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

Percentage Accurate: 69.7% → 77.3%

Time: 20.7s

Alternatives: 9

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 69.7% 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: 77.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.3333333333333333 \cdot \left(z \cdot t\right)\\ t_2 := \frac{a}{3 \cdot b}\\ t_3 := 2 \cdot \sqrt{x}\\ \mathbf{if}\;t\_3 \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - t\_2 \leq 2 \cdot 10^{+130}:\\ \;\;\;\;\mathsf{fma}\left(2, \sqrt{x} \cdot \mathsf{fma}\left(\cos y, \cos t\_1, \sin y \cdot \sin t\_1\right), a \cdot \frac{-0.3333333333333333}{b}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_3 \cdot \left|\cos y\right| - t\_2\\ \end{array} \end{array} \]

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 (<= (- (* t_3 (cos (- y (/ (* z t) 3.0)))) t_2) 2e+130)
     (fma
      2.0
      (* (sqrt x) (fma (cos y) (cos t_1) (* (sin y) (sin t_1))))
      (* a (/ -0.3333333333333333 b)))
     (- (* t_3 (fabs (cos y))) t_2))))

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 (((t_3 * cos((y - ((z * t) / 3.0)))) - t_2) <= 2e+130) {
		tmp = fma(2.0, (sqrt(x) * fma(cos(y), cos(t_1), (sin(y) * sin(t_1)))), (a * (-0.3333333333333333 / b)));
	} else {
		tmp = (t_3 * fabs(cos(y))) - t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(0.3333333333333333 * Float64(z * t))
	t_2 = Float64(a / Float64(3.0 * b))
	t_3 = Float64(2.0 * sqrt(x))
	tmp = 0.0
	if (Float64(Float64(t_3 * cos(Float64(y - Float64(Float64(z * t) / 3.0)))) - t_2) <= 2e+130)
		tmp = fma(2.0, Float64(sqrt(x) * fma(cos(y), cos(t_1), Float64(sin(y) * sin(t_1)))), Float64(a * Float64(-0.3333333333333333 / b)));
	else
		tmp = Float64(Float64(t_3 * abs(cos(y))) - t_2);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(0.3333333333333333 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a / N[(3.0 * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(t$95$3 * N[Cos[N[(y - N[(N[(z * t), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], 2e+130], N[(2.0 * N[(N[Sqrt[x], $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[(-0.3333333333333333 / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$3 * N[Abs[N[Cos[y], $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - t$95$2), $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)))) < 2.0000000000000001e130

   1. Initial program 75.4%

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

   3. Simplified 75.2%

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

   6. Applied egg-rr 74.9%

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

   8. Simplified 76.2%

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

   if 2.0000000000000001e130 < (-.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 48.7%

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

      1. *-commutative 48.7%

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

      2. *-commutative 48.7%

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

      3. *-commutative 48.7%

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

      4. *-commutative 48.7%

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

      5. associate-/l* 48.7%

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

      6. *-commutative 48.7%

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

   3. Simplified 48.7%

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

   5. Taylor expanded in z around 0 71.3%

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

      1. associate-*r* 71.3%

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

      2. *-commutative 71.3%

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

      3. *-commutative 71.3%

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

   7. Simplified 71.3%

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

      1. add-sqr-sqrt 51.8%

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

      2. sqrt-unprod 71.5%

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

      3. pow2 71.5%

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

   9. Applied egg-rr 71.5%

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

       1. unpow2 71.5%

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

       2. rem-sqrt-square 71.5%

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

   11. Simplified 71.5%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{3 \cdot b} \leq 2 \cdot 10^{+130}:\\ \;\;\;\;\mathsf{fma}\left(2, \sqrt{x} \cdot \mathsf{fma}\left(\cos y, \cos \left(0.3333333333333333 \cdot \left(z \cdot t\right)\right), \sin y \cdot \sin \left(0.3333333333333333 \cdot \left(z \cdot t\right)\right)\right), a \cdot \frac{-0.3333333333333333}{b}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \left|\cos y\right| - \frac{a}{3 \cdot b}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 77.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a}{3 \cdot b}\\ t_2 := 2 \cdot \sqrt{x}\\ \mathbf{if}\;t\_2 \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - t\_1 \leq 2 \cdot 10^{+130}:\\ \;\;\;\;t\_2 \cdot \left(\cos y \cdot \cos \left(z \cdot \left(t \cdot -0.3333333333333333\right)\right) + \sin y \cdot \sin \left(z \cdot \frac{1}{\frac{3}{t}}\right)\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2 \cdot \left|\cos y\right| - t\_1\\ \end{array} \end{array} \]

FPCore

(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) 2e+130)
     (-
      (*
       t_2
       (+
        (* (cos y) (cos (* z (* t -0.3333333333333333))))
        (* (sin y) (sin (* z (/ 1.0 (/ 3.0 t)))))))
      t_1)
     (- (* t_2 (fabs (cos y))) t_1))))

C

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) <= 2e+130) {
		tmp = (t_2 * ((cos(y) * cos((z * (t * -0.3333333333333333)))) + (sin(y) * sin((z * (1.0 / (3.0 / t))))))) - t_1;
	} else {
		tmp = (t_2 * fabs(cos(y))) - t_1;
	}
	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) :: tmp
    t_1 = a / (3.0d0 * b)
    t_2 = 2.0d0 * sqrt(x)
    if (((t_2 * cos((y - ((z * t) / 3.0d0)))) - t_1) <= 2d+130) then
        tmp = (t_2 * ((cos(y) * cos((z * (t * (-0.3333333333333333d0))))) + (sin(y) * sin((z * (1.0d0 / (3.0d0 / t))))))) - t_1
    else
        tmp = (t_2 * abs(cos(y))) - t_1
    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 = 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) <= 2e+130) {
		tmp = (t_2 * ((Math.cos(y) * Math.cos((z * (t * -0.3333333333333333)))) + (Math.sin(y) * Math.sin((z * (1.0 / (3.0 / t))))))) - t_1;
	} else {
		tmp = (t_2 * Math.abs(Math.cos(y))) - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a / (3.0 * b)
	t_2 = 2.0 * math.sqrt(x)
	tmp = 0
	if ((t_2 * math.cos((y - ((z * t) / 3.0)))) - t_1) <= 2e+130:
		tmp = (t_2 * ((math.cos(y) * math.cos((z * (t * -0.3333333333333333)))) + (math.sin(y) * math.sin((z * (1.0 / (3.0 / t))))))) - t_1
	else:
		tmp = (t_2 * math.fabs(math.cos(y))) - t_1
	return tmp

Julia

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) <= 2e+130)
		tmp = Float64(Float64(t_2 * Float64(Float64(cos(y) * cos(Float64(z * Float64(t * -0.3333333333333333)))) + Float64(sin(y) * sin(Float64(z * Float64(1.0 / Float64(3.0 / t))))))) - t_1);
	else
		tmp = Float64(Float64(t_2 * abs(cos(y))) - t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a / (3.0 * b);
	t_2 = 2.0 * sqrt(x);
	tmp = 0.0;
	if (((t_2 * cos((y - ((z * t) / 3.0)))) - t_1) <= 2e+130)
		tmp = (t_2 * ((cos(y) * cos((z * (t * -0.3333333333333333)))) + (sin(y) * sin((z * (1.0 / (3.0 / t))))))) - t_1;
	else
		tmp = (t_2 * abs(cos(y))) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

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], 2e+130], N[(N[(t$95$2 * N[(N[(N[Cos[y], $MachinePrecision] * N[Cos[N[(z * N[(t * -0.3333333333333333), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] + N[(N[Sin[y], $MachinePrecision] * N[Sin[N[(z * N[(1.0 / N[(3.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(t$95$2 * N[Abs[N[Cos[y], $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - t$95$1), $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)))) < 2.0000000000000001e130

   1. Initial program 75.4%

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

      1. *-commutative 75.4%

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

      2. *-commutative 75.4%

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

      3. *-commutative 75.4%

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

      4. *-commutative 75.4%

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

      5. associate-/l* 75.2%

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

      6. *-commutative 75.2%

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

   3. Simplified 75.2%

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

      1. add-sqr-sqrt 34.4%

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

      2. sqrt-unprod 63.4%

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

      3. div-inv 63.4%

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

      4. metadata-eval 63.4%

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

      5. metadata-eval 63.4%

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

      6. div-inv 63.4%

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

      7. metadata-eval 63.4%

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

      8. metadata-eval 63.4%

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

      9. swap-sqr 63.3%

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

      10. metadata-eval 63.3%

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

      11. metadata-eval 63.3%

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

      12. metadata-eval 63.3%

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - z \cdot \sqrt{\left(t \cdot t\right) \cdot \color{blue}{0.1111111111111111}}\right) - \frac{a}{3 \cdot b} \]

      13. metadata-eval 63.3%

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

      14. swap-sqr 63.4%

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

      15. sqrt-unprod 40.9%

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

      16. add-sqr-sqrt 75.2%

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

      17. add-cube-cbrt 74.9%

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

      18. pow3 75.0%

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

   6. Applied egg-rr 75.0%

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

      1. cos-diff 74.9%

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

      2. rem-cube-cbrt 74.8%

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

      3. rem-cube-cbrt 75.0%

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

   8. Applied egg-rr 75.0%

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

      1. add-sqr-sqrt 41.2%

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

      2. sqrt-unprod 63.2%

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

      3. swap-sqr 63.1%

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

      4. metadata-eval 63.1%

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \left(\cos y \cdot \cos \left(z \cdot \left(t \cdot -0.3333333333333333\right)\right) + \sin y \cdot \sin \left(z \cdot \sqrt{\left(t \cdot t\right) \cdot \color{blue}{0.1111111111111111}}\right)\right) - \frac{a}{3 \cdot b} \]

      5. metadata-eval 63.1%

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

      6. metadata-eval 63.1%

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

      7. metadata-eval 63.1%

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

      8. swap-sqr 63.2%

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

      9. metadata-eval 63.2%

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

      10. metadata-eval 63.2%

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

      11. div-inv 63.2%

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

      12. metadata-eval 63.2%

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

      13. metadata-eval 63.2%

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

      14. div-inv 63.2%

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

      15. sqrt-unprod 34.6%

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

      16. add-sqr-sqrt 75.8%

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

      17. clear-num 75.9%

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

   10. Applied egg-rr 75.9%

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

   if 2.0000000000000001e130 < (-.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 48.7%

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

      1. *-commutative 48.7%

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

      2. *-commutative 48.7%

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

      3. *-commutative 48.7%

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

      4. *-commutative 48.7%

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

      5. associate-/l* 48.7%

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

      6. *-commutative 48.7%

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

   3. Simplified 48.7%

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

   5. Taylor expanded in z around 0 71.3%

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

      1. associate-*r* 71.3%

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

      2. *-commutative 71.3%

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

      3. *-commutative 71.3%

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

   7. Simplified 71.3%

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

      1. add-sqr-sqrt 51.8%

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

      2. sqrt-unprod 71.5%

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

      3. pow2 71.5%

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

   9. Applied egg-rr 71.5%

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

       1. unpow2 71.5%

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

       2. rem-sqrt-square 71.5%

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

   11. Simplified 71.5%

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

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{3 \cdot b} \leq 2 \cdot 10^{+130}:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \left(\cos y \cdot \cos \left(z \cdot \left(t \cdot -0.3333333333333333\right)\right) + \sin y \cdot \sin \left(z \cdot \frac{1}{\frac{3}{t}}\right)\right) - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \left|\cos y\right| - \frac{a}{3 \cdot b}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 77.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a}{3 \cdot b}\\ t_2 := 2 \cdot \sqrt{x}\\ \mathbf{if}\;t\_2 \cdot \cos \left(y - \frac{z \cdot t}{3}\right) \leq 2 \cdot 10^{+130}:\\ \;\;\;\;t\_2 \cdot \left(\cos y \cdot \cos \left(z \cdot \left(t \cdot -0.3333333333333333\right)\right) + \sin y \cdot \sin \left(z \cdot \frac{t}{3}\right)\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2 \cdot \left|\cos y\right| - t\_1\\ \end{array} \end{array} \]

FPCore

(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)))) 2e+130)
     (-
      (*
       t_2
       (+
        (* (cos y) (cos (* z (* t -0.3333333333333333))))
        (* (sin y) (sin (* z (/ t 3.0))))))
      t_1)
     (- (* t_2 (fabs (cos y))) t_1))))

C

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)))) <= 2e+130) {
		tmp = (t_2 * ((cos(y) * cos((z * (t * -0.3333333333333333)))) + (sin(y) * sin((z * (t / 3.0)))))) - t_1;
	} else {
		tmp = (t_2 * fabs(cos(y))) - t_1;
	}
	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) :: tmp
    t_1 = a / (3.0d0 * b)
    t_2 = 2.0d0 * sqrt(x)
    if ((t_2 * cos((y - ((z * t) / 3.0d0)))) <= 2d+130) then
        tmp = (t_2 * ((cos(y) * cos((z * (t * (-0.3333333333333333d0))))) + (sin(y) * sin((z * (t / 3.0d0)))))) - t_1
    else
        tmp = (t_2 * abs(cos(y))) - t_1
    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 = a / (3.0 * b);
	double t_2 = 2.0 * Math.sqrt(x);
	double tmp;
	if ((t_2 * Math.cos((y - ((z * t) / 3.0)))) <= 2e+130) {
		tmp = (t_2 * ((Math.cos(y) * Math.cos((z * (t * -0.3333333333333333)))) + (Math.sin(y) * Math.sin((z * (t / 3.0)))))) - t_1;
	} else {
		tmp = (t_2 * Math.abs(Math.cos(y))) - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a / (3.0 * b)
	t_2 = 2.0 * math.sqrt(x)
	tmp = 0
	if (t_2 * math.cos((y - ((z * t) / 3.0)))) <= 2e+130:
		tmp = (t_2 * ((math.cos(y) * math.cos((z * (t * -0.3333333333333333)))) + (math.sin(y) * math.sin((z * (t / 3.0)))))) - t_1
	else:
		tmp = (t_2 * math.fabs(math.cos(y))) - t_1
	return tmp

Julia

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(t_2 * cos(Float64(y - Float64(Float64(z * t) / 3.0)))) <= 2e+130)
		tmp = Float64(Float64(t_2 * Float64(Float64(cos(y) * cos(Float64(z * Float64(t * -0.3333333333333333)))) + Float64(sin(y) * sin(Float64(z * Float64(t / 3.0)))))) - t_1);
	else
		tmp = Float64(Float64(t_2 * abs(cos(y))) - t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a / (3.0 * b);
	t_2 = 2.0 * sqrt(x);
	tmp = 0.0;
	if ((t_2 * cos((y - ((z * t) / 3.0)))) <= 2e+130)
		tmp = (t_2 * ((cos(y) * cos((z * (t * -0.3333333333333333)))) + (sin(y) * sin((z * (t / 3.0)))))) - t_1;
	else
		tmp = (t_2 * abs(cos(y))) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

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[(t$95$2 * N[Cos[N[(y - N[(N[(z * t), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2e+130], N[(N[(t$95$2 * N[(N[(N[Cos[y], $MachinePrecision] * N[Cos[N[(z * N[(t * -0.3333333333333333), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] + N[(N[Sin[y], $MachinePrecision] * N[Sin[N[(z * N[(t / 3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(t$95$2 * N[Abs[N[Cos[y], $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64))))) < 2.0000000000000001e130

   1. Initial program 77.9%

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

      1. *-commutative 77.9%

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

      2. *-commutative 77.9%

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

      3. *-commutative 77.9%

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

      4. *-commutative 77.9%

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

      5. associate-/l* 77.8%

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

      6. *-commutative 77.8%

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

   3. Simplified 77.8%

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

      1. add-sqr-sqrt 33.7%

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

      2. sqrt-unprod 62.5%

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

      3. div-inv 62.5%

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

      4. metadata-eval 62.5%

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

      5. metadata-eval 62.5%

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

      6. div-inv 62.5%

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

      7. metadata-eval 62.5%

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

      8. metadata-eval 62.5%

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

      9. swap-sqr 62.4%

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

      10. metadata-eval 62.4%

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

      11. metadata-eval 62.4%

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

      12. metadata-eval 62.4%

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - z \cdot \sqrt{\left(t \cdot t\right) \cdot \color{blue}{0.1111111111111111}}\right) - \frac{a}{3 \cdot b} \]

      13. metadata-eval 62.4%

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

      14. swap-sqr 62.5%

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

      15. sqrt-unprod 44.2%

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

      16. add-sqr-sqrt 77.8%

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

      17. add-cube-cbrt 77.5%

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

      18. pow3 77.6%

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

   6. Applied egg-rr 77.6%

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

      1. cos-diff 77.5%

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

      2. rem-cube-cbrt 77.4%

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

      3. rem-cube-cbrt 77.6%

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

   8. Applied egg-rr 77.6%

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

      1. add-sqr-sqrt 44.4%

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

      2. sqrt-unprod 62.3%

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

      3. swap-sqr 62.3%

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

      4. metadata-eval 62.3%

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \left(\cos y \cdot \cos \left(z \cdot \left(t \cdot -0.3333333333333333\right)\right) + \sin y \cdot \sin \left(z \cdot \sqrt{\left(t \cdot t\right) \cdot \color{blue}{0.1111111111111111}}\right)\right) - \frac{a}{3 \cdot b} \]

      5. metadata-eval 62.3%

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

      6. metadata-eval 62.3%

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

      7. metadata-eval 62.3%

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

      8. swap-sqr 62.3%

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

      9. metadata-eval 62.3%

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

      10. metadata-eval 62.3%

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

      11. div-inv 62.4%

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

      12. metadata-eval 62.4%

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

      13. metadata-eval 62.4%

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

      14. div-inv 62.4%

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

      15. sqrt-unprod 33.8%

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

      16. add-sqr-sqrt 78.3%

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

   10. Applied egg-rr 78.3%

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

   if 2.0000000000000001e130 < (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64)))))

   1. Initial program 23.1%

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

      1. *-commutative 23.1%

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

      2. *-commutative 23.1%

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

      3. *-commutative 23.1%

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

      4. *-commutative 23.1%

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

      5. associate-/l* 23.1%

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

      6. *-commutative 23.1%

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

   3. Simplified 23.1%

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

   5. Taylor expanded in z around 0 57.0%

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

      1. associate-*r* 57.0%

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

      2. *-commutative 57.0%

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

      3. *-commutative 57.0%

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

   7. Simplified 57.0%

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

      1. add-sqr-sqrt 48.1%

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

      2. sqrt-unprod 57.3%

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

      3. pow2 57.3%

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

   9. Applied egg-rr 57.3%

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

       1. unpow2 57.3%

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

       2. rem-sqrt-square 57.3%

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

   11. Simplified 57.3%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) \leq 2 \cdot 10^{+130}:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \left(\cos y \cdot \cos \left(z \cdot \left(t \cdot -0.3333333333333333\right)\right) + \sin y \cdot \sin \left(z \cdot \frac{t}{3}\right)\right) - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \left|\cos y\right| - \frac{a}{3 \cdot b}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 76.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \sqrt{x}\\ t_2 := \frac{a}{3 \cdot b}\\ \mathbf{if}\;t\_1 \cdot \cos \left(y - \frac{z \cdot t}{3}\right) \leq 2 \cdot 10^{+139}:\\ \;\;\;\;t\_1 \cdot \cos \left(y - z \cdot \frac{t}{3}\right) - t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1 - t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* 2.0 (sqrt x))) (t_2 (/ a (* 3.0 b))))
   (if (<= (* t_1 (cos (- y (/ (* z t) 3.0)))) 2e+139)
     (- (* t_1 (cos (- y (* z (/ t 3.0))))) t_2)
     (- t_1 t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 2.0 * sqrt(x);
	double t_2 = a / (3.0 * b);
	double tmp;
	if ((t_1 * cos((y - ((z * t) / 3.0)))) <= 2e+139) {
		tmp = (t_1 * cos((y - (z * (t / 3.0))))) - t_2;
	} else {
		tmp = t_1 - t_2;
	}
	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) :: tmp
    t_1 = 2.0d0 * sqrt(x)
    t_2 = a / (3.0d0 * b)
    if ((t_1 * cos((y - ((z * t) / 3.0d0)))) <= 2d+139) then
        tmp = (t_1 * cos((y - (z * (t / 3.0d0))))) - t_2
    else
        tmp = t_1 - t_2
    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 = 2.0 * Math.sqrt(x);
	double t_2 = a / (3.0 * b);
	double tmp;
	if ((t_1 * Math.cos((y - ((z * t) / 3.0)))) <= 2e+139) {
		tmp = (t_1 * Math.cos((y - (z * (t / 3.0))))) - t_2;
	} else {
		tmp = t_1 - t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = 2.0 * math.sqrt(x)
	t_2 = a / (3.0 * b)
	tmp = 0
	if (t_1 * math.cos((y - ((z * t) / 3.0)))) <= 2e+139:
		tmp = (t_1 * math.cos((y - (z * (t / 3.0))))) - t_2
	else:
		tmp = t_1 - t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(2.0 * sqrt(x))
	t_2 = Float64(a / Float64(3.0 * b))
	tmp = 0.0
	if (Float64(t_1 * cos(Float64(y - Float64(Float64(z * t) / 3.0)))) <= 2e+139)
		tmp = Float64(Float64(t_1 * cos(Float64(y - Float64(z * Float64(t / 3.0))))) - t_2);
	else
		tmp = Float64(t_1 - t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 2.0 * sqrt(x);
	t_2 = a / (3.0 * b);
	tmp = 0.0;
	if ((t_1 * cos((y - ((z * t) / 3.0)))) <= 2e+139)
		tmp = (t_1 * cos((y - (z * (t / 3.0))))) - t_2;
	else
		tmp = t_1 - t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a / N[(3.0 * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$1 * N[Cos[N[(y - N[(N[(z * t), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2e+139], N[(N[(t$95$1 * N[Cos[N[(y - N[(z * N[(t / 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], N[(t$95$1 - t$95$2), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64))))) < 2.00000000000000007e139

   1. Initial program 77.8%

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

      1. *-commutative 77.8%

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

      2. *-commutative 77.8%

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

      3. *-commutative 77.8%

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

      4. *-commutative 77.8%

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

      5. associate-/l* 77.7%

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

      6. *-commutative 77.7%

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

   3. Simplified 77.7%

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

   if 2.00000000000000007e139 < (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64)))))

   1. Initial program 13.5%

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

      1. *-commutative 13.5%

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

      2. *-commutative 13.5%

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

      3. *-commutative 13.5%

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

      4. *-commutative 13.5%

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

      5. associate-/l* 13.5%

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

      6. *-commutative 13.5%

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

   3. Simplified 13.5%

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

   5. Taylor expanded in z around 0 54.2%

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

      1. associate-*r* 54.2%

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

      2. *-commutative 54.2%

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

      3. *-commutative 54.2%

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

   7. Simplified 54.2%

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

   8. Taylor expanded in y around 0 54.3%

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

Alternative 5: 67.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{-153} \lor \neg \left(a \leq 1.35 \cdot 10^{-193}\right):\\ \;\;\;\;2 \cdot \sqrt{x} - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt{x} \cdot \cos \left(y + \left(z \cdot t\right) \cdot -0.3333333333333333\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -3.4e-153) (not (<= a 1.35e-193)))
   (- (* 2.0 (sqrt x)) (/ a (* 3.0 b)))
   (* 2.0 (* (sqrt x) (cos (+ y (* (* z t) -0.3333333333333333)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -3.4e-153) || !(a <= 1.35e-193)) {
		tmp = (2.0 * sqrt(x)) - (a / (3.0 * b));
	} else {
		tmp = 2.0 * (sqrt(x) * cos((y + ((z * t) * -0.3333333333333333))));
	}
	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) :: tmp
    if ((a <= (-3.4d-153)) .or. (.not. (a <= 1.35d-193))) then
        tmp = (2.0d0 * sqrt(x)) - (a / (3.0d0 * b))
    else
        tmp = 2.0d0 * (sqrt(x) * cos((y + ((z * t) * (-0.3333333333333333d0)))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -3.4e-153) || !(a <= 1.35e-193)) {
		tmp = (2.0 * Math.sqrt(x)) - (a / (3.0 * b));
	} else {
		tmp = 2.0 * (Math.sqrt(x) * Math.cos((y + ((z * t) * -0.3333333333333333))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -3.4e-153) or not (a <= 1.35e-193):
		tmp = (2.0 * math.sqrt(x)) - (a / (3.0 * b))
	else:
		tmp = 2.0 * (math.sqrt(x) * math.cos((y + ((z * t) * -0.3333333333333333))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -3.4e-153) || !(a <= 1.35e-193))
		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(Float64(z * t) * -0.3333333333333333)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -3.4e-153) || ~((a <= 1.35e-193)))
		tmp = (2.0 * sqrt(x)) - (a / (3.0 * b));
	else
		tmp = 2.0 * (sqrt(x) * cos((y + ((z * t) * -0.3333333333333333))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -3.4e-153], N[Not[LessEqual[a, 1.35e-193]], $MachinePrecision]], 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[(N[(z * t), $MachinePrecision] * -0.3333333333333333), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3.3999999999999998e-153 or 1.35e-193 < a

   1. Initial program 70.1%

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

      1. *-commutative 70.1%

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

      2. *-commutative 70.1%

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

      3. *-commutative 70.1%

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

      4. *-commutative 70.1%

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

      5. associate-/l* 70.0%

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

      6. *-commutative 70.0%

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

   3. Simplified 70.0%

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

   5. Taylor expanded in z around 0 76.0%

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

      1. associate-*r* 76.0%

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

      2. *-commutative 76.0%

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

      3. *-commutative 76.0%

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

   7. Simplified 76.0%

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

   8. Taylor expanded in y around 0 68.5%

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

   if -3.3999999999999998e-153 < a < 1.35e-193

   1. Initial program 62.5%

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

   3. Simplified 62.0%

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

   5. Taylor expanded in x around inf 58.1%

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

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.4 \cdot 10^{-153} \lor \neg \left(a \leq 1.35 \cdot 10^{-193}\right):\\ \;\;\;\;2 \cdot \sqrt{x} - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt{x} \cdot \cos \left(y + \left(z \cdot t\right) \cdot -0.3333333333333333\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 67.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -7 \cdot 10^{-233} \lor \neg \left(a \leq 9.8 \cdot 10^{-194}\right):\\ \;\;\;\;2 \cdot \sqrt{x} - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(\cos y \cdot \left(-\sqrt{x}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -7e-233) (not (<= a 9.8e-194)))
   (- (* 2.0 (sqrt x)) (/ a (* 3.0 b)))
   (* -2.0 (* (cos y) (- (sqrt x))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -7e-233) || !(a <= 9.8e-194)) {
		tmp = (2.0 * sqrt(x)) - (a / (3.0 * b));
	} else {
		tmp = -2.0 * (cos(y) * -sqrt(x));
	}
	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) :: tmp
    if ((a <= (-7d-233)) .or. (.not. (a <= 9.8d-194))) then
        tmp = (2.0d0 * sqrt(x)) - (a / (3.0d0 * b))
    else
        tmp = (-2.0d0) * (cos(y) * -sqrt(x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -7e-233) || !(a <= 9.8e-194)) {
		tmp = (2.0 * Math.sqrt(x)) - (a / (3.0 * b));
	} else {
		tmp = -2.0 * (Math.cos(y) * -Math.sqrt(x));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -7e-233) or not (a <= 9.8e-194):
		tmp = (2.0 * math.sqrt(x)) - (a / (3.0 * b))
	else:
		tmp = -2.0 * (math.cos(y) * -math.sqrt(x))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -7e-233) || !(a <= 9.8e-194))
		tmp = Float64(Float64(2.0 * sqrt(x)) - Float64(a / Float64(3.0 * b)));
	else
		tmp = Float64(-2.0 * Float64(cos(y) * Float64(-sqrt(x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -7e-233) || ~((a <= 9.8e-194)))
		tmp = (2.0 * sqrt(x)) - (a / (3.0 * b));
	else
		tmp = -2.0 * (cos(y) * -sqrt(x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -7e-233], N[Not[LessEqual[a, 9.8e-194]], $MachinePrecision]], N[(N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] - N[(a / N[(3.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-2.0 * N[(N[Cos[y], $MachinePrecision] * (-N[Sqrt[x], $MachinePrecision])), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -6.99999999999999982e-233 or 9.80000000000000008e-194 < a

   1. Initial program 68.5%

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

      1. *-commutative 68.5%

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

      2. *-commutative 68.5%

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

      3. *-commutative 68.5%

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

      4. *-commutative 68.5%

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

      5. associate-/l* 68.4%

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

      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 73.7%

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

      1. associate-*r* 73.7%

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

      2. *-commutative 73.7%

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

      3. *-commutative 73.7%

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

   7. Simplified 73.7%

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

   8. Taylor expanded in y around 0 66.1%

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

   if -6.99999999999999982e-233 < a < 9.80000000000000008e-194

   1. Initial program 68.6%

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

      1. *-commutative 68.6%

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

      2. *-commutative 68.6%

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

      3. *-commutative 68.6%

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

      4. *-commutative 68.6%

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

      5. associate-/l* 68.5%

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

      6. *-commutative 68.5%

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

   3. Simplified 68.5%

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

   5. Taylor expanded in z around 0 68.2%

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

      1. associate-*r* 68.2%

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

      2. *-commutative 68.2%

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

      3. *-commutative 68.2%

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

   7. Simplified 68.2%

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

      1. sub-neg 68.2%

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

      2. associate-/r* 68.2%

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

   9. Applied egg-rr 68.2%

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

   10. Taylor expanded in x around -inf 0.0%

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

       1. associate-*r* 0.0%

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

       2. unpow2 0.0%

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

       3. rem-square-sqrt 66.9%

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

   12. Simplified 66.9%

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

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -7 \cdot 10^{-233} \lor \neg \left(a \leq 9.8 \cdot 10^{-194}\right):\\ \;\;\;\;2 \cdot \sqrt{x} - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;-2 \cdot \left(\cos y \cdot \left(-\sqrt{x}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 76.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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

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

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

Julia

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

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

Wolfram

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 68.5%

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

   1. *-commutative 68.5%

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

   2. *-commutative 68.5%

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

   3. *-commutative 68.5%

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

   4. *-commutative 68.5%

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

   5. associate-/l* 68.4%

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

   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 72.8%

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

   1. associate-*r* 72.8%

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

   2. *-commutative 72.8%

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

   3. *-commutative 72.8%

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

7. Simplified 72.8%

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

8. Final simplification 72.8%

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

Alternative 8: 65.8% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ 2 \cdot \sqrt{x} - \frac{a}{3 \cdot b} \end{array} \]

FPCore

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

C

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

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)) - (a / (3.0d0 * b))
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)) - (a / (3.0 * b));
}

Python

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

Julia

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

MATLAB

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

Wolfram

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 68.5%

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

   1. *-commutative 68.5%

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

   2. *-commutative 68.5%

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

   3. *-commutative 68.5%

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

   4. *-commutative 68.5%

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

   5. associate-/l* 68.4%

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

   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 72.8%

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

   1. associate-*r* 72.8%

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

   2. *-commutative 72.8%

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

   3. *-commutative 72.8%

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

7. Simplified 72.8%

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

8. Taylor expanded in y around 0 62.3%

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

Alternative 9: 51.2% accurate, 43.4× speedup

Math

\[\begin{array}{l} \\ -0.3333333333333333 \cdot \frac{a}{b} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (* -0.3333333333333333 (/ a b)))

C

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

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 = (-0.3333333333333333d0) * (a / b)
end function

Java

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

Python

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

Julia

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

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = -0.3333333333333333 * (a / b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(-0.3333333333333333 * N[(a / b), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 68.5%

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

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 a around inf 45.5%

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

Developer Target 1: 74.5% 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 2024170 
(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))))