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

Percentage Accurate: 70.6% → 77.2%

Time: 37.0s

Alternatives: 13

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: 70.6% 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: 77.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \sin y \cdot \sin \left(t \cdot \frac{z}{-3}\right)\\ t_2 := 2 \cdot \sqrt{x}\\ t_3 := \cos \left(0.3333333333333333 \cdot \left(z \cdot t\right)\right)\\ t_4 := \cos y \cdot t\_3\\ \mathbf{if}\;t\_2 \cdot \cos \left(y - \frac{z \cdot t}{3}\right) \leq 10^{+140}:\\ \;\;\;\;t\_2 \cdot \frac{{t\_4}^{3} - {t\_1}^{3}}{\mathsf{fma}\left(t\_1, \mathsf{fma}\left(\cos y, t\_3, t\_1\right), t\_4 \cdot t\_4\right)} - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;t\_2 - \frac{\frac{a}{3}}{b}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (sin y) (sin (* t (/ z -3.0)))))
        (t_2 (* 2.0 (sqrt x)))
        (t_3 (cos (* 0.3333333333333333 (* z t))))
        (t_4 (* (cos y) t_3)))
   (if (<= (* t_2 (cos (- y (/ (* z t) 3.0)))) 1e+140)
     (-
      (*
       t_2
       (/
        (- (pow t_4 3.0) (pow t_1 3.0))
        (fma t_1 (fma (cos y) t_3 t_1) (* t_4 t_4))))
      (/ a (* 3.0 b)))
     (- t_2 (/ (/ a 3.0) b)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = sin(y) * sin((t * (z / -3.0)));
	double t_2 = 2.0 * sqrt(x);
	double t_3 = cos((0.3333333333333333 * (z * t)));
	double t_4 = cos(y) * t_3;
	double tmp;
	if ((t_2 * cos((y - ((z * t) / 3.0)))) <= 1e+140) {
		tmp = (t_2 * ((pow(t_4, 3.0) - pow(t_1, 3.0)) / fma(t_1, fma(cos(y), t_3, t_1), (t_4 * t_4)))) - (a / (3.0 * b));
	} else {
		tmp = t_2 - ((a / 3.0) / b);
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(sin(y) * sin(Float64(t * Float64(z / -3.0))))
	t_2 = Float64(2.0 * sqrt(x))
	t_3 = cos(Float64(0.3333333333333333 * Float64(z * t)))
	t_4 = Float64(cos(y) * t_3)
	tmp = 0.0
	if (Float64(t_2 * cos(Float64(y - Float64(Float64(z * t) / 3.0)))) <= 1e+140)
		tmp = Float64(Float64(t_2 * Float64(Float64((t_4 ^ 3.0) - (t_1 ^ 3.0)) / fma(t_1, fma(cos(y), t_3, t_1), Float64(t_4 * t_4)))) - Float64(a / Float64(3.0 * b)));
	else
		tmp = Float64(t_2 - Float64(Float64(a / 3.0) / b));
	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[(N[Sin[y], $MachinePrecision] * N[Sin[N[(t * N[(z / -3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[Cos[N[(0.3333333333333333 * N[(z * t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$4 = N[(N[Cos[y], $MachinePrecision] * t$95$3), $MachinePrecision]}, If[LessEqual[N[(t$95$2 * N[Cos[N[(y - N[(N[(z * t), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 1e+140], N[(N[(t$95$2 * N[(N[(N[Power[t$95$4, 3.0], $MachinePrecision] - N[Power[t$95$1, 3.0], $MachinePrecision]), $MachinePrecision] / N[(t$95$1 * N[(N[Cos[y], $MachinePrecision] * t$95$3 + t$95$1), $MachinePrecision] + N[(t$95$4 * t$95$4), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a / N[(3.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$2 - N[(N[(a / 3.0), $MachinePrecision] / b), $MachinePrecision]), $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))))) < 1.00000000000000006e140

   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* 78.0%

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

      6. *-commutative 78.0%

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

   3. Simplified 78.0%

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

   6. Applied egg-rr 79.7%

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

   8. Simplified 79.8%

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

   if 1.00000000000000006e140 < (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64)))))

   1. Initial program 21.9%

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

      1. *-commutative 21.9%

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

      2. *-commutative 21.9%

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

      3. *-commutative 21.9%

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

      4. *-commutative 21.9%

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

      5. associate-/l* 21.9%

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

      6. *-commutative 21.9%

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

   3. Simplified 21.9%

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

   5. Taylor expanded in z around 0 53.1%

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

   6. Taylor expanded in y around 0 54.8%

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

      1. *-commutative 54.8%

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

      2. associate-/r* 54.9%

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

      3. div-inv 54.9%

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

      4. metadata-eval 54.9%

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

   8. Applied egg-rr 54.9%

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

      1. metadata-eval 54.9%

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

      2. div-inv 54.9%

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

      3. associate-/l/ 54.8%

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

      4. associate-/r* 55.0%

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

   10. Applied egg-rr 55.0%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) \leq 10^{+140}:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \frac{{\left(\cos y \cdot \cos \left(0.3333333333333333 \cdot \left(z \cdot t\right)\right)\right)}^{3} - {\left(\sin y \cdot \sin \left(t \cdot \frac{z}{-3}\right)\right)}^{3}}{\mathsf{fma}\left(\sin y \cdot \sin \left(t \cdot \frac{z}{-3}\right), \mathsf{fma}\left(\cos y, \cos \left(0.3333333333333333 \cdot \left(z \cdot t\right)\right), \sin y \cdot \sin \left(t \cdot \frac{z}{-3}\right)\right), \left(\cos y \cdot \cos \left(0.3333333333333333 \cdot \left(z \cdot t\right)\right)\right) \cdot \left(\cos y \cdot \cos \left(0.3333333333333333 \cdot \left(z \cdot t\right)\right)\right)\right)} - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{x} - \frac{\frac{a}{3}}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 77.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := 2 \cdot \sqrt{x}\\ t_2 := 0.3333333333333333 \cdot \left(z \cdot t\right)\\ \mathbf{if}\;t\_1 \cdot \cos \left(y - \frac{z \cdot t}{3}\right) \leq 10^{+140}:\\ \;\;\;\;t\_1 \cdot \mathsf{fma}\left(\cos y, \cos t\_2, \sin y \cdot \sin t\_2\right) - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;t\_1 - \frac{\frac{a}{3}}{b}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* 2.0 (sqrt x))) (t_2 (* 0.3333333333333333 (* z t))))
   (if (<= (* t_1 (cos (- y (/ (* z t) 3.0)))) 1e+140)
     (- (* t_1 (fma (cos y) (cos t_2) (* (sin y) (sin t_2)))) (/ a (* 3.0 b)))
     (- t_1 (/ (/ a 3.0) b)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 2.0 * sqrt(x);
	double t_2 = 0.3333333333333333 * (z * t);
	double tmp;
	if ((t_1 * cos((y - ((z * t) / 3.0)))) <= 1e+140) {
		tmp = (t_1 * fma(cos(y), cos(t_2), (sin(y) * sin(t_2)))) - (a / (3.0 * b));
	} else {
		tmp = t_1 - ((a / 3.0) / b);
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(2.0 * sqrt(x))
	t_2 = Float64(0.3333333333333333 * Float64(z * t))
	tmp = 0.0
	if (Float64(t_1 * cos(Float64(y - Float64(Float64(z * t) / 3.0)))) <= 1e+140)
		tmp = Float64(Float64(t_1 * fma(cos(y), cos(t_2), Float64(sin(y) * sin(t_2)))) - Float64(a / Float64(3.0 * b)));
	else
		tmp = Float64(t_1 - Float64(Float64(a / 3.0) / b));
	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[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(0.3333333333333333 * N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$1 * N[Cos[N[(y - N[(N[(z * t), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 1e+140], N[(N[(t$95$1 * N[(N[Cos[y], $MachinePrecision] * N[Cos[t$95$2], $MachinePrecision] + N[(N[Sin[y], $MachinePrecision] * N[Sin[t$95$2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a / N[(3.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 - N[(N[(a / 3.0), $MachinePrecision] / b), $MachinePrecision]), $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))))) < 1.00000000000000006e140

   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* 78.0%

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

      6. *-commutative 78.0%

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

   3. Simplified 78.0%

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

   6. Applied egg-rr 79.7%

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

      1. fma-define 79.7%

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

      2. associate-*l* 79.9%

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

      3. *-commutative 79.9%

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

      4. associate-*r* 79.8%

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

      5. *-commutative 79.8%

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

      6. metadata-eval 79.8%

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

      7. *-commutative 79.8%

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

      8. distribute-lft-neg-in 79.8%

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

      9. cos-neg 79.8%

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

      10. distribute-rgt-neg-in 79.8%

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

      11. associate-*l* 79.8%

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

      12. *-commutative 79.8%

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

      13. associate-*r* 79.8%

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

      14. *-commutative 79.8%

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

      15. metadata-eval 79.8%

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

      16. *-commutative 79.8%

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

      17. distribute-lft-neg-in 79.8%

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

      18. sin-neg 79.8%

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

      19. remove-double-neg 79.8%

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

   8. Simplified 79.8%

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

   if 1.00000000000000006e140 < (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64)))))

   1. Initial program 21.9%

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

      1. *-commutative 21.9%

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

      2. *-commutative 21.9%

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

      3. *-commutative 21.9%

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

      4. *-commutative 21.9%

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

      5. associate-/l* 21.9%

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

      6. *-commutative 21.9%

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

   3. Simplified 21.9%

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

   5. Taylor expanded in z around 0 53.1%

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

   6. Taylor expanded in y around 0 54.8%

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

      1. *-commutative 54.8%

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

      2. associate-/r* 54.9%

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

      3. div-inv 54.9%

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

      4. metadata-eval 54.9%

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

   8. Applied egg-rr 54.9%

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

      1. metadata-eval 54.9%

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

      2. div-inv 54.9%

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

      3. associate-/l/ 54.8%

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

      4. associate-/r* 55.0%

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

   10. Applied egg-rr 55.0%

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

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) \leq 10^{+140}:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos y, \cos \left(0.3333333333333333 \cdot \left(z \cdot t\right)\right), \sin y \cdot \sin \left(0.3333333333333333 \cdot \left(z \cdot t\right)\right)\right) - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{x} - \frac{\frac{a}{3}}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 77.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := 2 \cdot \sqrt{x}\\ t_2 := t \cdot \left(z \cdot -0.3333333333333333\right)\\ \mathbf{if}\;t\_1 \cdot \cos \left(y - \frac{z \cdot t}{3}\right) \leq 10^{+140}:\\ \;\;\;\;t\_1 \cdot \left(\cos y \cdot \cos t\_2 - \sin y \cdot \sin t\_2\right) - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;t\_1 - \frac{\frac{a}{3}}{b}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* 2.0 (sqrt x))) (t_2 (* t (* z -0.3333333333333333))))
   (if (<= (* t_1 (cos (- y (/ (* z t) 3.0)))) 1e+140)
     (-
      (* t_1 (- (* (cos y) (cos t_2)) (* (sin y) (sin t_2))))
      (/ a (* 3.0 b)))
     (- t_1 (/ (/ a 3.0) b)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 2.0 * sqrt(x);
	double t_2 = t * (z * -0.3333333333333333);
	double tmp;
	if ((t_1 * cos((y - ((z * t) / 3.0)))) <= 1e+140) {
		tmp = (t_1 * ((cos(y) * cos(t_2)) - (sin(y) * sin(t_2)))) - (a / (3.0 * b));
	} else {
		tmp = t_1 - ((a / 3.0) / b);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 2.0d0 * sqrt(x)
    t_2 = t * (z * (-0.3333333333333333d0))
    if ((t_1 * cos((y - ((z * t) / 3.0d0)))) <= 1d+140) then
        tmp = (t_1 * ((cos(y) * cos(t_2)) - (sin(y) * sin(t_2)))) - (a / (3.0d0 * b))
    else
        tmp = t_1 - ((a / 3.0d0) / b)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 2.0 * Math.sqrt(x);
	double t_2 = t * (z * -0.3333333333333333);
	double tmp;
	if ((t_1 * Math.cos((y - ((z * t) / 3.0)))) <= 1e+140) {
		tmp = (t_1 * ((Math.cos(y) * Math.cos(t_2)) - (Math.sin(y) * Math.sin(t_2)))) - (a / (3.0 * b));
	} else {
		tmp = t_1 - ((a / 3.0) / b);
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = 2.0 * math.sqrt(x)
	t_2 = t * (z * -0.3333333333333333)
	tmp = 0
	if (t_1 * math.cos((y - ((z * t) / 3.0)))) <= 1e+140:
		tmp = (t_1 * ((math.cos(y) * math.cos(t_2)) - (math.sin(y) * math.sin(t_2)))) - (a / (3.0 * b))
	else:
		tmp = t_1 - ((a / 3.0) / b)
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(2.0 * sqrt(x))
	t_2 = Float64(t * Float64(z * -0.3333333333333333))
	tmp = 0.0
	if (Float64(t_1 * cos(Float64(y - Float64(Float64(z * t) / 3.0)))) <= 1e+140)
		tmp = Float64(Float64(t_1 * Float64(Float64(cos(y) * cos(t_2)) - Float64(sin(y) * sin(t_2)))) - Float64(a / Float64(3.0 * b)));
	else
		tmp = Float64(t_1 - Float64(Float64(a / 3.0) / b));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 2.0 * sqrt(x);
	t_2 = t * (z * -0.3333333333333333);
	tmp = 0.0;
	if ((t_1 * cos((y - ((z * t) / 3.0)))) <= 1e+140)
		tmp = (t_1 * ((cos(y) * cos(t_2)) - (sin(y) * sin(t_2)))) - (a / (3.0 * b));
	else
		tmp = t_1 - ((a / 3.0) / b);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(z * -0.3333333333333333), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$1 * N[Cos[N[(y - N[(N[(z * t), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 1e+140], N[(N[(t$95$1 * N[(N[(N[Cos[y], $MachinePrecision] * N[Cos[t$95$2], $MachinePrecision]), $MachinePrecision] - N[(N[Sin[y], $MachinePrecision] * N[Sin[t$95$2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a / N[(3.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 - N[(N[(a / 3.0), $MachinePrecision] / b), $MachinePrecision]), $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))))) < 1.00000000000000006e140

   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* 78.0%

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

      6. *-commutative 78.0%

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

   3. Simplified 78.0%

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

      1. associate-*r/ 77.9%

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

      2. div-inv 78.0%

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

      3. metadata-eval 78.0%

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

      4. metadata-eval 78.0%

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

      5. cancel-sign-sub-inv 78.0%

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

      6. metadata-eval 78.0%

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

      7. metadata-eval 78.0%

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

      8. div-inv 77.9%

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

      9. metadata-eval 77.9%

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

      10. frac-2neg 77.9%

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

      11. +-commutative 77.9%

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

      12. cos-sum 79.6%

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

      13. div-inv 79.7%

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

      14. metadata-eval 79.7%

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

      15. associate-*r* 79.8%

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

      16. *-commutative 79.8%

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

      17. associate-*r* 79.5%

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

   6. Applied egg-rr 79.7%

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

   if 1.00000000000000006e140 < (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64)))))

   1. Initial program 21.9%

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

      1. *-commutative 21.9%

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

      2. *-commutative 21.9%

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

      3. *-commutative 21.9%

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

      4. *-commutative 21.9%

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

      5. associate-/l* 21.9%

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

      6. *-commutative 21.9%

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

   3. Simplified 21.9%

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

   5. Taylor expanded in z around 0 53.1%

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

   6. Taylor expanded in y around 0 54.8%

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

      1. *-commutative 54.8%

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

      2. associate-/r* 54.9%

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

      3. div-inv 54.9%

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

      4. metadata-eval 54.9%

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

   8. Applied egg-rr 54.9%

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

      1. metadata-eval 54.9%

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

      2. div-inv 54.9%

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

      3. associate-/l/ 54.8%

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

      4. associate-/r* 55.0%

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

   10. Applied egg-rr 55.0%

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

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) \leq 10^{+140}:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \left(\cos y \cdot \cos \left(t \cdot \left(z \cdot -0.3333333333333333\right)\right) - \sin y \cdot \sin \left(t \cdot \left(z \cdot -0.3333333333333333\right)\right)\right) - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{x} - \frac{\frac{a}{3}}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 77.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := 2 \cdot \sqrt{x}\\ \mathbf{if}\;t\_1 \cdot \cos \left(y - \frac{z \cdot t}{3}\right) \leq 10^{+140}:\\ \;\;\;\;t\_1 \cdot \left(\cos y \cdot \cos \left(z \cdot \left(t \cdot 0.3333333333333333\right)\right) - \sin y \cdot \sin \left(t \cdot \left(z \cdot -0.3333333333333333\right)\right)\right) - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;t\_1 - \frac{\frac{a}{3}}{b}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* 2.0 (sqrt x))))
   (if (<= (* t_1 (cos (- y (/ (* z t) 3.0)))) 1e+140)
     (-
      (*
       t_1
       (-
        (* (cos y) (cos (* z (* t 0.3333333333333333))))
        (* (sin y) (sin (* t (* z -0.3333333333333333))))))
      (/ a (* 3.0 b)))
     (- t_1 (/ (/ a 3.0) b)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 2.0 * sqrt(x);
	double tmp;
	if ((t_1 * cos((y - ((z * t) / 3.0)))) <= 1e+140) {
		tmp = (t_1 * ((cos(y) * cos((z * (t * 0.3333333333333333)))) - (sin(y) * sin((t * (z * -0.3333333333333333)))))) - (a / (3.0 * b));
	} else {
		tmp = t_1 - ((a / 3.0) / b);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * sqrt(x)
    if ((t_1 * cos((y - ((z * t) / 3.0d0)))) <= 1d+140) then
        tmp = (t_1 * ((cos(y) * cos((z * (t * 0.3333333333333333d0)))) - (sin(y) * sin((t * (z * (-0.3333333333333333d0))))))) - (a / (3.0d0 * b))
    else
        tmp = t_1 - ((a / 3.0d0) / b)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 2.0 * Math.sqrt(x);
	double tmp;
	if ((t_1 * Math.cos((y - ((z * t) / 3.0)))) <= 1e+140) {
		tmp = (t_1 * ((Math.cos(y) * Math.cos((z * (t * 0.3333333333333333)))) - (Math.sin(y) * Math.sin((t * (z * -0.3333333333333333)))))) - (a / (3.0 * b));
	} else {
		tmp = t_1 - ((a / 3.0) / b);
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = 2.0 * math.sqrt(x)
	tmp = 0
	if (t_1 * math.cos((y - ((z * t) / 3.0)))) <= 1e+140:
		tmp = (t_1 * ((math.cos(y) * math.cos((z * (t * 0.3333333333333333)))) - (math.sin(y) * math.sin((t * (z * -0.3333333333333333)))))) - (a / (3.0 * b))
	else:
		tmp = t_1 - ((a / 3.0) / b)
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(2.0 * sqrt(x))
	tmp = 0.0
	if (Float64(t_1 * cos(Float64(y - Float64(Float64(z * t) / 3.0)))) <= 1e+140)
		tmp = Float64(Float64(t_1 * Float64(Float64(cos(y) * cos(Float64(z * Float64(t * 0.3333333333333333)))) - Float64(sin(y) * sin(Float64(t * Float64(z * -0.3333333333333333)))))) - Float64(a / Float64(3.0 * b)));
	else
		tmp = Float64(t_1 - Float64(Float64(a / 3.0) / b));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 2.0 * sqrt(x);
	tmp = 0.0;
	if ((t_1 * cos((y - ((z * t) / 3.0)))) <= 1e+140)
		tmp = (t_1 * ((cos(y) * cos((z * (t * 0.3333333333333333)))) - (sin(y) * sin((t * (z * -0.3333333333333333)))))) - (a / (3.0 * b));
	else
		tmp = t_1 - ((a / 3.0) / b);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$1 * N[Cos[N[(y - N[(N[(z * t), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 1e+140], N[(N[(t$95$1 * 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[(t * N[(z * -0.3333333333333333), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a / N[(3.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 - N[(N[(a / 3.0), $MachinePrecision] / b), $MachinePrecision]), $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))))) < 1.00000000000000006e140

   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* 78.0%

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

      6. *-commutative 78.0%

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

   3. Simplified 78.0%

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

   6. Applied egg-rr 79.7%

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

      1. sub-neg 79.7%

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

      2. *-rgt-identity 79.7%

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

      3. *-rgt-identity 79.7%

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

      4. associate-*l* 79.9%

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

      5. *-commutative 79.9%

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

      6. associate-*r* 79.8%

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

      7. *-commutative 79.8%

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

      8. metadata-eval 79.8%

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

      9. *-commutative 79.8%

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

      10. distribute-lft-neg-in 79.8%

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

      11. cos-neg 79.8%

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

      12. *-commutative 79.8%

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

      13. *-commutative 79.8%

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

      14. associate-*l* 79.9%

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

      15. *-commutative 79.9%

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

   8. Simplified 79.9%

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

   if 1.00000000000000006e140 < (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64)))))

   1. Initial program 21.9%

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

      1. *-commutative 21.9%

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

      2. *-commutative 21.9%

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

      3. *-commutative 21.9%

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

      4. *-commutative 21.9%

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

      5. associate-/l* 21.9%

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

      6. *-commutative 21.9%

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

   3. Simplified 21.9%

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

   5. Taylor expanded in z around 0 53.1%

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

   6. Taylor expanded in y around 0 54.8%

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

      1. *-commutative 54.8%

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

      2. associate-/r* 54.9%

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

      3. div-inv 54.9%

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

      4. metadata-eval 54.9%

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

   8. Applied egg-rr 54.9%

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

      1. metadata-eval 54.9%

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

      2. div-inv 54.9%

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

      3. associate-/l/ 54.8%

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

      4. associate-/r* 55.0%

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

   10. Applied egg-rr 55.0%

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

Alternative 5: 76.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 68.7%

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

   1. *-commutative 68.7%

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

   2. *-commutative 68.7%

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

   3. *-commutative 68.7%

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

   4. *-commutative 68.7%

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

   5. associate-/l* 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 73.5%

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

   1. *-commutative 73.5%

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

   2. clear-num 73.4%

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

   3. inv-pow 73.4%

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

   4. *-commutative 73.4%

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

   5. *-un-lft-identity 73.4%

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

   6. times-frac 73.5%

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

   7. metadata-eval 73.5%

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

7. Applied egg-rr 73.5%

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

   1. unpow-1 73.5%

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

   2. metadata-eval 73.5%

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

   3. *-commutative 73.5%

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

   4. associate-/r* 73.5%

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

   5. metadata-eval 73.5%

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

   6. clear-num 73.5%

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

9. Applied egg-rr 73.5%

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

Alternative 6: 76.4% 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 68.7%

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

   1. *-commutative 68.7%

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

   2. *-commutative 68.7%

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

   3. *-commutative 68.7%

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

   4. *-commutative 68.7%

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

   5. associate-/l* 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 73.5%

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

Alternative 7: 76.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 68.7%

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

   1. *-commutative 68.7%

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

   2. *-commutative 68.7%

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

   3. *-commutative 68.7%

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

   4. *-commutative 68.7%

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

   5. associate-/l* 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 73.5%

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

   1. *-commutative 64.6%

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

   2. associate-/r* 64.6%

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

   3. div-inv 64.5%

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

   4. metadata-eval 64.5%

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

7. Applied egg-rr 73.4%

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

8. Final simplification 73.4%

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

Alternative 8: 65.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -5.6 \cdot 10^{+107}:\\ \;\;\;\;2 \cdot \left(\sqrt{x} \cdot \cos y\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{x} - \frac{\frac{a}{b}}{3}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -5.6e+107)
   (* 2.0 (* (sqrt x) (cos y)))
   (- (* 2.0 (sqrt x)) (/ (/ a b) 3.0))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -5.6e+107) {
		tmp = 2.0 * (sqrt(x) * cos(y));
	} else {
		tmp = (2.0 * sqrt(x)) - ((a / b) / 3.0);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= (-5.6d+107)) then
        tmp = 2.0d0 * (sqrt(x) * cos(y))
    else
        tmp = (2.0d0 * sqrt(x)) - ((a / b) / 3.0d0)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -5.6e+107) {
		tmp = 2.0 * (Math.sqrt(x) * Math.cos(y));
	} else {
		tmp = (2.0 * Math.sqrt(x)) - ((a / b) / 3.0);
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -5.6e+107:
		tmp = 2.0 * (math.sqrt(x) * math.cos(y))
	else:
		tmp = (2.0 * math.sqrt(x)) - ((a / b) / 3.0)
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -5.6e+107)
		tmp = Float64(2.0 * Float64(sqrt(x) * cos(y)));
	else
		tmp = Float64(Float64(2.0 * sqrt(x)) - Float64(Float64(a / b) / 3.0));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -5.6e+107)
		tmp = 2.0 * (sqrt(x) * cos(y));
	else
		tmp = (2.0 * sqrt(x)) - ((a / b) / 3.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -5.6e+107], N[(2.0 * N[(N[Sqrt[x], $MachinePrecision] * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] - N[(N[(a / b), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -5.59999999999999969e107

   1. Initial program 57.7%

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

      1. *-commutative 57.7%

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

      2. *-commutative 57.7%

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

      3. *-commutative 57.7%

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

      4. *-commutative 57.7%

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

      5. associate-/l* 57.4%

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

      6. *-commutative 57.4%

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

   3. Simplified 57.4%

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

   5. Taylor expanded in z around 0 57.0%

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

      1. *-commutative 57.0%

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

      2. clear-num 57.0%

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

      3. inv-pow 57.0%

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

      4. *-commutative 57.0%

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

      5. *-un-lft-identity 57.0%

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

      6. times-frac 57.0%

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

      7. metadata-eval 57.0%

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

   7. Applied egg-rr 57.0%

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

      1. unpow-1 57.0%

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

      2. metadata-eval 57.0%

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

      3. *-commutative 57.0%

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

      4. associate-/r* 57.0%

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

      5. metadata-eval 57.0%

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

      6. clear-num 57.0%

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

   9. Applied egg-rr 57.0%

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

   10. Taylor expanded in x around inf 50.1%

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

   if -5.59999999999999969e107 < b

   1. Initial program 71.7%

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

      1. *-commutative 71.7%

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

      2. *-commutative 71.7%

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

      3. *-commutative 71.7%

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

      4. *-commutative 71.7%

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

      5. associate-/l* 71.9%

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

      6. *-commutative 71.9%

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

   3. Simplified 71.9%

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

   5. Taylor expanded in z around 0 78.0%

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

   6. Taylor expanded in y around 0 71.7%

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

      1. *-commutative 71.7%

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

      2. associate-/r* 71.8%

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

      3. div-inv 71.6%

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

      4. metadata-eval 71.6%

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

   8. Applied egg-rr 71.6%

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

      1. metadata-eval 71.6%

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

      2. div-inv 71.8%

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

   10. Applied egg-rr 71.8%

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

Alternative 9: 53.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -3.7 \cdot 10^{-122} \lor \neg \left(a \leq 3 \cdot 10^{-136}\right):\\ \;\;\;\;a \cdot \frac{-0.3333333333333333}{b}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{x}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -3.7e-122) (not (<= a 3e-136)))
   (* a (/ -0.3333333333333333 b))
   (* 2.0 (sqrt x))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -3.7e-122) || !(a <= 3e-136)) {
		tmp = a * (-0.3333333333333333 / b);
	} else {
		tmp = 2.0 * sqrt(x);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((a <= (-3.7d-122)) .or. (.not. (a <= 3d-136))) then
        tmp = a * ((-0.3333333333333333d0) / b)
    else
        tmp = 2.0d0 * sqrt(x)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -3.7e-122) || !(a <= 3e-136)) {
		tmp = a * (-0.3333333333333333 / b);
	} else {
		tmp = 2.0 * Math.sqrt(x);
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -3.7e-122) or not (a <= 3e-136):
		tmp = a * (-0.3333333333333333 / b)
	else:
		tmp = 2.0 * math.sqrt(x)
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -3.7e-122) || !(a <= 3e-136))
		tmp = Float64(a * Float64(-0.3333333333333333 / b));
	else
		tmp = Float64(2.0 * sqrt(x));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -3.7e-122) || ~((a <= 3e-136)))
		tmp = a * (-0.3333333333333333 / b);
	else
		tmp = 2.0 * sqrt(x);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -3.7e-122], N[Not[LessEqual[a, 3e-136]], $MachinePrecision]], N[(a * N[(-0.3333333333333333 / b), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3.6999999999999997e-122 or 2.9999999999999998e-136 < a

   1. Initial program 73.8%

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

      1. *-commutative 73.8%

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

      2. *-commutative 73.8%

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

      3. *-commutative 73.8%

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

      4. *-commutative 73.8%

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

      5. associate-/l* 73.8%

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

      6. *-commutative 73.8%

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

   3. Simplified 73.8%

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

   5. Taylor expanded in z around 0 78.9%

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

      1. *-commutative 78.9%

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

      2. clear-num 78.8%

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

      3. inv-pow 78.8%

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

      4. *-commutative 78.8%

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

      5. *-un-lft-identity 78.8%

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

      6. times-frac 78.8%

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

      7. metadata-eval 78.8%

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

   7. Applied egg-rr 78.8%

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

      1. unpow-1 78.8%

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

      2. metadata-eval 78.8%

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

      3. *-commutative 78.8%

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

      4. associate-/r* 78.8%

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

      5. metadata-eval 78.8%

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

      6. clear-num 78.9%

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

   9. Applied egg-rr 78.9%

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

   10. Taylor expanded in a around inf 60.6%

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

       1. *-commutative 60.6%

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

       2. associate-*l/ 60.6%

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

       3. associate-/l* 60.6%

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

   12. Simplified 60.6%

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

   if -3.6999999999999997e-122 < a < 2.9999999999999998e-136

   1. Initial program 55.7%

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

      1. *-commutative 55.7%

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

      2. *-commutative 55.7%

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

      3. *-commutative 55.7%

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

      4. *-commutative 55.7%

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

      5. associate-/l* 56.0%

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

      6. *-commutative 56.0%

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

   3. Simplified 56.0%

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

   5. Taylor expanded in z around 0 59.7%

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

   6. Taylor expanded in y around 0 49.5%

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

      1. *-commutative 49.5%

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

      2. associate-/r* 49.6%

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

      3. div-inv 49.5%

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

      4. metadata-eval 49.5%

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

   8. Applied egg-rr 49.5%

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

   9. Taylor expanded in x around inf 38.3%

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

4. Final simplification 54.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.7 \cdot 10^{-122} \lor \neg \left(a \leq 3 \cdot 10^{-136}\right):\\ \;\;\;\;a \cdot \frac{-0.3333333333333333}{b}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 65.0% accurate, 2.0× speedup

Math

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

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(Float64(a / 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[(N[(a / 3.0), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 68.7%

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

   1. *-commutative 68.7%

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

   2. *-commutative 68.7%

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

   3. *-commutative 68.7%

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

   4. *-commutative 68.7%

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

   5. associate-/l* 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 73.5%

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

6. Taylor expanded in y around 0 64.6%

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

   1. *-commutative 64.6%

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

   2. associate-/r* 64.6%

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

   3. div-inv 64.5%

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

   4. metadata-eval 64.5%

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

8. Applied egg-rr 64.5%

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

   1. metadata-eval 64.5%

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

   2. div-inv 64.6%

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

   3. associate-/l/ 64.6%

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

   4. associate-/r* 64.6%

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

10. Applied egg-rr 64.6%

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

Alternative 11: 65.0% 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 68.7%

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

   1. *-commutative 68.7%

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

   2. *-commutative 68.7%

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

   3. *-commutative 68.7%

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

   4. *-commutative 68.7%

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

   5. associate-/l* 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 73.5%

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

6. Taylor expanded in y around 0 64.6%

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

Alternative 12: 64.9% accurate, 2.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 68.7%

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

   1. *-commutative 68.7%

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

   2. *-commutative 68.7%

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

   3. *-commutative 68.7%

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

   4. *-commutative 68.7%

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

   5. associate-/l* 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 73.5%

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

6. Taylor expanded in y around 0 64.6%

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

   1. *-commutative 64.6%

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

   2. associate-/r* 64.6%

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

   3. div-inv 64.5%

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

   4. metadata-eval 64.5%

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

8. Applied egg-rr 64.5%

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

9. Final simplification 64.5%

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

Alternative 13: 50.8% accurate, 43.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 68.7%

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

   1. *-commutative 68.7%

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

   2. *-commutative 68.7%

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

   3. *-commutative 68.7%

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

   4. *-commutative 68.7%

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

   5. associate-/l* 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 73.5%

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

   1. *-commutative 73.5%

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

   2. clear-num 73.4%

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

   3. inv-pow 73.4%

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

   4. *-commutative 73.4%

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

   5. *-un-lft-identity 73.4%

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

   6. times-frac 73.5%

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

   7. metadata-eval 73.5%

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

7. Applied egg-rr 73.5%

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

   1. unpow-1 73.5%

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

   2. metadata-eval 73.5%

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

   3. *-commutative 73.5%

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

   4. associate-/r* 73.5%

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

   5. metadata-eval 73.5%

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

   6. clear-num 73.5%

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

9. Applied egg-rr 73.5%

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

10. Taylor expanded in a around inf 47.6%

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

    1. *-commutative 47.6%

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

    2. associate-*l/ 47.7%

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

    3. associate-/l* 47.6%

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

12. Simplified 47.6%

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

Developer target: 74.6% 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 2024092 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, K"
  :precision binary64

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

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