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

Percentage Accurate: 70.1% → 77.8%

Time: 21.8s

Alternatives: 6

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: 70.1% 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: 77.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \frac{a}{3 \cdot b}\\ t_2 := 2 \cdot \sqrt{x}\\ \mathbf{if}\;t\_2 \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - t\_1 \leq 10^{+249}:\\ \;\;\;\;t\_2 \cdot \left(\cos y \cdot \cos \left(z \cdot {\left(\sqrt[3]{t \cdot 0.3333333333333333}\right)}^{3}\right) + \sin y \cdot \sin \left(z \cdot \left(t \cdot 0.3333333333333333\right)\right)\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{-0.3333333333333333}{b} + x \cdot \left(2 \cdot {x}^{-0.5}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ a (* 3.0 b))) (t_2 (* 2.0 (sqrt x))))
   (if (<= (- (* t_2 (cos (- y (/ (* z t) 3.0)))) t_1) 1e+249)
     (-
      (*
       t_2
       (+
        (* (cos y) (cos (* z (pow (cbrt (* t 0.3333333333333333)) 3.0))))
        (* (sin y) (sin (* z (* t 0.3333333333333333))))))
      t_1)
     (+ (* a (/ -0.3333333333333333 b)) (* x (* 2.0 (pow x -0.5)))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a / (3.0 * b);
	double t_2 = 2.0 * sqrt(x);
	double tmp;
	if (((t_2 * cos((y - ((z * t) / 3.0)))) - t_1) <= 1e+249) {
		tmp = (t_2 * ((cos(y) * cos((z * pow(cbrt((t * 0.3333333333333333)), 3.0)))) + (sin(y) * sin((z * (t * 0.3333333333333333)))))) - t_1;
	} else {
		tmp = (a * (-0.3333333333333333 / b)) + (x * (2.0 * pow(x, -0.5)));
	}
	return tmp;
}

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a / (3.0 * b);
	double t_2 = 2.0 * Math.sqrt(x);
	double tmp;
	if (((t_2 * Math.cos((y - ((z * t) / 3.0)))) - t_1) <= 1e+249) {
		tmp = (t_2 * ((Math.cos(y) * Math.cos((z * Math.pow(Math.cbrt((t * 0.3333333333333333)), 3.0)))) + (Math.sin(y) * Math.sin((z * (t * 0.3333333333333333)))))) - t_1;
	} else {
		tmp = (a * (-0.3333333333333333 / b)) + (x * (2.0 * Math.pow(x, -0.5)));
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(a / Float64(3.0 * b))
	t_2 = Float64(2.0 * sqrt(x))
	tmp = 0.0
	if (Float64(Float64(t_2 * cos(Float64(y - Float64(Float64(z * t) / 3.0)))) - t_1) <= 1e+249)
		tmp = Float64(Float64(t_2 * Float64(Float64(cos(y) * cos(Float64(z * (cbrt(Float64(t * 0.3333333333333333)) ^ 3.0)))) + Float64(sin(y) * sin(Float64(z * Float64(t * 0.3333333333333333)))))) - t_1);
	else
		tmp = Float64(Float64(a * Float64(-0.3333333333333333 / b)) + Float64(x * Float64(2.0 * (x ^ -0.5))));
	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[(a / N[(3.0 * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(t$95$2 * N[Cos[N[(y - N[(N[(z * t), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], 1e+249], N[(N[(t$95$2 * N[(N[(N[Cos[y], $MachinePrecision] * N[Cos[N[(z * N[Power[N[Power[N[(t * 0.3333333333333333), $MachinePrecision], 1/3], $MachinePrecision], 3.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] + N[(N[Sin[y], $MachinePrecision] * N[Sin[N[(z * N[(t * 0.3333333333333333), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(a * N[(-0.3333333333333333 / b), $MachinePrecision]), $MachinePrecision] + N[(x * N[(2.0 * N[Power[x, -0.5], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64))))) (/.f64 a (*.f64 b #s(literal 3 binary64)))) < 9.9999999999999992e248

   1. Initial program 75.8%

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

      1. *-commutative 75.8%

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

      2. *-commutative 75.8%

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

      3. *-commutative 75.8%

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

      4. *-commutative 75.8%

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

      5. associate-/l* 75.8%

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

      6. *-commutative 75.8%

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

   3. Simplified 75.8%

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

      1. clear-num 76.0%

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

      2. inv-pow 76.0%

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

   6. Applied egg-rr 76.0%

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

      1. cos-diff 78.0%

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

      2. unpow-1 78.0%

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

      3. clear-num 77.8%

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

      4. div-inv 77.8%

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

      5. metadata-eval 77.8%

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

      6. unpow-1 77.8%

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

      7. clear-num 77.9%

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

      8. div-inv 78.1%

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

      9. metadata-eval 78.1%

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

   8. Applied egg-rr 78.1%

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

      1. add-cube-cbrt 78.3%

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

      2. pow3 78.1%

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

   10. Applied egg-rr 78.1%

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

   if 9.9999999999999992e248 < (-.f64 (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64))))) (/.f64 a (*.f64 b #s(literal 3 binary64))))

   1. Initial program 33.3%

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

   3. Simplified 33.3%

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

   5. Taylor expanded in x around inf 33.3%

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

   6. Taylor expanded in t around 0 57.9%

      \[\leadsto x \cdot \left(-0.3333333333333333 \cdot \frac{a}{b \cdot x} + 2 \cdot \color{blue}{\left(\sqrt{\frac{1}{x}} \cdot \cos y\right)}\right) \]
   7. Step-by-step derivation

      1. *-commutative 57.9%

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

      2. rem-exp-log 57.9%

         \[\leadsto x \cdot \left(-0.3333333333333333 \cdot \frac{a}{b \cdot x} + 2 \cdot \left(\cos y \cdot \sqrt{\frac{1}{\color{blue}{e^{\log x}}}}\right)\right) \]

      3. exp-neg 57.9%

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

      4. unpow1/2 57.9%

         \[\leadsto x \cdot \left(-0.3333333333333333 \cdot \frac{a}{b \cdot x} + 2 \cdot \left(\cos y \cdot \color{blue}{{\left(e^{-\log x}\right)}^{0.5}}\right)\right) \]

      5. exp-prod 57.9%

         \[\leadsto x \cdot \left(-0.3333333333333333 \cdot \frac{a}{b \cdot x} + 2 \cdot \left(\cos y \cdot \color{blue}{e^{\left(-\log x\right) \cdot 0.5}}\right)\right) \]

      6. distribute-lft-neg-out 57.9%

         \[\leadsto x \cdot \left(-0.3333333333333333 \cdot \frac{a}{b \cdot x} + 2 \cdot \left(\cos y \cdot e^{\color{blue}{-\log x \cdot 0.5}}\right)\right) \]

      7. exp-neg 57.9%

         \[\leadsto x \cdot \left(-0.3333333333333333 \cdot \frac{a}{b \cdot x} + 2 \cdot \left(\cos y \cdot \color{blue}{\frac{1}{e^{\log x \cdot 0.5}}}\right)\right) \]

      8. exp-to-pow 57.9%

         \[\leadsto x \cdot \left(-0.3333333333333333 \cdot \frac{a}{b \cdot x} + 2 \cdot \left(\cos y \cdot \frac{1}{\color{blue}{{x}^{0.5}}}\right)\right) \]

      9. unpow1/2 57.9%

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

   8. Simplified 57.9%

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

   9. Taylor expanded in y around 0 59.5%

      \[\leadsto \color{blue}{x \cdot \left(-0.3333333333333333 \cdot \frac{a}{b \cdot x} + 2 \cdot \sqrt{\frac{1}{x}}\right)} \]
   10. Step-by-step derivation

       1. distribute-lft-in 59.4%

          \[\leadsto \color{blue}{x \cdot \left(-0.3333333333333333 \cdot \frac{a}{b \cdot x}\right) + x \cdot \left(2 \cdot \sqrt{\frac{1}{x}}\right)} \]

       2. associate-*r/ 59.5%

          \[\leadsto x \cdot \color{blue}{\frac{-0.3333333333333333 \cdot a}{b \cdot x}} + x \cdot \left(2 \cdot \sqrt{\frac{1}{x}}\right) \]

       3. *-commutative 59.5%

          \[\leadsto x \cdot \frac{-0.3333333333333333 \cdot a}{\color{blue}{x \cdot b}} + x \cdot \left(2 \cdot \sqrt{\frac{1}{x}}\right) \]

       4. associate-*r/ 60.4%

          \[\leadsto \color{blue}{\frac{x \cdot \left(-0.3333333333333333 \cdot a\right)}{x \cdot b}} + x \cdot \left(2 \cdot \sqrt{\frac{1}{x}}\right) \]

       5. times-frac 65.8%

          \[\leadsto \color{blue}{\frac{x}{x} \cdot \frac{-0.3333333333333333 \cdot a}{b}} + x \cdot \left(2 \cdot \sqrt{\frac{1}{x}}\right) \]

       6. *-inverses 65.8%

          \[\leadsto \color{blue}{1} \cdot \frac{-0.3333333333333333 \cdot a}{b} + x \cdot \left(2 \cdot \sqrt{\frac{1}{x}}\right) \]

       7. associate-*l/ 65.9%

          \[\leadsto 1 \cdot \color{blue}{\left(\frac{-0.3333333333333333}{b} \cdot a\right)} + x \cdot \left(2 \cdot \sqrt{\frac{1}{x}}\right) \]

       8. *-lft-identity 65.9%

          \[\leadsto \color{blue}{\frac{-0.3333333333333333}{b} \cdot a} + x \cdot \left(2 \cdot \sqrt{\frac{1}{x}}\right) \]

       9. *-commutative 65.9%

          \[\leadsto \color{blue}{a \cdot \frac{-0.3333333333333333}{b}} + x \cdot \left(2 \cdot \sqrt{\frac{1}{x}}\right) \]

       10. rem-exp-log 65.9%

           \[\leadsto a \cdot \frac{-0.3333333333333333}{b} + x \cdot \left(2 \cdot \sqrt{\frac{1}{\color{blue}{e^{\log x}}}}\right) \]

       11. exp-neg 65.9%

           \[\leadsto a \cdot \frac{-0.3333333333333333}{b} + x \cdot \left(2 \cdot \sqrt{\color{blue}{e^{-\log x}}}\right) \]

       12. unpow1/2 65.9%

           \[\leadsto a \cdot \frac{-0.3333333333333333}{b} + x \cdot \left(2 \cdot \color{blue}{{\left(e^{-\log x}\right)}^{0.5}}\right) \]

       13. exp-prod 65.9%

           \[\leadsto a \cdot \frac{-0.3333333333333333}{b} + x \cdot \left(2 \cdot \color{blue}{e^{\left(-\log x\right) \cdot 0.5}}\right) \]

       14. distribute-lft-neg-out 65.9%

           \[\leadsto a \cdot \frac{-0.3333333333333333}{b} + x \cdot \left(2 \cdot e^{\color{blue}{-\log x \cdot 0.5}}\right) \]

       15. distribute-rgt-neg-in 65.9%

           \[\leadsto a \cdot \frac{-0.3333333333333333}{b} + x \cdot \left(2 \cdot e^{\color{blue}{\log x \cdot \left(-0.5\right)}}\right) \]

       16. metadata-eval 65.9%

           \[\leadsto a \cdot \frac{-0.3333333333333333}{b} + x \cdot \left(2 \cdot e^{\log x \cdot \color{blue}{-0.5}}\right) \]

       17. exp-to-pow 65.9%

           \[\leadsto a \cdot \frac{-0.3333333333333333}{b} + x \cdot \left(2 \cdot \color{blue}{{x}^{-0.5}}\right) \]

   11. Simplified 65.9%

       \[\leadsto \color{blue}{a \cdot \frac{-0.3333333333333333}{b} + x \cdot \left(2 \cdot {x}^{-0.5}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{3 \cdot b} \leq 10^{+249}:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \left(\cos y \cdot \cos \left(z \cdot {\left(\sqrt[3]{t \cdot 0.3333333333333333}\right)}^{3}\right) + \sin y \cdot \sin \left(z \cdot \left(t \cdot 0.3333333333333333\right)\right)\right) - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{-0.3333333333333333}{b} + x \cdot \left(2 \cdot {x}^{-0.5}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 77.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \frac{a}{3 \cdot b}\\ \mathbf{if}\;\cos \left(y - \frac{z \cdot t}{3}\right) \leq 0.99:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \left(\sin y \cdot \sin \left(z \cdot \left(t \cdot 0.3333333333333333\right)\right) + \cos y \cdot \cos \left(0.3333333333333333 \cdot \left(z \cdot t\right)\right)\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;\left|\cos y \cdot \sqrt{x \cdot 4}\right| - t\_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ a (* 3.0 b))))
   (if (<= (cos (- y (/ (* z t) 3.0))) 0.99)
     (-
      (*
       (* 2.0 (sqrt x))
       (+
        (* (sin y) (sin (* z (* t 0.3333333333333333))))
        (* (cos y) (cos (* 0.3333333333333333 (* z t))))))
      t_1)
     (- (fabs (* (cos y) (sqrt (* x 4.0)))) t_1))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a / (3.0 * b);
	double tmp;
	if (cos((y - ((z * t) / 3.0))) <= 0.99) {
		tmp = ((2.0 * sqrt(x)) * ((sin(y) * sin((z * (t * 0.3333333333333333)))) + (cos(y) * cos((0.3333333333333333 * (z * t)))))) - t_1;
	} else {
		tmp = fabs((cos(y) * sqrt((x * 4.0)))) - t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a / (3.0d0 * b)
    if (cos((y - ((z * t) / 3.0d0))) <= 0.99d0) then
        tmp = ((2.0d0 * sqrt(x)) * ((sin(y) * sin((z * (t * 0.3333333333333333d0)))) + (cos(y) * cos((0.3333333333333333d0 * (z * t)))))) - t_1
    else
        tmp = abs((cos(y) * sqrt((x * 4.0d0)))) - t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a / (3.0 * b);
	double tmp;
	if (Math.cos((y - ((z * t) / 3.0))) <= 0.99) {
		tmp = ((2.0 * Math.sqrt(x)) * ((Math.sin(y) * Math.sin((z * (t * 0.3333333333333333)))) + (Math.cos(y) * Math.cos((0.3333333333333333 * (z * t)))))) - t_1;
	} else {
		tmp = Math.abs((Math.cos(y) * Math.sqrt((x * 4.0)))) - t_1;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = a / (3.0 * b)
	tmp = 0
	if math.cos((y - ((z * t) / 3.0))) <= 0.99:
		tmp = ((2.0 * math.sqrt(x)) * ((math.sin(y) * math.sin((z * (t * 0.3333333333333333)))) + (math.cos(y) * math.cos((0.3333333333333333 * (z * t)))))) - t_1
	else:
		tmp = math.fabs((math.cos(y) * math.sqrt((x * 4.0)))) - t_1
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(a / Float64(3.0 * b))
	tmp = 0.0
	if (cos(Float64(y - Float64(Float64(z * t) / 3.0))) <= 0.99)
		tmp = Float64(Float64(Float64(2.0 * sqrt(x)) * Float64(Float64(sin(y) * sin(Float64(z * Float64(t * 0.3333333333333333)))) + Float64(cos(y) * cos(Float64(0.3333333333333333 * Float64(z * t)))))) - t_1);
	else
		tmp = Float64(abs(Float64(cos(y) * sqrt(Float64(x * 4.0)))) - t_1);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a / (3.0 * b);
	tmp = 0.0;
	if (cos((y - ((z * t) / 3.0))) <= 0.99)
		tmp = ((2.0 * sqrt(x)) * ((sin(y) * sin((z * (t * 0.3333333333333333)))) + (cos(y) * cos((0.3333333333333333 * (z * t)))))) - t_1;
	else
		tmp = abs((cos(y) * sqrt((x * 4.0)))) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a / N[(3.0 * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[Cos[N[(y - N[(N[(z * t), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], 0.99], N[(N[(N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] * N[(N[(N[Sin[y], $MachinePrecision] * N[Sin[N[(z * N[(t * 0.3333333333333333), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] + N[(N[Cos[y], $MachinePrecision] * N[Cos[N[(0.3333333333333333 * N[(z * t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[Abs[N[(N[Cos[y], $MachinePrecision] * N[Sqrt[N[(x * 4.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64)))) < 0.98999999999999999

   1. Initial program 68.0%

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

      1. *-commutative 68.0%

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

      2. *-commutative 68.0%

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

      3. *-commutative 68.0%

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

      4. *-commutative 68.0%

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

      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. Step-by-step derivation

      1. clear-num 68.3%

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

      2. inv-pow 68.3%

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

   6. Applied egg-rr 68.3%

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

      1. cos-diff 71.1%

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

      2. unpow-1 71.1%

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

      3. clear-num 70.8%

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

      4. div-inv 70.8%

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

      5. metadata-eval 70.8%

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

      6. unpow-1 70.8%

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

      7. clear-num 71.0%

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

      8. div-inv 71.2%

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

      9. metadata-eval 71.2%

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

   8. Applied egg-rr 71.2%

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

   9. Taylor expanded in y around inf 71.5%

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

   if 0.98999999999999999 < (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64))))

   1. Initial program 68.8%

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

      1. *-commutative 68.8%

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

      2. *-commutative 68.8%

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

      3. *-commutative 68.8%

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

      4. *-commutative 68.8%

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

      5. associate-/l* 68.8%

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

      6. *-commutative 68.8%

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

   3. Simplified 68.8%

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

   5. Taylor expanded in z around 0 82.9%

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

      1. associate-*r* 82.9%

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

      2. *-commutative 82.9%

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

      3. *-commutative 82.9%

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

   7. Simplified 82.9%

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

      1. add-sqr-sqrt 80.6%

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

      2. sqrt-unprod 83.4%

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

      3. *-commutative 83.4%

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

      4. *-commutative 83.4%

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

      5. swap-sqr 83.4%

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

      6. pow2 83.4%

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

      7. *-commutative 83.4%

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

      8. *-commutative 83.4%

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

      9. swap-sqr 83.4%

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

      10. add-sqr-sqrt 83.4%

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

      11. metadata-eval 83.4%

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

   9. Applied egg-rr 83.4%

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

       1. unpow2 83.4%

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

       2. rem-square-sqrt 83.4%

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

       3. swap-sqr 83.4%

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

       4. rem-sqrt-square 83.4%

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

   11. Simplified 83.4%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\cos \left(y - \frac{z \cdot t}{3}\right) \leq 0.99:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \left(\sin y \cdot \sin \left(z \cdot \left(t \cdot 0.3333333333333333\right)\right) + \cos y \cdot \cos \left(0.3333333333333333 \cdot \left(z \cdot t\right)\right)\right) - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\left|\cos y \cdot \sqrt{x \cdot 4}\right| - \frac{a}{3 \cdot b}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 66.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq 8.5 \cdot 10^{+234}:\\ \;\;\;\;2 \cdot \sqrt{x} - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt{x} \cdot \cos \left(y + -0.3333333333333333 \cdot \left(z \cdot t\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 8.5e+234)
   (- (* 2.0 (sqrt x)) (/ a (* 3.0 b)))
   (* 2.0 (* (sqrt x) (cos (+ y (* -0.3333333333333333 (* z t))))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 8.5e+234) {
		tmp = (2.0 * sqrt(x)) - (a / (3.0 * b));
	} else {
		tmp = 2.0 * (sqrt(x) * cos((y + (-0.3333333333333333 * (z * t)))));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 8.5d+234) then
        tmp = (2.0d0 * sqrt(x)) - (a / (3.0d0 * b))
    else
        tmp = 2.0d0 * (sqrt(x) * cos((y + ((-0.3333333333333333d0) * (z * t)))))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 8.5e+234) {
		tmp = (2.0 * Math.sqrt(x)) - (a / (3.0 * b));
	} else {
		tmp = 2.0 * (Math.sqrt(x) * Math.cos((y + (-0.3333333333333333 * (z * t)))));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 8.5e+234:
		tmp = (2.0 * math.sqrt(x)) - (a / (3.0 * b))
	else:
		tmp = 2.0 * (math.sqrt(x) * math.cos((y + (-0.3333333333333333 * (z * t)))))
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 8.5e+234)
		tmp = Float64(Float64(2.0 * sqrt(x)) - Float64(a / Float64(3.0 * b)));
	else
		tmp = Float64(2.0 * Float64(sqrt(x) * cos(Float64(y + Float64(-0.3333333333333333 * Float64(z * t))))));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 8.5e+234)
		tmp = (2.0 * sqrt(x)) - (a / (3.0 * b));
	else
		tmp = 2.0 * (sqrt(x) * cos((y + (-0.3333333333333333 * (z * t)))));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 8.5e+234], N[(N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] - N[(a / N[(3.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[Sqrt[x], $MachinePrecision] * N[Cos[N[(y + N[(-0.3333333333333333 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 8.49999999999999989e234

   1. Initial program 68.4%

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

      1. *-commutative 68.4%

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

      2. *-commutative 68.4%

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

      3. *-commutative 68.4%

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

      4. *-commutative 68.4%

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

      5. associate-/l* 68.4%

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

      6. *-commutative 68.4%

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

   3. Simplified 68.4%

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

   5. Taylor expanded in z around 0 74.2%

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

      1. associate-*r* 74.2%

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

      2. *-commutative 74.2%

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

      3. *-commutative 74.2%

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

   7. Simplified 74.2%

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

   8. Taylor expanded in y around 0 63.3%

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

   if 8.49999999999999989e234 < b

   1. Initial program 67.1%

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

   3. Simplified 68.4%

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

   5. Taylor expanded in x around inf 67.0%

      \[\leadsto \color{blue}{2 \cdot \left(\sqrt{x} \cdot \cos \left(y + -0.3333333333333333 \cdot \left(t \cdot z\right)\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 8.5 \cdot 10^{+234}:\\ \;\;\;\;2 \cdot \sqrt{x} - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt{x} \cdot \cos \left(y + -0.3333333333333333 \cdot \left(z \cdot t\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 76.8% 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 68.3%

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

   1. *-commutative 68.3%

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

   2. *-commutative 68.3%

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

   3. *-commutative 68.3%

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

   4. *-commutative 68.3%

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

   5. associate-/l* 68.4%

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

   6. *-commutative 68.4%

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

3. Simplified 68.4%

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

5. Taylor expanded in z around 0 73.5%

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

   1. associate-*r* 73.5%

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

   2. *-commutative 73.5%

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

   3. *-commutative 73.5%

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

7. Simplified 73.5%

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

8. Final simplification 73.5%

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

Alternative 5: 65.7% 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 68.3%

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

   1. *-commutative 68.3%

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

   2. *-commutative 68.3%

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

   3. *-commutative 68.3%

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

   4. *-commutative 68.3%

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

   5. associate-/l* 68.4%

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

   6. *-commutative 68.4%

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

3. Simplified 68.4%

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

5. Taylor expanded in z around 0 73.5%

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

   1. associate-*r* 73.5%

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

   2. *-commutative 73.5%

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

   3. *-commutative 73.5%

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

7. Simplified 73.5%

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

8. Taylor expanded in y around 0 62.0%

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

Alternative 6: 51.1% accurate, 43.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 68.3%

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

3. Simplified 68.3%

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

5. Taylor expanded in a around inf 45.2%

   \[\leadsto \color{blue}{-0.3333333333333333 \cdot \frac{a}{b}} \]
6. Add Preprocessing

Developer Target 1: 74.4% 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 2024160 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, K"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< z -1379333748723514100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (* (* 2 (sqrt x)) (cos (- (/ 1 y) (/ (/ 3333333333333333/10000000000000000 z) t)))) (/ (/ a 3) b)) (if (< z 35162906135559870000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (* (* (sqrt x) 2) (cos (- y (* (/ t 3) z)))) (/ (/ a 3) b)) (- (* (cos (- y (/ (/ 3333333333333333/10000000000000000 z) t))) (* 2 (sqrt x))) (/ (/ a b) 3)))))

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