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

Percentage Accurate: 69.6% → 77.0%

Time: 38.4s

Alternatives: 12

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 69.6% 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: 77.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := t \cdot \left(z \cdot -0.3333333333333333\right)\\ t_2 := \frac{a}{3 \cdot b}\\ t_3 := 2 \cdot \sqrt{x}\\ \mathbf{if}\;t\_3 \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - t\_2 \leq 2 \cdot 10^{+151}:\\ \;\;\;\;t\_3 \cdot \left(\cos t\_1 \cdot \cos y - \sin t\_1 \cdot \sin y\right) - t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3 - \frac{a \cdot 0.3333333333333333}{b}\\ \end{array} \end{array} \]

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 (* t (* z -0.3333333333333333)))
        (t_2 (/ a (* 3.0 b)))
        (t_3 (* 2.0 (sqrt x))))
   (if (<= (- (* t_3 (cos (- y (/ (* z t) 3.0)))) t_2) 2e+151)
     (- (* t_3 (- (* (cos t_1) (cos y)) (* (sin t_1) (sin y)))) t_2)
     (- t_3 (/ (* 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) {
	double t_1 = t * (z * -0.3333333333333333);
	double t_2 = a / (3.0 * b);
	double t_3 = 2.0 * sqrt(x);
	double tmp;
	if (((t_3 * cos((y - ((z * t) / 3.0)))) - t_2) <= 2e+151) {
		tmp = (t_3 * ((cos(t_1) * cos(y)) - (sin(t_1) * sin(y)))) - t_2;
	} else {
		tmp = t_3 - ((a * 0.3333333333333333) / 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) :: t_3
    real(8) :: tmp
    t_1 = t * (z * (-0.3333333333333333d0))
    t_2 = a / (3.0d0 * b)
    t_3 = 2.0d0 * sqrt(x)
    if (((t_3 * cos((y - ((z * t) / 3.0d0)))) - t_2) <= 2d+151) then
        tmp = (t_3 * ((cos(t_1) * cos(y)) - (sin(t_1) * sin(y)))) - t_2
    else
        tmp = t_3 - ((a * 0.3333333333333333d0) / 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 = t * (z * -0.3333333333333333);
	double t_2 = a / (3.0 * b);
	double t_3 = 2.0 * Math.sqrt(x);
	double tmp;
	if (((t_3 * Math.cos((y - ((z * t) / 3.0)))) - t_2) <= 2e+151) {
		tmp = (t_3 * ((Math.cos(t_1) * Math.cos(y)) - (Math.sin(t_1) * Math.sin(y)))) - t_2;
	} else {
		tmp = t_3 - ((a * 0.3333333333333333) / 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 = t * (z * -0.3333333333333333)
	t_2 = a / (3.0 * b)
	t_3 = 2.0 * math.sqrt(x)
	tmp = 0
	if ((t_3 * math.cos((y - ((z * t) / 3.0)))) - t_2) <= 2e+151:
		tmp = (t_3 * ((math.cos(t_1) * math.cos(y)) - (math.sin(t_1) * math.sin(y)))) - t_2
	else:
		tmp = t_3 - ((a * 0.3333333333333333) / 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(t * Float64(z * -0.3333333333333333))
	t_2 = Float64(a / Float64(3.0 * b))
	t_3 = Float64(2.0 * sqrt(x))
	tmp = 0.0
	if (Float64(Float64(t_3 * cos(Float64(y - Float64(Float64(z * t) / 3.0)))) - t_2) <= 2e+151)
		tmp = Float64(Float64(t_3 * Float64(Float64(cos(t_1) * cos(y)) - Float64(sin(t_1) * sin(y)))) - t_2);
	else
		tmp = Float64(t_3 - Float64(Float64(a * 0.3333333333333333) / 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 = t * (z * -0.3333333333333333);
	t_2 = a / (3.0 * b);
	t_3 = 2.0 * sqrt(x);
	tmp = 0.0;
	if (((t_3 * cos((y - ((z * t) / 3.0)))) - t_2) <= 2e+151)
		tmp = (t_3 * ((cos(t_1) * cos(y)) - (sin(t_1) * sin(y)))) - t_2;
	else
		tmp = t_3 - ((a * 0.3333333333333333) / 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[(t * N[(z * -0.3333333333333333), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a / N[(3.0 * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(t$95$3 * N[Cos[N[(y - N[(N[(z * t), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], 2e+151], N[(N[(t$95$3 * N[(N[(N[Cos[t$95$1], $MachinePrecision] * N[Cos[y], $MachinePrecision]), $MachinePrecision] - N[(N[Sin[t$95$1], $MachinePrecision] * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], N[(t$95$3 - N[(N[(a * 0.3333333333333333), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64))))) (/.f64 a (*.f64 b #s(literal 3 binary64)))) < 2.00000000000000003e151

   1. Initial program 75.5%

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

      1. *-commutative 75.5%

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

      2. *-commutative 75.5%

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

      3. *-commutative 75.5%

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

      4. *-commutative 75.5%

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

      5. associate-/l* 75.1%

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

      6. *-commutative 75.1%

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

   3. Simplified 75.1%

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

      1. associate-*r/ 75.5%

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

      2. div-inv 75.5%

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

      3. metadata-eval 75.5%

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

      4. metadata-eval 75.5%

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

      5. cancel-sign-sub-inv 75.5%

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

      6. metadata-eval 75.5%

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

      7. metadata-eval 75.5%

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

      8. div-inv 75.5%

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

      9. metadata-eval 75.5%

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

      10. frac-2neg 75.5%

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

      11. +-commutative 75.5%

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

      12. cos-sum 75.6%

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

   6. Applied egg-rr 75.5%

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

   if 2.00000000000000003e151 < (-.f64 (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64))))) (/.f64 a (*.f64 b #s(literal 3 binary64))))

   1. Initial program 58.6%

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

      1. *-commutative 58.6%

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

      2. *-commutative 58.6%

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

      3. *-commutative 58.6%

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

      4. *-commutative 58.6%

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

      5. associate-/l* 60.1%

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

      6. *-commutative 60.1%

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

   3. Simplified 60.1%

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

   5. Taylor expanded in z around 0 85.1%

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

   6. Taylor expanded in a around 0 85.0%

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

      1. associate-*r/ 85.2%

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

   8. Simplified 85.2%

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

   9. Taylor expanded in y around 0 85.6%

      \[\leadsto \color{blue}{2 \cdot \sqrt{x}} - \frac{0.3333333333333333 \cdot a}{b} \]
3. Recombined 2 regimes into one program.

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{3 \cdot b} \leq 2 \cdot 10^{+151}:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \left(\cos \left(t \cdot \left(z \cdot -0.3333333333333333\right)\right) \cdot \cos y - \sin \left(t \cdot \left(z \cdot -0.3333333333333333\right)\right) \cdot \sin y\right) - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{x} - \frac{a \cdot 0.3333333333333333}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 76.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := t \cdot \left(z \cdot -0.3333333333333333\right)\\ t_2 := \frac{a}{3 \cdot b}\\ t_3 := 2 \cdot \sqrt{x}\\ \mathbf{if}\;t\_3 \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - t\_2 \leq 2 \cdot 10^{+151}:\\ \;\;\;\;t\_3 \cdot \left(\cos t\_1 \cdot \cos y + \sin t\_1 \cdot \sin y\right) - t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3 - \frac{a \cdot 0.3333333333333333}{b}\\ \end{array} \end{array} \]

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 (* t (* z -0.3333333333333333)))
        (t_2 (/ a (* 3.0 b)))
        (t_3 (* 2.0 (sqrt x))))
   (if (<= (- (* t_3 (cos (- y (/ (* z t) 3.0)))) t_2) 2e+151)
     (- (* t_3 (+ (* (cos t_1) (cos y)) (* (sin t_1) (sin y)))) t_2)
     (- t_3 (/ (* 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) {
	double t_1 = t * (z * -0.3333333333333333);
	double t_2 = a / (3.0 * b);
	double t_3 = 2.0 * sqrt(x);
	double tmp;
	if (((t_3 * cos((y - ((z * t) / 3.0)))) - t_2) <= 2e+151) {
		tmp = (t_3 * ((cos(t_1) * cos(y)) + (sin(t_1) * sin(y)))) - t_2;
	} else {
		tmp = t_3 - ((a * 0.3333333333333333) / 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) :: t_3
    real(8) :: tmp
    t_1 = t * (z * (-0.3333333333333333d0))
    t_2 = a / (3.0d0 * b)
    t_3 = 2.0d0 * sqrt(x)
    if (((t_3 * cos((y - ((z * t) / 3.0d0)))) - t_2) <= 2d+151) then
        tmp = (t_3 * ((cos(t_1) * cos(y)) + (sin(t_1) * sin(y)))) - t_2
    else
        tmp = t_3 - ((a * 0.3333333333333333d0) / 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 = t * (z * -0.3333333333333333);
	double t_2 = a / (3.0 * b);
	double t_3 = 2.0 * Math.sqrt(x);
	double tmp;
	if (((t_3 * Math.cos((y - ((z * t) / 3.0)))) - t_2) <= 2e+151) {
		tmp = (t_3 * ((Math.cos(t_1) * Math.cos(y)) + (Math.sin(t_1) * Math.sin(y)))) - t_2;
	} else {
		tmp = t_3 - ((a * 0.3333333333333333) / 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 = t * (z * -0.3333333333333333)
	t_2 = a / (3.0 * b)
	t_3 = 2.0 * math.sqrt(x)
	tmp = 0
	if ((t_3 * math.cos((y - ((z * t) / 3.0)))) - t_2) <= 2e+151:
		tmp = (t_3 * ((math.cos(t_1) * math.cos(y)) + (math.sin(t_1) * math.sin(y)))) - t_2
	else:
		tmp = t_3 - ((a * 0.3333333333333333) / 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(t * Float64(z * -0.3333333333333333))
	t_2 = Float64(a / Float64(3.0 * b))
	t_3 = Float64(2.0 * sqrt(x))
	tmp = 0.0
	if (Float64(Float64(t_3 * cos(Float64(y - Float64(Float64(z * t) / 3.0)))) - t_2) <= 2e+151)
		tmp = Float64(Float64(t_3 * Float64(Float64(cos(t_1) * cos(y)) + Float64(sin(t_1) * sin(y)))) - t_2);
	else
		tmp = Float64(t_3 - Float64(Float64(a * 0.3333333333333333) / 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 = t * (z * -0.3333333333333333);
	t_2 = a / (3.0 * b);
	t_3 = 2.0 * sqrt(x);
	tmp = 0.0;
	if (((t_3 * cos((y - ((z * t) / 3.0)))) - t_2) <= 2e+151)
		tmp = (t_3 * ((cos(t_1) * cos(y)) + (sin(t_1) * sin(y)))) - t_2;
	else
		tmp = t_3 - ((a * 0.3333333333333333) / 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[(t * N[(z * -0.3333333333333333), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a / N[(3.0 * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(t$95$3 * N[Cos[N[(y - N[(N[(z * t), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], 2e+151], N[(N[(t$95$3 * N[(N[(N[Cos[t$95$1], $MachinePrecision] * N[Cos[y], $MachinePrecision]), $MachinePrecision] + N[(N[Sin[t$95$1], $MachinePrecision] * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], N[(t$95$3 - N[(N[(a * 0.3333333333333333), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64))))) (/.f64 a (*.f64 b #s(literal 3 binary64)))) < 2.00000000000000003e151

   1. Initial program 75.5%

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

      1. *-commutative 75.5%

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

      2. *-commutative 75.5%

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

      3. *-commutative 75.5%

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

      4. *-commutative 75.5%

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

      5. associate-/l* 75.1%

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

      6. *-commutative 75.1%

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

   3. Simplified 75.1%

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

   6. Applied egg-rr 75.5%

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

   if 2.00000000000000003e151 < (-.f64 (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64))))) (/.f64 a (*.f64 b #s(literal 3 binary64))))

   1. Initial program 58.6%

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

      1. *-commutative 58.6%

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

      2. *-commutative 58.6%

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

      3. *-commutative 58.6%

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

      4. *-commutative 58.6%

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

      5. associate-/l* 60.1%

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

      6. *-commutative 60.1%

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

   3. Simplified 60.1%

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

   5. Taylor expanded in z around 0 85.1%

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

   6. Taylor expanded in a around 0 85.0%

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

      1. associate-*r/ 85.2%

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

   8. Simplified 85.2%

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

   9. Taylor expanded in y around 0 85.6%

      \[\leadsto \color{blue}{2 \cdot \sqrt{x}} - \frac{0.3333333333333333 \cdot a}{b} \]
3. Recombined 2 regimes into one program.

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{3 \cdot b} \leq 2 \cdot 10^{+151}:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \left(\cos \left(t \cdot \left(z \cdot -0.3333333333333333\right)\right) \cdot \cos y + \sin \left(t \cdot \left(z \cdot -0.3333333333333333\right)\right) \cdot \sin y\right) - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{x} - \frac{a \cdot 0.3333333333333333}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 65.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -3.6 \cdot 10^{+212} \lor \neg \left(b \leq 2.6 \cdot 10^{+82}\right):\\ \;\;\;\;2 \cdot \left(\sqrt{x} \cdot \cos y\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{x} - \frac{a \cdot 0.3333333333333333}{b}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -3.6e+212) (not (<= b 2.6e+82)))
   (* 2.0 (* (sqrt x) (cos y)))
   (- (* 2.0 (sqrt x)) (/ (* a 0.3333333333333333) b))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -3.6e+212) || !(b <= 2.6e+82)) {
		tmp = 2.0 * (sqrt(x) * cos(y));
	} else {
		tmp = (2.0 * sqrt(x)) - ((a * 0.3333333333333333) / b);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-3.6d+212)) .or. (.not. (b <= 2.6d+82))) then
        tmp = 2.0d0 * (sqrt(x) * cos(y))
    else
        tmp = (2.0d0 * sqrt(x)) - ((a * 0.3333333333333333d0) / b)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -3.6e+212) || !(b <= 2.6e+82)) {
		tmp = 2.0 * (Math.sqrt(x) * Math.cos(y));
	} else {
		tmp = (2.0 * Math.sqrt(x)) - ((a * 0.3333333333333333) / b);
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -3.6e+212) or not (b <= 2.6e+82):
		tmp = 2.0 * (math.sqrt(x) * math.cos(y))
	else:
		tmp = (2.0 * math.sqrt(x)) - ((a * 0.3333333333333333) / b)
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -3.6e+212) || !(b <= 2.6e+82))
		tmp = Float64(2.0 * Float64(sqrt(x) * cos(y)));
	else
		tmp = Float64(Float64(2.0 * sqrt(x)) - Float64(Float64(a * 0.3333333333333333) / b));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -3.6e+212) || ~((b <= 2.6e+82)))
		tmp = 2.0 * (sqrt(x) * cos(y));
	else
		tmp = (2.0 * sqrt(x)) - ((a * 0.3333333333333333) / b);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -3.6e+212], N[Not[LessEqual[b, 2.6e+82]], $MachinePrecision]], 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 * 0.3333333333333333), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -3.6e212 or 2.5999999999999998e82 < b

   1. Initial program 58.3%

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

      1. *-commutative 58.3%

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

      2. *-commutative 58.3%

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

      3. *-commutative 58.3%

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

      4. *-commutative 58.3%

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

      5. associate-/l* 58.0%

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

      6. *-commutative 58.0%

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

   3. Simplified 58.0%

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

   5. Taylor expanded in z around 0 56.7%

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

   6. Taylor expanded in a around 0 56.7%

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

      1. associate-*r/ 56.6%

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

   8. Simplified 56.6%

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

   9. Taylor expanded in x around inf 50.8%

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

   if -3.6e212 < b < 2.5999999999999998e82

   1. Initial program 75.2%

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

      1. *-commutative 75.2%

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

      2. *-commutative 75.2%

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

      3. *-commutative 75.2%

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

      4. *-commutative 75.2%

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

      5. associate-/l* 75.3%

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

      6. *-commutative 75.3%

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

   3. Simplified 75.3%

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

   5. Taylor expanded in z around 0 83.3%

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

   6. Taylor expanded in a around 0 83.2%

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

      1. associate-*r/ 83.3%

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

   8. Simplified 83.3%

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

   9. Taylor expanded in y around 0 77.8%

      \[\leadsto \color{blue}{2 \cdot \sqrt{x}} - \frac{0.3333333333333333 \cdot a}{b} \]
3. Recombined 2 regimes into one program.

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.6 \cdot 10^{+212} \lor \neg \left(b \leq 2.6 \cdot 10^{+82}\right):\\ \;\;\;\;2 \cdot \left(\sqrt{x} \cdot \cos y\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{x} - \frac{a \cdot 0.3333333333333333}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 75.9% 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 71.0%

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

   1. *-commutative 71.0%

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

   2. *-commutative 71.0%

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

   3. *-commutative 71.0%

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

   4. *-commutative 71.0%

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

   5. associate-/l* 71.1%

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

   6. *-commutative 71.1%

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

3. Simplified 71.1%

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

5. Taylor expanded in z around 0 76.7%

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

   1. *-commutative 76.7%

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

   2. clear-num 76.6%

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

   3. inv-pow 76.6%

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

   4. *-commutative 76.6%

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

   5. *-un-lft-identity 76.6%

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

   6. times-frac 76.7%

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

   7. metadata-eval 76.7%

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

7. Applied egg-rr 76.7%

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

   1. unpow-1 76.7%

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

   2. metadata-eval 76.7%

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

   3. *-commutative 76.7%

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

   4. associate-/r* 76.7%

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

   5. metadata-eval 76.7%

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

   6. clear-num 76.8%

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

9. Applied egg-rr 76.8%

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

Alternative 5: 75.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 71.0%

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

   1. *-commutative 71.0%

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

   2. *-commutative 71.0%

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

   3. *-commutative 71.0%

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

   4. *-commutative 71.0%

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

   5. associate-/l* 71.1%

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

   6. *-commutative 71.1%

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

3. Simplified 71.1%

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

5. Taylor expanded in z around 0 76.7%

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

6. Taylor expanded in a around 0 76.7%

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

   1. associate-*r/ 76.8%

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

8. Simplified 76.8%

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

9. Final simplification 76.8%

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

Alternative 6: 76.0% 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 71.0%

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

   1. *-commutative 71.0%

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

   2. *-commutative 71.0%

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

   3. *-commutative 71.0%

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

   4. *-commutative 71.0%

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

   5. associate-/l* 71.1%

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

   6. *-commutative 71.1%

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

3. Simplified 71.1%

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

5. Taylor expanded in z around 0 76.7%

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

Alternative 7: 65.4% accurate, 2.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 71.0%

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

   1. *-commutative 71.0%

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

   2. *-commutative 71.0%

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

   3. *-commutative 71.0%

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

   4. *-commutative 71.0%

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

   5. associate-/l* 71.1%

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

   6. *-commutative 71.1%

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

3. Simplified 71.1%

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

5. Taylor expanded in z around 0 76.7%

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

6. Taylor expanded in a around 0 76.7%

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

   1. associate-*r/ 76.8%

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

8. Simplified 76.8%

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

9. Taylor expanded in y around 0 67.0%

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

10. Final simplification 67.0%

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

Alternative 8: 65.4% accurate, 2.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 71.0%

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

   1. *-commutative 71.0%

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

   2. *-commutative 71.0%

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

   3. *-commutative 71.0%

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

   4. *-commutative 71.0%

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

   5. associate-/l* 71.1%

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

   6. *-commutative 71.1%

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

3. Simplified 71.1%

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

5. Taylor expanded in z around 0 76.7%

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

6. Taylor expanded in y around 0 67.0%

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

   1. associate-*r/ 67.0%

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

   2. *-commutative 67.0%

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

   3. associate-/l* 67.0%

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

8. Simplified 67.0%

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

Alternative 9: 65.4% 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 71.0%

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

   1. *-commutative 71.0%

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

   2. *-commutative 71.0%

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

   3. *-commutative 71.0%

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

   4. *-commutative 71.0%

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

   5. associate-/l* 71.1%

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

   6. *-commutative 71.1%

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

3. Simplified 71.1%

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

5. Taylor expanded in z around 0 76.7%

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

6. Taylor expanded in y around 0 67.0%

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

Alternative 10: 50.6% accurate, 43.4× speedup

Math

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

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(Float64(a * -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[(N[(a * -0.3333333333333333), $MachinePrecision] / b), $MachinePrecision]

Derivation

1. Initial program 71.0%

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

   1. *-commutative 71.0%

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

   2. *-commutative 71.0%

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

   3. *-commutative 71.0%

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

   4. *-commutative 71.0%

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

   5. associate-/l* 71.1%

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

   6. *-commutative 71.1%

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

3. Simplified 71.1%

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

5. Taylor expanded in z around 0 76.7%

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

6. Taylor expanded in a around inf 53.6%

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

   1. *-commutative 53.6%

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

8. Simplified 53.6%

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

   1. associate-*l/ 53.7%

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

10. Applied egg-rr 53.7%

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

Alternative 11: 50.7% accurate, 43.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 71.0%

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

   1. *-commutative 71.0%

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

   2. *-commutative 71.0%

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

   3. *-commutative 71.0%

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

   4. *-commutative 71.0%

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

   5. associate-/l* 71.1%

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

   6. *-commutative 71.1%

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

3. Simplified 71.1%

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

5. Taylor expanded in z around 0 76.7%

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

6. Taylor expanded in a around inf 53.6%

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

   1. metadata-eval 53.6%

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

   2. times-frac 53.7%

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

   3. *-lft-identity 53.7%

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

   4. *-commutative 53.7%

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

8. Simplified 53.7%

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

Alternative 12: 50.6% 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 71.0%

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

   1. *-commutative 71.0%

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

   2. *-commutative 71.0%

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

   3. *-commutative 71.0%

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

   4. *-commutative 71.0%

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

   5. associate-/l* 71.1%

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

   6. *-commutative 71.1%

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

3. Simplified 71.1%

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

5. Taylor expanded in z around 0 76.7%

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

6. Taylor expanded in a around inf 53.6%

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

   1. metadata-eval 53.6%

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

   2. times-frac 53.7%

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

   3. *-lft-identity 53.7%

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

   4. *-commutative 53.7%

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

8. Simplified 53.7%

   \[\leadsto \color{blue}{\frac{a}{b \cdot -3}} \]
9. Step-by-step derivation

   1. div-inv 53.6%

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

   2. *-commutative 53.6%

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

   3. metadata-eval 53.6%

      \[\leadsto \frac{\color{blue}{3 \cdot 0.3333333333333333}}{b \cdot -3} \cdot a \]

   4. *-commutative 53.6%

      \[\leadsto \frac{3 \cdot 0.3333333333333333}{\color{blue}{-3 \cdot b}} \cdot a \]

   5. associate-/r* 53.6%

      \[\leadsto \color{blue}{\frac{\frac{3 \cdot 0.3333333333333333}{-3}}{b}} \cdot a \]

   6. metadata-eval 53.6%

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

   7. metadata-eval 53.6%

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

10. Applied egg-rr 53.6%

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

11. Final simplification 53.6%

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

Developer target: 73.7% 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 2024091 
(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))))