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

Percentage Accurate: 98.0% → 99.5%

Time: 36.9s

Alternatives: 2

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: 98.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(\sqrt{\pi} \cdot -0.16666666666666666, \sqrt{\pi}, \mathsf{fma}\left(0.3333333333333333, \cos^{-1} \left(\frac{\sqrt{t} \cdot 0.05555555555555555}{y \cdot z} \cdot x\right), \pi \cdot 0.16666666666666666\right)\right) \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (fma
  (* (sqrt PI) -0.16666666666666666)
  (sqrt PI)
  (fma
   0.3333333333333333
   (acos (* (/ (* (sqrt t) 0.05555555555555555) (* y z)) x))
   (* PI 0.16666666666666666))))

C

double code(double x, double y, double z, double t) {
	return fma((sqrt(((double) M_PI)) * -0.16666666666666666), sqrt(((double) M_PI)), fma(0.3333333333333333, acos((((sqrt(t) * 0.05555555555555555) / (y * z)) * x)), (((double) M_PI) * 0.16666666666666666)));
}

Julia

function code(x, y, z, t)
	return fma(Float64(sqrt(pi) * -0.16666666666666666), sqrt(pi), fma(0.3333333333333333, acos(Float64(Float64(Float64(sqrt(t) * 0.05555555555555555) / Float64(y * z)) * x)), Float64(pi * 0.16666666666666666)))
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[Sqrt[Pi], $MachinePrecision] * -0.16666666666666666), $MachinePrecision] * N[Sqrt[Pi], $MachinePrecision] + N[(0.3333333333333333 * N[ArcCos[N[(N[(N[(N[Sqrt[t], $MachinePrecision] * 0.05555555555555555), $MachinePrecision] / N[(y * z), $MachinePrecision]), $MachinePrecision] * x), $MachinePrecision]], $MachinePrecision] + N[(Pi * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 96.7%

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

   1. acos-asin N/A

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

   2. sub-neg N/A

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

   3. distribute-rgt-in N/A

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

   4. accelerator-lowering-fma.f64 N/A

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{\mathsf{PI}\left(\right)}{2}, \frac{1}{3}, \left(\mathsf{neg}\left(\sin^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right)\right)\right) \cdot \frac{1}{3}\right)} \]

   5. div-inv N/A

      \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{PI}\left(\right) \cdot \frac{1}{2}}, \frac{1}{3}, \left(\mathsf{neg}\left(\sin^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right)\right)\right) \cdot \frac{1}{3}\right) \]

   6. metadata-eval N/A

      \[\leadsto \mathsf{fma}\left(\mathsf{PI}\left(\right) \cdot \color{blue}{\frac{1}{2}}, \frac{1}{3}, \left(\mathsf{neg}\left(\sin^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right)\right)\right) \cdot \frac{1}{3}\right) \]

   7. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{PI}\left(\right) \cdot \frac{1}{2}}, \frac{1}{3}, \left(\mathsf{neg}\left(\sin^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right)\right)\right) \cdot \frac{1}{3}\right) \]

   8. PI-lowering-PI.f64 N/A

      \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{PI}\left(\right)} \cdot \frac{1}{2}, \frac{1}{3}, \left(\mathsf{neg}\left(\sin^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right)\right)\right) \cdot \frac{1}{3}\right) \]

   9. metadata-eval N/A

      \[\leadsto \mathsf{fma}\left(\mathsf{PI}\left(\right) \cdot \frac{1}{2}, \color{blue}{\frac{1}{3}}, \left(\mathsf{neg}\left(\sin^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right)\right)\right) \cdot \frac{1}{3}\right) \]

   10. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{fma}\left(\mathsf{PI}\left(\right) \cdot \frac{1}{2}, \frac{1}{3}, \color{blue}{\left(\mathsf{neg}\left(\sin^{-1} \left(\frac{3 \cdot \frac{x}{y \cdot 27}}{z \cdot 2} \cdot \sqrt{t}\right)\right)\right) \cdot \frac{1}{3}}\right) \]

4. Applied egg-rr 97.3%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\pi \cdot 0.5, 0.3333333333333333, \left(-\sin^{-1} \left(\frac{x \cdot \left(3 \cdot \sqrt{t}\right)}{z \cdot \left(54 \cdot y\right)}\right)\right) \cdot 0.3333333333333333\right)} \]

6. Applied egg-rr 98.8%

   \[\leadsto \mathsf{fma}\left(\pi \cdot 0.5, 0.3333333333333333, \color{blue}{\mathsf{fma}\left(\sqrt{\pi}, -\sqrt{\pi} \cdot 0.16666666666666666, 0.3333333333333333 \cdot \cos^{-1} \left(\frac{x \cdot \left(\sqrt{t} \cdot 0.05555555555555555\right)}{y \cdot z}\right)\right)}\right) \]
7. Step-by-step derivation

   1. +-commutative N/A

      \[\leadsto \color{blue}{\left(\sqrt{\mathsf{PI}\left(\right)} \cdot \left(\mathsf{neg}\left(\sqrt{\mathsf{PI}\left(\right)} \cdot \frac{1}{6}\right)\right) + \frac{1}{3} \cdot \cos^{-1} \left(\frac{x \cdot \left(\sqrt{t} \cdot \frac{1}{18}\right)}{y \cdot z}\right)\right) + \left(\mathsf{PI}\left(\right) \cdot \frac{1}{2}\right) \cdot \frac{1}{3}} \]

   2. associate-+l+ N/A

      \[\leadsto \color{blue}{\sqrt{\mathsf{PI}\left(\right)} \cdot \left(\mathsf{neg}\left(\sqrt{\mathsf{PI}\left(\right)} \cdot \frac{1}{6}\right)\right) + \left(\frac{1}{3} \cdot \cos^{-1} \left(\frac{x \cdot \left(\sqrt{t} \cdot \frac{1}{18}\right)}{y \cdot z}\right) + \left(\mathsf{PI}\left(\right) \cdot \frac{1}{2}\right) \cdot \frac{1}{3}\right)} \]

   3. *-commutative N/A

      \[\leadsto \sqrt{\mathsf{PI}\left(\right)} \cdot \left(\mathsf{neg}\left(\sqrt{\mathsf{PI}\left(\right)} \cdot \frac{1}{6}\right)\right) + \left(\frac{1}{3} \cdot \cos^{-1} \left(\frac{x \cdot \left(\sqrt{t} \cdot \frac{1}{18}\right)}{y \cdot z}\right) + \color{blue}{\frac{1}{3} \cdot \left(\mathsf{PI}\left(\right) \cdot \frac{1}{2}\right)}\right) \]

   4. distribute-lft-in N/A

      \[\leadsto \sqrt{\mathsf{PI}\left(\right)} \cdot \left(\mathsf{neg}\left(\sqrt{\mathsf{PI}\left(\right)} \cdot \frac{1}{6}\right)\right) + \color{blue}{\frac{1}{3} \cdot \left(\cos^{-1} \left(\frac{x \cdot \left(\sqrt{t} \cdot \frac{1}{18}\right)}{y \cdot z}\right) + \mathsf{PI}\left(\right) \cdot \frac{1}{2}\right)} \]

   5. +-commutative N/A

      \[\leadsto \sqrt{\mathsf{PI}\left(\right)} \cdot \left(\mathsf{neg}\left(\sqrt{\mathsf{PI}\left(\right)} \cdot \frac{1}{6}\right)\right) + \frac{1}{3} \cdot \color{blue}{\left(\mathsf{PI}\left(\right) \cdot \frac{1}{2} + \cos^{-1} \left(\frac{x \cdot \left(\sqrt{t} \cdot \frac{1}{18}\right)}{y \cdot z}\right)\right)} \]

   6. *-commutative N/A

      \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\sqrt{\mathsf{PI}\left(\right)} \cdot \frac{1}{6}\right)\right) \cdot \sqrt{\mathsf{PI}\left(\right)}} + \frac{1}{3} \cdot \left(\mathsf{PI}\left(\right) \cdot \frac{1}{2} + \cos^{-1} \left(\frac{x \cdot \left(\sqrt{t} \cdot \frac{1}{18}\right)}{y \cdot z}\right)\right) \]

   7. accelerator-lowering-fma.f64 N/A

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(\sqrt{\mathsf{PI}\left(\right)} \cdot \frac{1}{6}\right), \sqrt{\mathsf{PI}\left(\right)}, \frac{1}{3} \cdot \left(\mathsf{PI}\left(\right) \cdot \frac{1}{2} + \cos^{-1} \left(\frac{x \cdot \left(\sqrt{t} \cdot \frac{1}{18}\right)}{y \cdot z}\right)\right)\right)} \]

8. Applied egg-rr 98.8%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\sqrt{\pi} \cdot -0.16666666666666666, \sqrt{\pi}, \mathsf{fma}\left(0.3333333333333333, \cos^{-1} \left(\frac{x \cdot \left(\sqrt{t} \cdot 0.05555555555555555\right)}{y \cdot z}\right), \pi \cdot 0.16666666666666666\right)\right)} \]
9. Step-by-step derivation

   1. associate-/l* N/A

      \[\leadsto \mathsf{fma}\left(\sqrt{\mathsf{PI}\left(\right)} \cdot \frac{-1}{6}, \sqrt{\mathsf{PI}\left(\right)}, \mathsf{fma}\left(\frac{1}{3}, \cos^{-1} \color{blue}{\left(x \cdot \frac{\sqrt{t} \cdot \frac{1}{18}}{y \cdot z}\right)}, \mathsf{PI}\left(\right) \cdot \frac{1}{6}\right)\right) \]

   2. *-commutative N/A

      \[\leadsto \mathsf{fma}\left(\sqrt{\mathsf{PI}\left(\right)} \cdot \frac{-1}{6}, \sqrt{\mathsf{PI}\left(\right)}, \mathsf{fma}\left(\frac{1}{3}, \cos^{-1} \color{blue}{\left(\frac{\sqrt{t} \cdot \frac{1}{18}}{y \cdot z} \cdot x\right)}, \mathsf{PI}\left(\right) \cdot \frac{1}{6}\right)\right) \]

   3. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{fma}\left(\sqrt{\mathsf{PI}\left(\right)} \cdot \frac{-1}{6}, \sqrt{\mathsf{PI}\left(\right)}, \mathsf{fma}\left(\frac{1}{3}, \cos^{-1} \color{blue}{\left(\frac{\sqrt{t} \cdot \frac{1}{18}}{y \cdot z} \cdot x\right)}, \mathsf{PI}\left(\right) \cdot \frac{1}{6}\right)\right) \]

   4. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{fma}\left(\sqrt{\mathsf{PI}\left(\right)} \cdot \frac{-1}{6}, \sqrt{\mathsf{PI}\left(\right)}, \mathsf{fma}\left(\frac{1}{3}, \cos^{-1} \left(\color{blue}{\frac{\sqrt{t} \cdot \frac{1}{18}}{y \cdot z}} \cdot x\right), \mathsf{PI}\left(\right) \cdot \frac{1}{6}\right)\right) \]

   5. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{fma}\left(\sqrt{\mathsf{PI}\left(\right)} \cdot \frac{-1}{6}, \sqrt{\mathsf{PI}\left(\right)}, \mathsf{fma}\left(\frac{1}{3}, \cos^{-1} \left(\frac{\color{blue}{\sqrt{t} \cdot \frac{1}{18}}}{y \cdot z} \cdot x\right), \mathsf{PI}\left(\right) \cdot \frac{1}{6}\right)\right) \]

   6. sqrt-lowering-sqrt.f64 N/A

      \[\leadsto \mathsf{fma}\left(\sqrt{\mathsf{PI}\left(\right)} \cdot \frac{-1}{6}, \sqrt{\mathsf{PI}\left(\right)}, \mathsf{fma}\left(\frac{1}{3}, \cos^{-1} \left(\frac{\color{blue}{\sqrt{t}} \cdot \frac{1}{18}}{y \cdot z} \cdot x\right), \mathsf{PI}\left(\right) \cdot \frac{1}{6}\right)\right) \]

   7. *-lowering-*.f64 99.7

      \[\leadsto \mathsf{fma}\left(\sqrt{\pi} \cdot -0.16666666666666666, \sqrt{\pi}, \mathsf{fma}\left(0.3333333333333333, \cos^{-1} \left(\frac{\sqrt{t} \cdot 0.05555555555555555}{\color{blue}{y \cdot z}} \cdot x\right), \pi \cdot 0.16666666666666666\right)\right) \]

10. Applied egg-rr 99.7%

    \[\leadsto \mathsf{fma}\left(\sqrt{\pi} \cdot -0.16666666666666666, \sqrt{\pi}, \mathsf{fma}\left(0.3333333333333333, \cos^{-1} \color{blue}{\left(\frac{\sqrt{t} \cdot 0.05555555555555555}{y \cdot z} \cdot x\right)}, \pi \cdot 0.16666666666666666\right)\right) \]
11. Add Preprocessing

Alternative 2: 98.1% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.7%

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

   1. metadata-eval 96.7

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

4. Applied egg-rr 96.7%

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

   1. associate-*r/ N/A

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

   2. *-commutative N/A

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

   3. times-frac N/A

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

   4. *-commutative N/A

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

   5. times-frac N/A

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

   6. metadata-eval N/A

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

   7. metadata-eval N/A

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

   8. associate-/r* N/A

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

   9. associate-*r/ N/A

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

   10. /-lowering-/.f64 N/A

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

   11. *-commutative N/A

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

   12. *-lowering-*.f64 N/A

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

   13. *-lowering-*.f64 98.3

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

6. Applied egg-rr 98.3%

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

7. Final simplification 98.3%

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

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 2024199 
(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)))))