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

Percentage Accurate: 69.3% → 76.7%

Time: 25.8s

Alternatives: 9

Speedup: 1.0×

Specification

Math

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

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (- (* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0)))) (/ a (* b 3.0))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((2.0 * sqrt(x)) * cos((y - ((z * t) / 3.0)))) - (a / (b * 3.0));
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = ((2.0d0 * sqrt(x)) * cos((y - ((z * t) / 3.0d0)))) - (a / (b * 3.0d0))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return ((2.0 * Math.sqrt(x)) * Math.cos((y - ((z * t) / 3.0)))) - (a / (b * 3.0));
}

Python

def code(x, y, z, t, a, b):
	return ((2.0 * math.sqrt(x)) * math.cos((y - ((z * t) / 3.0)))) - (a / (b * 3.0))

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(2.0 * sqrt(x)) * cos(Float64(y - Float64(Float64(z * t) / 3.0)))) - Float64(a / Float64(b * 3.0)))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((2.0 * sqrt(x)) * cos((y - ((z * t) / 3.0)))) - (a / (b * 3.0));
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] * N[Cos[N[(y - N[(N[(z * t), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - N[(a / N[(b * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 69.3% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (- (* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0)))) (/ a (* b 3.0))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((2.0 * sqrt(x)) * cos((y - ((z * t) / 3.0)))) - (a / (b * 3.0));
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = ((2.0d0 * sqrt(x)) * cos((y - ((z * t) / 3.0d0)))) - (a / (b * 3.0d0))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return ((2.0 * Math.sqrt(x)) * Math.cos((y - ((z * t) / 3.0)))) - (a / (b * 3.0));
}

Python

def code(x, y, z, t, a, b):
	return ((2.0 * math.sqrt(x)) * math.cos((y - ((z * t) / 3.0)))) - (a / (b * 3.0))

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(2.0 * sqrt(x)) * cos(Float64(y - Float64(Float64(z * t) / 3.0)))) - Float64(a / Float64(b * 3.0)))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((2.0 * sqrt(x)) * cos((y - ((z * t) / 3.0)))) - (a / (b * 3.0));
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] * N[Cos[N[(y - N[(N[(z * t), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - N[(a / N[(b * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 76.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := 2 \cdot \sqrt{x}\\ t_2 := \frac{z}{\frac{3}{t}}\\ \mathbf{if}\;t_1 \cdot \cos \left(y - \frac{z \cdot t}{3}\right) \leq 4 \cdot 10^{+136}:\\ \;\;\;\;t_1 \cdot \left(\cos y \cdot \cos t_2 + \sin y \cdot \sin t_2\right) - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;t_1 \cdot \left|\cos y\right| + \frac{a}{3} \cdot \frac{-1}{b}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* 2.0 (sqrt x))) (t_2 (/ z (/ 3.0 t))))
   (if (<= (* t_1 (cos (- y (/ (* z t) 3.0)))) 4e+136)
     (-
      (* t_1 (+ (* (cos y) (cos t_2)) (* (sin y) (sin t_2))))
      (/ a (* 3.0 b)))
     (+ (* t_1 (fabs (cos y))) (* (/ a 3.0) (/ -1.0 b))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 2.0 * sqrt(x);
	double t_2 = z / (3.0 / t);
	double tmp;
	if ((t_1 * cos((y - ((z * t) / 3.0)))) <= 4e+136) {
		tmp = (t_1 * ((cos(y) * cos(t_2)) + (sin(y) * sin(t_2)))) - (a / (3.0 * b));
	} else {
		tmp = (t_1 * fabs(cos(y))) + ((a / 3.0) * (-1.0 / b));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 2.0d0 * sqrt(x)
    t_2 = z / (3.0d0 / t)
    if ((t_1 * cos((y - ((z * t) / 3.0d0)))) <= 4d+136) then
        tmp = (t_1 * ((cos(y) * cos(t_2)) + (sin(y) * sin(t_2)))) - (a / (3.0d0 * b))
    else
        tmp = (t_1 * abs(cos(y))) + ((a / 3.0d0) * ((-1.0d0) / b))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 2.0 * Math.sqrt(x);
	double t_2 = z / (3.0 / t);
	double tmp;
	if ((t_1 * Math.cos((y - ((z * t) / 3.0)))) <= 4e+136) {
		tmp = (t_1 * ((Math.cos(y) * Math.cos(t_2)) + (Math.sin(y) * Math.sin(t_2)))) - (a / (3.0 * b));
	} else {
		tmp = (t_1 * Math.abs(Math.cos(y))) + ((a / 3.0) * (-1.0 / b));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = 2.0 * math.sqrt(x)
	t_2 = z / (3.0 / t)
	tmp = 0
	if (t_1 * math.cos((y - ((z * t) / 3.0)))) <= 4e+136:
		tmp = (t_1 * ((math.cos(y) * math.cos(t_2)) + (math.sin(y) * math.sin(t_2)))) - (a / (3.0 * b))
	else:
		tmp = (t_1 * math.fabs(math.cos(y))) + ((a / 3.0) * (-1.0 / b))
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(2.0 * sqrt(x))
	t_2 = Float64(z / Float64(3.0 / t))
	tmp = 0.0
	if (Float64(t_1 * cos(Float64(y - Float64(Float64(z * t) / 3.0)))) <= 4e+136)
		tmp = Float64(Float64(t_1 * Float64(Float64(cos(y) * cos(t_2)) + Float64(sin(y) * sin(t_2)))) - Float64(a / Float64(3.0 * b)));
	else
		tmp = Float64(Float64(t_1 * abs(cos(y))) + Float64(Float64(a / 3.0) * Float64(-1.0 / b)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 2.0 * sqrt(x);
	t_2 = z / (3.0 / t);
	tmp = 0.0;
	if ((t_1 * cos((y - ((z * t) / 3.0)))) <= 4e+136)
		tmp = (t_1 * ((cos(y) * cos(t_2)) + (sin(y) * sin(t_2)))) - (a / (3.0 * b));
	else
		tmp = (t_1 * abs(cos(y))) + ((a / 3.0) * (-1.0 / b));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z / N[(3.0 / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$1 * N[Cos[N[(y - N[(N[(z * t), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 4e+136], N[(N[(t$95$1 * N[(N[(N[Cos[y], $MachinePrecision] * N[Cos[t$95$2], $MachinePrecision]), $MachinePrecision] + N[(N[Sin[y], $MachinePrecision] * N[Sin[t$95$2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a / N[(3.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$1 * N[Abs[N[Cos[y], $MachinePrecision]], $MachinePrecision]), $MachinePrecision] + N[(N[(a / 3.0), $MachinePrecision] * N[(-1.0 / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3)))) < 4.00000000000000023e136

   1. Initial program 76.5%

      \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
   2. Step-by-step derivation

      1. *-commutative 76.5%

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

      2. *-commutative 76.5%

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

      3. associate-/l* 76.4%

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

      4. *-commutative 76.4%

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

   3. Simplified 76.4%

      \[\leadsto \color{blue}{\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z}{\frac{3}{t}}\right) - \frac{a}{3 \cdot b}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. *-un-lft-identity 76.4%

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

      2. add-cube-cbrt 76.6%

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

      3. times-frac 76.1%

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

      4. pow2 76.1%

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

   6. Applied egg-rr 76.1%

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

      1. associate-*l/ 76.5%

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

      2. *-lft-identity 76.5%

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

   8. Simplified 76.5%

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

      1. cos-diff 78.1%

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

      2. associate-/l/ 78.2%

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

      3. unpow2 78.2%

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

      4. add-cube-cbrt 78.1%

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

      5. associate-/l/ 78.2%

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

      6. unpow2 78.2%

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \left(\cos y \cdot \cos \left(\frac{z}{\frac{3}{t}}\right) + \sin y \cdot \sin \left(\frac{z}{\color{blue}{\left(\sqrt[3]{\frac{3}{t}} \cdot \sqrt[3]{\frac{3}{t}}\right)} \cdot \sqrt[3]{\frac{3}{t}}}\right)\right) - \frac{a}{3 \cdot b} \]

      7. add-cube-cbrt 78.6%

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \left(\cos y \cdot \cos \left(\frac{z}{\frac{3}{t}}\right) + \sin y \cdot \sin \left(\frac{z}{\color{blue}{\frac{3}{t}}}\right)\right) - \frac{a}{3 \cdot b} \]

   10. Applied egg-rr 78.6%

       \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\left(\cos y \cdot \cos \left(\frac{z}{\frac{3}{t}}\right) + \sin y \cdot \sin \left(\frac{z}{\frac{3}{t}}\right)\right)} - \frac{a}{3 \cdot b} \]

   if 4.00000000000000023e136 < (*.f64 (*.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3))))

   1. Initial program 13.6%

      \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
   2. Step-by-step derivation

      1. *-commutative 13.6%

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

      2. *-commutative 13.6%

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

      3. associate-/l* 13.6%

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

      4. *-commutative 13.6%

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

   3. Simplified 13.6%

      \[\leadsto \color{blue}{\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z}{\frac{3}{t}}\right) - \frac{a}{3 \cdot b}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 62.7%

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\cos y} - \frac{a}{3 \cdot b} \]
   6. Step-by-step derivation

      1. *-un-lft-identity 62.7%

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \frac{\color{blue}{1 \cdot a}}{3 \cdot b} \]

      2. *-commutative 62.7%

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \frac{1 \cdot a}{\color{blue}{b \cdot 3}} \]

      3. times-frac 62.7%

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \color{blue}{\frac{1}{b} \cdot \frac{a}{3}} \]

   7. Applied egg-rr 62.7%

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \color{blue}{\frac{1}{b} \cdot \frac{a}{3}} \]
   8. Step-by-step derivation

      1. add-sqr-sqrt 47.9%

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\left(\sqrt{\cos y} \cdot \sqrt{\cos y}\right)} - \frac{1}{b} \cdot \frac{a}{3} \]

      2. sqrt-unprod 63.5%

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\sqrt{\cos y \cdot \cos y}} - \frac{1}{b} \cdot \frac{a}{3} \]

      3. pow2 63.5%

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

   9. Applied egg-rr 63.5%

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\sqrt{{\cos y}^{2}}} - \frac{1}{b} \cdot \frac{a}{3} \]
   10. Step-by-step derivation

       1. unpow2 63.5%

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \sqrt{\color{blue}{\cos y \cdot \cos y}} - \frac{1}{b} \cdot \frac{a}{3} \]

       2. rem-sqrt-square 63.5%

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\left|\cos y\right|} - \frac{1}{b} \cdot \frac{a}{3} \]

   11. Simplified 63.5%

       \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\left|\cos y\right|} - \frac{1}{b} \cdot \frac{a}{3} \]
3. Recombined 2 regimes into one program.

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) \leq 4 \cdot 10^{+136}:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \left(\cos y \cdot \cos \left(\frac{z}{\frac{3}{t}}\right) + \sin y \cdot \sin \left(\frac{z}{\frac{3}{t}}\right)\right) - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \left|\cos y\right| + \frac{a}{3} \cdot \frac{-1}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 76.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \frac{a}{3 \cdot b}\\ t_2 := \left(z \cdot t\right) \cdot 0.3333333333333333\\ \mathbf{if}\;\cos \left(y - \frac{z \cdot t}{3}\right) \leq 0.9998:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \left(\cos y \cdot \cos t_2 + \sin y \cdot \sin t_2\right) - t_1\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1 + \cos \left(2 \cdot y\right)}{2} \cdot \left(x \cdot 4\right)} - t_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ a (* 3.0 b))) (t_2 (* (* z t) 0.3333333333333333)))
   (if (<= (cos (- y (/ (* z t) 3.0))) 0.9998)
     (-
      (* (* 2.0 (sqrt x)) (+ (* (cos y) (cos t_2)) (* (sin y) (sin t_2))))
      t_1)
     (- (sqrt (* (/ (+ 1.0 (cos (* 2.0 y))) 2.0) (* x 4.0))) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a / (3.0 * b);
	double t_2 = (z * t) * 0.3333333333333333;
	double tmp;
	if (cos((y - ((z * t) / 3.0))) <= 0.9998) {
		tmp = ((2.0 * sqrt(x)) * ((cos(y) * cos(t_2)) + (sin(y) * sin(t_2)))) - t_1;
	} else {
		tmp = sqrt((((1.0 + cos((2.0 * y))) / 2.0) * (x * 4.0))) - t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a / (3.0d0 * b)
    t_2 = (z * t) * 0.3333333333333333d0
    if (cos((y - ((z * t) / 3.0d0))) <= 0.9998d0) then
        tmp = ((2.0d0 * sqrt(x)) * ((cos(y) * cos(t_2)) + (sin(y) * sin(t_2)))) - t_1
    else
        tmp = sqrt((((1.0d0 + cos((2.0d0 * y))) / 2.0d0) * (x * 4.0d0))) - t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a / (3.0 * b);
	double t_2 = (z * t) * 0.3333333333333333;
	double tmp;
	if (Math.cos((y - ((z * t) / 3.0))) <= 0.9998) {
		tmp = ((2.0 * Math.sqrt(x)) * ((Math.cos(y) * Math.cos(t_2)) + (Math.sin(y) * Math.sin(t_2)))) - t_1;
	} else {
		tmp = Math.sqrt((((1.0 + Math.cos((2.0 * y))) / 2.0) * (x * 4.0))) - t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = a / (3.0 * b)
	t_2 = (z * t) * 0.3333333333333333
	tmp = 0
	if math.cos((y - ((z * t) / 3.0))) <= 0.9998:
		tmp = ((2.0 * math.sqrt(x)) * ((math.cos(y) * math.cos(t_2)) + (math.sin(y) * math.sin(t_2)))) - t_1
	else:
		tmp = math.sqrt((((1.0 + math.cos((2.0 * y))) / 2.0) * (x * 4.0))) - t_1
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(a / Float64(3.0 * b))
	t_2 = Float64(Float64(z * t) * 0.3333333333333333)
	tmp = 0.0
	if (cos(Float64(y - Float64(Float64(z * t) / 3.0))) <= 0.9998)
		tmp = Float64(Float64(Float64(2.0 * sqrt(x)) * Float64(Float64(cos(y) * cos(t_2)) + Float64(sin(y) * sin(t_2)))) - t_1);
	else
		tmp = Float64(sqrt(Float64(Float64(Float64(1.0 + cos(Float64(2.0 * y))) / 2.0) * Float64(x * 4.0))) - t_1);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a / (3.0 * b);
	t_2 = (z * t) * 0.3333333333333333;
	tmp = 0.0;
	if (cos((y - ((z * t) / 3.0))) <= 0.9998)
		tmp = ((2.0 * sqrt(x)) * ((cos(y) * cos(t_2)) + (sin(y) * sin(t_2)))) - t_1;
	else
		tmp = sqrt((((1.0 + cos((2.0 * y))) / 2.0) * (x * 4.0))) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a / N[(3.0 * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z * t), $MachinePrecision] * 0.3333333333333333), $MachinePrecision]}, If[LessEqual[N[Cos[N[(y - N[(N[(z * t), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], 0.9998], N[(N[(N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] * N[(N[(N[Cos[y], $MachinePrecision] * N[Cos[t$95$2], $MachinePrecision]), $MachinePrecision] + N[(N[Sin[y], $MachinePrecision] * N[Sin[t$95$2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[Sqrt[N[(N[(N[(1.0 + N[Cos[N[(2.0 * y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision] * N[(x * 4.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3))) < 0.99980000000000002

   1. Initial program 68.0%

      \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
   2. Step-by-step derivation

      1. *-commutative 68.0%

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

      2. *-commutative 68.0%

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

      3. associate-/l* 67.8%

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

      4. *-commutative 67.8%

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

   3. Simplified 67.8%

      \[\leadsto \color{blue}{\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z}{\frac{3}{t}}\right) - \frac{a}{3 \cdot b}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. cos-diff 70.6%

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\left(\cos y \cdot \cos \left(\frac{z}{\frac{3}{t}}\right) + \sin y \cdot \sin \left(\frac{z}{\frac{3}{t}}\right)\right)} - \frac{a}{3 \cdot b} \]

   6. Applied egg-rr 70.5%

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\left(\cos y \cdot \cos \left(\left(z \cdot t\right) \cdot 0.3333333333333333\right) + \sin y \cdot \sin \left(\left(z \cdot t\right) \cdot 0.3333333333333333\right)\right)} - \frac{a}{3 \cdot b} \]

   if 0.99980000000000002 < (cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3)))

   1. Initial program 64.2%

      \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
   2. Step-by-step derivation

      1. *-commutative 64.2%

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

      2. *-commutative 64.2%

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

      3. associate-/l* 64.2%

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

      4. *-commutative 64.2%

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

   3. Simplified 64.2%

      \[\leadsto \color{blue}{\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z}{\frac{3}{t}}\right) - \frac{a}{3 \cdot b}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 86.1%

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\cos y} - \frac{a}{3 \cdot b} \]
   6. Step-by-step derivation

      1. add-sqr-sqrt 79.4%

         \[\leadsto \color{blue}{\sqrt{\left(2 \cdot \sqrt{x}\right) \cdot \cos y} \cdot \sqrt{\left(2 \cdot \sqrt{x}\right) \cdot \cos y}} - \frac{a}{3 \cdot b} \]

      2. sqrt-unprod 86.7%

         \[\leadsto \color{blue}{\sqrt{\left(\left(2 \cdot \sqrt{x}\right) \cdot \cos y\right) \cdot \left(\left(2 \cdot \sqrt{x}\right) \cdot \cos y\right)}} - \frac{a}{3 \cdot b} \]

      3. *-commutative 86.7%

         \[\leadsto \sqrt{\color{blue}{\left(\cos y \cdot \left(2 \cdot \sqrt{x}\right)\right)} \cdot \left(\left(2 \cdot \sqrt{x}\right) \cdot \cos y\right)} - \frac{a}{3 \cdot b} \]

      4. *-commutative 86.7%

         \[\leadsto \sqrt{\left(\cos y \cdot \left(2 \cdot \sqrt{x}\right)\right) \cdot \color{blue}{\left(\cos y \cdot \left(2 \cdot \sqrt{x}\right)\right)}} - \frac{a}{3 \cdot b} \]

      5. swap-sqr 86.7%

         \[\leadsto \sqrt{\color{blue}{\left(\cos y \cdot \cos y\right) \cdot \left(\left(2 \cdot \sqrt{x}\right) \cdot \left(2 \cdot \sqrt{x}\right)\right)}} - \frac{a}{3 \cdot b} \]

      6. pow2 86.7%

         \[\leadsto \sqrt{\color{blue}{{\cos y}^{2}} \cdot \left(\left(2 \cdot \sqrt{x}\right) \cdot \left(2 \cdot \sqrt{x}\right)\right)} - \frac{a}{3 \cdot b} \]

      7. *-commutative 86.7%

         \[\leadsto \sqrt{{\cos y}^{2} \cdot \left(\color{blue}{\left(\sqrt{x} \cdot 2\right)} \cdot \left(2 \cdot \sqrt{x}\right)\right)} - \frac{a}{3 \cdot b} \]

      8. *-commutative 86.7%

         \[\leadsto \sqrt{{\cos y}^{2} \cdot \left(\left(\sqrt{x} \cdot 2\right) \cdot \color{blue}{\left(\sqrt{x} \cdot 2\right)}\right)} - \frac{a}{3 \cdot b} \]

      9. swap-sqr 86.7%

         \[\leadsto \sqrt{{\cos y}^{2} \cdot \color{blue}{\left(\left(\sqrt{x} \cdot \sqrt{x}\right) \cdot \left(2 \cdot 2\right)\right)}} - \frac{a}{3 \cdot b} \]

      10. add-sqr-sqrt 86.7%

          \[\leadsto \sqrt{{\cos y}^{2} \cdot \left(\color{blue}{x} \cdot \left(2 \cdot 2\right)\right)} - \frac{a}{3 \cdot b} \]

      11. metadata-eval 86.7%

          \[\leadsto \sqrt{{\cos y}^{2} \cdot \left(x \cdot \color{blue}{4}\right)} - \frac{a}{3 \cdot b} \]

   7. Applied egg-rr 86.7%

      \[\leadsto \color{blue}{\sqrt{{\cos y}^{2} \cdot \left(x \cdot 4\right)}} - \frac{a}{3 \cdot b} \]
   8. Step-by-step derivation

      1. unpow2 86.7%

         \[\leadsto \sqrt{\color{blue}{\left(\cos y \cdot \cos y\right)} \cdot \left(x \cdot 4\right)} - \frac{a}{3 \cdot b} \]

      2. cos-mult 86.7%

         \[\leadsto \sqrt{\color{blue}{\frac{\cos \left(y + y\right) + \cos \left(y - y\right)}{2}} \cdot \left(x \cdot 4\right)} - \frac{a}{3 \cdot b} \]

   9. Applied egg-rr 86.7%

      \[\leadsto \sqrt{\color{blue}{\frac{\cos \left(y + y\right) + \cos \left(y - y\right)}{2}} \cdot \left(x \cdot 4\right)} - \frac{a}{3 \cdot b} \]
   10. Step-by-step derivation

       1. +-commutative 86.7%

          \[\leadsto \sqrt{\frac{\color{blue}{\cos \left(y - y\right) + \cos \left(y + y\right)}}{2} \cdot \left(x \cdot 4\right)} - \frac{a}{3 \cdot b} \]

       2. +-inverses 86.7%

          \[\leadsto \sqrt{\frac{\cos \color{blue}{0} + \cos \left(y + y\right)}{2} \cdot \left(x \cdot 4\right)} - \frac{a}{3 \cdot b} \]

       3. cos-0 86.7%

          \[\leadsto \sqrt{\frac{\color{blue}{1} + \cos \left(y + y\right)}{2} \cdot \left(x \cdot 4\right)} - \frac{a}{3 \cdot b} \]

       4. count-2 86.7%

          \[\leadsto \sqrt{\frac{1 + \cos \color{blue}{\left(2 \cdot y\right)}}{2} \cdot \left(x \cdot 4\right)} - \frac{a}{3 \cdot b} \]

   11. Simplified 86.7%

       \[\leadsto \sqrt{\color{blue}{\frac{1 + \cos \left(2 \cdot y\right)}{2}} \cdot \left(x \cdot 4\right)} - \frac{a}{3 \cdot b} \]
3. Recombined 2 regimes into one program.

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\cos \left(y - \frac{z \cdot t}{3}\right) \leq 0.9998:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \left(\cos y \cdot \cos \left(\left(z \cdot t\right) \cdot 0.3333333333333333\right) + \sin y \cdot \sin \left(\left(z \cdot t\right) \cdot 0.3333333333333333\right)\right) - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\frac{1 + \cos \left(2 \cdot y\right)}{2} \cdot \left(x \cdot 4\right)} - \frac{a}{3 \cdot b}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \left(2 \cdot \sqrt{x}\right) \cdot \cos y - 0.3333333333333333 \cdot \frac{a}{b} \end{array} \]

FPCore

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

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	return ((2.0 * sqrt(x)) * cos(y)) - (0.3333333333333333 * (a / b));
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = ((2.0d0 * sqrt(x)) * cos(y)) - (0.3333333333333333d0 * (a / b))
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	return ((2.0 * Math.sqrt(x)) * Math.cos(y)) - (0.3333333333333333 * (a / b));
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	return ((2.0 * math.sqrt(x)) * math.cos(y)) - (0.3333333333333333 * (a / b))

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(2.0 * sqrt(x)) * cos(y)) - Float64(0.3333333333333333 * Float64(a / b)))
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp = code(x, y, z, t, a, b)
	tmp = ((2.0 * sqrt(x)) * cos(y)) - (0.3333333333333333 * (a / b));
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] * N[Cos[y], $MachinePrecision]), $MachinePrecision] - N[(0.3333333333333333 * N[(a / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 66.7%

   \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
2. Step-by-step derivation

   1. *-commutative 66.7%

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

   2. *-commutative 66.7%

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

   3. associate-/l* 66.6%

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

   4. *-commutative 66.6%

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

3. Simplified 66.6%

   \[\leadsto \color{blue}{\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z}{\frac{3}{t}}\right) - \frac{a}{3 \cdot b}} \]
4. Add Preprocessing

5. Taylor expanded in z around 0 74.2%

   \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\cos y} - \frac{a}{3 \cdot b} \]

6. Taylor expanded in a around 0 74.1%

   \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \color{blue}{0.3333333333333333 \cdot \frac{a}{b}} \]

7. Final simplification 74.1%

   \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - 0.3333333333333333 \cdot \frac{a}{b} \]
8. Add Preprocessing

Alternative 4: 75.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \frac{a}{3 \cdot b} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (- (* (* 2.0 (sqrt x)) (cos y)) (/ a (* 3.0 b))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	return ((2.0 * sqrt(x)) * cos(y)) - (a / (3.0 * b));
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = ((2.0d0 * sqrt(x)) * cos(y)) - (a / (3.0d0 * b))
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	return ((2.0 * Math.sqrt(x)) * Math.cos(y)) - (a / (3.0 * b));
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	return ((2.0 * math.sqrt(x)) * math.cos(y)) - (a / (3.0 * b))

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(2.0 * sqrt(x)) * cos(y)) - Float64(a / Float64(3.0 * b)))
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp = code(x, y, z, t, a, b)
	tmp = ((2.0 * sqrt(x)) * cos(y)) - (a / (3.0 * b));
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] * N[Cos[y], $MachinePrecision]), $MachinePrecision] - N[(a / N[(3.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 66.7%

   \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
2. Step-by-step derivation

   1. *-commutative 66.7%

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

   2. *-commutative 66.7%

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

   3. associate-/l* 66.6%

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

   4. *-commutative 66.6%

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

3. Simplified 66.6%

   \[\leadsto \color{blue}{\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z}{\frac{3}{t}}\right) - \frac{a}{3 \cdot b}} \]
4. Add Preprocessing

5. Taylor expanded in z around 0 74.2%

   \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\cos y} - \frac{a}{3 \cdot b} \]

6. Final simplification 74.2%

   \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \frac{a}{3 \cdot b} \]
7. Add Preprocessing

Alternative 5: 65.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -1.8 \cdot 10^{+158}:\\ \;\;\;\;\sqrt{x} \cdot \left(2 \cdot \cos y\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{x} - \frac{a}{3 \cdot b}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.8e+158)
   (* (sqrt x) (* 2.0 (cos y)))
   (- (* 2.0 (sqrt x)) (/ a (* 3.0 b)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.8e+158) {
		tmp = sqrt(x) * (2.0 * cos(y));
	} else {
		tmp = (2.0 * sqrt(x)) - (a / (3.0 * b));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-1.8d+158)) then
        tmp = sqrt(x) * (2.0d0 * cos(y))
    else
        tmp = (2.0d0 * sqrt(x)) - (a / (3.0d0 * b))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.8e+158) {
		tmp = Math.sqrt(x) * (2.0 * Math.cos(y));
	} else {
		tmp = (2.0 * Math.sqrt(x)) - (a / (3.0 * b));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.8e+158:
		tmp = math.sqrt(x) * (2.0 * math.cos(y))
	else:
		tmp = (2.0 * math.sqrt(x)) - (a / (3.0 * b))
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.8e+158)
		tmp = Float64(sqrt(x) * Float64(2.0 * cos(y)));
	else
		tmp = Float64(Float64(2.0 * sqrt(x)) - Float64(a / Float64(3.0 * b)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.8e+158)
		tmp = sqrt(x) * (2.0 * cos(y));
	else
		tmp = (2.0 * sqrt(x)) - (a / (3.0 * b));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.8e+158], N[(N[Sqrt[x], $MachinePrecision] * N[(2.0 * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] - N[(a / N[(3.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.79999999999999994e158

   1. Initial program 45.5%

      \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
   2. Step-by-step derivation

      1. *-commutative 45.5%

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

      2. *-commutative 45.5%

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

      3. associate-/l* 45.5%

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

      4. *-commutative 45.5%

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

   3. Simplified 45.5%

      \[\leadsto \color{blue}{\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z}{\frac{3}{t}}\right) - \frac{a}{3 \cdot b}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 45.6%

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\cos y} - \frac{a}{3 \cdot b} \]
   6. Step-by-step derivation

      1. *-un-lft-identity 45.6%

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \frac{\color{blue}{1 \cdot a}}{3 \cdot b} \]

      2. *-commutative 45.6%

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \frac{1 \cdot a}{\color{blue}{b \cdot 3}} \]

      3. times-frac 45.6%

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \color{blue}{\frac{1}{b} \cdot \frac{a}{3}} \]

   7. Applied egg-rr 45.6%

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \color{blue}{\frac{1}{b} \cdot \frac{a}{3}} \]

   8. Taylor expanded in b around inf 41.1%

      \[\leadsto \color{blue}{2 \cdot \left(\sqrt{x} \cdot \cos y\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 41.1%

         \[\leadsto \color{blue}{\left(2 \cdot \sqrt{x}\right) \cdot \cos y} \]

      2. *-commutative 41.1%

         \[\leadsto \color{blue}{\left(\sqrt{x} \cdot 2\right)} \cdot \cos y \]

      3. associate-*l* 41.1%

         \[\leadsto \color{blue}{\sqrt{x} \cdot \left(2 \cdot \cos y\right)} \]

   10. Simplified 41.1%

       \[\leadsto \color{blue}{\sqrt{x} \cdot \left(2 \cdot \cos y\right)} \]

   if -1.79999999999999994e158 < b

   1. Initial program 68.6%

      \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
   2. Step-by-step derivation

      1. *-commutative 68.6%

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

      2. *-commutative 68.6%

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

      3. associate-/l* 68.5%

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

      4. *-commutative 68.5%

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

   3. Simplified 68.5%

      \[\leadsto \color{blue}{\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z}{\frac{3}{t}}\right) - \frac{a}{3 \cdot b}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 76.8%

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\cos y} - \frac{a}{3 \cdot b} \]

   6. Taylor expanded in y around 0 67.4%

      \[\leadsto \color{blue}{2 \cdot \sqrt{x}} - \frac{a}{3 \cdot b} \]
3. Recombined 2 regimes into one program.

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.8 \cdot 10^{+158}:\\ \;\;\;\;\sqrt{x} \cdot \left(2 \cdot \cos y\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{x} - \frac{a}{3 \cdot b}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 65.2% accurate, 2.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ 2 \cdot \sqrt{x} - \frac{a}{3 \cdot b} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b) :precision binary64 (- (* 2.0 (sqrt x)) (/ a (* 3.0 b))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	return (2.0 * sqrt(x)) - (a / (3.0 * b));
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = (2.0d0 * sqrt(x)) - (a / (3.0d0 * b))
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	return (2.0 * Math.sqrt(x)) - (a / (3.0 * b));
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	return (2.0 * math.sqrt(x)) - (a / (3.0 * b))

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	return Float64(Float64(2.0 * sqrt(x)) - Float64(a / Float64(3.0 * b)))
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp = code(x, y, z, t, a, b)
	tmp = (2.0 * sqrt(x)) - (a / (3.0 * b));
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := N[(N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] - N[(a / N[(3.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 66.7%

   \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
2. Step-by-step derivation

   1. *-commutative 66.7%

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

   2. *-commutative 66.7%

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

   3. associate-/l* 66.6%

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

   4. *-commutative 66.6%

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

3. Simplified 66.6%

   \[\leadsto \color{blue}{\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z}{\frac{3}{t}}\right) - \frac{a}{3 \cdot b}} \]
4. Add Preprocessing

5. Taylor expanded in z around 0 74.2%

   \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\cos y} - \frac{a}{3 \cdot b} \]

6. Taylor expanded in y around 0 63.5%

   \[\leadsto \color{blue}{2 \cdot \sqrt{x}} - \frac{a}{3 \cdot b} \]

7. Final simplification 63.5%

   \[\leadsto 2 \cdot \sqrt{x} - \frac{a}{3 \cdot b} \]
8. Add Preprocessing

Alternative 7: 49.8% accurate, 43.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \frac{a}{b} \cdot -0.3333333333333333 \end{array} \]

FPCore

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

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	return (a / b) * -0.3333333333333333;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = (a / b) * (-0.3333333333333333d0)
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	return (a / b) * -0.3333333333333333;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	return (a / b) * -0.3333333333333333

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	return Float64(Float64(a / b) * -0.3333333333333333)
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp = code(x, y, z, t, a, b)
	tmp = (a / b) * -0.3333333333333333;
end

Wolfram

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

Derivation

1. Initial program 66.7%

   \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
2. Step-by-step derivation

   1. *-commutative 66.7%

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

   2. *-commutative 66.7%

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

   3. associate-/l* 66.6%

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

   4. *-commutative 66.6%

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

3. Simplified 66.6%

   \[\leadsto \color{blue}{\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z}{\frac{3}{t}}\right) - \frac{a}{3 \cdot b}} \]
4. Add Preprocessing

5. Taylor expanded in z around 0 74.2%

   \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\cos y} - \frac{a}{3 \cdot b} \]

6. Taylor expanded in x around 0 51.8%

   \[\leadsto \color{blue}{-0.3333333333333333 \cdot \frac{a}{b}} \]

7. Final simplification 51.8%

   \[\leadsto \frac{a}{b} \cdot -0.3333333333333333 \]
8. Add Preprocessing

Alternative 8: 49.8% accurate, 43.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ a \cdot \frac{-0.3333333333333333}{b} \end{array} \]

FPCore

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

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	return a * (-0.3333333333333333 / b);
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = a * ((-0.3333333333333333d0) / b)
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	return a * (-0.3333333333333333 / b);
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	return a * (-0.3333333333333333 / b)

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	return Float64(a * Float64(-0.3333333333333333 / b))
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp = code(x, y, z, t, a, b)
	tmp = a * (-0.3333333333333333 / b);
end

Wolfram

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

Derivation

1. Initial program 66.7%

   \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
2. Step-by-step derivation

   1. *-commutative 66.7%

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

   2. *-commutative 66.7%

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

   3. associate-/l* 66.6%

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

   4. *-commutative 66.6%

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

3. Simplified 66.6%

   \[\leadsto \color{blue}{\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z}{\frac{3}{t}}\right) - \frac{a}{3 \cdot b}} \]
4. Add Preprocessing

5. Taylor expanded in z around 0 74.2%

   \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\cos y} - \frac{a}{3 \cdot b} \]

6. Taylor expanded in x around 0 51.8%

   \[\leadsto \color{blue}{-0.3333333333333333 \cdot \frac{a}{b}} \]
7. Step-by-step derivation

   1. metadata-eval 51.8%

      \[\leadsto \color{blue}{\left(-0.3333333333333333\right)} \cdot \frac{a}{b} \]

   2. distribute-lft-neg-in 51.8%

      \[\leadsto \color{blue}{-0.3333333333333333 \cdot \frac{a}{b}} \]

   3. metadata-eval 51.8%

      \[\leadsto -\color{blue}{\frac{1}{3}} \cdot \frac{a}{b} \]

   4. times-frac 51.9%

      \[\leadsto -\color{blue}{\frac{1 \cdot a}{3 \cdot b}} \]

   5. associate-*l/ 51.8%

      \[\leadsto -\color{blue}{\frac{1}{3 \cdot b} \cdot a} \]

   6. *-commutative 51.8%

      \[\leadsto -\color{blue}{a \cdot \frac{1}{3 \cdot b}} \]

   7. distribute-rgt-neg-in 51.8%

      \[\leadsto \color{blue}{a \cdot \left(-\frac{1}{3 \cdot b}\right)} \]

   8. associate-/r* 51.8%

      \[\leadsto a \cdot \left(-\color{blue}{\frac{\frac{1}{3}}{b}}\right) \]

   9. metadata-eval 51.8%

      \[\leadsto a \cdot \left(-\frac{\color{blue}{0.3333333333333333}}{b}\right) \]

   10. distribute-neg-frac 51.8%

       \[\leadsto a \cdot \color{blue}{\frac{-0.3333333333333333}{b}} \]

   11. metadata-eval 51.8%

       \[\leadsto a \cdot \frac{\color{blue}{-0.3333333333333333}}{b} \]

8. Simplified 51.8%

   \[\leadsto \color{blue}{a \cdot \frac{-0.3333333333333333}{b}} \]

9. Final simplification 51.8%

   \[\leadsto a \cdot \frac{-0.3333333333333333}{b} \]
10. Add Preprocessing

Alternative 9: 49.9% accurate, 43.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \frac{a}{b \cdot -3} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b) :precision binary64 (/ a (* b -3.0)))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	return a / (b * -3.0);
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = a / (b * (-3.0d0))
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	return a / (b * -3.0);
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	return a / (b * -3.0)

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	return Float64(a / Float64(b * -3.0))
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp = code(x, y, z, t, a, b)
	tmp = a / (b * -3.0);
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := N[(a / N[(b * -3.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 66.7%

   \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
2. Step-by-step derivation

   1. *-commutative 66.7%

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

   2. *-commutative 66.7%

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

   3. associate-/l* 66.6%

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

   4. *-commutative 66.6%

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

3. Simplified 66.6%

   \[\leadsto \color{blue}{\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z}{\frac{3}{t}}\right) - \frac{a}{3 \cdot b}} \]
4. Add Preprocessing

5. Taylor expanded in z around 0 74.2%

   \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\cos y} - \frac{a}{3 \cdot b} \]
6. Step-by-step derivation

   1. *-un-lft-identity 74.2%

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \frac{\color{blue}{1 \cdot a}}{3 \cdot b} \]

   2. *-commutative 74.2%

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \frac{1 \cdot a}{\color{blue}{b \cdot 3}} \]

   3. times-frac 74.2%

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \color{blue}{\frac{1}{b} \cdot \frac{a}{3}} \]

7. Applied egg-rr 74.2%

   \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos y - \color{blue}{\frac{1}{b} \cdot \frac{a}{3}} \]

8. Taylor expanded in x around 0 51.8%

   \[\leadsto \color{blue}{-0.3333333333333333 \cdot \frac{a}{b}} \]
9. Step-by-step derivation

   1. *-commutative 51.8%

      \[\leadsto \color{blue}{\frac{a}{b} \cdot -0.3333333333333333} \]

   2. metadata-eval 51.8%

      \[\leadsto \frac{a}{b} \cdot \color{blue}{\frac{1}{-3}} \]

   3. times-frac 51.9%

      \[\leadsto \color{blue}{\frac{a \cdot 1}{b \cdot -3}} \]

   4. *-rgt-identity 51.9%

      \[\leadsto \frac{\color{blue}{a}}{b \cdot -3} \]

10. Simplified 51.9%

    \[\leadsto \color{blue}{\frac{a}{b \cdot -3}} \]

11. Final simplification 51.9%

    \[\leadsto \frac{a}{b \cdot -3} \]
12. Add Preprocessing

Developer target: 73.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{0.3333333333333333}{z}}{t}\\ t_2 := \frac{\frac{a}{3}}{b}\\ t_3 := 2 \cdot \sqrt{x}\\ \mathbf{if}\;z < -1.3793337487235141 \cdot 10^{+129}:\\ \;\;\;\;t_3 \cdot \cos \left(\frac{1}{y} - t_1\right) - t_2\\ \mathbf{elif}\;z < 3.516290613555987 \cdot 10^{+106}:\\ \;\;\;\;\left(\sqrt{x} \cdot 2\right) \cdot \cos \left(y - \frac{t}{3} \cdot z\right) - t_2\\ \mathbf{else}:\\ \;\;\;\;\cos \left(y - t_1\right) \cdot t_3 - \frac{\frac{a}{b}}{3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (/ 0.3333333333333333 z) t))
        (t_2 (/ (/ a 3.0) b))
        (t_3 (* 2.0 (sqrt x))))
   (if (< z -1.3793337487235141e+129)
     (- (* t_3 (cos (- (/ 1.0 y) t_1))) t_2)
     (if (< z 3.516290613555987e+106)
       (- (* (* (sqrt x) 2.0) (cos (- y (* (/ t 3.0) z)))) t_2)
       (- (* (cos (- y t_1)) t_3) (/ (/ a b) 3.0))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (0.3333333333333333 / z) / t;
	double t_2 = (a / 3.0) / b;
	double t_3 = 2.0 * sqrt(x);
	double tmp;
	if (z < -1.3793337487235141e+129) {
		tmp = (t_3 * cos(((1.0 / y) - t_1))) - t_2;
	} else if (z < 3.516290613555987e+106) {
		tmp = ((sqrt(x) * 2.0) * cos((y - ((t / 3.0) * z)))) - t_2;
	} else {
		tmp = (cos((y - t_1)) * t_3) - ((a / b) / 3.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (0.3333333333333333d0 / z) / t
    t_2 = (a / 3.0d0) / b
    t_3 = 2.0d0 * sqrt(x)
    if (z < (-1.3793337487235141d+129)) then
        tmp = (t_3 * cos(((1.0d0 / y) - t_1))) - t_2
    else if (z < 3.516290613555987d+106) then
        tmp = ((sqrt(x) * 2.0d0) * cos((y - ((t / 3.0d0) * z)))) - t_2
    else
        tmp = (cos((y - t_1)) * t_3) - ((a / b) / 3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (0.3333333333333333 / z) / t;
	double t_2 = (a / 3.0) / b;
	double t_3 = 2.0 * Math.sqrt(x);
	double tmp;
	if (z < -1.3793337487235141e+129) {
		tmp = (t_3 * Math.cos(((1.0 / y) - t_1))) - t_2;
	} else if (z < 3.516290613555987e+106) {
		tmp = ((Math.sqrt(x) * 2.0) * Math.cos((y - ((t / 3.0) * z)))) - t_2;
	} else {
		tmp = (Math.cos((y - t_1)) * t_3) - ((a / b) / 3.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (0.3333333333333333 / z) / t
	t_2 = (a / 3.0) / b
	t_3 = 2.0 * math.sqrt(x)
	tmp = 0
	if z < -1.3793337487235141e+129:
		tmp = (t_3 * math.cos(((1.0 / y) - t_1))) - t_2
	elif z < 3.516290613555987e+106:
		tmp = ((math.sqrt(x) * 2.0) * math.cos((y - ((t / 3.0) * z)))) - t_2
	else:
		tmp = (math.cos((y - t_1)) * t_3) - ((a / b) / 3.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(0.3333333333333333 / z) / t)
	t_2 = Float64(Float64(a / 3.0) / b)
	t_3 = Float64(2.0 * sqrt(x))
	tmp = 0.0
	if (z < -1.3793337487235141e+129)
		tmp = Float64(Float64(t_3 * cos(Float64(Float64(1.0 / y) - t_1))) - t_2);
	elseif (z < 3.516290613555987e+106)
		tmp = Float64(Float64(Float64(sqrt(x) * 2.0) * cos(Float64(y - Float64(Float64(t / 3.0) * z)))) - t_2);
	else
		tmp = Float64(Float64(cos(Float64(y - t_1)) * t_3) - Float64(Float64(a / b) / 3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (0.3333333333333333 / z) / t;
	t_2 = (a / 3.0) / b;
	t_3 = 2.0 * sqrt(x);
	tmp = 0.0;
	if (z < -1.3793337487235141e+129)
		tmp = (t_3 * cos(((1.0 / y) - t_1))) - t_2;
	elseif (z < 3.516290613555987e+106)
		tmp = ((sqrt(x) * 2.0) * cos((y - ((t / 3.0) * z)))) - t_2;
	else
		tmp = (cos((y - t_1)) * t_3) - ((a / b) / 3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(0.3333333333333333 / z), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a / 3.0), $MachinePrecision] / b), $MachinePrecision]}, Block[{t$95$3 = N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]}, If[Less[z, -1.3793337487235141e+129], N[(N[(t$95$3 * N[Cos[N[(N[(1.0 / y), $MachinePrecision] - t$95$1), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], If[Less[z, 3.516290613555987e+106], N[(N[(N[(N[Sqrt[x], $MachinePrecision] * 2.0), $MachinePrecision] * N[Cos[N[(y - N[(N[(t / 3.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], N[(N[(N[Cos[N[(y - t$95$1), $MachinePrecision]], $MachinePrecision] * t$95$3), $MachinePrecision] - N[(N[(a / b), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]]]]]]

Reproduce

herbie shell --seed 2024021 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, K"
  :precision binary64

  :herbie-target
  (if (< z -1.3793337487235141e+129) (- (* (* 2.0 (sqrt x)) (cos (- (/ 1.0 y) (/ (/ 0.3333333333333333 z) t)))) (/ (/ a 3.0) b)) (if (< z 3.516290613555987e+106) (- (* (* (sqrt x) 2.0) (cos (- y (* (/ t 3.0) z)))) (/ (/ a 3.0) b)) (- (* (cos (- y (/ (/ 0.3333333333333333 z) t))) (* 2.0 (sqrt x))) (/ (/ a b) 3.0))))

  (- (* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0)))) (/ a (* b 3.0))))