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

Percentage Accurate: 71.5% → 78.3%

Time: 30.8s

Alternatives: 14

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: 71.5% 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: 78.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \frac{z}{\frac{3}{t}}\\ \mathbf{if}\;\cos \left(y - \frac{z \cdot t}{3}\right) \leq 0.965:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos y, \cos t\_1, \sin y \cdot \sin t\_1\right) - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{{\cos y}^{2} \cdot \left(x \cdot 4\right)} - \frac{\frac{a}{b}}{3}\\ \end{array} \end{array} \]

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 (/ z (/ 3.0 t))))
   (if (<= (cos (- y (/ (* z t) 3.0))) 0.965)
     (-
      (* (* 2.0 (sqrt x)) (fma (cos y) (cos t_1) (* (sin y) (sin t_1))))
      (/ a (* 3.0 b)))
     (- (sqrt (* (pow (cos y) 2.0) (* x 4.0))) (/ (/ 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) {
	double t_1 = z / (3.0 / t);
	double tmp;
	if (cos((y - ((z * t) / 3.0))) <= 0.965) {
		tmp = ((2.0 * sqrt(x)) * fma(cos(y), cos(t_1), (sin(y) * sin(t_1)))) - (a / (3.0 * b));
	} else {
		tmp = sqrt((pow(cos(y), 2.0) * (x * 4.0))) - ((a / b) / 3.0);
	}
	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(z / Float64(3.0 / t))
	tmp = 0.0
	if (cos(Float64(y - Float64(Float64(z * t) / 3.0))) <= 0.965)
		tmp = Float64(Float64(Float64(2.0 * sqrt(x)) * fma(cos(y), cos(t_1), Float64(sin(y) * sin(t_1)))) - Float64(a / Float64(3.0 * b)));
	else
		tmp = Float64(sqrt(Float64((cos(y) ^ 2.0) * Float64(x * 4.0))) - Float64(Float64(a / b) / 3.0));
	end
	return 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[(z / N[(3.0 / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[Cos[N[(y - N[(N[(z * t), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], 0.965], N[(N[(N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] * N[(N[Cos[y], $MachinePrecision] * N[Cos[t$95$1], $MachinePrecision] + N[(N[Sin[y], $MachinePrecision] * N[Sin[t$95$1], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a / N[(3.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Sqrt[N[(N[Power[N[Cos[y], $MachinePrecision], 2.0], $MachinePrecision] * N[(x * 4.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - N[(N[(a / b), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64)))) < 0.964999999999999969

   1. Initial program 72.2%

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

      1. *-commutative 72.2%

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

      2. *-commutative 72.2%

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

      3. *-commutative 72.2%

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

      4. *-commutative 72.2%

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

      5. associate-/l* 71.8%

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

      6. *-commutative 71.8%

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

   3. Simplified 71.8%

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

   6. Applied egg-rr 73.3%

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

      1. fma-define 73.3%

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

      2. cos-neg 73.3%

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

      3. distribute-lft-neg-in 73.3%

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

      4. distribute-rgt-neg-in 73.3%

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

      5. metadata-eval 73.3%

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

      6. metadata-eval 73.3%

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

      7. associate-/l* 73.4%

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

      8. *-rgt-identity 73.4%

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

      9. associate-/r/ 73.3%

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

      10. distribute-rgt-neg-in 73.3%

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

      11. sin-neg 73.3%

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

      12. distribute-lft-neg-in 73.3%

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

      13. distribute-rgt-neg-in 73.3%

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

      14. metadata-eval 73.3%

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

      15. metadata-eval 73.3%

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

      16. associate-/l* 73.4%

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

      17. *-rgt-identity 73.4%

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

      18. associate-/r/ 73.3%

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

   8. Simplified 73.3%

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

   if 0.964999999999999969 < (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64))))

   1. Initial program 67.5%

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

      1. *-commutative 67.5%

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

      2. *-commutative 67.5%

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

      3. *-commutative 67.5%

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

      4. *-commutative 67.5%

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

      5. associate-/l* 68.1%

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

      6. *-commutative 68.1%

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

   3. Simplified 68.1%

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

   5. Taylor expanded in z around 0 85.3%

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

      1. *-commutative 85.3%

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

      2. clear-num 85.2%

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

      3. inv-pow 85.2%

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

      4. *-commutative 85.2%

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

      5. *-un-lft-identity 85.2%

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

      6. times-frac 85.2%

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

      7. metadata-eval 85.2%

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

   7. Applied egg-rr 85.2%

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

      1. unpow-1 85.2%

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

      2. *-commutative 85.2%

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

      3. associate-/r* 85.3%

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

      4. clear-num 85.3%

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

   9. Applied egg-rr 85.3%

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

       1. add-sqr-sqrt 81.4%

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

       2. sqrt-unprod 85.8%

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

       3. *-commutative 85.8%

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

       4. *-commutative 85.8%

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

       5. swap-sqr 85.8%

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

       6. pow2 85.8%

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

       7. *-commutative 85.8%

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

       8. *-commutative 85.8%

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

       9. swap-sqr 85.8%

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

       10. add-sqr-sqrt 85.8%

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

       11. metadata-eval 85.8%

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

   11. Applied egg-rr 85.8%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\cos \left(y - \frac{z \cdot t}{3}\right) \leq 0.965:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos y, \cos \left(\frac{z}{\frac{3}{t}}\right), \sin y \cdot \sin \left(\frac{z}{\frac{3}{t}}\right)\right) - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{{\cos y}^{2} \cdot \left(x \cdot 4\right)} - \frac{\frac{a}{b}}{3}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 78.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := 0.3333333333333333 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;\cos \left(y - \frac{z \cdot t}{3}\right) \leq 0.862:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos y, \cos t\_1, \sin y \cdot \sin t\_1\right) - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{{\cos y}^{2} \cdot \left(x \cdot 4\right)} - \frac{\frac{a}{b}}{3}\\ \end{array} \end{array} \]

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 (* 0.3333333333333333 (* z t))))
   (if (<= (cos (- y (/ (* z t) 3.0))) 0.862)
     (-
      (* (* 2.0 (sqrt x)) (fma (cos y) (cos t_1) (* (sin y) (sin t_1))))
      (/ a (* 3.0 b)))
     (- (sqrt (* (pow (cos y) 2.0) (* x 4.0))) (/ (/ 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) {
	double t_1 = 0.3333333333333333 * (z * t);
	double tmp;
	if (cos((y - ((z * t) / 3.0))) <= 0.862) {
		tmp = ((2.0 * sqrt(x)) * fma(cos(y), cos(t_1), (sin(y) * sin(t_1)))) - (a / (3.0 * b));
	} else {
		tmp = sqrt((pow(cos(y), 2.0) * (x * 4.0))) - ((a / b) / 3.0);
	}
	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(0.3333333333333333 * Float64(z * t))
	tmp = 0.0
	if (cos(Float64(y - Float64(Float64(z * t) / 3.0))) <= 0.862)
		tmp = Float64(Float64(Float64(2.0 * sqrt(x)) * fma(cos(y), cos(t_1), Float64(sin(y) * sin(t_1)))) - Float64(a / Float64(3.0 * b)));
	else
		tmp = Float64(sqrt(Float64((cos(y) ^ 2.0) * Float64(x * 4.0))) - Float64(Float64(a / b) / 3.0));
	end
	return 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[(0.3333333333333333 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[Cos[N[(y - N[(N[(z * t), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], 0.862], N[(N[(N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] * N[(N[Cos[y], $MachinePrecision] * N[Cos[t$95$1], $MachinePrecision] + N[(N[Sin[y], $MachinePrecision] * N[Sin[t$95$1], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a / N[(3.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Sqrt[N[(N[Power[N[Cos[y], $MachinePrecision], 2.0], $MachinePrecision] * N[(x * 4.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - N[(N[(a / b), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64)))) < 0.861999999999999988

   1. Initial program 70.8%

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

      1. *-commutative 70.8%

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

      2. *-commutative 70.8%

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

      3. *-commutative 70.8%

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

      4. *-commutative 70.8%

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

      5. associate-/l* 70.4%

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

      6. *-commutative 70.4%

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

   3. Simplified 70.4%

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

   6. Applied egg-rr 71.9%

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

      1. fma-define 71.9%

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

      2. associate-*l* 72.1%

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

      3. *-commutative 72.1%

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

      4. associate-*r* 72.1%

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

      5. *-commutative 72.1%

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

      6. metadata-eval 72.1%

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

      7. *-commutative 72.1%

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

      8. distribute-lft-neg-in 72.1%

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

      9. cos-neg 72.1%

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

      10. distribute-rgt-neg-in 72.1%

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

      11. associate-*l* 71.8%

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

      12. *-commutative 71.8%

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

      13. associate-*r* 72.1%

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

      14. *-commutative 72.1%

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

      15. metadata-eval 72.1%

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

      16. *-commutative 72.1%

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

      17. distribute-lft-neg-in 72.1%

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

      18. sin-neg 72.1%

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

      19. remove-double-neg 72.1%

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

   8. Simplified 72.1%

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

   if 0.861999999999999988 < (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64))))

   1. Initial program 69.8%

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

      1. *-commutative 69.8%

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

      2. *-commutative 69.8%

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

      3. *-commutative 69.8%

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

      4. *-commutative 69.8%

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

      5. associate-/l* 70.3%

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

      6. *-commutative 70.3%

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

   3. Simplified 70.3%

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

   5. Taylor expanded in z around 0 85.9%

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

      1. *-commutative 85.9%

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

      2. clear-num 85.7%

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

      3. inv-pow 85.7%

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

      4. *-commutative 85.7%

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

      5. *-un-lft-identity 85.7%

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

      6. times-frac 85.8%

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

      7. metadata-eval 85.8%

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

   7. Applied egg-rr 85.8%

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

      1. unpow-1 85.8%

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

      2. *-commutative 85.8%

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

      3. associate-/r* 85.8%

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

      4. clear-num 85.9%

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

   9. Applied egg-rr 85.9%

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

       1. add-sqr-sqrt 82.2%

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

       2. sqrt-unprod 86.2%

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

       3. *-commutative 86.2%

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

       4. *-commutative 86.2%

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

       5. swap-sqr 86.2%

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

       6. pow2 86.2%

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

       7. *-commutative 86.2%

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

       8. *-commutative 86.2%

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

       9. swap-sqr 86.2%

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

       10. add-sqr-sqrt 86.2%

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

       11. metadata-eval 86.2%

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

   11. Applied egg-rr 86.2%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\cos \left(y - \frac{z \cdot t}{3}\right) \leq 0.862:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos y, \cos \left(0.3333333333333333 \cdot \left(z \cdot t\right)\right), \sin y \cdot \sin \left(0.3333333333333333 \cdot \left(z \cdot t\right)\right)\right) - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{{\cos y}^{2} \cdot \left(x \cdot 4\right)} - \frac{\frac{a}{b}}{3}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 78.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;\cos \left(y - \frac{z \cdot t}{3}\right) \leq 0.862:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \left(\cos y \cdot \cos \left(0.3333333333333333 \cdot \left(z \cdot t\right)\right) - \sin y \cdot \sin \left(z \cdot \left(t \cdot -0.3333333333333333\right)\right)\right) - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{{\cos y}^{2} \cdot \left(x \cdot 4\right)} - \frac{\frac{a}{b}}{3}\\ \end{array} \end{array} \]

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 (<= (cos (- y (/ (* z t) 3.0))) 0.862)
   (-
    (*
     (* 2.0 (sqrt x))
     (-
      (* (cos y) (cos (* 0.3333333333333333 (* z t))))
      (* (sin y) (sin (* z (* t -0.3333333333333333))))))
    (/ a (* 3.0 b)))
   (- (sqrt (* (pow (cos y) 2.0) (* x 4.0))) (/ (/ 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) {
	double tmp;
	if (cos((y - ((z * t) / 3.0))) <= 0.862) {
		tmp = ((2.0 * sqrt(x)) * ((cos(y) * cos((0.3333333333333333 * (z * t)))) - (sin(y) * sin((z * (t * -0.3333333333333333)))))) - (a / (3.0 * b));
	} else {
		tmp = sqrt((pow(cos(y), 2.0) * (x * 4.0))) - ((a / b) / 3.0);
	}
	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 (cos((y - ((z * t) / 3.0d0))) <= 0.862d0) then
        tmp = ((2.0d0 * sqrt(x)) * ((cos(y) * cos((0.3333333333333333d0 * (z * t)))) - (sin(y) * sin((z * (t * (-0.3333333333333333d0))))))) - (a / (3.0d0 * b))
    else
        tmp = sqrt(((cos(y) ** 2.0d0) * (x * 4.0d0))) - ((a / b) / 3.0d0)
    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 (Math.cos((y - ((z * t) / 3.0))) <= 0.862) {
		tmp = ((2.0 * Math.sqrt(x)) * ((Math.cos(y) * Math.cos((0.3333333333333333 * (z * t)))) - (Math.sin(y) * Math.sin((z * (t * -0.3333333333333333)))))) - (a / (3.0 * b));
	} else {
		tmp = Math.sqrt((Math.pow(Math.cos(y), 2.0) * (x * 4.0))) - ((a / b) / 3.0);
	}
	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 math.cos((y - ((z * t) / 3.0))) <= 0.862:
		tmp = ((2.0 * math.sqrt(x)) * ((math.cos(y) * math.cos((0.3333333333333333 * (z * t)))) - (math.sin(y) * math.sin((z * (t * -0.3333333333333333)))))) - (a / (3.0 * b))
	else:
		tmp = math.sqrt((math.pow(math.cos(y), 2.0) * (x * 4.0))) - ((a / b) / 3.0)
	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 (cos(Float64(y - Float64(Float64(z * t) / 3.0))) <= 0.862)
		tmp = Float64(Float64(Float64(2.0 * sqrt(x)) * Float64(Float64(cos(y) * cos(Float64(0.3333333333333333 * Float64(z * t)))) - Float64(sin(y) * sin(Float64(z * Float64(t * -0.3333333333333333)))))) - Float64(a / Float64(3.0 * b)));
	else
		tmp = Float64(sqrt(Float64((cos(y) ^ 2.0) * Float64(x * 4.0))) - Float64(Float64(a / b) / 3.0));
	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 (cos((y - ((z * t) / 3.0))) <= 0.862)
		tmp = ((2.0 * sqrt(x)) * ((cos(y) * cos((0.3333333333333333 * (z * t)))) - (sin(y) * sin((z * (t * -0.3333333333333333)))))) - (a / (3.0 * b));
	else
		tmp = sqrt(((cos(y) ^ 2.0) * (x * 4.0))) - ((a / b) / 3.0);
	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[N[Cos[N[(y - N[(N[(z * t), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], 0.862], N[(N[(N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] * N[(N[(N[Cos[y], $MachinePrecision] * N[Cos[N[(0.3333333333333333 * N[(z * t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - N[(N[Sin[y], $MachinePrecision] * N[Sin[N[(z * N[(t * -0.3333333333333333), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a / N[(3.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Sqrt[N[(N[Power[N[Cos[y], $MachinePrecision], 2.0], $MachinePrecision] * N[(x * 4.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - N[(N[(a / b), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64)))) < 0.861999999999999988

   1. Initial program 70.8%

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

      1. *-commutative 70.8%

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

      2. *-commutative 70.8%

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

      3. *-commutative 70.8%

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

      4. *-commutative 70.8%

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

      5. associate-/l* 70.4%

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

      6. *-commutative 70.4%

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

   3. Simplified 70.4%

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

   6. Applied egg-rr 71.9%

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

      1. sub-neg 71.9%

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

      2. *-rgt-identity 71.9%

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

      3. *-rgt-identity 71.9%

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

      4. *-rgt-identity 71.9%

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

      5. associate-*l* 72.1%

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

      6. *-commutative 72.1%

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

      7. associate-*r* 72.1%

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

      8. *-commutative 72.1%

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

      9. metadata-eval 72.1%

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

      10. *-commutative 72.1%

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

      11. distribute-lft-neg-in 72.1%

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

      12. cos-neg 72.1%

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

      13. *-rgt-identity 72.1%

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

      14. associate-*l* 71.8%

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

      15. *-commutative 71.8%

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

   8. Simplified 71.8%

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

   if 0.861999999999999988 < (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64))))

   1. Initial program 69.8%

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

      1. *-commutative 69.8%

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

      2. *-commutative 69.8%

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

      3. *-commutative 69.8%

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

      4. *-commutative 69.8%

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

      5. associate-/l* 70.3%

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

      6. *-commutative 70.3%

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

   3. Simplified 70.3%

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

   5. Taylor expanded in z around 0 85.9%

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

      1. *-commutative 85.9%

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

      2. clear-num 85.7%

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

      3. inv-pow 85.7%

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

      4. *-commutative 85.7%

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

      5. *-un-lft-identity 85.7%

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

      6. times-frac 85.8%

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

      7. metadata-eval 85.8%

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

   7. Applied egg-rr 85.8%

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

      1. unpow-1 85.8%

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

      2. *-commutative 85.8%

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

      3. associate-/r* 85.8%

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

      4. clear-num 85.9%

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

   9. Applied egg-rr 85.9%

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

       1. add-sqr-sqrt 82.2%

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

       2. sqrt-unprod 86.2%

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

       3. *-commutative 86.2%

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

       4. *-commutative 86.2%

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

       5. swap-sqr 86.2%

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

       6. pow2 86.2%

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

       7. *-commutative 86.2%

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

       8. *-commutative 86.2%

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

       9. swap-sqr 86.2%

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

       10. add-sqr-sqrt 86.2%

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

       11. metadata-eval 86.2%

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

   11. Applied egg-rr 86.2%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\cos \left(y - \frac{z \cdot t}{3}\right) \leq 0.862:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \left(\cos y \cdot \cos \left(0.3333333333333333 \cdot \left(z \cdot t\right)\right) - \sin y \cdot \sin \left(z \cdot \left(t \cdot -0.3333333333333333\right)\right)\right) - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{{\cos y}^{2} \cdot \left(x \cdot 4\right)} - \frac{\frac{a}{b}}{3}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 67.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := 2 \cdot \sqrt{x}\\ \mathbf{if}\;a \leq -1.5 \cdot 10^{-155}:\\ \;\;\;\;t\_1 - \frac{\frac{a}{b}}{3}\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-230}:\\ \;\;\;\;t\_1 \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;t\_1 - \frac{a}{3 \cdot b}\\ \end{array} \end{array} \]

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
 (let* ((t_1 (* 2.0 (sqrt x))))
   (if (<= a -1.5e-155)
     (- t_1 (/ (/ a b) 3.0))
     (if (<= a 1.5e-230) (* t_1 (cos y)) (- t_1 (/ 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 t_1 = 2.0 * sqrt(x);
	double tmp;
	if (a <= -1.5e-155) {
		tmp = t_1 - ((a / b) / 3.0);
	} else if (a <= 1.5e-230) {
		tmp = t_1 * cos(y);
	} else {
		tmp = t_1 - (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) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * sqrt(x)
    if (a <= (-1.5d-155)) then
        tmp = t_1 - ((a / b) / 3.0d0)
    else if (a <= 1.5d-230) then
        tmp = t_1 * cos(y)
    else
        tmp = t_1 - (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 t_1 = 2.0 * Math.sqrt(x);
	double tmp;
	if (a <= -1.5e-155) {
		tmp = t_1 - ((a / b) / 3.0);
	} else if (a <= 1.5e-230) {
		tmp = t_1 * Math.cos(y);
	} else {
		tmp = t_1 - (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):
	t_1 = 2.0 * math.sqrt(x)
	tmp = 0
	if a <= -1.5e-155:
		tmp = t_1 - ((a / b) / 3.0)
	elif a <= 1.5e-230:
		tmp = t_1 * math.cos(y)
	else:
		tmp = t_1 - (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)
	t_1 = Float64(2.0 * sqrt(x))
	tmp = 0.0
	if (a <= -1.5e-155)
		tmp = Float64(t_1 - Float64(Float64(a / b) / 3.0));
	elseif (a <= 1.5e-230)
		tmp = Float64(t_1 * cos(y));
	else
		tmp = Float64(t_1 - 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)
	t_1 = 2.0 * sqrt(x);
	tmp = 0.0;
	if (a <= -1.5e-155)
		tmp = t_1 - ((a / b) / 3.0);
	elseif (a <= 1.5e-230)
		tmp = t_1 * cos(y);
	else
		tmp = t_1 - (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_] := Block[{t$95$1 = N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.5e-155], N[(t$95$1 - N[(N[(a / b), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.5e-230], N[(t$95$1 * N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(t$95$1 - N[(a / N[(3.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.49999999999999992e-155

   1. Initial program 78.5%

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

      1. *-commutative 78.5%

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

      2. *-commutative 78.5%

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

      3. *-commutative 78.5%

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

      4. *-commutative 78.5%

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

      5. associate-/l* 79.6%

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

      6. *-commutative 79.6%

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

   3. Simplified 79.6%

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

   5. Taylor expanded in z around 0 82.9%

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

      1. *-commutative 82.9%

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

      2. clear-num 82.8%

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

      3. inv-pow 82.8%

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

      4. *-commutative 82.8%

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

      5. *-un-lft-identity 82.8%

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

      6. times-frac 82.9%

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

      7. metadata-eval 82.9%

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

   7. Applied egg-rr 82.9%

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

      1. unpow-1 82.9%

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

      2. *-commutative 82.9%

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

      3. associate-/r* 82.9%

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

      4. clear-num 82.9%

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

   9. Applied egg-rr 82.9%

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

   10. Taylor expanded in y around 0 76.2%

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

   if -1.49999999999999992e-155 < a < 1.5e-230

   1. Initial program 60.4%

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

      1. *-commutative 60.4%

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

      2. *-commutative 60.4%

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

      3. *-commutative 60.4%

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

      4. *-commutative 60.4%

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

      5. associate-/l* 59.9%

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

      6. *-commutative 59.9%

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

   3. Simplified 59.9%

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

   5. Taylor expanded in z around 0 61.8%

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

      1. *-commutative 61.8%

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

      2. clear-num 61.8%

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

      3. inv-pow 61.8%

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

      4. *-commutative 61.8%

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

      5. *-un-lft-identity 61.8%

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

      6. times-frac 61.8%

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

      7. metadata-eval 61.8%

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

   7. Applied egg-rr 61.8%

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

      1. unpow-1 61.8%

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

      2. *-commutative 61.8%

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

      3. associate-/r* 61.8%

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

      4. clear-num 61.8%

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

   9. Applied egg-rr 61.8%

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

   10. Taylor expanded in x around inf 57.0%

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

       1. associate-*r* 57.0%

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

       2. *-commutative 57.0%

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

   12. Simplified 57.0%

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

   if 1.5e-230 < a

   1. Initial program 69.2%

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

      1. *-commutative 69.2%

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

      2. *-commutative 69.2%

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

      3. *-commutative 69.2%

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

      4. *-commutative 69.2%

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

      5. associate-/l* 68.6%

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

      6. *-commutative 68.6%

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

   3. Simplified 68.6%

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

   5. Taylor expanded in z around 0 79.6%

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

   6. Taylor expanded in y around 0 68.4%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.5 \cdot 10^{-155}:\\ \;\;\;\;2 \cdot \sqrt{x} - \frac{\frac{a}{b}}{3}\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-230}:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{x} - \frac{a}{3 \cdot b}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 77.5% accurate, 1.0× speedup

Math

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

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
 (- (* (* 2.0 (sqrt x)) (cos y)) (* (/ 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 ((2.0 * sqrt(x)) * cos(y)) - ((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 = ((2.0d0 * sqrt(x)) * cos(y)) - ((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 ((2.0 * Math.sqrt(x)) * Math.cos(y)) - ((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 ((2.0 * math.sqrt(x)) * math.cos(y)) - ((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(Float64(2.0 * sqrt(x)) * cos(y)) - 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 = ((2.0 * sqrt(x)) * cos(y)) - ((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[(N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] * N[Cos[y], $MachinePrecision]), $MachinePrecision] - N[(N[(a / b), $MachinePrecision] * 0.3333333333333333), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 70.3%

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

   1. *-commutative 70.3%

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

   2. *-commutative 70.3%

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

   3. *-commutative 70.3%

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

   4. *-commutative 70.3%

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

   5. associate-/l* 70.3%

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

   6. *-commutative 70.3%

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

3. Simplified 70.3%

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

5. Taylor expanded in z around 0 76.6%

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

   1. *-commutative 62.6%

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

   2. associate-/r* 62.6%

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

   3. div-inv 62.5%

      \[\leadsto 2 \cdot \sqrt{x} - \color{blue}{\frac{a}{b} \cdot \frac{1}{3}} \]

   4. metadata-eval 62.5%

      \[\leadsto 2 \cdot \sqrt{x} - \frac{a}{b} \cdot \color{blue}{0.3333333333333333} \]

7. Applied egg-rr 76.5%

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

8. Final simplification 76.5%

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

Alternative 6: 77.5% 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 70.3%

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

   1. *-commutative 70.3%

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

   2. *-commutative 70.3%

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

   3. *-commutative 70.3%

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

   4. *-commutative 70.3%

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

   5. associate-/l* 70.3%

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

   6. *-commutative 70.3%

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

3. Simplified 70.3%

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

5. Taylor expanded in z around 0 76.6%

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

6. Final simplification 76.6%

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

Alternative 7: 77.5% accurate, 1.0× speedup

Math

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

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
 (- (* (* 2.0 (sqrt x)) (cos y)) (/ (/ 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 ((2.0 * sqrt(x)) * cos(y)) - ((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 = ((2.0d0 * sqrt(x)) * cos(y)) - ((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 ((2.0 * Math.sqrt(x)) * Math.cos(y)) - ((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 ((2.0 * math.sqrt(x)) * math.cos(y)) - ((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(Float64(Float64(2.0 * sqrt(x)) * cos(y)) - Float64(Float64(a / 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 = ((2.0 * sqrt(x)) * cos(y)) - ((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[(N[(N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] * N[Cos[y], $MachinePrecision]), $MachinePrecision] - N[(N[(a / b), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 70.3%

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

   1. *-commutative 70.3%

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

   2. *-commutative 70.3%

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

   3. *-commutative 70.3%

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

   4. *-commutative 70.3%

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

   5. associate-/l* 70.3%

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

   6. *-commutative 70.3%

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

3. Simplified 70.3%

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

5. Taylor expanded in z around 0 76.6%

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

   1. *-commutative 76.6%

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

   2. clear-num 76.5%

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

   3. inv-pow 76.5%

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

   4. *-commutative 76.5%

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

   5. *-un-lft-identity 76.5%

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

   6. times-frac 76.5%

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

   7. metadata-eval 76.5%

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

7. Applied egg-rr 76.5%

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

   1. unpow-1 76.5%

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

   2. *-commutative 76.5%

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

   3. associate-/r* 76.5%

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

   4. clear-num 76.6%

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

9. Applied egg-rr 76.6%

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

10. Final simplification 76.6%

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

Alternative 8: 53.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -4 \cdot 10^{-136} \lor \neg \left(a \leq 7.4 \cdot 10^{-141}\right):\\ \;\;\;\;\frac{a}{b \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{x}\\ \end{array} \end{array} \]

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 (or (<= a -4e-136) (not (<= a 7.4e-141)))
   (/ a (* b -3.0))
   (* 2.0 (sqrt x))))

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 ((a <= -4e-136) || !(a <= 7.4e-141)) {
		tmp = a / (b * -3.0);
	} else {
		tmp = 2.0 * sqrt(x);
	}
	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 ((a <= (-4d-136)) .or. (.not. (a <= 7.4d-141))) then
        tmp = a / (b * (-3.0d0))
    else
        tmp = 2.0d0 * sqrt(x)
    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 ((a <= -4e-136) || !(a <= 7.4e-141)) {
		tmp = a / (b * -3.0);
	} else {
		tmp = 2.0 * Math.sqrt(x);
	}
	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 (a <= -4e-136) or not (a <= 7.4e-141):
		tmp = a / (b * -3.0)
	else:
		tmp = 2.0 * math.sqrt(x)
	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 ((a <= -4e-136) || !(a <= 7.4e-141))
		tmp = Float64(a / Float64(b * -3.0));
	else
		tmp = Float64(2.0 * sqrt(x));
	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 ((a <= -4e-136) || ~((a <= 7.4e-141)))
		tmp = a / (b * -3.0);
	else
		tmp = 2.0 * sqrt(x);
	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[Or[LessEqual[a, -4e-136], N[Not[LessEqual[a, 7.4e-141]], $MachinePrecision]], N[(a / N[(b * -3.0), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -4.00000000000000001e-136 or 7.4e-141 < a

   1. Initial program 74.1%

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

      1. *-commutative 74.1%

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

      2. *-commutative 74.1%

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

      3. *-commutative 74.1%

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

      4. *-commutative 74.1%

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

      5. associate-/l* 74.4%

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

      6. *-commutative 74.4%

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

   3. Simplified 74.4%

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

   5. Taylor expanded in z around 0 83.2%

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

      1. *-commutative 83.2%

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

      2. clear-num 83.2%

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

      3. inv-pow 83.2%

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

      4. *-commutative 83.2%

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

      5. *-un-lft-identity 83.2%

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

      6. times-frac 83.2%

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

      7. metadata-eval 83.2%

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

   7. Applied egg-rr 83.2%

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

      1. unpow-1 83.2%

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

      2. *-commutative 83.2%

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

      3. associate-/r* 83.2%

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

      4. clear-num 83.2%

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

   9. Applied egg-rr 83.2%

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

   10. Taylor expanded in a around inf 64.1%

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

       1. metadata-eval 64.1%

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

       2. times-frac 64.2%

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

       3. neg-mul-1 64.2%

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

       4. distribute-neg-frac 64.2%

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

       5. distribute-neg-frac2 64.2%

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

       6. *-commutative 64.2%

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

       7. distribute-rgt-neg-in 64.2%

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

       8. metadata-eval 64.2%

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

   12. Simplified 64.2%

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

   if -4.00000000000000001e-136 < a < 7.4e-141

   1. Initial program 62.7%

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

      1. *-commutative 62.7%

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

      2. *-commutative 62.7%

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

      3. *-commutative 62.7%

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

      4. *-commutative 62.7%

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

      5. associate-/l* 62.2%

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

      6. *-commutative 62.2%

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

   3. Simplified 62.2%

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

   5. Taylor expanded in z around 0 63.1%

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

   6. Taylor expanded in y around 0 41.5%

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

   7. Taylor expanded in a around 0 41.5%

      \[\leadsto 2 \cdot \sqrt{x} - \color{blue}{0.3333333333333333 \cdot \frac{a}{b}} \]
   8. Step-by-step derivation

      1. *-commutative 41.5%

         \[\leadsto 2 \cdot \sqrt{x} - \color{blue}{\frac{a}{b} \cdot 0.3333333333333333} \]

      2. rem-square-sqrt 25.4%

         \[\leadsto 2 \cdot \sqrt{x} - \color{blue}{\sqrt{\frac{a}{b} \cdot 0.3333333333333333} \cdot \sqrt{\frac{a}{b} \cdot 0.3333333333333333}} \]

      3. fabs-sqr 25.4%

         \[\leadsto 2 \cdot \sqrt{x} - \color{blue}{\left|\sqrt{\frac{a}{b} \cdot 0.3333333333333333} \cdot \sqrt{\frac{a}{b} \cdot 0.3333333333333333}\right|} \]

      4. rem-square-sqrt 36.8%

         \[\leadsto 2 \cdot \sqrt{x} - \left|\color{blue}{\frac{a}{b} \cdot 0.3333333333333333}\right| \]

      5. *-commutative 36.8%

         \[\leadsto 2 \cdot \sqrt{x} - \left|\color{blue}{0.3333333333333333 \cdot \frac{a}{b}}\right| \]

      6. metadata-eval 36.8%

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

      7. times-frac 36.8%

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

      8. associate-*l/ 36.8%

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

      9. associate-/r/ 36.8%

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

      10. associate-*r/ 36.8%

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

      11. associate-/r* 36.8%

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

      12. metadata-eval 36.8%

          \[\leadsto 2 \cdot \sqrt{x} - \left|\frac{\color{blue}{0.3333333333333333}}{\frac{b}{a}}\right| \]

      13. fabs-div 36.8%

          \[\leadsto 2 \cdot \sqrt{x} - \color{blue}{\frac{\left|0.3333333333333333\right|}{\left|\frac{b}{a}\right|}} \]

      14. metadata-eval 36.8%

          \[\leadsto 2 \cdot \sqrt{x} - \frac{\color{blue}{0.3333333333333333}}{\left|\frac{b}{a}\right|} \]

      15. metadata-eval 36.8%

          \[\leadsto 2 \cdot \sqrt{x} - \frac{\color{blue}{\left|-0.3333333333333333\right|}}{\left|\frac{b}{a}\right|} \]

      16. fabs-div 36.8%

          \[\leadsto 2 \cdot \sqrt{x} - \color{blue}{\left|\frac{-0.3333333333333333}{\frac{b}{a}}\right|} \]

      17. rem-square-sqrt 20.4%

          \[\leadsto 2 \cdot \sqrt{x} - \left|\color{blue}{\sqrt{\frac{-0.3333333333333333}{\frac{b}{a}}} \cdot \sqrt{\frac{-0.3333333333333333}{\frac{b}{a}}}}\right| \]

      18. fabs-sqr 20.4%

          \[\leadsto 2 \cdot \sqrt{x} - \color{blue}{\sqrt{\frac{-0.3333333333333333}{\frac{b}{a}}} \cdot \sqrt{\frac{-0.3333333333333333}{\frac{b}{a}}}} \]

      19. rem-square-sqrt 31.1%

          \[\leadsto 2 \cdot \sqrt{x} - \color{blue}{\frac{-0.3333333333333333}{\frac{b}{a}}} \]

      20. associate-/r/ 31.1%

          \[\leadsto 2 \cdot \sqrt{x} - \color{blue}{\frac{-0.3333333333333333}{b} \cdot a} \]

      21. *-commutative 31.1%

          \[\leadsto 2 \cdot \sqrt{x} - \color{blue}{a \cdot \frac{-0.3333333333333333}{b}} \]

   9. Simplified 31.1%

      \[\leadsto 2 \cdot \sqrt{x} - \color{blue}{a \cdot \frac{-0.3333333333333333}{b}} \]

   10. Taylor expanded in x around inf 31.4%

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

4. Final simplification 53.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4 \cdot 10^{-136} \lor \neg \left(a \leq 7.4 \cdot 10^{-141}\right):\\ \;\;\;\;\frac{a}{b \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 66.2% accurate, 2.0× speedup

Math

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

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
 (- (* 2.0 (sqrt x)) (* 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 (2.0 * sqrt(x)) - (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 = (2.0d0 * sqrt(x)) - (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 (2.0 * Math.sqrt(x)) - (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 (2.0 * math.sqrt(x)) - (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(Float64(2.0 * sqrt(x)) - 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 = (2.0 * sqrt(x)) - (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[(N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] - N[(a * N[(0.3333333333333333 / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 70.3%

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

   1. *-commutative 70.3%

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

   2. *-commutative 70.3%

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

   3. *-commutative 70.3%

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

   4. *-commutative 70.3%

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

   5. associate-/l* 70.3%

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

   6. *-commutative 70.3%

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

3. Simplified 70.3%

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

5. Taylor expanded in z around 0 76.6%

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

6. Taylor expanded in y around 0 62.6%

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

7. Taylor expanded in a around 0 62.5%

   \[\leadsto 2 \cdot \sqrt{x} - \color{blue}{0.3333333333333333 \cdot \frac{a}{b}} \]
8. Step-by-step derivation

   1. associate-*r/ 62.5%

      \[\leadsto 2 \cdot \sqrt{x} - \color{blue}{\frac{0.3333333333333333 \cdot a}{b}} \]

   2. associate-*l/ 62.5%

      \[\leadsto 2 \cdot \sqrt{x} - \color{blue}{\frac{0.3333333333333333}{b} \cdot a} \]

   3. *-commutative 62.5%

      \[\leadsto 2 \cdot \sqrt{x} - \color{blue}{a \cdot \frac{0.3333333333333333}{b}} \]

9. Simplified 62.5%

   \[\leadsto 2 \cdot \sqrt{x} - \color{blue}{a \cdot \frac{0.3333333333333333}{b}} \]

10. Final simplification 62.5%

    \[\leadsto 2 \cdot \sqrt{x} - a \cdot \frac{0.3333333333333333}{b} \]
11. Add Preprocessing

Alternative 10: 66.2% accurate, 2.0× speedup

Math

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

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
 (- (* 2.0 (sqrt x)) (* (/ 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 (2.0 * sqrt(x)) - ((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 = (2.0d0 * sqrt(x)) - ((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 (2.0 * Math.sqrt(x)) - ((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 (2.0 * math.sqrt(x)) - ((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(2.0 * sqrt(x)) - 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 = (2.0 * sqrt(x)) - ((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[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] - N[(N[(a / b), $MachinePrecision] * 0.3333333333333333), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 70.3%

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

   1. *-commutative 70.3%

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

   2. *-commutative 70.3%

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

   3. *-commutative 70.3%

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

   4. *-commutative 70.3%

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

   5. associate-/l* 70.3%

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

   6. *-commutative 70.3%

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

3. Simplified 70.3%

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

5. Taylor expanded in z around 0 76.6%

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

6. Taylor expanded in y around 0 62.6%

   \[\leadsto \color{blue}{2 \cdot \sqrt{x}} - \frac{a}{3 \cdot b} \]
7. Step-by-step derivation

   1. *-commutative 62.6%

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

   2. associate-/r* 62.6%

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

   3. div-inv 62.5%

      \[\leadsto 2 \cdot \sqrt{x} - \color{blue}{\frac{a}{b} \cdot \frac{1}{3}} \]

   4. metadata-eval 62.5%

      \[\leadsto 2 \cdot \sqrt{x} - \frac{a}{b} \cdot \color{blue}{0.3333333333333333} \]

8. Applied egg-rr 62.5%

   \[\leadsto 2 \cdot \sqrt{x} - \color{blue}{\frac{a}{b} \cdot 0.3333333333333333} \]

9. Final simplification 62.5%

   \[\leadsto 2 \cdot \sqrt{x} - \frac{a}{b} \cdot 0.3333333333333333 \]
10. Add Preprocessing

Alternative 11: 66.3% 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 70.3%

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

   1. *-commutative 70.3%

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

   2. *-commutative 70.3%

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

   3. *-commutative 70.3%

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

   4. *-commutative 70.3%

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

   5. associate-/l* 70.3%

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

   6. *-commutative 70.3%

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

3. Simplified 70.3%

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

5. Taylor expanded in z around 0 76.6%

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

6. Taylor expanded in y around 0 62.6%

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

7. Final simplification 62.6%

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

Alternative 12: 66.3% accurate, 2.0× speedup

Math

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

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 (- (* 2.0 (sqrt x)) (/ (/ 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 (2.0 * sqrt(x)) - ((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 = (2.0d0 * sqrt(x)) - ((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 (2.0 * Math.sqrt(x)) - ((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 (2.0 * math.sqrt(x)) - ((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(Float64(2.0 * sqrt(x)) - Float64(Float64(a / 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 = (2.0 * sqrt(x)) - ((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[(N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] - N[(N[(a / b), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 70.3%

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

   1. *-commutative 70.3%

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

   2. *-commutative 70.3%

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

   3. *-commutative 70.3%

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

   4. *-commutative 70.3%

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

   5. associate-/l* 70.3%

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

   6. *-commutative 70.3%

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

3. Simplified 70.3%

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

5. Taylor expanded in z around 0 76.6%

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

   1. *-commutative 76.6%

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

   2. clear-num 76.5%

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

   3. inv-pow 76.5%

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

   4. *-commutative 76.5%

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

   5. *-un-lft-identity 76.5%

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

   6. times-frac 76.5%

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

   7. metadata-eval 76.5%

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

7. Applied egg-rr 76.5%

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

   1. unpow-1 76.5%

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

   2. *-commutative 76.5%

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

   3. associate-/r* 76.5%

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

   4. clear-num 76.6%

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

9. Applied egg-rr 76.6%

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

10. Taylor expanded in y around 0 62.6%

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

11. Final simplification 62.6%

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

Alternative 13: 51.1% 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 70.3%

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

   1. *-commutative 70.3%

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

   2. *-commutative 70.3%

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

   3. *-commutative 70.3%

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

   4. *-commutative 70.3%

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

   5. associate-/l* 70.3%

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

   6. *-commutative 70.3%

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

3. Simplified 70.3%

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

5. Taylor expanded in z around 0 76.6%

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

   1. *-commutative 76.6%

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

   2. clear-num 76.5%

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

   3. inv-pow 76.5%

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

   4. *-commutative 76.5%

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

   5. *-un-lft-identity 76.5%

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

   6. times-frac 76.5%

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

   7. metadata-eval 76.5%

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

7. Applied egg-rr 76.5%

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

   1. unpow-1 76.5%

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

   2. *-commutative 76.5%

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

   3. associate-/r* 76.5%

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

   4. clear-num 76.6%

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

9. Applied egg-rr 76.6%

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

10. Taylor expanded in a around inf 47.3%

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

11. Final simplification 47.3%

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

Alternative 14: 51.2% 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 70.3%

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

   1. *-commutative 70.3%

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

   2. *-commutative 70.3%

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

   3. *-commutative 70.3%

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

   4. *-commutative 70.3%

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

   5. associate-/l* 70.3%

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

   6. *-commutative 70.3%

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

3. Simplified 70.3%

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

5. Taylor expanded in z around 0 76.6%

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

   1. *-commutative 76.6%

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

   2. clear-num 76.5%

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

   3. inv-pow 76.5%

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

   4. *-commutative 76.5%

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

   5. *-un-lft-identity 76.5%

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

   6. times-frac 76.5%

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

   7. metadata-eval 76.5%

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

7. Applied egg-rr 76.5%

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

   1. unpow-1 76.5%

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

   2. *-commutative 76.5%

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

   3. associate-/r* 76.5%

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

   4. clear-num 76.6%

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

9. Applied egg-rr 76.6%

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

10. Taylor expanded in a around inf 47.3%

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

    1. metadata-eval 47.3%

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

    2. times-frac 47.4%

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

    3. neg-mul-1 47.4%

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

    4. distribute-neg-frac 47.4%

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

    5. distribute-neg-frac2 47.4%

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

    6. *-commutative 47.4%

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

    7. distribute-rgt-neg-in 47.4%

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

    8. metadata-eval 47.4%

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

12. Simplified 47.4%

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

13. Final simplification 47.4%

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

Developer target: 75.0% 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 2024072 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, K"
  :precision binary64

  :alt
  (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))))