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

Percentage Accurate: 98.0% → 99.5%

Time: 1.3min

Alternatives: 5

Speedup: 1.2×

Specification

Math

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

FPCore

(FPCore (x y z t)
  :precision binary64
  (* (/ 1 3) (acos (* (/ (* 3 (/ x (* y 27))) (* z 2)) (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 / 3), $MachinePrecision] * N[ArcCos[N[(N[(N[(3 * N[(x / N[(y * 27), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * 2), $MachinePrecision]), $MachinePrecision] * N[Sqrt[t], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Initial Program: 98.0% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z t)
  :precision binary64
  (* (/ 1 3) (acos (* (/ (* 3 (/ x (* y 27))) (* z 2)) (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 / 3), $MachinePrecision] * N[ArcCos[N[(N[(N[(3 * N[(x / N[(y * 27), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * 2), $MachinePrecision]), $MachinePrecision] * N[Sqrt[t], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.5% accurate, 0.4× speedup

Math

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

FPCore

(FPCore (x y z t)
  :precision binary64
  (*
 1/3
 (*
  (/ (* PI 1/2) (pow PI 2/3))
  (/ (acos (* (* (/ x (* z y)) 1/18) (sqrt t))) (* (cbrt PI) 1/2)))))

C

double code(double x, double y, double z, double t) {
	return 0.3333333333333333 * (((((double) M_PI) * 0.5) / pow(((double) M_PI), 0.6666666666666666)) * (acos((((x / (z * y)) * 0.05555555555555555) * sqrt(t))) / (cbrt(((double) M_PI)) * 0.5)));
}

Java

public static double code(double x, double y, double z, double t) {
	return 0.3333333333333333 * (((Math.PI * 0.5) / Math.pow(Math.PI, 0.6666666666666666)) * (Math.acos((((x / (z * y)) * 0.05555555555555555) * Math.sqrt(t))) / (Math.cbrt(Math.PI) * 0.5)));
}

Julia

function code(x, y, z, t)
	return Float64(0.3333333333333333 * Float64(Float64(Float64(pi * 0.5) / (pi ^ 0.6666666666666666)) * Float64(acos(Float64(Float64(Float64(x / Float64(z * y)) * 0.05555555555555555) * sqrt(t))) / Float64(cbrt(pi) * 0.5))))
end

Wolfram

code[x_, y_, z_, t_] := N[(1/3 * N[(N[(N[(Pi * 1/2), $MachinePrecision] / N[Power[Pi, 2/3], $MachinePrecision]), $MachinePrecision] * N[(N[ArcCos[N[(N[(N[(x / N[(z * y), $MachinePrecision]), $MachinePrecision] * 1/18), $MachinePrecision] * N[Sqrt[t], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / N[(N[Power[Pi, 1/3], $MachinePrecision] * 1/2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 98.0%

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

2. Taylor expanded in x around 0

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

   1. metadata-eval N/A

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

   2. lower-*.f64 N/A

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

   3. metadata-eval N/A

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

   4. lower-acos.f64 N/A

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

   5. lower-*.f64 N/A

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

   6. lower-/.f64 N/A

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

   7. lower-*.f64 N/A

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

   8. lower-sqrt.f64 N/A

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

   9. lower-*.f64 97.0%

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

4. Applied rewrites 97.0%

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

6. Applied rewrites 99.5%

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

Alternative 2: 99.5% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t)
  :precision binary64
  (*
 (/
  (* (acos (* (* (sqrt t) 1/18) (/ x (* z y)))) (* 1/2 (cbrt PI)))
  (cbrt PI))
 2/3))

C

double code(double x, double y, double z, double t) {
	return ((acos(((sqrt(t) * 0.05555555555555555) * (x / (z * y)))) * (0.5 * cbrt(((double) M_PI)))) / cbrt(((double) M_PI))) * 0.6666666666666666;
}

Java

public static double code(double x, double y, double z, double t) {
	return ((Math.acos(((Math.sqrt(t) * 0.05555555555555555) * (x / (z * y)))) * (0.5 * Math.cbrt(Math.PI))) / Math.cbrt(Math.PI)) * 0.6666666666666666;
}

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(acos(Float64(Float64(sqrt(t) * 0.05555555555555555) * Float64(x / Float64(z * y)))) * Float64(0.5 * cbrt(pi))) / cbrt(pi)) * 0.6666666666666666)
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(N[ArcCos[N[(N[(N[Sqrt[t], $MachinePrecision] * 1/18), $MachinePrecision] * N[(x / N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(1/2 * N[Power[Pi, 1/3], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[Power[Pi, 1/3], $MachinePrecision]), $MachinePrecision] * 2/3), $MachinePrecision]

Derivation

1. Initial program 98.0%

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

2. Taylor expanded in x around 0

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

   1. metadata-eval N/A

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

   2. lower-*.f64 N/A

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

   3. metadata-eval N/A

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

   4. lower-acos.f64 N/A

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

   5. lower-*.f64 N/A

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

   6. lower-/.f64 N/A

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

   7. lower-*.f64 N/A

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

   8. lower-sqrt.f64 N/A

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

   9. lower-*.f64 97.0%

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

4. Applied rewrites 97.0%

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

6. Applied rewrites 99.5%

   \[\leadsto \frac{1}{3} \cdot \left(\frac{\pi \cdot \frac{1}{2}}{{\pi}^{\frac{2}{3}}} \cdot \color{blue}{\frac{\cos^{-1} \left(\left(\frac{x}{z \cdot y} \cdot \frac{1}{18}\right) \cdot \sqrt{t}\right)}{\sqrt[3]{\pi} \cdot \frac{1}{2}}}\right) \]
7. Step-by-step derivation

   1. lift-/.f64 N/A

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

   2. lift-*.f64 N/A

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

   3. *-commutative N/A

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

   4. associate-/l* N/A

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

   5. unpow1 N/A

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

   6. lift-pow.f64 N/A

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

   7. pow-div N/A

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

   8. metadata-eval N/A

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

   9. pow1/3 N/A

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

   10. lift-cbrt.f64 N/A

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

   11. *-commutative N/A

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

   12. lift-*.f64 99.5%

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

8. Applied rewrites 99.5%

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

10. Applied rewrites 99.5%

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

Alternative 3: 98.0% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z t)
  :precision binary64
  (* (* (acos (* (* (sqrt t) 1/18) (/ x (* z y)))) (* (/ 1 PI) 1/3)) PI))

C

double code(double x, double y, double z, double t) {
	return (acos(((sqrt(t) * 0.05555555555555555) * (x / (z * y)))) * ((1.0 / ((double) M_PI)) * 0.3333333333333333)) * ((double) M_PI);
}

Java

public static double code(double x, double y, double z, double t) {
	return (Math.acos(((Math.sqrt(t) * 0.05555555555555555) * (x / (z * y)))) * ((1.0 / Math.PI) * 0.3333333333333333)) * Math.PI;
}

Python

def code(x, y, z, t):
	return (math.acos(((math.sqrt(t) * 0.05555555555555555) * (x / (z * y)))) * ((1.0 / math.pi) * 0.3333333333333333)) * math.pi

Julia

function code(x, y, z, t)
	return Float64(Float64(acos(Float64(Float64(sqrt(t) * 0.05555555555555555) * Float64(x / Float64(z * y)))) * Float64(Float64(1.0 / pi) * 0.3333333333333333)) * pi)
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (acos(((sqrt(t) * 0.05555555555555555) * (x / (z * y)))) * ((1.0 / pi) * 0.3333333333333333)) * pi;
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[ArcCos[N[(N[(N[Sqrt[t], $MachinePrecision] * 1/18), $MachinePrecision] * N[(x / N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[(N[(1 / Pi), $MachinePrecision] * 1/3), $MachinePrecision]), $MachinePrecision] * Pi), $MachinePrecision]

Derivation

1. Initial program 98.0%

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

2. Taylor expanded in x around 0

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

   1. metadata-eval N/A

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

   2. lower-*.f64 N/A

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

   3. metadata-eval N/A

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

   4. lower-acos.f64 N/A

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

   5. lower-*.f64 N/A

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

   6. lower-/.f64 N/A

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

   7. lower-*.f64 N/A

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

   8. lower-sqrt.f64 N/A

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

   9. lower-*.f64 97.0%

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

4. Applied rewrites 97.0%

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

6. Applied rewrites 99.5%

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

8. Applied rewrites 96.8%

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

   1. metadata-eval N/A

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

   2. lift-*.f64 N/A

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

   3. *-commutative N/A

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

   4. lift-/.f64 N/A

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

   5. mult-flip N/A

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

   6. associate-*l* N/A

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

   7. lower-*.f64 N/A

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

10. Applied rewrites 98.0%

    \[\leadsto \left(\cos^{-1} \left(\left(\sqrt{t} \cdot \frac{1}{18}\right) \cdot \frac{x}{z \cdot y}\right) \cdot \left(\frac{1}{\pi} \cdot \frac{1}{3}\right)\right) \cdot \pi \]
11. Add Preprocessing

Alternative 4: 98.0% accurate, 1.2× speedup

Math

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

FPCore

(FPCore (x y z t)
  :precision binary64
  (* 1/3 (acos (* (/ (* x 1/18) (* z y)) (sqrt t)))))

C

double code(double x, double y, double z, double t) {
	return 0.3333333333333333 * acos((((x * 0.05555555555555555) / (z * y)) * 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 = 0.3333333333333333d0 * acos((((x * 0.05555555555555555d0) / (z * y)) * 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) / (z * y)) * Math.sqrt(t)));
}

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(1/3 * N[ArcCos[N[(N[(N[(x * 1/18), $MachinePrecision] / N[(z * y), $MachinePrecision]), $MachinePrecision] * N[Sqrt[t], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 98.0%

   \[\frac{1}{3} \cdot \cos^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right) \]
2. 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 98.0%

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

3. Applied rewrites 98.0%

   \[\leadsto \color{blue}{\frac{1}{3}} \cdot \cos^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right) \]
4. 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. mult-flip N/A

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

   3. lift-*.f64 N/A

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

   4. lift-/.f64 N/A

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

   5. lift-*.f64 N/A

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

   6. lift-*.f64 N/A

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

   7. associate-*r/ N/A

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

   8. lift-*.f64 N/A

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

   9. *-commutative N/A

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

   10. times-frac N/A

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

   11. metadata-eval N/A

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

   12. associate-/l* N/A

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

   13. *-commutative N/A

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

   14. lift-*.f64 N/A

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

   15. mult-flip N/A

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

   16. lift-*.f64 N/A

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

   17. *-commutative N/A

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

   18. count-2 N/A

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

   19. lift-+.f64 N/A

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

   20. associate-/r* N/A

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

   21. lift-*.f64 N/A

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

   22. lift-*.f64 N/A

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

   23. lift-*.f64 N/A

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

   24. times-frac N/A

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

   25. lift-+.f64 N/A

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

   26. count-2 N/A

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

   27. associate-/r* N/A

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

5. Applied rewrites 98.0%

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

Alternative 5: 97.0% accurate, 1.2× speedup

Math

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

FPCore

(FPCore (x y z t)
  :precision binary64
  (* 1/3 (acos (* 1/18 (/ (* x (sqrt t)) (* y z))))))

C

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

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 = 0.3333333333333333d0 * acos((0.05555555555555555d0 * ((x * sqrt(t)) / (y * z))))
end function

Java

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

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(1/3 * N[ArcCos[N[(1/18 * N[(N[(x * N[Sqrt[t], $MachinePrecision]), $MachinePrecision] / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 98.0%

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

2. Taylor expanded in x around 0

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

   1. metadata-eval N/A

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

   2. lower-*.f64 N/A

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

   3. metadata-eval N/A

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

   4. lower-acos.f64 N/A

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

   5. lower-*.f64 N/A

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

   6. lower-/.f64 N/A

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

   7. lower-*.f64 N/A

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

   8. lower-sqrt.f64 N/A

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

   9. lower-*.f64 97.0%

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

4. Applied rewrites 97.0%

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

Reproduce

herbie shell --seed 2025271 -o generate:evaluate
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, D"
  :precision binary64
  (* (/ 1 3) (acos (* (/ (* 3 (/ x (* y 27))) (* z 2)) (sqrt t)))))