift-/.f64 N/A

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

   2. metadata-eval 96.9

      \[\leadsto \color{blue}{0.3333333333333333} \cdot \cos^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right) \]

4. Applied rewrites 96.9%

   \[\leadsto \color{blue}{0.3333333333333333} \cdot \cos^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right) \]
5. Step-by-step derivation

   1. lift-/.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. lift-*.f64 N/A

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

   4. *-commutative N/A

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

   5. lift-/.f64 N/A

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

   6. associate-*r/ N/A

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

   7. lift-*.f64 N/A

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

   8. *-commutative N/A

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

   9. times-frac N/A

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

   10. times-frac N/A

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

   11. metadata-eval N/A

       \[\leadsto \frac{1}{3} \cdot \cos^{-1} \left(\left(\frac{\color{blue}{\frac{1}{9}}}{2} \cdot \frac{\frac{x}{y}}{z}\right) \cdot \sqrt{t}\right) \]

   12. metadata-eval N/A

       \[\leadsto \frac{1}{3} \cdot \cos^{-1} \left(\left(\color{blue}{\frac{1}{18}} \cdot \frac{\frac{x}{y}}{z}\right) \cdot \sqrt{t}\right) \]

   13. associate-/r* N/A

       \[\leadsto \frac{1}{3} \cdot \cos^{-1} \left(\left(\frac{1}{18} \cdot \color{blue}{\frac{x}{y \cdot z}}\right) \cdot \sqrt{t}\right) \]

   14. lift-*.f64 N/A

       \[\leadsto \frac{1}{3} \cdot \cos^{-1} \left(\left(\frac{1}{18} \cdot \frac{x}{\color{blue}{y \cdot z}}\right) \cdot \sqrt{t}\right) \]

   15. associate-*r/ N/A

       \[\leadsto \frac{1}{3} \cdot \cos^{-1} \left(\color{blue}{\frac{\frac{1}{18} \cdot x}{y \cdot z}} \cdot \sqrt{t}\right) \]

   16. lift-*.f64 N/A

       \[\leadsto \frac{1}{3} \cdot \cos^{-1} \left(\frac{\frac{1}{18} \cdot x}{\color{blue}{y \cdot z}} \cdot \sqrt{t}\right) \]

   17. *-commutative N/A

       \[\leadsto \frac{1}{3} \cdot \cos^{-1} \left(\frac{\frac{1}{18} \cdot x}{\color{blue}{z \cdot y}} \cdot \sqrt{t}\right) \]

   18. associate-/r* N/A

       \[\leadsto \frac{1}{3} \cdot \cos^{-1} \left(\color{blue}{\frac{\frac{\frac{1}{18} \cdot x}{z}}{y}} \cdot \sqrt{t}\right) \]

   19. lower-/.f64 N/A

       \[\leadsto \frac{1}{3} \cdot \cos^{-1} \left(\color{blue}{\frac{\frac{\frac{1}{18} \cdot x}{z}}{y}} \cdot \sqrt{t}\right) \]

   20. lower-/.f64 N/A

       \[\leadsto \frac{1}{3} \cdot \cos^{-1} \left(\frac{\color{blue}{\frac{\frac{1}{18} \cdot x}{z}}}{y} \cdot \sqrt{t}\right) \]

   21. *-commutative N/A

       \[\leadsto \frac{1}{3} \cdot \cos^{-1} \left(\frac{\frac{\color{blue}{x \cdot \frac{1}{18}}}{z}}{y} \cdot \sqrt{t}\right) \]

   22. lower-*.f64 98.1

       \[\leadsto 0.3333333333333333 \cdot \cos^{-1} \left(\frac{\frac{\color{blue}{x \cdot 0.05555555555555555}}{z}}{y} \cdot \sqrt{t}\right) \]

6. Applied rewrites 98.1%

   \[\leadsto 0.3333333333333333 \cdot \cos^{-1} \left(\color{blue}{\frac{\frac{x \cdot 0.05555555555555555}{z}}{y}} \cdot \sqrt{t}\right) \]

7. Final simplification 98.1%

   \[\leadsto 0.3333333333333333 \cdot \cos^{-1} \left(\sqrt{t} \cdot \frac{\frac{x \cdot 0.05555555555555555}{z}}{y}\right) \]
8. Add Preprocessing

Alternative 3: 98.2% accurate, 1.2× speedup

Math

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

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (*
  0.3333333333333333
  (acos (* (sqrt t) (* 0.05555555555555555 (/ x (* y z)))))))

C

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

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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) * (0.05555555555555555d0 * (x / (y * z)))))
end function

Java

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

Python

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

Julia

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

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp = code(x, y, z, t)
	tmp = 0.3333333333333333 * acos((sqrt(t) * (0.05555555555555555 * (x / (y * z)))));
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := N[(0.3333333333333333 * N[ArcCos[N[(N[Sqrt[t], $MachinePrecision] * N[(0.05555555555555555 * N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 96.9%

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

3. Taylor expanded in x around 0

   \[\leadsto \frac{1}{3} \cdot \cos^{-1} \left(\color{blue}{\left(\frac{1}{18} \cdot \frac{x}{y \cdot z}\right)} \cdot \sqrt{t}\right) \]
4. Step-by-step derivation

   1. lower-*.f64 N/A

      \[\leadsto \frac{1}{3} \cdot \cos^{-1} \left(\color{blue}{\left(\frac{1}{18} \cdot \frac{x}{y \cdot z}\right)} \cdot \sqrt{t}\right) \]

   2. lower-/.f64 N/A

      \[\leadsto \frac{1}{3} \cdot \cos^{-1} \left(\left(\frac{1}{18} \cdot \color{blue}{\frac{x}{y \cdot z}}\right) \cdot \sqrt{t}\right) \]

   3. lower-*.f64 96.9

      \[\leadsto \frac{1}{3} \cdot \cos^{-1} \left(\left(0.05555555555555555 \cdot \frac{x}{\color{blue}{y \cdot z}}\right) \cdot \sqrt{t}\right) \]

5. Applied rewrites 96.9%

   \[\leadsto \frac{1}{3} \cdot \cos^{-1} \left(\color{blue}{\left(0.05555555555555555 \cdot \frac{x}{y \cdot z}\right)} \cdot \sqrt{t}\right) \]
6. Step-by-step derivation

   1. lift-*.f64 N/A

      \[\leadsto \color{blue}{\frac{1}{3} \cdot \cos^{-1} \left(\left(\frac{1}{18} \cdot \frac{x}{y \cdot z}\right) \cdot \sqrt{t}\right)} \]

   2. lift-/.f64 N/A

      \[\leadsto \color{blue}{\frac{1}{3}} \cdot \cos^{-1} \left(\left(\frac{1}{18} \cdot \frac{x}{y \cdot z}\right) \cdot \sqrt{t}\right) \]

   3. *-commutative N/A

      \[\leadsto \color{blue}{\cos^{-1} \left(\left(\frac{1}{18} \cdot \frac{x}{y \cdot z}\right) \cdot \sqrt{t}\right) \cdot \frac{1}{3}} \]

   4. lower-*.f64 N/A

      \[\leadsto \color{blue}{\cos^{-1} \left(\left(\frac{1}{18} \cdot \frac{x}{y \cdot z}\right) \cdot \sqrt{t}\right) \cdot \frac{1}{3}} \]

   5. lift-*.f64 N/A

      \[\leadsto \cos^{-1} \color{blue}{\left(\left(\frac{1}{18} \cdot \frac{x}{y \cdot z}\right) \cdot \sqrt{t}\right)} \cdot \frac{1}{3} \]

   6. *-commutative N/A

      \[\leadsto \cos^{-1} \color{blue}{\left(\sqrt{t} \cdot \left(\frac{1}{18} \cdot \frac{x}{y \cdot z}\right)\right)} \cdot \frac{1}{3} \]

   7. lower-*.f64 N/A

      \[\leadsto \cos^{-1} \color{blue}{\left(\sqrt{t} \cdot \left(\frac{1}{18} \cdot \frac{x}{y \cdot z}\right)\right)} \cdot \frac{1}{3} \]

   8. metadata-eval 96.9

      \[\leadsto \cos^{-1} \left(\sqrt{t} \cdot \left(0.05555555555555555 \cdot \frac{x}{y \cdot z}\right)\right) \cdot \color{blue}{0.3333333333333333} \]

7. Applied rewrites 96.9%

   \[\leadsto \color{blue}{\cos^{-1} \left(\sqrt{t} \cdot \left(0.05555555555555555 \cdot \frac{x}{y \cdot z}\right)\right) \cdot 0.3333333333333333} \]

8. Final simplification 96.9%

   \[\leadsto 0.3333333333333333 \cdot \cos^{-1} \left(\sqrt{t} \cdot \left(0.05555555555555555 \cdot \frac{x}{y \cdot z}\right)\right) \]
9. Add Preprocessing

Alternative 4: 96.9% accurate, 1.2× speedup

Math

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

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (*
  0.3333333333333333
  (acos (/ (* 0.05555555555555555 (* x (sqrt t))) (* y z)))))

C

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

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
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(((0.05555555555555555d0 * (x * sqrt(t))) / (y * z)))
end function

Java

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

Python

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

Julia

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

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp = code(x, y, z, t)
	tmp = 0.3333333333333333 * acos(((0.05555555555555555 * (x * sqrt(t))) / (y * z)));
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := N[(0.3333333333333333 * N[ArcCos[N[(N[(0.05555555555555555 * N[(x * N[Sqrt[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y * z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 96.9%

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

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{\frac{1}{3} \cdot \cos^{-1} \left(\frac{1}{18} \cdot \left(\sqrt{t} \cdot \frac{x}{y \cdot z}\right)\right)} \]
4. Step-by-step derivation

   1. lower-*.f64 N/A

      \[\leadsto \color{blue}{\frac{1}{3} \cdot \cos^{-1} \left(\frac{1}{18} \cdot \left(\sqrt{t} \cdot \frac{x}{y \cdot z}\right)\right)} \]

   2. lower-acos.f64 N/A

      \[\leadsto \frac{1}{3} \cdot \color{blue}{\cos^{-1} \left(\frac{1}{18} \cdot \left(\sqrt{t} \cdot \frac{x}{y \cdot z}\right)\right)} \]

   3. associate-*r/ N/A

      \[\leadsto \frac{1}{3} \cdot \cos^{-1} \left(\frac{1}{18} \cdot \color{blue}{\frac{\sqrt{t} \cdot x}{y \cdot z}}\right) \]

   4. associate-*r/ N/A

      \[\leadsto \frac{1}{3} \cdot \cos^{-1} \color{blue}{\left(\frac{\frac{1}{18} \cdot \left(\sqrt{t} \cdot x\right)}{y \cdot z}\right)} \]

   5. lower-/.f64 N/A

      \[\leadsto \frac{1}{3} \cdot \cos^{-1} \color{blue}{\left(\frac{\frac{1}{18} \cdot \left(\sqrt{t} \cdot x\right)}{y \cdot z}\right)} \]

   6. lower-*.f64 N/A

      \[\leadsto \frac{1}{3} \cdot \cos^{-1} \left(\frac{\color{blue}{\frac{1}{18} \cdot \left(\sqrt{t} \cdot x\right)}}{y \cdot z}\right) \]

   7. *-commutative N/A

      \[\leadsto \frac{1}{3} \cdot \cos^{-1} \left(\frac{\frac{1}{18} \cdot \color{blue}{\left(x \cdot \sqrt{t}\right)}}{y \cdot z}\right) \]

   8. lower-*.f64 N/A

      \[\leadsto \frac{1}{3} \cdot \cos^{-1} \left(\frac{\frac{1}{18} \cdot \color{blue}{\left(x \cdot \sqrt{t}\right)}}{y \cdot z}\right) \]

   9. lower-sqrt.f64 N/A

      \[\leadsto \frac{1}{3} \cdot \cos^{-1} \left(\frac{\frac{1}{18} \cdot \left(x \cdot \color{blue}{\sqrt{t}}\right)}{y \cdot z}\right) \]

   10. lower-*.f64 95.8

       \[\leadsto 0.3333333333333333 \cdot \cos^{-1} \left(\frac{0.05555555555555555 \cdot \left(x \cdot \sqrt{t}\right)}{\color{blue}{y \cdot z}}\right) \]

5. Applied rewrites 95.8%

   \[\leadsto \color{blue}{0.3333333333333333 \cdot \cos^{-1} \left(\frac{0.05555555555555555 \cdot \left(x \cdot \sqrt{t}\right)}{y \cdot z}\right)} \]
6. Add Preprocessing

Developer Target 1: 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 2024220 
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, D"
  :precision binary64

  :alt
  (! :herbie-platform default (/ (acos (* (/ (/ x 27) (* y z)) (/ (sqrt t) (/ 2 3)))) 3))

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