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

Percentage Accurate: 98.0% → 99.1%

Time: 17.1s

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

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    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

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    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: 99.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\mathsf{PI}\left(\right)}{2}\\ t_2 := \left(\sqrt{t} \cdot -0.05555555555555555\right) \cdot \frac{\frac{x}{y}}{z}\\ t_3 := \sin^{-1} t\_2\\ t_4 := \cos^{-1} t\_2\\ \frac{\left({t\_1}^{3} - {t\_3}^{3}\right) \cdot 0.3333333333333333}{{t\_1}^{4} - {\left(t\_3 \cdot t\_4\right)}^{2}} \cdot \mathsf{fma}\left(t\_3, t\_4, {t\_1}^{2}\right) \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (PI) 2.0))
        (t_2 (* (* (sqrt t) -0.05555555555555555) (/ (/ x y) z)))
        (t_3 (asin t_2))
        (t_4 (acos t_2)))
   (*
    (/
     (* (- (pow t_1 3.0) (pow t_3 3.0)) 0.3333333333333333)
     (- (pow t_1 4.0) (pow (* t_3 t_4) 2.0)))
    (fma t_3 t_4 (pow t_1 2.0)))))

Derivation

1. Initial program 97.7%

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

4. Applied rewrites 99.0%

   \[\leadsto \color{blue}{\frac{\left({\left(\frac{\mathsf{PI}\left(\right)}{2}\right)}^{3} - {\sin^{-1} \left(\left(\sqrt{t} \cdot -0.05555555555555555\right) \cdot \frac{\frac{x}{y}}{z}\right)}^{3}\right) \cdot 0.3333333333333333}{{\left(\frac{\mathsf{PI}\left(\right)}{2}\right)}^{4} - {\left(\sin^{-1} \left(\left(\sqrt{t} \cdot -0.05555555555555555\right) \cdot \frac{\frac{x}{y}}{z}\right) \cdot \cos^{-1} \left(\left(\sqrt{t} \cdot -0.05555555555555555\right) \cdot \frac{\frac{x}{y}}{z}\right)\right)}^{2}} \cdot \mathsf{fma}\left(\sin^{-1} \left(\left(\sqrt{t} \cdot -0.05555555555555555\right) \cdot \frac{\frac{x}{y}}{z}\right), \cos^{-1} \left(\left(\sqrt{t} \cdot -0.05555555555555555\right) \cdot \frac{\frac{x}{y}}{z}\right), {\left(\frac{\mathsf{PI}\left(\right)}{2}\right)}^{2}\right)} \]
5. Add Preprocessing

Alternative 2: 98.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \sqrt{t} \cdot -0.05555555555555555\\ t_2 := t\_1 \cdot \frac{x}{z \cdot y}\\ t_3 := \frac{\mathsf{PI}\left(\right)}{2}\\ t_4 := t\_1 \cdot \frac{\frac{x}{y}}{z}\\ t_5 := \sin^{-1} t\_4\\ \frac{\left({t\_3}^{3} - {t\_5}^{3}\right) \cdot 0.3333333333333333}{{t\_3}^{4} - {\left(t\_5 \cdot \cos^{-1} t\_4\right)}^{2}} \cdot \mathsf{fma}\left(\sin^{-1} t\_2, \cos^{-1} t\_2, {t\_3}^{2}\right) \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (sqrt t) -0.05555555555555555))
        (t_2 (* t_1 (/ x (* z y))))
        (t_3 (/ (PI) 2.0))
        (t_4 (* t_1 (/ (/ x y) z)))
        (t_5 (asin t_4)))
   (*
    (/
     (* (- (pow t_3 3.0) (pow t_5 3.0)) 0.3333333333333333)
     (- (pow t_3 4.0) (pow (* t_5 (acos t_4)) 2.0)))
    (fma (asin t_2) (acos t_2) (pow t_3 2.0)))))

Derivation

1. Initial program 97.7%

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

4. Applied rewrites 99.0%

   \[\leadsto \color{blue}{\frac{\left({\left(\frac{\mathsf{PI}\left(\right)}{2}\right)}^{3} - {\sin^{-1} \left(\left(\sqrt{t} \cdot -0.05555555555555555\right) \cdot \frac{\frac{x}{y}}{z}\right)}^{3}\right) \cdot 0.3333333333333333}{{\left(\frac{\mathsf{PI}\left(\right)}{2}\right)}^{4} - {\left(\sin^{-1} \left(\left(\sqrt{t} \cdot -0.05555555555555555\right) \cdot \frac{\frac{x}{y}}{z}\right) \cdot \cos^{-1} \left(\left(\sqrt{t} \cdot -0.05555555555555555\right) \cdot \frac{\frac{x}{y}}{z}\right)\right)}^{2}} \cdot \mathsf{fma}\left(\sin^{-1} \left(\left(\sqrt{t} \cdot -0.05555555555555555\right) \cdot \frac{\frac{x}{y}}{z}\right), \cos^{-1} \left(\left(\sqrt{t} \cdot -0.05555555555555555\right) \cdot \frac{\frac{x}{y}}{z}\right), {\left(\frac{\mathsf{PI}\left(\right)}{2}\right)}^{2}\right)} \]
5. Step-by-step derivation

   1. lift-/.f64 N/A

      \[\leadsto \frac{\left({\left(\frac{\mathsf{PI}\left(\right)}{2}\right)}^{3} - {\sin^{-1} \left(\left(\sqrt{t} \cdot \frac{-1}{18}\right) \cdot \frac{\frac{x}{y}}{z}\right)}^{3}\right) \cdot \frac{1}{3}}{{\left(\frac{\mathsf{PI}\left(\right)}{2}\right)}^{4} - {\left(\sin^{-1} \left(\left(\sqrt{t} \cdot \frac{-1}{18}\right) \cdot \frac{\frac{x}{y}}{z}\right) \cdot \cos^{-1} \left(\left(\sqrt{t} \cdot \frac{-1}{18}\right) \cdot \frac{\frac{x}{y}}{z}\right)\right)}^{2}} \cdot \mathsf{fma}\left(\sin^{-1} \left(\left(\sqrt{t} \cdot \frac{-1}{18}\right) \cdot \frac{\frac{x}{y}}{z}\right), \cos^{-1} \left(\left(\sqrt{t} \cdot \frac{-1}{18}\right) \cdot \color{blue}{\frac{\frac{x}{y}}{z}}\right), {\left(\frac{\mathsf{PI}\left(\right)}{2}\right)}^{2}\right) \]

   2. lift-/.f64 N/A

      \[\leadsto \frac{\left({\left(\frac{\mathsf{PI}\left(\right)}{2}\right)}^{3} - {\sin^{-1} \left(\left(\sqrt{t} \cdot \frac{-1}{18}\right) \cdot \frac{\frac{x}{y}}{z}\right)}^{3}\right) \cdot \frac{1}{3}}{{\left(\frac{\mathsf{PI}\left(\right)}{2}\right)}^{4} - {\left(\sin^{-1} \left(\left(\sqrt{t} \cdot \frac{-1}{18}\right) \cdot \frac{\frac{x}{y}}{z}\right) \cdot \cos^{-1} \left(\left(\sqrt{t} \cdot \frac{-1}{18}\right) \cdot \frac{\frac{x}{y}}{z}\right)\right)}^{2}} \cdot \mathsf{fma}\left(\sin^{-1} \left(\left(\sqrt{t} \cdot \frac{-1}{18}\right) \cdot \frac{\frac{x}{y}}{z}\right), \cos^{-1} \left(\left(\sqrt{t} \cdot \frac{-1}{18}\right) \cdot \frac{\color{blue}{\frac{x}{y}}}{z}\right), {\left(\frac{\mathsf{PI}\left(\right)}{2}\right)}^{2}\right) \]

   3. associate-/l/ N/A

      \[\leadsto \frac{\left({\left(\frac{\mathsf{PI}\left(\right)}{2}\right)}^{3} - {\sin^{-1} \left(\left(\sqrt{t} \cdot \frac{-1}{18}\right) \cdot \frac{\frac{x}{y}}{z}\right)}^{3}\right) \cdot \frac{1}{3}}{{\left(\frac{\mathsf{PI}\left(\right)}{2}\right)}^{4} - {\left(\sin^{-1} \left(\left(\sqrt{t} \cdot \frac{-1}{18}\right) \cdot \frac{\frac{x}{y}}{z}\right) \cdot \cos^{-1} \left(\left(\sqrt{t} \cdot \frac{-1}{18}\right) \cdot \frac{\frac{x}{y}}{z}\right)\right)}^{2}} \cdot \mathsf{fma}\left(\sin^{-1} \left(\left(\sqrt{t} \cdot \frac{-1}{18}\right) \cdot \frac{\frac{x}{y}}{z}\right), \cos^{-1} \left(\left(\sqrt{t} \cdot \frac{-1}{18}\right) \cdot \color{blue}{\frac{x}{y \cdot z}}\right), {\left(\frac{\mathsf{PI}\left(\right)}{2}\right)}^{2}\right) \]

   4. lower-/.f64 N/A

      \[\leadsto \frac{\left({\left(\frac{\mathsf{PI}\left(\right)}{2}\right)}^{3} - {\sin^{-1} \left(\left(\sqrt{t} \cdot \frac{-1}{18}\right) \cdot \frac{\frac{x}{y}}{z}\right)}^{3}\right) \cdot \frac{1}{3}}{{\left(\frac{\mathsf{PI}\left(\right)}{2}\right)}^{4} - {\left(\sin^{-1} \left(\left(\sqrt{t} \cdot \frac{-1}{18}\right) \cdot \frac{\frac{x}{y}}{z}\right) \cdot \cos^{-1} \left(\left(\sqrt{t} \cdot \frac{-1}{18}\right) \cdot \frac{\frac{x}{y}}{z}\right)\right)}^{2}} \cdot \mathsf{fma}\left(\sin^{-1} \left(\left(\sqrt{t} \cdot \frac{-1}{18}\right) \cdot \frac{\frac{x}{y}}{z}\right), \cos^{-1} \left(\left(\sqrt{t} \cdot \frac{-1}{18}\right) \cdot \color{blue}{\frac{x}{y \cdot z}}\right), {\left(\frac{\mathsf{PI}\left(\right)}{2}\right)}^{2}\right) \]

   5. *-commutative N/A

      \[\leadsto \frac{\left({\left(\frac{\mathsf{PI}\left(\right)}{2}\right)}^{3} - {\sin^{-1} \left(\left(\sqrt{t} \cdot \frac{-1}{18}\right) \cdot \frac{\frac{x}{y}}{z}\right)}^{3}\right) \cdot \frac{1}{3}}{{\left(\frac{\mathsf{PI}\left(\right)}{2}\right)}^{4} - {\left(\sin^{-1} \left(\left(\sqrt{t} \cdot \frac{-1}{18}\right) \cdot \frac{\frac{x}{y}}{z}\right) \cdot \cos^{-1} \left(\left(\sqrt{t} \cdot \frac{-1}{18}\right) \cdot \frac{\frac{x}{y}}{z}\right)\right)}^{2}} \cdot \mathsf{fma}\left(\sin^{-1} \left(\left(\sqrt{t} \cdot \frac{-1}{18}\right) \cdot \frac{\frac{x}{y}}{z}\right), \cos^{-1} \left(\left(\sqrt{t} \cdot \frac{-1}{18}\right) \cdot \frac{x}{\color{blue}{z \cdot y}}\right), {\left(\frac{\mathsf{PI}\left(\right)}{2}\right)}^{2}\right) \]

   6. lower-*.f64 98.6

      \[\leadsto \frac{\left({\left(\frac{\mathsf{PI}\left(\right)}{2}\right)}^{3} - {\sin^{-1} \left(\left(\sqrt{t} \cdot -0.05555555555555555\right) \cdot \frac{\frac{x}{y}}{z}\right)}^{3}\right) \cdot 0.3333333333333333}{{\left(\frac{\mathsf{PI}\left(\right)}{2}\right)}^{4} - {\left(\sin^{-1} \left(\left(\sqrt{t} \cdot -0.05555555555555555\right) \cdot \frac{\frac{x}{y}}{z}\right) \cdot \cos^{-1} \left(\left(\sqrt{t} \cdot -0.05555555555555555\right) \cdot \frac{\frac{x}{y}}{z}\right)\right)}^{2}} \cdot \mathsf{fma}\left(\sin^{-1} \left(\left(\sqrt{t} \cdot -0.05555555555555555\right) \cdot \frac{\frac{x}{y}}{z}\right), \cos^{-1} \left(\left(\sqrt{t} \cdot -0.05555555555555555\right) \cdot \frac{x}{\color{blue}{z \cdot y}}\right), {\left(\frac{\mathsf{PI}\left(\right)}{2}\right)}^{2}\right) \]

6. Applied rewrites 98.6%

   \[\leadsto \frac{\left({\left(\frac{\mathsf{PI}\left(\right)}{2}\right)}^{3} - {\sin^{-1} \left(\left(\sqrt{t} \cdot -0.05555555555555555\right) \cdot \frac{\frac{x}{y}}{z}\right)}^{3}\right) \cdot 0.3333333333333333}{{\left(\frac{\mathsf{PI}\left(\right)}{2}\right)}^{4} - {\left(\sin^{-1} \left(\left(\sqrt{t} \cdot -0.05555555555555555\right) \cdot \frac{\frac{x}{y}}{z}\right) \cdot \cos^{-1} \left(\left(\sqrt{t} \cdot -0.05555555555555555\right) \cdot \frac{\frac{x}{y}}{z}\right)\right)}^{2}} \cdot \mathsf{fma}\left(\sin^{-1} \left(\left(\sqrt{t} \cdot -0.05555555555555555\right) \cdot \frac{\frac{x}{y}}{z}\right), \cos^{-1} \left(\left(\sqrt{t} \cdot -0.05555555555555555\right) \cdot \color{blue}{\frac{x}{z \cdot y}}\right), {\left(\frac{\mathsf{PI}\left(\right)}{2}\right)}^{2}\right) \]
7. Step-by-step derivation

   1. lift-/.f64 N/A

      \[\leadsto \frac{\left({\left(\frac{\mathsf{PI}\left(\right)}{2}\right)}^{3} - {\sin^{-1} \left(\left(\sqrt{t} \cdot \frac{-1}{18}\right) \cdot \frac{\frac{x}{y}}{z}\right)}^{3}\right) \cdot \frac{1}{3}}{{\left(\frac{\mathsf{PI}\left(\right)}{2}\right)}^{4} - {\left(\sin^{-1} \left(\left(\sqrt{t} \cdot \frac{-1}{18}\right) \cdot \frac{\frac{x}{y}}{z}\right) \cdot \cos^{-1} \left(\left(\sqrt{t} \cdot \frac{-1}{18}\right) \cdot \frac{\frac{x}{y}}{z}\right)\right)}^{2}} \cdot \mathsf{fma}\left(\sin^{-1} \left(\left(\sqrt{t} \cdot \frac{-1}{18}\right) \cdot \color{blue}{\frac{\frac{x}{y}}{z}}\right), \cos^{-1} \left(\left(\sqrt{t} \cdot \frac{-1}{18}\right) \cdot \frac{x}{z \cdot y}\right), {\left(\frac{\mathsf{PI}\left(\right)}{2}\right)}^{2}\right) \]

   2. lift-/.f64 N/A

      \[\leadsto \frac{\left({\left(\frac{\mathsf{PI}\left(\right)}{2}\right)}^{3} - {\sin^{-1} \left(\left(\sqrt{t} \cdot \frac{-1}{18}\right) \cdot \frac{\frac{x}{y}}{z}\right)}^{3}\right) \cdot \frac{1}{3}}{{\left(\frac{\mathsf{PI}\left(\right)}{2}\right)}^{4} - {\left(\sin^{-1} \left(\left(\sqrt{t} \cdot \frac{-1}{18}\right) \cdot \frac{\frac{x}{y}}{z}\right) \cdot \cos^{-1} \left(\left(\sqrt{t} \cdot \frac{-1}{18}\right) \cdot \frac{\frac{x}{y}}{z}\right)\right)}^{2}} \cdot \mathsf{fma}\left(\sin^{-1} \left(\left(\sqrt{t} \cdot \frac{-1}{18}\right) \cdot \frac{\color{blue}{\frac{x}{y}}}{z}\right), \cos^{-1} \left(\left(\sqrt{t} \cdot \frac{-1}{18}\right) \cdot \frac{x}{z \cdot y}\right), {\left(\frac{\mathsf{PI}\left(\right)}{2}\right)}^{2}\right) \]

   3. associate-/l/ N/A

      \[\leadsto \frac{\left({\left(\frac{\mathsf{PI}\left(\right)}{2}\right)}^{3} - {\sin^{-1} \left(\left(\sqrt{t} \cdot \frac{-1}{18}\right) \cdot \frac{\frac{x}{y}}{z}\right)}^{3}\right) \cdot \frac{1}{3}}{{\left(\frac{\mathsf{PI}\left(\right)}{2}\right)}^{4} - {\left(\sin^{-1} \left(\left(\sqrt{t} \cdot \frac{-1}{18}\right) \cdot \frac{\frac{x}{y}}{z}\right) \cdot \cos^{-1} \left(\left(\sqrt{t} \cdot \frac{-1}{18}\right) \cdot \frac{\frac{x}{y}}{z}\right)\right)}^{2}} \cdot \mathsf{fma}\left(\sin^{-1} \left(\left(\sqrt{t} \cdot \frac{-1}{18}\right) \cdot \color{blue}{\frac{x}{y \cdot z}}\right), \cos^{-1} \left(\left(\sqrt{t} \cdot \frac{-1}{18}\right) \cdot \frac{x}{z \cdot y}\right), {\left(\frac{\mathsf{PI}\left(\right)}{2}\right)}^{2}\right) \]

   4. *-commutative N/A

      \[\leadsto \frac{\left({\left(\frac{\mathsf{PI}\left(\right)}{2}\right)}^{3} - {\sin^{-1} \left(\left(\sqrt{t} \cdot \frac{-1}{18}\right) \cdot \frac{\frac{x}{y}}{z}\right)}^{3}\right) \cdot \frac{1}{3}}{{\left(\frac{\mathsf{PI}\left(\right)}{2}\right)}^{4} - {\left(\sin^{-1} \left(\left(\sqrt{t} \cdot \frac{-1}{18}\right) \cdot \frac{\frac{x}{y}}{z}\right) \cdot \cos^{-1} \left(\left(\sqrt{t} \cdot \frac{-1}{18}\right) \cdot \frac{\frac{x}{y}}{z}\right)\right)}^{2}} \cdot \mathsf{fma}\left(\sin^{-1} \left(\left(\sqrt{t} \cdot \frac{-1}{18}\right) \cdot \frac{x}{\color{blue}{z \cdot y}}\right), \cos^{-1} \left(\left(\sqrt{t} \cdot \frac{-1}{18}\right) \cdot \frac{x}{z \cdot y}\right), {\left(\frac{\mathsf{PI}\left(\right)}{2}\right)}^{2}\right) \]

   5. lift-*.f64 N/A

      \[\leadsto \frac{\left({\left(\frac{\mathsf{PI}\left(\right)}{2}\right)}^{3} - {\sin^{-1} \left(\left(\sqrt{t} \cdot \frac{-1}{18}\right) \cdot \frac{\frac{x}{y}}{z}\right)}^{3}\right) \cdot \frac{1}{3}}{{\left(\frac{\mathsf{PI}\left(\right)}{2}\right)}^{4} - {\left(\sin^{-1} \left(\left(\sqrt{t} \cdot \frac{-1}{18}\right) \cdot \frac{\frac{x}{y}}{z}\right) \cdot \cos^{-1} \left(\left(\sqrt{t} \cdot \frac{-1}{18}\right) \cdot \frac{\frac{x}{y}}{z}\right)\right)}^{2}} \cdot \mathsf{fma}\left(\sin^{-1} \left(\left(\sqrt{t} \cdot \frac{-1}{18}\right) \cdot \frac{x}{\color{blue}{z \cdot y}}\right), \cos^{-1} \left(\left(\sqrt{t} \cdot \frac{-1}{18}\right) \cdot \frac{x}{z \cdot y}\right), {\left(\frac{\mathsf{PI}\left(\right)}{2}\right)}^{2}\right) \]

   6. lift-/.f64 98.6

      \[\leadsto \frac{\left({\left(\frac{\mathsf{PI}\left(\right)}{2}\right)}^{3} - {\sin^{-1} \left(\left(\sqrt{t} \cdot -0.05555555555555555\right) \cdot \frac{\frac{x}{y}}{z}\right)}^{3}\right) \cdot 0.3333333333333333}{{\left(\frac{\mathsf{PI}\left(\right)}{2}\right)}^{4} - {\left(\sin^{-1} \left(\left(\sqrt{t} \cdot -0.05555555555555555\right) \cdot \frac{\frac{x}{y}}{z}\right) \cdot \cos^{-1} \left(\left(\sqrt{t} \cdot -0.05555555555555555\right) \cdot \frac{\frac{x}{y}}{z}\right)\right)}^{2}} \cdot \mathsf{fma}\left(\sin^{-1} \left(\left(\sqrt{t} \cdot -0.05555555555555555\right) \cdot \color{blue}{\frac{x}{z \cdot y}}\right), \cos^{-1} \left(\left(\sqrt{t} \cdot -0.05555555555555555\right) \cdot \frac{x}{z \cdot y}\right), {\left(\frac{\mathsf{PI}\left(\right)}{2}\right)}^{2}\right) \]

8. Applied rewrites 98.6%

   \[\leadsto \frac{\left({\left(\frac{\mathsf{PI}\left(\right)}{2}\right)}^{3} - {\sin^{-1} \left(\left(\sqrt{t} \cdot -0.05555555555555555\right) \cdot \frac{\frac{x}{y}}{z}\right)}^{3}\right) \cdot 0.3333333333333333}{{\left(\frac{\mathsf{PI}\left(\right)}{2}\right)}^{4} - {\left(\sin^{-1} \left(\left(\sqrt{t} \cdot -0.05555555555555555\right) \cdot \frac{\frac{x}{y}}{z}\right) \cdot \cos^{-1} \left(\left(\sqrt{t} \cdot -0.05555555555555555\right) \cdot \frac{\frac{x}{y}}{z}\right)\right)}^{2}} \cdot \mathsf{fma}\left(\sin^{-1} \left(\left(\sqrt{t} \cdot -0.05555555555555555\right) \cdot \color{blue}{\frac{x}{z \cdot y}}\right), \cos^{-1} \left(\left(\sqrt{t} \cdot -0.05555555555555555\right) \cdot \frac{x}{z \cdot y}\right), {\left(\frac{\mathsf{PI}\left(\right)}{2}\right)}^{2}\right) \]
9. Add Preprocessing

Alternative 3: 98.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\frac{x}{y} \cdot -0.05555555555555555\right) \cdot \frac{\sqrt{t}}{z}\\ t_2 := \sin^{-1} t\_1\\ t_3 := \mathsf{PI}\left(\right) \cdot \mathsf{PI}\left(\right)\\ t_4 := \cos^{-1} t\_1\\ \frac{\left(\left(0.125 \cdot \left(t\_3 \cdot \mathsf{PI}\left(\right)\right) - {t\_2}^{3}\right) \cdot \mathsf{fma}\left(t\_4, t\_2, 0.25 \cdot t\_3\right)\right) \cdot 0.3333333333333333}{0.0625 \cdot {\mathsf{PI}\left(\right)}^{4} - {\left(t\_4 \cdot t\_2\right)}^{2}} \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (* (/ x y) -0.05555555555555555) (/ (sqrt t) z)))
        (t_2 (asin t_1))
        (t_3 (* (PI) (PI)))
        (t_4 (acos t_1)))
   (/
    (*
     (* (- (* 0.125 (* t_3 (PI))) (pow t_2 3.0)) (fma t_4 t_2 (* 0.25 t_3)))
     0.3333333333333333)
    (- (* 0.0625 (pow (PI) 4.0)) (pow (* t_4 t_2) 2.0)))))

Derivation

1. Initial program 97.7%

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

4. Applied rewrites 99.0%

   \[\leadsto \color{blue}{\frac{\left({\left(\frac{\mathsf{PI}\left(\right)}{2}\right)}^{3} - {\sin^{-1} \left(\left(\sqrt{t} \cdot -0.05555555555555555\right) \cdot \frac{\frac{x}{y}}{z}\right)}^{3}\right) \cdot 0.3333333333333333}{{\left(\frac{\mathsf{PI}\left(\right)}{2}\right)}^{4} - {\left(\sin^{-1} \left(\left(\sqrt{t} \cdot -0.05555555555555555\right) \cdot \frac{\frac{x}{y}}{z}\right) \cdot \cos^{-1} \left(\left(\sqrt{t} \cdot -0.05555555555555555\right) \cdot \frac{\frac{x}{y}}{z}\right)\right)}^{2}} \cdot \mathsf{fma}\left(\sin^{-1} \left(\left(\sqrt{t} \cdot -0.05555555555555555\right) \cdot \frac{\frac{x}{y}}{z}\right), \cos^{-1} \left(\left(\sqrt{t} \cdot -0.05555555555555555\right) \cdot \frac{\frac{x}{y}}{z}\right), {\left(\frac{\mathsf{PI}\left(\right)}{2}\right)}^{2}\right)} \]

5. Taylor expanded in x around 0

   \[\leadsto \color{blue}{\frac{1}{3} \cdot \frac{\left(\frac{1}{4} \cdot {\mathsf{PI}\left(\right)}^{2} + \cos^{-1} \left(\frac{-1}{18} \cdot \left(\sqrt{t} \cdot \frac{x}{y \cdot z}\right)\right) \cdot \sin^{-1} \left(\frac{-1}{18} \cdot \left(\sqrt{t} \cdot \frac{x}{y \cdot z}\right)\right)\right) \cdot \left(\frac{1}{8} \cdot {\mathsf{PI}\left(\right)}^{3} - {\sin^{-1} \left(\frac{-1}{18} \cdot \left(\sqrt{t} \cdot \frac{x}{y \cdot z}\right)\right)}^{3}\right)}{\frac{1}{16} \cdot {\mathsf{PI}\left(\right)}^{4} - {\cos^{-1} \left(\frac{-1}{18} \cdot \left(\sqrt{t} \cdot \frac{x}{y \cdot z}\right)\right)}^{2} \cdot {\sin^{-1} \left(\frac{-1}{18} \cdot \left(\sqrt{t} \cdot \frac{x}{y \cdot z}\right)\right)}^{2}}} \]

7. Applied rewrites 96.7%

   \[\leadsto \color{blue}{\frac{\left(\mathsf{fma}\left(\sin^{-1} \left(\left(-0.05555555555555555 \cdot \frac{\sqrt{t}}{z}\right) \cdot \frac{x}{y}\right), \cos^{-1} \left(\left(-0.05555555555555555 \cdot \frac{\sqrt{t}}{z}\right) \cdot \frac{x}{y}\right), \left(\mathsf{PI}\left(\right) \cdot \mathsf{PI}\left(\right)\right) \cdot 0.25\right) \cdot 0.3333333333333333\right) \cdot \left({\mathsf{PI}\left(\right)}^{3} \cdot 0.125 - {\sin^{-1} \left(\left(-0.05555555555555555 \cdot \frac{\sqrt{t}}{z}\right) \cdot \frac{x}{y}\right)}^{3}\right)}{\mathsf{fma}\left(-{\sin^{-1} \left(\left(-0.05555555555555555 \cdot \frac{\sqrt{t}}{z}\right) \cdot \frac{x}{y}\right)}^{2}, {\cos^{-1} \left(\left(-0.05555555555555555 \cdot \frac{\sqrt{t}}{z}\right) \cdot \frac{x}{y}\right)}^{2}, {\mathsf{PI}\left(\right)}^{4} \cdot 0.0625\right)}} \]

9. Applied rewrites 98.2%

   \[\leadsto \color{blue}{\frac{\left(\left(0.125 \cdot {\mathsf{PI}\left(\right)}^{3} - {\sin^{-1} \left(\left(\frac{x}{y} \cdot -0.05555555555555555\right) \cdot \frac{\sqrt{t}}{z}\right)}^{3}\right) \cdot \mathsf{fma}\left(\cos^{-1} \left(\left(\frac{x}{y} \cdot -0.05555555555555555\right) \cdot \frac{\sqrt{t}}{z}\right), \sin^{-1} \left(\left(\frac{x}{y} \cdot -0.05555555555555555\right) \cdot \frac{\sqrt{t}}{z}\right), 0.25 \cdot \left(\mathsf{PI}\left(\right) \cdot \mathsf{PI}\left(\right)\right)\right)\right) \cdot 0.3333333333333333}{0.0625 \cdot {\mathsf{PI}\left(\right)}^{4} - {\left(\cos^{-1} \left(\left(\frac{x}{y} \cdot -0.05555555555555555\right) \cdot \frac{\sqrt{t}}{z}\right) \cdot \sin^{-1} \left(\left(\frac{x}{y} \cdot -0.05555555555555555\right) \cdot \frac{\sqrt{t}}{z}\right)\right)}^{2}}} \]
10. Step-by-step derivation

11. Applied rewrites 98.2%

    \[\leadsto \frac{\left(\left(0.125 \cdot \left(\left(\mathsf{PI}\left(\right) \cdot \mathsf{PI}\left(\right)\right) \cdot \mathsf{PI}\left(\right)\right) - {\sin^{-1} \left(\left(\frac{x}{y} \cdot -0.05555555555555555\right) \cdot \frac{\sqrt{t}}{z}\right)}^{3}\right) \cdot \mathsf{fma}\left(\cos^{-1} \left(\left(\frac{x}{y} \cdot -0.05555555555555555\right) \cdot \frac{\sqrt{t}}{z}\right), \sin^{-1} \left(\left(\frac{x}{y} \cdot -0.05555555555555555\right) \cdot \frac{\sqrt{t}}{z}\right), 0.25 \cdot \left(\mathsf{PI}\left(\right) \cdot \mathsf{PI}\left(\right)\right)\right)\right) \cdot 0.3333333333333333}{0.0625 \cdot {\mathsf{PI}\left(\right)}^{4} - {\left(\cos^{-1} \left(\left(\frac{x}{y} \cdot -0.05555555555555555\right) \cdot \frac{\sqrt{t}}{z}\right) \cdot \sin^{-1} \left(\left(\frac{x}{y} \cdot -0.05555555555555555\right) \cdot \frac{\sqrt{t}}{z}\right)\right)}^{2}} \]
12. Add Preprocessing

Alternative 4: 98.1% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.7%

   \[\frac{1}{3} \cdot \cos^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right) \]
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. *-commutative N/A

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

   2. lower-*.f64 N/A

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

5. Applied rewrites 97.7%

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

7. Applied rewrites 98.1%

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

Developer Target 1: 98.1% 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

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(x, y, z, t)
use fmin_fmax_functions
    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 2024359 
(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)))))