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

Percentage Accurate: 69.8% → 77.3%

Time: 27.8s

Alternatives: 9

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 69.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 77.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := 2 \cdot \sqrt{x}\\ t_2 := \frac{z}{\frac{3}{t}}\\ \mathbf{if}\;\cos \left(y - \frac{z \cdot t}{3}\right) \leq 0.99999999999996:\\ \;\;\;\;t\_1 \cdot \mathsf{fma}\left(\cos y, \cos t\_2, \sin y \cdot \sin t\_2\right) - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;t\_1 - \frac{a \cdot 0.3333333333333333}{b}\\ \end{array} \end{array} \]

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 (* 2.0 (sqrt x))) (t_2 (/ z (/ 3.0 t))))
   (if (<= (cos (- y (/ (* z t) 3.0))) 0.99999999999996)
     (- (* t_1 (fma (cos y) (cos t_2) (* (sin y) (sin t_2)))) (/ a (* 3.0 b)))
     (- t_1 (/ (* 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 = 2.0 * sqrt(x);
	double t_2 = z / (3.0 / t);
	double tmp;
	if (cos((y - ((z * t) / 3.0))) <= 0.99999999999996) {
		tmp = (t_1 * fma(cos(y), cos(t_2), (sin(y) * sin(t_2)))) - (a / (3.0 * b));
	} else {
		tmp = t_1 - ((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(2.0 * sqrt(x))
	t_2 = Float64(z / Float64(3.0 / t))
	tmp = 0.0
	if (cos(Float64(y - Float64(Float64(z * t) / 3.0))) <= 0.99999999999996)
		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 * 0.3333333333333333) / 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[(z / N[(3.0 / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[Cos[N[(y - N[(N[(z * t), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], 0.99999999999996], 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 * 0.3333333333333333), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64)))) < 0.99999999999996003

   1. Initial program 78.6%

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

      1. *-commutative 78.6%

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

      2. *-commutative 78.6%

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

      3. *-commutative 78.6%

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

      4. *-commutative 78.6%

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

      5. associate-/l* 79.1%

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

      6. *-commutative 79.1%

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

   3. Simplified 79.1%

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

   6. Applied egg-rr 80.6%

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

      1. fma-define 80.6%

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

      2. cos-neg 80.6%

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

      3. distribute-lft-neg-in 80.6%

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

      4. distribute-rgt-neg-in 80.6%

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

      5. metadata-eval 80.6%

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

      6. metadata-eval 80.6%

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

      7. associate-/l* 80.9%

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

      8. *-rgt-identity 80.9%

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

      9. associate-/r/ 80.6%

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

      10. distribute-rgt-neg-in 80.6%

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

      11. sin-neg 80.6%

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

      12. distribute-lft-neg-in 80.6%

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

      13. distribute-rgt-neg-in 80.6%

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

      14. metadata-eval 80.6%

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

      15. metadata-eval 80.6%

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

      16. associate-/l* 80.6%

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

      17. *-rgt-identity 80.6%

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

      18. associate-/r/ 80.6%

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

   8. Simplified 80.6%

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

   if 0.99999999999996003 < (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64))))

   1. Initial program 69.5%

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

      1. *-commutative 69.5%

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

      2. *-commutative 69.5%

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

      3. *-commutative 69.5%

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

      4. *-commutative 69.5%

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

      5. associate-/l* 69.5%

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

      6. *-commutative 69.5%

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

   3. Simplified 69.5%

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

   5. Taylor expanded in z around 0 86.3%

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

   6. Taylor expanded in y around 0 86.7%

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

      1. associate-*r/ 86.7%

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

   8. Simplified 86.7%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\cos \left(y - \frac{z \cdot t}{3}\right) \leq 0.99999999999996:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos y, \cos \left(\frac{z}{\frac{3}{t}}\right), \sin y \cdot \sin \left(\frac{z}{\frac{3}{t}}\right)\right) - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{x} - \frac{a \cdot 0.3333333333333333}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 77.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := 2 \cdot \sqrt{x}\\ \mathbf{if}\;\cos \left(y - \frac{z \cdot t}{3}\right) \leq 0.99999999999996:\\ \;\;\;\;t\_1 \cdot \left(\cos y \cdot \cos \left(0.3333333333333333 \cdot \left(z \cdot t\right)\right) - \sin y \cdot \sin \left(z \cdot \left(t \cdot -0.3333333333333333\right)\right)\right) - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;t\_1 - \frac{a \cdot 0.3333333333333333}{b}\\ \end{array} \end{array} \]

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 (* 2.0 (sqrt x))))
   (if (<= (cos (- y (/ (* z t) 3.0))) 0.99999999999996)
     (-
      (*
       t_1
       (-
        (* (cos y) (cos (* 0.3333333333333333 (* z t))))
        (* (sin y) (sin (* z (* t -0.3333333333333333))))))
      (/ a (* 3.0 b)))
     (- t_1 (/ (* 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 = 2.0 * sqrt(x);
	double tmp;
	if (cos((y - ((z * t) / 3.0))) <= 0.99999999999996) {
		tmp = (t_1 * ((cos(y) * cos((0.3333333333333333 * (z * t)))) - (sin(y) * sin((z * (t * -0.3333333333333333)))))) - (a / (3.0 * b));
	} else {
		tmp = t_1 - ((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) :: tmp
    t_1 = 2.0d0 * sqrt(x)
    if (cos((y - ((z * t) / 3.0d0))) <= 0.99999999999996d0) then
        tmp = (t_1 * ((cos(y) * cos((0.3333333333333333d0 * (z * t)))) - (sin(y) * sin((z * (t * (-0.3333333333333333d0))))))) - (a / (3.0d0 * b))
    else
        tmp = t_1 - ((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 = 2.0 * Math.sqrt(x);
	double tmp;
	if (Math.cos((y - ((z * t) / 3.0))) <= 0.99999999999996) {
		tmp = (t_1 * ((Math.cos(y) * Math.cos((0.3333333333333333 * (z * t)))) - (Math.sin(y) * Math.sin((z * (t * -0.3333333333333333)))))) - (a / (3.0 * b));
	} else {
		tmp = t_1 - ((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 = 2.0 * math.sqrt(x)
	tmp = 0
	if math.cos((y - ((z * t) / 3.0))) <= 0.99999999999996:
		tmp = (t_1 * ((math.cos(y) * math.cos((0.3333333333333333 * (z * t)))) - (math.sin(y) * math.sin((z * (t * -0.3333333333333333)))))) - (a / (3.0 * b))
	else:
		tmp = t_1 - ((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(2.0 * sqrt(x))
	tmp = 0.0
	if (cos(Float64(y - Float64(Float64(z * t) / 3.0))) <= 0.99999999999996)
		tmp = Float64(Float64(t_1 * Float64(Float64(cos(y) * cos(Float64(0.3333333333333333 * Float64(z * t)))) - Float64(sin(y) * sin(Float64(z * Float64(t * -0.3333333333333333)))))) - Float64(a / Float64(3.0 * b)));
	else
		tmp = Float64(t_1 - 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 = 2.0 * sqrt(x);
	tmp = 0.0;
	if (cos((y - ((z * t) / 3.0))) <= 0.99999999999996)
		tmp = (t_1 * ((cos(y) * cos((0.3333333333333333 * (z * t)))) - (sin(y) * sin((z * (t * -0.3333333333333333)))))) - (a / (3.0 * b));
	else
		tmp = t_1 - ((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[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[Cos[N[(y - N[(N[(z * t), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], 0.99999999999996], N[(N[(t$95$1 * N[(N[(N[Cos[y], $MachinePrecision] * N[Cos[N[(0.3333333333333333 * N[(z * t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - N[(N[Sin[y], $MachinePrecision] * N[Sin[N[(z * N[(t * -0.3333333333333333), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a / N[(3.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 - N[(N[(a * 0.3333333333333333), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64)))) < 0.99999999999996003

   1. Initial program 78.6%

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

      1. *-commutative 78.6%

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

      2. *-commutative 78.6%

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

      3. *-commutative 78.6%

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

      4. *-commutative 78.6%

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

      5. associate-/l* 79.1%

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

      6. *-commutative 79.1%

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

   3. Simplified 79.1%

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

   6. Applied egg-rr 80.6%

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

      1. sub-neg 80.6%

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

      2. *-rgt-identity 80.6%

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

      3. *-rgt-identity 80.6%

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

      4. *-rgt-identity 80.6%

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

      5. associate-*l* 80.8%

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

      6. *-commutative 80.8%

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

      7. associate-*r* 80.5%

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

      8. *-commutative 80.5%

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

      9. metadata-eval 80.5%

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

      10. *-commutative 80.5%

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

      11. distribute-lft-neg-in 80.5%

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

      12. cos-neg 80.5%

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

      13. *-rgt-identity 80.5%

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

      14. associate-*l* 80.6%

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

      15. *-commutative 80.6%

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

   8. Simplified 80.6%

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

   if 0.99999999999996003 < (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64))))

   1. Initial program 69.5%

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

      1. *-commutative 69.5%

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

      2. *-commutative 69.5%

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

      3. *-commutative 69.5%

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

      4. *-commutative 69.5%

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

      5. associate-/l* 69.5%

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

      6. *-commutative 69.5%

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

   3. Simplified 69.5%

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

   5. Taylor expanded in z around 0 86.3%

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

   6. Taylor expanded in y around 0 86.7%

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

      1. associate-*r/ 86.7%

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

   8. Simplified 86.7%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\cos \left(y - \frac{z \cdot t}{3}\right) \leq 0.99999999999996:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \left(\cos y \cdot \cos \left(0.3333333333333333 \cdot \left(z \cdot t\right)\right) - \sin y \cdot \sin \left(z \cdot \left(t \cdot -0.3333333333333333\right)\right)\right) - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{x} - \frac{a \cdot 0.3333333333333333}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 77.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := 2 \cdot \sqrt{x}\\ \mathbf{if}\;\cos \left(y - \frac{z \cdot t}{3}\right) \leq 0.99999999999996:\\ \;\;\;\;t\_1 \cdot \left(\cos y \cdot \cos \left(0.3333333333333333 \cdot \left(z \cdot t\right)\right) - \sin y \cdot \sin \left(z \cdot \frac{t}{-3}\right)\right) - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;t\_1 - \frac{a \cdot 0.3333333333333333}{b}\\ \end{array} \end{array} \]

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 (* 2.0 (sqrt x))))
   (if (<= (cos (- y (/ (* z t) 3.0))) 0.99999999999996)
     (-
      (*
       t_1
       (-
        (* (cos y) (cos (* 0.3333333333333333 (* z t))))
        (* (sin y) (sin (* z (/ t -3.0))))))
      (/ a (* 3.0 b)))
     (- t_1 (/ (* 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 = 2.0 * sqrt(x);
	double tmp;
	if (cos((y - ((z * t) / 3.0))) <= 0.99999999999996) {
		tmp = (t_1 * ((cos(y) * cos((0.3333333333333333 * (z * t)))) - (sin(y) * sin((z * (t / -3.0)))))) - (a / (3.0 * b));
	} else {
		tmp = t_1 - ((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) :: tmp
    t_1 = 2.0d0 * sqrt(x)
    if (cos((y - ((z * t) / 3.0d0))) <= 0.99999999999996d0) then
        tmp = (t_1 * ((cos(y) * cos((0.3333333333333333d0 * (z * t)))) - (sin(y) * sin((z * (t / (-3.0d0))))))) - (a / (3.0d0 * b))
    else
        tmp = t_1 - ((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 = 2.0 * Math.sqrt(x);
	double tmp;
	if (Math.cos((y - ((z * t) / 3.0))) <= 0.99999999999996) {
		tmp = (t_1 * ((Math.cos(y) * Math.cos((0.3333333333333333 * (z * t)))) - (Math.sin(y) * Math.sin((z * (t / -3.0)))))) - (a / (3.0 * b));
	} else {
		tmp = t_1 - ((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 = 2.0 * math.sqrt(x)
	tmp = 0
	if math.cos((y - ((z * t) / 3.0))) <= 0.99999999999996:
		tmp = (t_1 * ((math.cos(y) * math.cos((0.3333333333333333 * (z * t)))) - (math.sin(y) * math.sin((z * (t / -3.0)))))) - (a / (3.0 * b))
	else:
		tmp = t_1 - ((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(2.0 * sqrt(x))
	tmp = 0.0
	if (cos(Float64(y - Float64(Float64(z * t) / 3.0))) <= 0.99999999999996)
		tmp = Float64(Float64(t_1 * Float64(Float64(cos(y) * cos(Float64(0.3333333333333333 * Float64(z * t)))) - Float64(sin(y) * sin(Float64(z * Float64(t / -3.0)))))) - Float64(a / Float64(3.0 * b)));
	else
		tmp = Float64(t_1 - 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 = 2.0 * sqrt(x);
	tmp = 0.0;
	if (cos((y - ((z * t) / 3.0))) <= 0.99999999999996)
		tmp = (t_1 * ((cos(y) * cos((0.3333333333333333 * (z * t)))) - (sin(y) * sin((z * (t / -3.0)))))) - (a / (3.0 * b));
	else
		tmp = t_1 - ((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[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[Cos[N[(y - N[(N[(z * t), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], 0.99999999999996], N[(N[(t$95$1 * N[(N[(N[Cos[y], $MachinePrecision] * N[Cos[N[(0.3333333333333333 * N[(z * t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - N[(N[Sin[y], $MachinePrecision] * N[Sin[N[(z * N[(t / -3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a / N[(3.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 - N[(N[(a * 0.3333333333333333), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64)))) < 0.99999999999996003

   1. Initial program 78.6%

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

      1. *-commutative 78.6%

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

      2. *-commutative 78.6%

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

      3. *-commutative 78.6%

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

      4. *-commutative 78.6%

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

      5. associate-/l* 79.1%

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

      6. *-commutative 79.1%

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

   3. Simplified 79.1%

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

   6. Applied egg-rr 80.6%

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

      1. sub-neg 80.6%

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

      2. *-rgt-identity 80.6%

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

      3. *-rgt-identity 80.6%

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

      4. *-rgt-identity 80.6%

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

      5. associate-*l* 80.8%

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

      6. *-commutative 80.8%

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

      7. associate-*r* 80.5%

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

      8. *-commutative 80.5%

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

      9. metadata-eval 80.5%

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

      10. *-commutative 80.5%

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

      11. distribute-lft-neg-in 80.5%

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

      12. cos-neg 80.5%

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

      13. *-rgt-identity 80.5%

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

      14. associate-*l* 80.6%

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

      15. *-commutative 80.6%

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

   8. Simplified 80.6%

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

      1. metadata-eval 80.6%

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

      2. div-inv 80.7%

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

   10. Applied egg-rr 80.7%

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

   if 0.99999999999996003 < (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64))))

   1. Initial program 69.5%

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

      1. *-commutative 69.5%

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

      2. *-commutative 69.5%

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

      3. *-commutative 69.5%

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

      4. *-commutative 69.5%

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

      5. associate-/l* 69.5%

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

      6. *-commutative 69.5%

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

   3. Simplified 69.5%

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

   5. Taylor expanded in z around 0 86.3%

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

   6. Taylor expanded in y around 0 86.7%

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

      1. associate-*r/ 86.7%

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

   8. Simplified 86.7%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\cos \left(y - \frac{z \cdot t}{3}\right) \leq 0.99999999999996:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \left(\cos y \cdot \cos \left(0.3333333333333333 \cdot \left(z \cdot t\right)\right) - \sin y \cdot \sin \left(z \cdot \frac{t}{-3}\right)\right) - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{x} - \frac{a \cdot 0.3333333333333333}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 77.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := 2 \cdot \sqrt{x}\\ t_2 := t \cdot \left(z \cdot -0.3333333333333333\right)\\ \mathbf{if}\;\cos \left(y - \frac{z \cdot t}{3}\right) \leq 0.99999999999996:\\ \;\;\;\;t\_1 \cdot \left(\cos y \cdot \cos t\_2 - \sin y \cdot \sin t\_2\right) - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;t\_1 - \frac{a \cdot 0.3333333333333333}{b}\\ \end{array} \end{array} \]

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 (* 2.0 (sqrt x))) (t_2 (* t (* z -0.3333333333333333))))
   (if (<= (cos (- y (/ (* z t) 3.0))) 0.99999999999996)
     (-
      (* t_1 (- (* (cos y) (cos t_2)) (* (sin y) (sin t_2))))
      (/ a (* 3.0 b)))
     (- t_1 (/ (* 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 = 2.0 * sqrt(x);
	double t_2 = t * (z * -0.3333333333333333);
	double tmp;
	if (cos((y - ((z * t) / 3.0))) <= 0.99999999999996) {
		tmp = (t_1 * ((cos(y) * cos(t_2)) - (sin(y) * sin(t_2)))) - (a / (3.0 * b));
	} else {
		tmp = t_1 - ((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) :: tmp
    t_1 = 2.0d0 * sqrt(x)
    t_2 = t * (z * (-0.3333333333333333d0))
    if (cos((y - ((z * t) / 3.0d0))) <= 0.99999999999996d0) then
        tmp = (t_1 * ((cos(y) * cos(t_2)) - (sin(y) * sin(t_2)))) - (a / (3.0d0 * b))
    else
        tmp = t_1 - ((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 = 2.0 * Math.sqrt(x);
	double t_2 = t * (z * -0.3333333333333333);
	double tmp;
	if (Math.cos((y - ((z * t) / 3.0))) <= 0.99999999999996) {
		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 * 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 = 2.0 * math.sqrt(x)
	t_2 = t * (z * -0.3333333333333333)
	tmp = 0
	if math.cos((y - ((z * t) / 3.0))) <= 0.99999999999996:
		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 * 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(2.0 * sqrt(x))
	t_2 = Float64(t * Float64(z * -0.3333333333333333))
	tmp = 0.0
	if (cos(Float64(y - Float64(Float64(z * t) / 3.0))) <= 0.99999999999996)
		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 * 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 = 2.0 * sqrt(x);
	t_2 = t * (z * -0.3333333333333333);
	tmp = 0.0;
	if (cos((y - ((z * t) / 3.0))) <= 0.99999999999996)
		tmp = (t_1 * ((cos(y) * cos(t_2)) - (sin(y) * sin(t_2)))) - (a / (3.0 * b));
	else
		tmp = t_1 - ((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[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(z * -0.3333333333333333), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[Cos[N[(y - N[(N[(z * t), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], 0.99999999999996], 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 * 0.3333333333333333), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64)))) < 0.99999999999996003

   1. Initial program 78.6%

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

      1. *-commutative 78.6%

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

      2. *-commutative 78.6%

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

      3. *-commutative 78.6%

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

      4. *-commutative 78.6%

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

      5. associate-/l* 79.1%

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

      6. *-commutative 79.1%

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

   3. Simplified 79.1%

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

      1. associate-*r/ 78.6%

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

      2. div-inv 78.7%

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

      3. metadata-eval 78.7%

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

      4. metadata-eval 78.7%

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

      5. cancel-sign-sub-inv 78.7%

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

      6. metadata-eval 78.7%

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

      7. metadata-eval 78.7%

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

      8. div-inv 78.6%

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

      9. metadata-eval 78.6%

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

      10. frac-2neg 78.6%

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

      11. +-commutative 78.6%

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

      12. cos-sum 80.6%

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

      13. div-inv 80.5%

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

      14. metadata-eval 80.5%

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

      15. associate-*r* 80.8%

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

      16. *-commutative 80.8%

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

      17. associate-*r* 80.6%

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

   6. Applied egg-rr 80.6%

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

   if 0.99999999999996003 < (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64))))

   1. Initial program 69.5%

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

      1. *-commutative 69.5%

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

      2. *-commutative 69.5%

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

      3. *-commutative 69.5%

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

      4. *-commutative 69.5%

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

      5. associate-/l* 69.5%

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

      6. *-commutative 69.5%

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

   3. Simplified 69.5%

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

   5. Taylor expanded in z around 0 86.3%

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

   6. Taylor expanded in y around 0 86.7%

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

      1. associate-*r/ 86.7%

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

   8. Simplified 86.7%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\cos \left(y - \frac{z \cdot t}{3}\right) \leq 0.99999999999996:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \left(\cos y \cdot \cos \left(t \cdot \left(z \cdot -0.3333333333333333\right)\right) - \sin y \cdot \sin \left(t \cdot \left(z \cdot -0.3333333333333333\right)\right)\right) - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{x} - \frac{a \cdot 0.3333333333333333}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 76.2% 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 75.4%

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

   1. *-commutative 75.4%

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

   2. *-commutative 75.4%

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

   3. *-commutative 75.4%

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

   4. *-commutative 75.4%

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

   5. associate-/l* 75.7%

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

   6. *-commutative 75.7%

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

3. Simplified 75.7%

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

5. Taylor expanded in z around 0 80.4%

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

6. Final simplification 80.4%

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

Alternative 6: 66.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -3.5 \cdot 10^{+214}:\\ \;\;\;\;2 \cdot \left(\sqrt{x} \cdot \cos y\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{x} - \frac{a}{3 \cdot b}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -3.5e+214)
   (* 2.0 (* (sqrt x) (cos y)))
   (- (* 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) {
	double tmp;
	if (b <= -3.5e+214) {
		tmp = 2.0 * (sqrt(x) * cos(y));
	} else {
		tmp = (2.0 * sqrt(x)) - (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) :: tmp
    if (b <= (-3.5d+214)) then
        tmp = 2.0d0 * (sqrt(x) * cos(y))
    else
        tmp = (2.0d0 * sqrt(x)) - (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 tmp;
	if (b <= -3.5e+214) {
		tmp = 2.0 * (Math.sqrt(x) * Math.cos(y));
	} else {
		tmp = (2.0 * Math.sqrt(x)) - (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):
	tmp = 0
	if b <= -3.5e+214:
		tmp = 2.0 * (math.sqrt(x) * math.cos(y))
	else:
		tmp = (2.0 * math.sqrt(x)) - (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)
	tmp = 0.0
	if (b <= -3.5e+214)
		tmp = Float64(2.0 * Float64(sqrt(x) * cos(y)));
	else
		tmp = Float64(Float64(2.0 * sqrt(x)) - Float64(a / Float64(3.0 * b)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -3.5e+214)
		tmp = 2.0 * (sqrt(x) * cos(y));
	else
		tmp = (2.0 * sqrt(x)) - (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_] := If[LessEqual[b, -3.5e+214], N[(2.0 * N[(N[Sqrt[x], $MachinePrecision] * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] - N[(a / N[(3.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -3.5e214

   1. Initial program 66.6%

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

      1. *-commutative 66.6%

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

      2. *-commutative 66.6%

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

      3. *-commutative 66.6%

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

      4. *-commutative 66.6%

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

      5. associate-/l* 66.6%

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

      6. *-commutative 66.6%

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

   3. Simplified 66.6%

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

   5. Taylor expanded in z around 0 73.1%

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

   6. Taylor expanded in a around 0 73.1%

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

      1. associate-*r/ 73.1%

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

   8. Simplified 73.1%

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

   9. Taylor expanded in x around inf 67.3%

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

   if -3.5e214 < b

   1. Initial program 76.1%

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

      1. *-commutative 76.1%

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

      2. *-commutative 76.1%

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

      3. *-commutative 76.1%

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

      4. *-commutative 76.1%

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

      5. associate-/l* 76.4%

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

      6. *-commutative 76.4%

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

   3. Simplified 76.4%

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

   5. Taylor expanded in z around 0 81.0%

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

   6. Taylor expanded in y around 0 72.6%

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

4. Final simplification 72.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -3.5 \cdot 10^{+214}:\\ \;\;\;\;2 \cdot \left(\sqrt{x} \cdot \cos y\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{x} - \frac{a}{3 \cdot b}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 65.2% accurate, 2.0× speedup

Math

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

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 75.4%

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

   1. *-commutative 75.4%

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

   2. *-commutative 75.4%

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

   3. *-commutative 75.4%

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

   4. *-commutative 75.4%

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

   5. associate-/l* 75.7%

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

   6. *-commutative 75.7%

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

3. Simplified 75.7%

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

5. Taylor expanded in z around 0 80.4%

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

6. Taylor expanded in y around 0 69.9%

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

7. Final simplification 69.9%

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

Alternative 8: 50.4% 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 75.4%

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

   1. *-commutative 75.4%

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

   2. *-commutative 75.4%

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

   3. *-commutative 75.4%

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

   4. *-commutative 75.4%

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

   5. associate-/l* 75.7%

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

   6. *-commutative 75.7%

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

3. Simplified 75.7%

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

5. Taylor expanded in z around 0 80.4%

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

6. Taylor expanded in a around inf 56.2%

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

   1. metadata-eval 56.2%

      \[\leadsto \color{blue}{\left(-0.3333333333333333\right)} \cdot \frac{a}{b} \]

   2. distribute-lft-neg-in 56.2%

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

   3. associate-*r/ 56.2%

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

   4. *-commutative 56.2%

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

   5. associate-*r/ 56.2%

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

   6. metadata-eval 56.2%

      \[\leadsto -a \cdot \frac{\color{blue}{0.3333333333333333 \cdot 1}}{b} \]

   7. associate-*r/ 56.2%

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

   8. *-commutative 56.2%

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

   9. *-commutative 56.2%

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

   10. distribute-rgt-neg-in 56.2%

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

   11. associate-*r/ 56.2%

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

   12. metadata-eval 56.2%

       \[\leadsto a \cdot \left(-\frac{\color{blue}{0.3333333333333333}}{b}\right) \]

   13. distribute-neg-frac 56.2%

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

   14. metadata-eval 56.2%

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

8. Simplified 56.2%

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

9. Final simplification 56.2%

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

Alternative 9: 50.5% 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 75.4%

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

   1. *-commutative 75.4%

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

   2. *-commutative 75.4%

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

   3. *-commutative 75.4%

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

   4. *-commutative 75.4%

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

   5. associate-/l* 75.7%

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

   6. *-commutative 75.7%

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

3. Simplified 75.7%

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

5. Taylor expanded in z around 0 80.4%

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

6. Taylor expanded in a around inf 56.2%

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

   1. metadata-eval 56.2%

      \[\leadsto \color{blue}{\left(-0.3333333333333333\right)} \cdot \frac{a}{b} \]

   2. distribute-lft-neg-in 56.2%

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

   3. associate-*r/ 56.2%

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

   4. *-commutative 56.2%

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

   5. associate-*r/ 56.2%

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

   6. metadata-eval 56.2%

      \[\leadsto -a \cdot \frac{\color{blue}{0.3333333333333333 \cdot 1}}{b} \]

   7. associate-*r/ 56.2%

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

   8. *-commutative 56.2%

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

   9. *-commutative 56.2%

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

   10. distribute-rgt-neg-in 56.2%

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

   11. associate-*r/ 56.2%

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

   12. metadata-eval 56.2%

       \[\leadsto a \cdot \left(-\frac{\color{blue}{0.3333333333333333}}{b}\right) \]

   13. distribute-neg-frac 56.2%

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

   14. metadata-eval 56.2%

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

8. Simplified 56.2%

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

   1. clear-num 56.1%

      \[\leadsto a \cdot \color{blue}{\frac{1}{\frac{b}{-0.3333333333333333}}} \]

   2. un-div-inv 56.2%

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

   3. div-inv 56.3%

      \[\leadsto \frac{a}{\color{blue}{b \cdot \frac{1}{-0.3333333333333333}}} \]

   4. metadata-eval 56.3%

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

10. Applied egg-rr 56.3%

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

11. Final simplification 56.3%

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

Developer target: 73.9% 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 2024073 
(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))))