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

Percentage Accurate: 70.1% → 77.8%

Time: 20.8s

Alternatives: 11

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 70.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 77.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \frac{a}{3 \cdot b}\\ t_2 := 2 \cdot \sqrt{x}\\ \mathbf{if}\;t\_2 \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - t\_1 \leq 10^{+271}:\\ \;\;\;\;t\_2 \cdot \mathsf{fma}\left(\sin \left(t \cdot \frac{z}{3}\right), \sin y, \cos y \cdot \cos \left(\left(z \cdot t\right) \cdot 0.3333333333333333\right)\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;2 \cdot {\left({x}^{0.25}\right)}^{2} - \frac{\frac{a}{b}}{3}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ a (* 3.0 b))) (t_2 (* 2.0 (sqrt x))))
   (if (<= (- (* t_2 (cos (- y (/ (* z t) 3.0)))) t_1) 1e+271)
     (-
      (*
       t_2
       (fma
        (sin (* t (/ z 3.0)))
        (sin y)
        (* (cos y) (cos (* (* z t) 0.3333333333333333)))))
      t_1)
     (- (* 2.0 (pow (pow x 0.25) 2.0)) (/ (/ a b) 3.0)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a / (3.0 * b);
	double t_2 = 2.0 * sqrt(x);
	double tmp;
	if (((t_2 * cos((y - ((z * t) / 3.0)))) - t_1) <= 1e+271) {
		tmp = (t_2 * fma(sin((t * (z / 3.0))), sin(y), (cos(y) * cos(((z * t) * 0.3333333333333333))))) - t_1;
	} else {
		tmp = (2.0 * pow(pow(x, 0.25), 2.0)) - ((a / b) / 3.0);
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(a / Float64(3.0 * b))
	t_2 = Float64(2.0 * sqrt(x))
	tmp = 0.0
	if (Float64(Float64(t_2 * cos(Float64(y - Float64(Float64(z * t) / 3.0)))) - t_1) <= 1e+271)
		tmp = Float64(Float64(t_2 * fma(sin(Float64(t * Float64(z / 3.0))), sin(y), Float64(cos(y) * cos(Float64(Float64(z * t) * 0.3333333333333333))))) - t_1);
	else
		tmp = Float64(Float64(2.0 * ((x ^ 0.25) ^ 2.0)) - Float64(Float64(a / b) / 3.0));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a / N[(3.0 * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(t$95$2 * N[Cos[N[(y - N[(N[(z * t), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], 1e+271], N[(N[(t$95$2 * N[(N[Sin[N[(t * N[(z / 3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[Sin[y], $MachinePrecision] + N[(N[Cos[y], $MachinePrecision] * N[Cos[N[(N[(z * t), $MachinePrecision] * 0.3333333333333333), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(2.0 * N[Power[N[Power[x, 0.25], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] - N[(N[(a / b), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64))))) (/.f64 a (*.f64 b #s(literal 3 binary64)))) < 9.99999999999999953e270

   1. Initial program 75.9%

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

      1. cos-diff N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \left(\cos y \cdot \cos \left(\frac{z \cdot t}{3}\right) + \sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \left(\sin y \cdot \sin \left(\frac{z \cdot t}{3}\right) + \cos y \cdot \cos \left(\frac{z \cdot t}{3}\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \left(\sin \left(\frac{z \cdot t}{3}\right) \cdot \sin y + \cos y \cdot \cos \left(\frac{z \cdot t}{3}\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      4. fma-define N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \left(\mathsf{fma}\left(\sin \left(\frac{z \cdot t}{3}\right), \sin y, \cos y \cdot \cos \left(\frac{z \cdot t}{3}\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      5. fma-lowering-fma.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{fma.f64}\left(\sin \left(\frac{z \cdot t}{3}\right), \sin y, \left(\cos y \cdot \cos \left(\frac{z \cdot t}{3}\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      6. sin-lowering-sin.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{fma.f64}\left(\mathsf{sin.f64}\left(\left(\frac{z \cdot t}{3}\right)\right), \sin y, \left(\cos y \cdot \cos \left(\frac{z \cdot t}{3}\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{fma.f64}\left(\mathsf{sin.f64}\left(\left(\frac{t \cdot z}{3}\right)\right), \sin y, \left(\cos y \cdot \cos \left(\frac{z \cdot t}{3}\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      8. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{fma.f64}\left(\mathsf{sin.f64}\left(\left(t \cdot \frac{z}{3}\right)\right), \sin y, \left(\cos y \cdot \cos \left(\frac{z \cdot t}{3}\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{fma.f64}\left(\mathsf{sin.f64}\left(\mathsf{*.f64}\left(t, \left(\frac{z}{3}\right)\right)\right), \sin y, \left(\cos y \cdot \cos \left(\frac{z \cdot t}{3}\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{fma.f64}\left(\mathsf{sin.f64}\left(\mathsf{*.f64}\left(t, \mathsf{/.f64}\left(z, 3\right)\right)\right), \sin y, \left(\cos y \cdot \cos \left(\frac{z \cdot t}{3}\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      11. sin-lowering-sin.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{fma.f64}\left(\mathsf{sin.f64}\left(\mathsf{*.f64}\left(t, \mathsf{/.f64}\left(z, 3\right)\right)\right), \mathsf{sin.f64}\left(y\right), \left(\cos y \cdot \cos \left(\frac{z \cdot t}{3}\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{fma.f64}\left(\mathsf{sin.f64}\left(\mathsf{*.f64}\left(t, \mathsf{/.f64}\left(z, 3\right)\right)\right), \mathsf{sin.f64}\left(y\right), \mathsf{*.f64}\left(\cos y, \cos \left(\frac{z \cdot t}{3}\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      13. cos-lowering-cos.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{fma.f64}\left(\mathsf{sin.f64}\left(\mathsf{*.f64}\left(t, \mathsf{/.f64}\left(z, 3\right)\right)\right), \mathsf{sin.f64}\left(y\right), \mathsf{*.f64}\left(\mathsf{cos.f64}\left(y\right), \cos \left(\frac{z \cdot t}{3}\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      14. cos-lowering-cos.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{fma.f64}\left(\mathsf{sin.f64}\left(\mathsf{*.f64}\left(t, \mathsf{/.f64}\left(z, 3\right)\right)\right), \mathsf{sin.f64}\left(y\right), \mathsf{*.f64}\left(\mathsf{cos.f64}\left(y\right), \mathsf{cos.f64}\left(\left(\frac{z \cdot t}{3}\right)\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      15. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{fma.f64}\left(\mathsf{sin.f64}\left(\mathsf{*.f64}\left(t, \mathsf{/.f64}\left(z, 3\right)\right)\right), \mathsf{sin.f64}\left(y\right), \mathsf{*.f64}\left(\mathsf{cos.f64}\left(y\right), \mathsf{cos.f64}\left(\left(\frac{t \cdot z}{3}\right)\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      16. associate-/l* N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{fma.f64}\left(\mathsf{sin.f64}\left(\mathsf{*.f64}\left(t, \mathsf{/.f64}\left(z, 3\right)\right)\right), \mathsf{sin.f64}\left(y\right), \mathsf{*.f64}\left(\mathsf{cos.f64}\left(y\right), \mathsf{cos.f64}\left(\left(t \cdot \frac{z}{3}\right)\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      17. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{fma.f64}\left(\mathsf{sin.f64}\left(\mathsf{*.f64}\left(t, \mathsf{/.f64}\left(z, 3\right)\right)\right), \mathsf{sin.f64}\left(y\right), \mathsf{*.f64}\left(\mathsf{cos.f64}\left(y\right), \mathsf{cos.f64}\left(\mathsf{*.f64}\left(t, \left(\frac{z}{3}\right)\right)\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      18. /-lowering-/.f64 78.2%

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{fma.f64}\left(\mathsf{sin.f64}\left(\mathsf{*.f64}\left(t, \mathsf{/.f64}\left(z, 3\right)\right)\right), \mathsf{sin.f64}\left(y\right), \mathsf{*.f64}\left(\mathsf{cos.f64}\left(y\right), \mathsf{cos.f64}\left(\mathsf{*.f64}\left(t, \mathsf{/.f64}\left(z, 3\right)\right)\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

   4. Applied egg-rr 78.2%

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

   5. Taylor expanded in t around inf

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{fma.f64}\left(\mathsf{sin.f64}\left(\mathsf{*.f64}\left(t, \mathsf{/.f64}\left(z, 3\right)\right)\right), \mathsf{sin.f64}\left(y\right), \mathsf{*.f64}\left(\mathsf{cos.f64}\left(y\right), \color{blue}{\cos \left(\frac{1}{3} \cdot \left(t \cdot z\right)\right)}\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]
   6. Step-by-step derivation

      1. cos-lowering-cos.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{fma.f64}\left(\mathsf{sin.f64}\left(\mathsf{*.f64}\left(t, \mathsf{/.f64}\left(z, 3\right)\right)\right), \mathsf{sin.f64}\left(y\right), \mathsf{*.f64}\left(\mathsf{cos.f64}\left(y\right), \mathsf{cos.f64}\left(\left(\frac{1}{3} \cdot \left(t \cdot z\right)\right)\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{fma.f64}\left(\mathsf{sin.f64}\left(\mathsf{*.f64}\left(t, \mathsf{/.f64}\left(z, 3\right)\right)\right), \mathsf{sin.f64}\left(y\right), \mathsf{*.f64}\left(\mathsf{cos.f64}\left(y\right), \mathsf{cos.f64}\left(\mathsf{*.f64}\left(\frac{1}{3}, \left(t \cdot z\right)\right)\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      3. *-lowering-*.f64 78.4%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{fma.f64}\left(\mathsf{sin.f64}\left(\mathsf{*.f64}\left(t, \mathsf{/.f64}\left(z, 3\right)\right)\right), \mathsf{sin.f64}\left(y\right), \mathsf{*.f64}\left(\mathsf{cos.f64}\left(y\right), \mathsf{cos.f64}\left(\mathsf{*.f64}\left(\frac{1}{3}, \mathsf{*.f64}\left(t, z\right)\right)\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

   7. Simplified 78.4%

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

   if 9.99999999999999953e270 < (-.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 31.7%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \color{blue}{\cos y}\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]
   4. Step-by-step derivation

      1. cos-lowering-cos.f64 63.5%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

   5. Simplified 63.5%

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

      1. associate-/r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{cos.f64}\left(y\right)\right), \left(\frac{\frac{a}{b}}{\color{blue}{3}}\right)\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{/.f64}\left(\left(\frac{a}{b}\right), \color{blue}{3}\right)\right) \]

      3. /-lowering-/.f64 63.5%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{/.f64}\left(\mathsf{/.f64}\left(a, b\right), 3\right)\right) \]

   7. Applied egg-rr 63.5%

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

      1. pow1/2 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \left({x}^{\frac{1}{2}}\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{/.f64}\left(\mathsf{/.f64}\left(a, b\right), 3\right)\right) \]

      2. rem-exp-log N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \left({\left(e^{\log x}\right)}^{\frac{1}{2}}\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{/.f64}\left(\mathsf{/.f64}\left(a, b\right), 3\right)\right) \]

      3. sqr-pow N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \left({\left(e^{\log x}\right)}^{\left(\frac{\frac{1}{2}}{2}\right)} \cdot {\left(e^{\log x}\right)}^{\left(\frac{\frac{1}{2}}{2}\right)}\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{/.f64}\left(\mathsf{/.f64}\left(a, b\right), 3\right)\right) \]

      4. pow2 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \left({\left({\left(e^{\log x}\right)}^{\left(\frac{\frac{1}{2}}{2}\right)}\right)}^{2}\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{/.f64}\left(\mathsf{/.f64}\left(a, b\right), 3\right)\right) \]

      5. pow-lowering-pow.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\left({\left(e^{\log x}\right)}^{\left(\frac{\frac{1}{2}}{2}\right)}\right), 2\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{/.f64}\left(\mathsf{/.f64}\left(a, b\right), 3\right)\right) \]

      6. rem-square-sqrt N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\left({\left(\sqrt{e^{\log x}} \cdot \sqrt{e^{\log x}}\right)}^{\left(\frac{\frac{1}{2}}{2}\right)}\right), 2\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{/.f64}\left(\mathsf{/.f64}\left(a, b\right), 3\right)\right) \]

      7. rem-exp-log N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\left({\left(\sqrt{x} \cdot \sqrt{e^{\log x}}\right)}^{\left(\frac{\frac{1}{2}}{2}\right)}\right), 2\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{/.f64}\left(\mathsf{/.f64}\left(a, b\right), 3\right)\right) \]

      8. rem-exp-log N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\left({\left(\sqrt{x} \cdot \sqrt{x}\right)}^{\left(\frac{\frac{1}{2}}{2}\right)}\right), 2\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{/.f64}\left(\mathsf{/.f64}\left(a, b\right), 3\right)\right) \]

      9. pow-lowering-pow.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\mathsf{pow.f64}\left(\left(\sqrt{x} \cdot \sqrt{x}\right), \left(\frac{\frac{1}{2}}{2}\right)\right), 2\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{/.f64}\left(\mathsf{/.f64}\left(a, b\right), 3\right)\right) \]

      10. rem-exp-log N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\mathsf{pow.f64}\left(\left(\sqrt{e^{\log x}} \cdot \sqrt{x}\right), \left(\frac{\frac{1}{2}}{2}\right)\right), 2\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{/.f64}\left(\mathsf{/.f64}\left(a, b\right), 3\right)\right) \]

      11. rem-exp-log N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\mathsf{pow.f64}\left(\left(\sqrt{e^{\log x}} \cdot \sqrt{e^{\log x}}\right), \left(\frac{\frac{1}{2}}{2}\right)\right), 2\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{/.f64}\left(\mathsf{/.f64}\left(a, b\right), 3\right)\right) \]

      12. rem-square-sqrt N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\mathsf{pow.f64}\left(\left(e^{\log x}\right), \left(\frac{\frac{1}{2}}{2}\right)\right), 2\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{/.f64}\left(\mathsf{/.f64}\left(a, b\right), 3\right)\right) \]

      13. rem-exp-log N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\mathsf{pow.f64}\left(x, \left(\frac{\frac{1}{2}}{2}\right)\right), 2\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{/.f64}\left(\mathsf{/.f64}\left(a, b\right), 3\right)\right) \]

      14. metadata-eval 63.5%

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\mathsf{pow.f64}\left(x, \frac{1}{4}\right), 2\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{/.f64}\left(\mathsf{/.f64}\left(a, b\right), 3\right)\right) \]

   9. Applied egg-rr 63.5%

      \[\leadsto \left(2 \cdot \color{blue}{{\left({x}^{0.25}\right)}^{2}}\right) \cdot \cos y - \frac{\frac{a}{b}}{3} \]

   10. Taylor expanded in y around 0

       \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\mathsf{pow.f64}\left(x, \frac{1}{4}\right), 2\right)\right), \color{blue}{1}\right), \mathsf{/.f64}\left(\mathsf{/.f64}\left(a, b\right), 3\right)\right) \]
   11. Step-by-step derivation

   12. Simplified 65.1%

       \[\leadsto \left(2 \cdot {\left({x}^{0.25}\right)}^{2}\right) \cdot \color{blue}{1} - \frac{\frac{a}{b}}{3} \]
3. Recombined 2 regimes into one program.

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{3 \cdot b} \leq 10^{+271}:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\sin \left(t \cdot \frac{z}{3}\right), \sin y, \cos y \cdot \cos \left(\left(z \cdot t\right) \cdot 0.3333333333333333\right)\right) - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot {\left({x}^{0.25}\right)}^{2} - \frac{\frac{a}{b}}{3}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 77.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \frac{a}{3 \cdot b}\\ t_2 := 2 \cdot \sqrt{x}\\ t_3 := t \cdot \frac{z}{3}\\ \mathbf{if}\;t\_2 \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - t\_1 \leq 10^{+271}:\\ \;\;\;\;t\_2 \cdot \mathsf{fma}\left(\cos t\_3, \cos y, \sin t\_3 \cdot \sin y\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;2 \cdot {\left({x}^{0.25}\right)}^{2} - \frac{\frac{a}{b}}{3}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ a (* 3.0 b))) (t_2 (* 2.0 (sqrt x))) (t_3 (* t (/ z 3.0))))
   (if (<= (- (* t_2 (cos (- y (/ (* z t) 3.0)))) t_1) 1e+271)
     (- (* t_2 (fma (cos t_3) (cos y) (* (sin t_3) (sin y)))) t_1)
     (- (* 2.0 (pow (pow x 0.25) 2.0)) (/ (/ a b) 3.0)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a / (3.0 * b);
	double t_2 = 2.0 * sqrt(x);
	double t_3 = t * (z / 3.0);
	double tmp;
	if (((t_2 * cos((y - ((z * t) / 3.0)))) - t_1) <= 1e+271) {
		tmp = (t_2 * fma(cos(t_3), cos(y), (sin(t_3) * sin(y)))) - t_1;
	} else {
		tmp = (2.0 * pow(pow(x, 0.25), 2.0)) - ((a / b) / 3.0);
	}
	return tmp;
}

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(a / Float64(3.0 * b))
	t_2 = Float64(2.0 * sqrt(x))
	t_3 = Float64(t * Float64(z / 3.0))
	tmp = 0.0
	if (Float64(Float64(t_2 * cos(Float64(y - Float64(Float64(z * t) / 3.0)))) - t_1) <= 1e+271)
		tmp = Float64(Float64(t_2 * fma(cos(t_3), cos(y), Float64(sin(t_3) * sin(y)))) - t_1);
	else
		tmp = Float64(Float64(2.0 * ((x ^ 0.25) ^ 2.0)) - Float64(Float64(a / b) / 3.0));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a / N[(3.0 * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(z / 3.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(t$95$2 * N[Cos[N[(y - N[(N[(z * t), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], 1e+271], N[(N[(t$95$2 * N[(N[Cos[t$95$3], $MachinePrecision] * N[Cos[y], $MachinePrecision] + N[(N[Sin[t$95$3], $MachinePrecision] * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(2.0 * N[Power[N[Power[x, 0.25], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] - N[(N[(a / b), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64))))) (/.f64 a (*.f64 b #s(literal 3 binary64)))) < 9.99999999999999953e270

   1. Initial program 75.9%

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

      1. cos-diff N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \left(\cos y \cdot \cos \left(\frac{z \cdot t}{3}\right) + \sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \left(\cos \left(\frac{z \cdot t}{3}\right) \cdot \cos y + \sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      3. fma-define N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \left(\mathsf{fma}\left(\cos \left(\frac{z \cdot t}{3}\right), \cos y, \sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      4. fma-lowering-fma.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{fma.f64}\left(\cos \left(\frac{z \cdot t}{3}\right), \cos y, \left(\sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      5. cos-lowering-cos.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{fma.f64}\left(\mathsf{cos.f64}\left(\left(\frac{z \cdot t}{3}\right)\right), \cos y, \left(\sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{fma.f64}\left(\mathsf{cos.f64}\left(\left(\frac{t \cdot z}{3}\right)\right), \cos y, \left(\sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      7. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{fma.f64}\left(\mathsf{cos.f64}\left(\left(t \cdot \frac{z}{3}\right)\right), \cos y, \left(\sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{fma.f64}\left(\mathsf{cos.f64}\left(\mathsf{*.f64}\left(t, \left(\frac{z}{3}\right)\right)\right), \cos y, \left(\sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{fma.f64}\left(\mathsf{cos.f64}\left(\mathsf{*.f64}\left(t, \mathsf{/.f64}\left(z, 3\right)\right)\right), \cos y, \left(\sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      10. cos-lowering-cos.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{fma.f64}\left(\mathsf{cos.f64}\left(\mathsf{*.f64}\left(t, \mathsf{/.f64}\left(z, 3\right)\right)\right), \mathsf{cos.f64}\left(y\right), \left(\sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{fma.f64}\left(\mathsf{cos.f64}\left(\mathsf{*.f64}\left(t, \mathsf{/.f64}\left(z, 3\right)\right)\right), \mathsf{cos.f64}\left(y\right), \mathsf{*.f64}\left(\sin y, \sin \left(\frac{z \cdot t}{3}\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      12. sin-lowering-sin.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{fma.f64}\left(\mathsf{cos.f64}\left(\mathsf{*.f64}\left(t, \mathsf{/.f64}\left(z, 3\right)\right)\right), \mathsf{cos.f64}\left(y\right), \mathsf{*.f64}\left(\mathsf{sin.f64}\left(y\right), \sin \left(\frac{z \cdot t}{3}\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      13. sin-lowering-sin.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{fma.f64}\left(\mathsf{cos.f64}\left(\mathsf{*.f64}\left(t, \mathsf{/.f64}\left(z, 3\right)\right)\right), \mathsf{cos.f64}\left(y\right), \mathsf{*.f64}\left(\mathsf{sin.f64}\left(y\right), \mathsf{sin.f64}\left(\left(\frac{z \cdot t}{3}\right)\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{fma.f64}\left(\mathsf{cos.f64}\left(\mathsf{*.f64}\left(t, \mathsf{/.f64}\left(z, 3\right)\right)\right), \mathsf{cos.f64}\left(y\right), \mathsf{*.f64}\left(\mathsf{sin.f64}\left(y\right), \mathsf{sin.f64}\left(\left(\frac{t \cdot z}{3}\right)\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      15. associate-/l* N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{fma.f64}\left(\mathsf{cos.f64}\left(\mathsf{*.f64}\left(t, \mathsf{/.f64}\left(z, 3\right)\right)\right), \mathsf{cos.f64}\left(y\right), \mathsf{*.f64}\left(\mathsf{sin.f64}\left(y\right), \mathsf{sin.f64}\left(\left(t \cdot \frac{z}{3}\right)\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{fma.f64}\left(\mathsf{cos.f64}\left(\mathsf{*.f64}\left(t, \mathsf{/.f64}\left(z, 3\right)\right)\right), \mathsf{cos.f64}\left(y\right), \mathsf{*.f64}\left(\mathsf{sin.f64}\left(y\right), \mathsf{sin.f64}\left(\mathsf{*.f64}\left(t, \left(\frac{z}{3}\right)\right)\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      17. /-lowering-/.f64 78.2%

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{fma.f64}\left(\mathsf{cos.f64}\left(\mathsf{*.f64}\left(t, \mathsf{/.f64}\left(z, 3\right)\right)\right), \mathsf{cos.f64}\left(y\right), \mathsf{*.f64}\left(\mathsf{sin.f64}\left(y\right), \mathsf{sin.f64}\left(\mathsf{*.f64}\left(t, \mathsf{/.f64}\left(z, 3\right)\right)\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

   4. Applied egg-rr 78.2%

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

   if 9.99999999999999953e270 < (-.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 31.7%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \color{blue}{\cos y}\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]
   4. Step-by-step derivation

      1. cos-lowering-cos.f64 63.5%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

   5. Simplified 63.5%

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

      1. associate-/r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{cos.f64}\left(y\right)\right), \left(\frac{\frac{a}{b}}{\color{blue}{3}}\right)\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{/.f64}\left(\left(\frac{a}{b}\right), \color{blue}{3}\right)\right) \]

      3. /-lowering-/.f64 63.5%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{/.f64}\left(\mathsf{/.f64}\left(a, b\right), 3\right)\right) \]

   7. Applied egg-rr 63.5%

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

      1. pow1/2 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \left({x}^{\frac{1}{2}}\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{/.f64}\left(\mathsf{/.f64}\left(a, b\right), 3\right)\right) \]

      2. rem-exp-log N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \left({\left(e^{\log x}\right)}^{\frac{1}{2}}\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{/.f64}\left(\mathsf{/.f64}\left(a, b\right), 3\right)\right) \]

      3. sqr-pow N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \left({\left(e^{\log x}\right)}^{\left(\frac{\frac{1}{2}}{2}\right)} \cdot {\left(e^{\log x}\right)}^{\left(\frac{\frac{1}{2}}{2}\right)}\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{/.f64}\left(\mathsf{/.f64}\left(a, b\right), 3\right)\right) \]

      4. pow2 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \left({\left({\left(e^{\log x}\right)}^{\left(\frac{\frac{1}{2}}{2}\right)}\right)}^{2}\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{/.f64}\left(\mathsf{/.f64}\left(a, b\right), 3\right)\right) \]

      5. pow-lowering-pow.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\left({\left(e^{\log x}\right)}^{\left(\frac{\frac{1}{2}}{2}\right)}\right), 2\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{/.f64}\left(\mathsf{/.f64}\left(a, b\right), 3\right)\right) \]

      6. rem-square-sqrt N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\left({\left(\sqrt{e^{\log x}} \cdot \sqrt{e^{\log x}}\right)}^{\left(\frac{\frac{1}{2}}{2}\right)}\right), 2\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{/.f64}\left(\mathsf{/.f64}\left(a, b\right), 3\right)\right) \]

      7. rem-exp-log N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\left({\left(\sqrt{x} \cdot \sqrt{e^{\log x}}\right)}^{\left(\frac{\frac{1}{2}}{2}\right)}\right), 2\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{/.f64}\left(\mathsf{/.f64}\left(a, b\right), 3\right)\right) \]

      8. rem-exp-log N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\left({\left(\sqrt{x} \cdot \sqrt{x}\right)}^{\left(\frac{\frac{1}{2}}{2}\right)}\right), 2\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{/.f64}\left(\mathsf{/.f64}\left(a, b\right), 3\right)\right) \]

      9. pow-lowering-pow.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\mathsf{pow.f64}\left(\left(\sqrt{x} \cdot \sqrt{x}\right), \left(\frac{\frac{1}{2}}{2}\right)\right), 2\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{/.f64}\left(\mathsf{/.f64}\left(a, b\right), 3\right)\right) \]

      10. rem-exp-log N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\mathsf{pow.f64}\left(\left(\sqrt{e^{\log x}} \cdot \sqrt{x}\right), \left(\frac{\frac{1}{2}}{2}\right)\right), 2\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{/.f64}\left(\mathsf{/.f64}\left(a, b\right), 3\right)\right) \]

      11. rem-exp-log N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\mathsf{pow.f64}\left(\left(\sqrt{e^{\log x}} \cdot \sqrt{e^{\log x}}\right), \left(\frac{\frac{1}{2}}{2}\right)\right), 2\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{/.f64}\left(\mathsf{/.f64}\left(a, b\right), 3\right)\right) \]

      12. rem-square-sqrt N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\mathsf{pow.f64}\left(\left(e^{\log x}\right), \left(\frac{\frac{1}{2}}{2}\right)\right), 2\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{/.f64}\left(\mathsf{/.f64}\left(a, b\right), 3\right)\right) \]

      13. rem-exp-log N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\mathsf{pow.f64}\left(x, \left(\frac{\frac{1}{2}}{2}\right)\right), 2\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{/.f64}\left(\mathsf{/.f64}\left(a, b\right), 3\right)\right) \]

      14. metadata-eval 63.5%

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\mathsf{pow.f64}\left(x, \frac{1}{4}\right), 2\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{/.f64}\left(\mathsf{/.f64}\left(a, b\right), 3\right)\right) \]

   9. Applied egg-rr 63.5%

      \[\leadsto \left(2 \cdot \color{blue}{{\left({x}^{0.25}\right)}^{2}}\right) \cdot \cos y - \frac{\frac{a}{b}}{3} \]

   10. Taylor expanded in y around 0

       \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\mathsf{pow.f64}\left(x, \frac{1}{4}\right), 2\right)\right), \color{blue}{1}\right), \mathsf{/.f64}\left(\mathsf{/.f64}\left(a, b\right), 3\right)\right) \]
   11. Step-by-step derivation

   12. Simplified 65.1%

       \[\leadsto \left(2 \cdot {\left({x}^{0.25}\right)}^{2}\right) \cdot \color{blue}{1} - \frac{\frac{a}{b}}{3} \]
3. Recombined 2 regimes into one program.

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{3 \cdot b} \leq 10^{+271}:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos \left(t \cdot \frac{z}{3}\right), \cos y, \sin \left(t \cdot \frac{z}{3}\right) \cdot \sin y\right) - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot {\left({x}^{0.25}\right)}^{2} - \frac{\frac{a}{b}}{3}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 77.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := t \cdot \frac{z}{3}\\ t_2 := \frac{a}{3 \cdot b}\\ t_3 := 2 \cdot \sqrt{x}\\ \mathbf{if}\;t\_3 \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - t\_2 \leq 10^{+271}:\\ \;\;\;\;t\_3 \cdot \left(\sin t\_1 \cdot \sin y + \cos y \cdot \cos t\_1\right) - t\_2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot {\left({x}^{0.25}\right)}^{2} - \frac{\frac{a}{b}}{3}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (/ z 3.0))) (t_2 (/ a (* 3.0 b))) (t_3 (* 2.0 (sqrt x))))
   (if (<= (- (* t_3 (cos (- y (/ (* z t) 3.0)))) t_2) 1e+271)
     (- (* t_3 (+ (* (sin t_1) (sin y)) (* (cos y) (cos t_1)))) t_2)
     (- (* 2.0 (pow (pow x 0.25) 2.0)) (/ (/ a b) 3.0)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (z / 3.0);
	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) <= 1e+271) {
		tmp = (t_3 * ((sin(t_1) * sin(y)) + (cos(y) * cos(t_1)))) - t_2;
	} else {
		tmp = (2.0 * pow(pow(x, 0.25), 2.0)) - ((a / b) / 3.0);
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = t * (z / 3.0d0)
    t_2 = a / (3.0d0 * b)
    t_3 = 2.0d0 * sqrt(x)
    if (((t_3 * cos((y - ((z * t) / 3.0d0)))) - t_2) <= 1d+271) then
        tmp = (t_3 * ((sin(t_1) * sin(y)) + (cos(y) * cos(t_1)))) - t_2
    else
        tmp = (2.0d0 * ((x ** 0.25d0) ** 2.0d0)) - ((a / b) / 3.0d0)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (z / 3.0);
	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) <= 1e+271) {
		tmp = (t_3 * ((Math.sin(t_1) * Math.sin(y)) + (Math.cos(y) * Math.cos(t_1)))) - t_2;
	} else {
		tmp = (2.0 * Math.pow(Math.pow(x, 0.25), 2.0)) - ((a / b) / 3.0);
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = t * (z / 3.0)
	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) <= 1e+271:
		tmp = (t_3 * ((math.sin(t_1) * math.sin(y)) + (math.cos(y) * math.cos(t_1)))) - t_2
	else:
		tmp = (2.0 * math.pow(math.pow(x, 0.25), 2.0)) - ((a / b) / 3.0)
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(z / 3.0))
	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) <= 1e+271)
		tmp = Float64(Float64(t_3 * Float64(Float64(sin(t_1) * sin(y)) + Float64(cos(y) * cos(t_1)))) - t_2);
	else
		tmp = Float64(Float64(2.0 * ((x ^ 0.25) ^ 2.0)) - Float64(Float64(a / b) / 3.0));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (z / 3.0);
	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) <= 1e+271)
		tmp = (t_3 * ((sin(t_1) * sin(y)) + (cos(y) * cos(t_1)))) - t_2;
	else
		tmp = (2.0 * ((x ^ 0.25) ^ 2.0)) - ((a / b) / 3.0);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(z / 3.0), $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], 1e+271], N[(N[(t$95$3 * N[(N[(N[Sin[t$95$1], $MachinePrecision] * N[Sin[y], $MachinePrecision]), $MachinePrecision] + N[(N[Cos[y], $MachinePrecision] * N[Cos[t$95$1], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], N[(N[(2.0 * N[Power[N[Power[x, 0.25], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] - N[(N[(a / b), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64))))) (/.f64 a (*.f64 b #s(literal 3 binary64)))) < 9.99999999999999953e270

   1. Initial program 75.9%

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

      1. cos-diff N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \left(\cos y \cdot \cos \left(\frac{z \cdot t}{3}\right) + \sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \left(\sin y \cdot \sin \left(\frac{z \cdot t}{3}\right) + \cos y \cdot \cos \left(\frac{z \cdot t}{3}\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{+.f64}\left(\left(\sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right), \left(\cos y \cdot \cos \left(\frac{z \cdot t}{3}\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\sin y, \sin \left(\frac{z \cdot t}{3}\right)\right), \left(\cos y \cdot \cos \left(\frac{z \cdot t}{3}\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      5. sin-lowering-sin.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{sin.f64}\left(y\right), \sin \left(\frac{z \cdot t}{3}\right)\right), \left(\cos y \cdot \cos \left(\frac{z \cdot t}{3}\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      6. sin-lowering-sin.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{sin.f64}\left(y\right), \mathsf{sin.f64}\left(\left(\frac{z \cdot t}{3}\right)\right)\right), \left(\cos y \cdot \cos \left(\frac{z \cdot t}{3}\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{sin.f64}\left(y\right), \mathsf{sin.f64}\left(\left(\frac{t \cdot z}{3}\right)\right)\right), \left(\cos y \cdot \cos \left(\frac{z \cdot t}{3}\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      8. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{sin.f64}\left(y\right), \mathsf{sin.f64}\left(\left(t \cdot \frac{z}{3}\right)\right)\right), \left(\cos y \cdot \cos \left(\frac{z \cdot t}{3}\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{sin.f64}\left(y\right), \mathsf{sin.f64}\left(\mathsf{*.f64}\left(t, \left(\frac{z}{3}\right)\right)\right)\right), \left(\cos y \cdot \cos \left(\frac{z \cdot t}{3}\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{sin.f64}\left(y\right), \mathsf{sin.f64}\left(\mathsf{*.f64}\left(t, \mathsf{/.f64}\left(z, 3\right)\right)\right)\right), \left(\cos y \cdot \cos \left(\frac{z \cdot t}{3}\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{sin.f64}\left(y\right), \mathsf{sin.f64}\left(\mathsf{*.f64}\left(t, \mathsf{/.f64}\left(z, 3\right)\right)\right)\right), \mathsf{*.f64}\left(\cos y, \cos \left(\frac{z \cdot t}{3}\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      12. cos-lowering-cos.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{sin.f64}\left(y\right), \mathsf{sin.f64}\left(\mathsf{*.f64}\left(t, \mathsf{/.f64}\left(z, 3\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{cos.f64}\left(y\right), \cos \left(\frac{z \cdot t}{3}\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      13. cos-lowering-cos.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{sin.f64}\left(y\right), \mathsf{sin.f64}\left(\mathsf{*.f64}\left(t, \mathsf{/.f64}\left(z, 3\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{cos.f64}\left(y\right), \mathsf{cos.f64}\left(\left(\frac{z \cdot t}{3}\right)\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{sin.f64}\left(y\right), \mathsf{sin.f64}\left(\mathsf{*.f64}\left(t, \mathsf{/.f64}\left(z, 3\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{cos.f64}\left(y\right), \mathsf{cos.f64}\left(\left(\frac{t \cdot z}{3}\right)\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      15. associate-/l* N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{sin.f64}\left(y\right), \mathsf{sin.f64}\left(\mathsf{*.f64}\left(t, \mathsf{/.f64}\left(z, 3\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{cos.f64}\left(y\right), \mathsf{cos.f64}\left(\left(t \cdot \frac{z}{3}\right)\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{sin.f64}\left(y\right), \mathsf{sin.f64}\left(\mathsf{*.f64}\left(t, \mathsf{/.f64}\left(z, 3\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{cos.f64}\left(y\right), \mathsf{cos.f64}\left(\mathsf{*.f64}\left(t, \left(\frac{z}{3}\right)\right)\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      17. /-lowering-/.f64 78.2%

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{sin.f64}\left(y\right), \mathsf{sin.f64}\left(\mathsf{*.f64}\left(t, \mathsf{/.f64}\left(z, 3\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{cos.f64}\left(y\right), \mathsf{cos.f64}\left(\mathsf{*.f64}\left(t, \mathsf{/.f64}\left(z, 3\right)\right)\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

   4. Applied egg-rr 78.2%

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

   if 9.99999999999999953e270 < (-.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 31.7%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \color{blue}{\cos y}\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]
   4. Step-by-step derivation

      1. cos-lowering-cos.f64 63.5%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

   5. Simplified 63.5%

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

      1. associate-/r* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{cos.f64}\left(y\right)\right), \left(\frac{\frac{a}{b}}{\color{blue}{3}}\right)\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{/.f64}\left(\left(\frac{a}{b}\right), \color{blue}{3}\right)\right) \]

      3. /-lowering-/.f64 63.5%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{/.f64}\left(\mathsf{/.f64}\left(a, b\right), 3\right)\right) \]

   7. Applied egg-rr 63.5%

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

      1. pow1/2 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \left({x}^{\frac{1}{2}}\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{/.f64}\left(\mathsf{/.f64}\left(a, b\right), 3\right)\right) \]

      2. rem-exp-log N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \left({\left(e^{\log x}\right)}^{\frac{1}{2}}\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{/.f64}\left(\mathsf{/.f64}\left(a, b\right), 3\right)\right) \]

      3. sqr-pow N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \left({\left(e^{\log x}\right)}^{\left(\frac{\frac{1}{2}}{2}\right)} \cdot {\left(e^{\log x}\right)}^{\left(\frac{\frac{1}{2}}{2}\right)}\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{/.f64}\left(\mathsf{/.f64}\left(a, b\right), 3\right)\right) \]

      4. pow2 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \left({\left({\left(e^{\log x}\right)}^{\left(\frac{\frac{1}{2}}{2}\right)}\right)}^{2}\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{/.f64}\left(\mathsf{/.f64}\left(a, b\right), 3\right)\right) \]

      5. pow-lowering-pow.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\left({\left(e^{\log x}\right)}^{\left(\frac{\frac{1}{2}}{2}\right)}\right), 2\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{/.f64}\left(\mathsf{/.f64}\left(a, b\right), 3\right)\right) \]

      6. rem-square-sqrt N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\left({\left(\sqrt{e^{\log x}} \cdot \sqrt{e^{\log x}}\right)}^{\left(\frac{\frac{1}{2}}{2}\right)}\right), 2\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{/.f64}\left(\mathsf{/.f64}\left(a, b\right), 3\right)\right) \]

      7. rem-exp-log N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\left({\left(\sqrt{x} \cdot \sqrt{e^{\log x}}\right)}^{\left(\frac{\frac{1}{2}}{2}\right)}\right), 2\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{/.f64}\left(\mathsf{/.f64}\left(a, b\right), 3\right)\right) \]

      8. rem-exp-log N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\left({\left(\sqrt{x} \cdot \sqrt{x}\right)}^{\left(\frac{\frac{1}{2}}{2}\right)}\right), 2\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{/.f64}\left(\mathsf{/.f64}\left(a, b\right), 3\right)\right) \]

      9. pow-lowering-pow.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\mathsf{pow.f64}\left(\left(\sqrt{x} \cdot \sqrt{x}\right), \left(\frac{\frac{1}{2}}{2}\right)\right), 2\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{/.f64}\left(\mathsf{/.f64}\left(a, b\right), 3\right)\right) \]

      10. rem-exp-log N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\mathsf{pow.f64}\left(\left(\sqrt{e^{\log x}} \cdot \sqrt{x}\right), \left(\frac{\frac{1}{2}}{2}\right)\right), 2\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{/.f64}\left(\mathsf{/.f64}\left(a, b\right), 3\right)\right) \]

      11. rem-exp-log N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\mathsf{pow.f64}\left(\left(\sqrt{e^{\log x}} \cdot \sqrt{e^{\log x}}\right), \left(\frac{\frac{1}{2}}{2}\right)\right), 2\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{/.f64}\left(\mathsf{/.f64}\left(a, b\right), 3\right)\right) \]

      12. rem-square-sqrt N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\mathsf{pow.f64}\left(\left(e^{\log x}\right), \left(\frac{\frac{1}{2}}{2}\right)\right), 2\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{/.f64}\left(\mathsf{/.f64}\left(a, b\right), 3\right)\right) \]

      13. rem-exp-log N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\mathsf{pow.f64}\left(x, \left(\frac{\frac{1}{2}}{2}\right)\right), 2\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{/.f64}\left(\mathsf{/.f64}\left(a, b\right), 3\right)\right) \]

      14. metadata-eval 63.5%

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\mathsf{pow.f64}\left(x, \frac{1}{4}\right), 2\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{/.f64}\left(\mathsf{/.f64}\left(a, b\right), 3\right)\right) \]

   9. Applied egg-rr 63.5%

      \[\leadsto \left(2 \cdot \color{blue}{{\left({x}^{0.25}\right)}^{2}}\right) \cdot \cos y - \frac{\frac{a}{b}}{3} \]

   10. Taylor expanded in y around 0

       \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\mathsf{pow.f64}\left(x, \frac{1}{4}\right), 2\right)\right), \color{blue}{1}\right), \mathsf{/.f64}\left(\mathsf{/.f64}\left(a, b\right), 3\right)\right) \]
   11. Step-by-step derivation

   12. Simplified 65.1%

       \[\leadsto \left(2 \cdot {\left({x}^{0.25}\right)}^{2}\right) \cdot \color{blue}{1} - \frac{\frac{a}{b}}{3} \]
3. Recombined 2 regimes into one program.

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{3 \cdot b} \leq 10^{+271}:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \left(\sin \left(t \cdot \frac{z}{3}\right) \cdot \sin y + \cos y \cdot \cos \left(t \cdot \frac{z}{3}\right)\right) - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot {\left({x}^{0.25}\right)}^{2} - \frac{\frac{a}{b}}{3}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 71.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \frac{a}{3 \cdot b}\\ t_2 := 2 \cdot \sqrt{x} - t\_1\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{-67}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-142}:\\ \;\;\;\;2 \cdot \left(\sqrt{x} \cdot \cos \left(t \cdot \left(z \cdot 0.3333333333333333\right) - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ a (* 3.0 b))) (t_2 (- (* 2.0 (sqrt x)) t_1)))
   (if (<= t_1 -4e-67)
     t_2
     (if (<= t_1 5e-142)
       (* 2.0 (* (sqrt x) (cos (- (* t (* z 0.3333333333333333)) y))))
       t_2))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a / (3.0 * b);
	double t_2 = (2.0 * sqrt(x)) - t_1;
	double tmp;
	if (t_1 <= -4e-67) {
		tmp = t_2;
	} else if (t_1 <= 5e-142) {
		tmp = 2.0 * (sqrt(x) * cos(((t * (z * 0.3333333333333333)) - y)));
	} else {
		tmp = t_2;
	}
	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 = a / (3.0d0 * b)
    t_2 = (2.0d0 * sqrt(x)) - t_1
    if (t_1 <= (-4d-67)) then
        tmp = t_2
    else if (t_1 <= 5d-142) then
        tmp = 2.0d0 * (sqrt(x) * cos(((t * (z * 0.3333333333333333d0)) - y)))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a / (3.0 * b);
	double t_2 = (2.0 * Math.sqrt(x)) - t_1;
	double tmp;
	if (t_1 <= -4e-67) {
		tmp = t_2;
	} else if (t_1 <= 5e-142) {
		tmp = 2.0 * (Math.sqrt(x) * Math.cos(((t * (z * 0.3333333333333333)) - y)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = a / (3.0 * b)
	t_2 = (2.0 * math.sqrt(x)) - t_1
	tmp = 0
	if t_1 <= -4e-67:
		tmp = t_2
	elif t_1 <= 5e-142:
		tmp = 2.0 * (math.sqrt(x) * math.cos(((t * (z * 0.3333333333333333)) - y)))
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(a / Float64(3.0 * b))
	t_2 = Float64(Float64(2.0 * sqrt(x)) - t_1)
	tmp = 0.0
	if (t_1 <= -4e-67)
		tmp = t_2;
	elseif (t_1 <= 5e-142)
		tmp = Float64(2.0 * Float64(sqrt(x) * cos(Float64(Float64(t * Float64(z * 0.3333333333333333)) - y))));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a / (3.0 * b);
	t_2 = (2.0 * sqrt(x)) - t_1;
	tmp = 0.0;
	if (t_1 <= -4e-67)
		tmp = t_2;
	elseif (t_1 <= 5e-142)
		tmp = 2.0 * (sqrt(x) * cos(((t * (z * 0.3333333333333333)) - y)));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a / N[(3.0 * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]}, If[LessEqual[t$95$1, -4e-67], t$95$2, If[LessEqual[t$95$1, 5e-142], N[(2.0 * N[(N[Sqrt[x], $MachinePrecision] * N[Cos[N[(N[(t * N[(z * 0.3333333333333333), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 a (*.f64 b #s(literal 3 binary64))) < -3.99999999999999977e-67 or 5.0000000000000002e-142 < (/.f64 a (*.f64 b #s(literal 3 binary64)))

   1. Initial program 74.4%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \color{blue}{\cos y}\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]
   4. Step-by-step derivation

      1. cos-lowering-cos.f64 83.2%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

   5. Simplified 83.2%

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

   6. Taylor expanded in y around 0

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(2 \cdot \sqrt{x}\right)}, \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(2, \left(\sqrt{x}\right)\right), \mathsf{/.f64}\left(\color{blue}{a}, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      2. sqrt-lowering-sqrt.f64 78.1%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

   8. Simplified 78.1%

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

   if -3.99999999999999977e-67 < (/.f64 a (*.f64 b #s(literal 3 binary64))) < 5.0000000000000002e-142

   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. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{\left(\sqrt{x} \cdot \cos \left(y - \frac{1}{3} \cdot \left(t \cdot z\right)\right)\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\left(\sqrt{x}\right), \color{blue}{\cos \left(y - \frac{1}{3} \cdot \left(t \cdot z\right)\right)}\right)\right) \]

      3. sqrt-lowering-sqrt.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \cos \color{blue}{\left(y - \frac{1}{3} \cdot \left(t \cdot z\right)\right)}\right)\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \cos \left(y + \left(\mathsf{neg}\left(\frac{1}{3} \cdot \left(t \cdot z\right)\right)\right)\right)\right)\right) \]

      5. remove-double-neg N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \cos \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(y\right)\right)\right)\right) + \left(\mathsf{neg}\left(\frac{1}{3} \cdot \left(t \cdot z\right)\right)\right)\right)\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \cos \left(\left(\mathsf{neg}\left(-1 \cdot y\right)\right) + \left(\mathsf{neg}\left(\frac{1}{3} \cdot \left(t \cdot z\right)\right)\right)\right)\right)\right) \]

      7. distribute-neg-in N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \cos \left(\mathsf{neg}\left(\left(-1 \cdot y + \frac{1}{3} \cdot \left(t \cdot z\right)\right)\right)\right)\right)\right) \]

      8. cos-neg N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \cos \left(-1 \cdot y + \frac{1}{3} \cdot \left(t \cdot z\right)\right)\right)\right) \]

      9. cos-lowering-cos.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{cos.f64}\left(\left(-1 \cdot y + \frac{1}{3} \cdot \left(t \cdot z\right)\right)\right)\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{cos.f64}\left(\left(\frac{1}{3} \cdot \left(t \cdot z\right) + -1 \cdot y\right)\right)\right)\right) \]

      11. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{cos.f64}\left(\left(\frac{1}{3} \cdot \left(t \cdot z\right) + \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right)\right) \]

      12. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{cos.f64}\left(\left(\frac{1}{3} \cdot \left(t \cdot z\right) - y\right)\right)\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{cos.f64}\left(\mathsf{\_.f64}\left(\left(\frac{1}{3} \cdot \left(t \cdot z\right)\right), y\right)\right)\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{cos.f64}\left(\mathsf{\_.f64}\left(\left(\left(t \cdot z\right) \cdot \frac{1}{3}\right), y\right)\right)\right)\right) \]

      15. associate-*l* N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{cos.f64}\left(\mathsf{\_.f64}\left(\left(t \cdot \left(z \cdot \frac{1}{3}\right)\right), y\right)\right)\right)\right) \]

      16. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{cos.f64}\left(\mathsf{\_.f64}\left(\left(t \cdot \left(z \cdot \left(\mathsf{neg}\left(\frac{-1}{3}\right)\right)\right)\right), y\right)\right)\right)\right) \]

      17. distribute-rgt-neg-in N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{cos.f64}\left(\mathsf{\_.f64}\left(\left(t \cdot \left(\mathsf{neg}\left(z \cdot \frac{-1}{3}\right)\right)\right), y\right)\right)\right)\right) \]

      18. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{cos.f64}\left(\mathsf{\_.f64}\left(\left(t \cdot \left(\mathsf{neg}\left(\frac{-1}{3} \cdot z\right)\right)\right), y\right)\right)\right)\right) \]

      19. distribute-lft-neg-in N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{cos.f64}\left(\mathsf{\_.f64}\left(\left(t \cdot \left(\left(\mathsf{neg}\left(\frac{-1}{3}\right)\right) \cdot z\right)\right), y\right)\right)\right)\right) \]

      20. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{cos.f64}\left(\mathsf{\_.f64}\left(\left(t \cdot \left(\frac{1}{3} \cdot z\right)\right), y\right)\right)\right)\right) \]

      21. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{cos.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \left(\frac{1}{3} \cdot z\right)\right), y\right)\right)\right)\right) \]

      22. *-lowering-*.f64 57.3%

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{cos.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(t, \mathsf{*.f64}\left(\frac{1}{3}, z\right)\right), y\right)\right)\right)\right) \]

   5. Simplified 57.3%

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

4. Final simplification 70.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{a}{3 \cdot b} \leq -4 \cdot 10^{-67}:\\ \;\;\;\;2 \cdot \sqrt{x} - \frac{a}{3 \cdot b}\\ \mathbf{elif}\;\frac{a}{3 \cdot b} \leq 5 \cdot 10^{-142}:\\ \;\;\;\;2 \cdot \left(\sqrt{x} \cdot \cos \left(t \cdot \left(z \cdot 0.3333333333333333\right) - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{x} - \frac{a}{3 \cdot b}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 72.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \frac{a}{3 \cdot b}\\ t_2 := 2 \cdot \sqrt{x} - t\_1\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-66}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-110}:\\ \;\;\;\;\sqrt{x} \cdot \left(2 \cdot \cos y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ a (* 3.0 b))) (t_2 (- (* 2.0 (sqrt x)) t_1)))
   (if (<= t_1 -5e-66)
     t_2
     (if (<= t_1 5e-110) (* (sqrt x) (* 2.0 (cos y))) t_2))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a / (3.0 * b);
	double t_2 = (2.0 * sqrt(x)) - t_1;
	double tmp;
	if (t_1 <= -5e-66) {
		tmp = t_2;
	} else if (t_1 <= 5e-110) {
		tmp = sqrt(x) * (2.0 * cos(y));
	} else {
		tmp = t_2;
	}
	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 = a / (3.0d0 * b)
    t_2 = (2.0d0 * sqrt(x)) - t_1
    if (t_1 <= (-5d-66)) then
        tmp = t_2
    else if (t_1 <= 5d-110) then
        tmp = sqrt(x) * (2.0d0 * cos(y))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a / (3.0 * b);
	double t_2 = (2.0 * Math.sqrt(x)) - t_1;
	double tmp;
	if (t_1 <= -5e-66) {
		tmp = t_2;
	} else if (t_1 <= 5e-110) {
		tmp = Math.sqrt(x) * (2.0 * Math.cos(y));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = a / (3.0 * b)
	t_2 = (2.0 * math.sqrt(x)) - t_1
	tmp = 0
	if t_1 <= -5e-66:
		tmp = t_2
	elif t_1 <= 5e-110:
		tmp = math.sqrt(x) * (2.0 * math.cos(y))
	else:
		tmp = t_2
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(a / Float64(3.0 * b))
	t_2 = Float64(Float64(2.0 * sqrt(x)) - t_1)
	tmp = 0.0
	if (t_1 <= -5e-66)
		tmp = t_2;
	elseif (t_1 <= 5e-110)
		tmp = Float64(sqrt(x) * Float64(2.0 * cos(y)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a / (3.0 * b);
	t_2 = (2.0 * sqrt(x)) - t_1;
	tmp = 0.0;
	if (t_1 <= -5e-66)
		tmp = t_2;
	elseif (t_1 <= 5e-110)
		tmp = sqrt(x) * (2.0 * cos(y));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a / N[(3.0 * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]}, If[LessEqual[t$95$1, -5e-66], t$95$2, If[LessEqual[t$95$1, 5e-110], N[(N[Sqrt[x], $MachinePrecision] * N[(2.0 * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 a (*.f64 b #s(literal 3 binary64))) < -4.99999999999999962e-66 or 5e-110 < (/.f64 a (*.f64 b #s(literal 3 binary64)))

   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. Add Preprocessing

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \color{blue}{\cos y}\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]
   4. Step-by-step derivation

      1. cos-lowering-cos.f64 84.3%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

   5. Simplified 84.3%

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

   6. Taylor expanded in y around 0

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(2 \cdot \sqrt{x}\right)}, \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(2, \left(\sqrt{x}\right)\right), \mathsf{/.f64}\left(\color{blue}{a}, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      2. sqrt-lowering-sqrt.f64 79.0%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

   8. Simplified 79.0%

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

   if -4.99999999999999962e-66 < (/.f64 a (*.f64 b #s(literal 3 binary64))) < 5e-110

   1. Initial program 57.9%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \color{blue}{\cos y}\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]
   4. Step-by-step derivation

      1. cos-lowering-cos.f64 57.6%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

   5. Simplified 57.6%

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

   6. Taylor expanded in x around inf

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

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

      3. associate-*l* N/A

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

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\sqrt{x}\right), \color{blue}{\left(2 \cdot \cos y\right)}\right) \]

      5. sqrt-lowering-sqrt.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(\color{blue}{2} \cdot \cos y\right)\right) \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{*.f64}\left(2, \color{blue}{\cos y}\right)\right) \]

      7. cos-lowering-cos.f64 56.3%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{*.f64}\left(2, \mathsf{cos.f64}\left(y\right)\right)\right) \]

   8. Simplified 56.3%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{a}{3 \cdot b} \leq -5 \cdot 10^{-66}:\\ \;\;\;\;2 \cdot \sqrt{x} - \frac{a}{3 \cdot b}\\ \mathbf{elif}\;\frac{a}{3 \cdot b} \leq 5 \cdot 10^{-110}:\\ \;\;\;\;\sqrt{x} \cdot \left(2 \cdot \cos y\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{x} - \frac{a}{3 \cdot b}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 76.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 68.3%

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

3. Taylor expanded in z around 0

   \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \color{blue}{\cos y}\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]
4. Step-by-step derivation

   1. cos-lowering-cos.f64 73.5%

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

5. Simplified 73.5%

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

6. Final simplification 73.5%

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

Alternative 7: 58.9% accurate, 1.7× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \frac{a}{3 \cdot b}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-101}:\\ \;\;\;\;\frac{a}{b} \cdot -0.3333333333333333\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-42}:\\ \;\;\;\;\sqrt{x} \cdot \left(2 - y \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{-0.3333333333333333}{b}\\ \end{array} \end{array} \]

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 (/ a (* 3.0 b))))
   (if (<= t_1 -1e-101)
     (* (/ a b) -0.3333333333333333)
     (if (<= t_1 2e-42)
       (* (sqrt x) (- 2.0 (* y 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) {
	double t_1 = a / (3.0 * b);
	double tmp;
	if (t_1 <= -1e-101) {
		tmp = (a / b) * -0.3333333333333333;
	} else if (t_1 <= 2e-42) {
		tmp = sqrt(x) * (2.0 - (y * y));
	} else {
		tmp = 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 = a / (3.0d0 * b)
    if (t_1 <= (-1d-101)) then
        tmp = (a / b) * (-0.3333333333333333d0)
    else if (t_1 <= 2d-42) then
        tmp = sqrt(x) * (2.0d0 - (y * y))
    else
        tmp = 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 = a / (3.0 * b);
	double tmp;
	if (t_1 <= -1e-101) {
		tmp = (a / b) * -0.3333333333333333;
	} else if (t_1 <= 2e-42) {
		tmp = Math.sqrt(x) * (2.0 - (y * y));
	} else {
		tmp = 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 = a / (3.0 * b)
	tmp = 0
	if t_1 <= -1e-101:
		tmp = (a / b) * -0.3333333333333333
	elif t_1 <= 2e-42:
		tmp = math.sqrt(x) * (2.0 - (y * y))
	else:
		tmp = 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(a / Float64(3.0 * b))
	tmp = 0.0
	if (t_1 <= -1e-101)
		tmp = Float64(Float64(a / b) * -0.3333333333333333);
	elseif (t_1 <= 2e-42)
		tmp = Float64(sqrt(x) * Float64(2.0 - Float64(y * y)));
	else
		tmp = Float64(a * Float64(-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 = a / (3.0 * b);
	tmp = 0.0;
	if (t_1 <= -1e-101)
		tmp = (a / b) * -0.3333333333333333;
	elseif (t_1 <= 2e-42)
		tmp = sqrt(x) * (2.0 - (y * y));
	else
		tmp = 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[(a / N[(3.0 * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-101], N[(N[(a / b), $MachinePrecision] * -0.3333333333333333), $MachinePrecision], If[LessEqual[t$95$1, 2e-42], N[(N[Sqrt[x], $MachinePrecision] * N[(2.0 - N[(y * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(-0.3333333333333333 / b), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 a (*.f64 b #s(literal 3 binary64))) < -1.00000000000000005e-101

   1. Initial program 71.9%

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

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{\frac{-1}{3} \cdot \frac{a}{b}} \]
   4. Step-by-step derivation

      1. *-commutative N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{a}{b}\right), \color{blue}{\frac{-1}{3}}\right) \]

      3. /-lowering-/.f64 68.8%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(a, b\right), \frac{-1}{3}\right) \]

   5. Simplified 68.8%

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

   if -1.00000000000000005e-101 < (/.f64 a (*.f64 b #s(literal 3 binary64))) < 2.00000000000000008e-42

   1. Initial program 57.2%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \color{blue}{\cos y}\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]
   4. Step-by-step derivation

      1. cos-lowering-cos.f64 57.2%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

   5. Simplified 57.2%

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

   6. Taylor expanded in y around 0

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(-1 \cdot \left(\sqrt{x} \cdot {y}^{2}\right) + 2 \cdot \sqrt{x}\right)}, \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]
   7. Step-by-step derivation

      1. +-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(2 \cdot \sqrt{x} + -1 \cdot \left(\sqrt{x} \cdot {y}^{2}\right)\right), \mathsf{/.f64}\left(\color{blue}{a}, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      2. mul-1-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(2 \cdot \sqrt{x} + \left(\mathsf{neg}\left(\sqrt{x} \cdot {y}^{2}\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      3. unsub-neg N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(2 \cdot \sqrt{x} - \sqrt{x} \cdot {y}^{2}\right), \mathsf{/.f64}\left(\color{blue}{a}, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      4. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\left(2 \cdot \sqrt{x}\right), \left(\sqrt{x} \cdot {y}^{2}\right)\right), \mathsf{/.f64}\left(\color{blue}{a}, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(2, \left(\sqrt{x}\right)\right), \left(\sqrt{x} \cdot {y}^{2}\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      6. sqrt-lowering-sqrt.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \left(\sqrt{x} \cdot {y}^{2}\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \left({y}^{2} \cdot \sqrt{x}\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      8. unpow2 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \left(\left(y \cdot y\right) \cdot \sqrt{x}\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      9. associate-*l* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \left(y \cdot \left(y \cdot \sqrt{x}\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \left(y \cdot \left(\sqrt{x} \cdot y\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{*.f64}\left(y, \left(\sqrt{x} \cdot y\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(\left(\sqrt{x}\right), y\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      13. sqrt-lowering-sqrt.f64 36.7%

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), y\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

   8. Simplified 36.7%

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

   9. Taylor expanded in a around 0

      \[\leadsto \color{blue}{2 \cdot \sqrt{x} - \sqrt{x} \cdot {y}^{2}} \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \sqrt{x} \cdot 2 - \color{blue}{\sqrt{x}} \cdot {y}^{2} \]

       2. distribute-lft-out-- N/A

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

       3. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(\sqrt{x}\right), \color{blue}{\left(2 - {y}^{2}\right)}\right) \]

       4. sqrt-lowering-sqrt.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(\color{blue}{2} - {y}^{2}\right)\right) \]

       5. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{\_.f64}\left(2, \color{blue}{\left({y}^{2}\right)}\right)\right) \]

       6. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{\_.f64}\left(2, \left(y \cdot \color{blue}{y}\right)\right)\right) \]

       7. *-lowering-*.f64 34.8%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{\_.f64}\left(2, \mathsf{*.f64}\left(y, \color{blue}{y}\right)\right)\right) \]

   11. Simplified 34.8%

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

   if 2.00000000000000008e-42 < (/.f64 a (*.f64 b #s(literal 3 binary64)))

   1. Initial program 81.2%

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

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{\frac{-1}{3} \cdot \frac{a}{b}} \]
   4. Step-by-step derivation

      1. *-commutative N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{a}{b}\right), \color{blue}{\frac{-1}{3}}\right) \]

      3. /-lowering-/.f64 78.5%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(a, b\right), \frac{-1}{3}\right) \]

   5. Simplified 78.5%

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

      1. associate-*l/ N/A

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

      2. associate-/l* N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(\frac{\frac{-1}{3}}{b}\right)}\right) \]

      4. /-lowering-/.f64 78.5%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{/.f64}\left(\frac{-1}{3}, \color{blue}{b}\right)\right) \]

   7. Applied egg-rr 78.5%

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

4. Final simplification 57.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{a}{3 \cdot b} \leq -1 \cdot 10^{-101}:\\ \;\;\;\;\frac{a}{b} \cdot -0.3333333333333333\\ \mathbf{elif}\;\frac{a}{3 \cdot b} \leq 2 \cdot 10^{-42}:\\ \;\;\;\;\sqrt{x} \cdot \left(2 - y \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;a \cdot \frac{-0.3333333333333333}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 65.7% accurate, 2.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 68.3%

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

3. Taylor expanded in z around 0

   \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \color{blue}{\cos y}\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]
4. Step-by-step derivation

   1. cos-lowering-cos.f64 73.5%

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

5. Simplified 73.5%

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

6. Taylor expanded in y around 0

   \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(2 \cdot \sqrt{x}\right)}, \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]
7. Step-by-step derivation

   1. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(2, \left(\sqrt{x}\right)\right), \mathsf{/.f64}\left(\color{blue}{a}, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

   2. sqrt-lowering-sqrt.f64 62.0%

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

8. Simplified 62.0%

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

9. Final simplification 62.0%

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

Alternative 9: 51.1% 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 68.3%

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

3. Taylor expanded in a around inf

   \[\leadsto \color{blue}{\frac{-1}{3} \cdot \frac{a}{b}} \]
4. Step-by-step derivation

   1. *-commutative N/A

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

   2. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\left(\frac{a}{b}\right), \color{blue}{\frac{-1}{3}}\right) \]

   3. /-lowering-/.f64 45.2%

      \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(a, b\right), \frac{-1}{3}\right) \]

5. Simplified 45.2%

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

   1. *-commutative N/A

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

   2. clear-num N/A

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

   3. un-div-inv N/A

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

   4. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\frac{-1}{3}, \color{blue}{\left(\frac{b}{a}\right)}\right) \]

   5. /-lowering-/.f64 45.2%

      \[\leadsto \mathsf{/.f64}\left(\frac{-1}{3}, \mathsf{/.f64}\left(b, \color{blue}{a}\right)\right) \]

7. Applied egg-rr 45.2%

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

   1. clear-num N/A

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

   2. associate-/r/ N/A

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

   3. clear-num N/A

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

   4. metadata-eval N/A

      \[\leadsto \frac{a}{b} \cdot \left(\mathsf{neg}\left(\frac{1}{3}\right)\right) \]

   5. distribute-rgt-neg-in N/A

      \[\leadsto \mathsf{neg}\left(\frac{a}{b} \cdot \frac{1}{3}\right) \]

   6. metadata-eval N/A

      \[\leadsto \mathsf{neg}\left(\frac{a}{b} \cdot \frac{1}{3}\right) \]

   7. div-inv N/A

      \[\leadsto \mathsf{neg}\left(\frac{\frac{a}{b}}{3}\right) \]

   8. associate-/r* N/A

      \[\leadsto \mathsf{neg}\left(\frac{a}{b \cdot 3}\right) \]

   9. distribute-neg-frac2 N/A

      \[\leadsto \frac{a}{\color{blue}{\mathsf{neg}\left(b \cdot 3\right)}} \]

   10. /-lowering-/.f64 N/A

       \[\leadsto \mathsf{/.f64}\left(a, \color{blue}{\left(\mathsf{neg}\left(b \cdot 3\right)\right)}\right) \]

   11. distribute-rgt-neg-in N/A

       \[\leadsto \mathsf{/.f64}\left(a, \left(b \cdot \color{blue}{\left(\mathsf{neg}\left(3\right)\right)}\right)\right) \]

   12. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, \color{blue}{\left(\mathsf{neg}\left(3\right)\right)}\right)\right) \]

   13. metadata-eval 45.2%

       \[\leadsto \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, -3\right)\right) \]

9. Applied egg-rr 45.2%

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

Alternative 10: 51.1% accurate, 43.4× speedup

Math

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

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) -0.3333333333333333))

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) * -0.3333333333333333;
}

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) * (-0.3333333333333333d0)
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) * -0.3333333333333333;
}

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) * -0.3333333333333333

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 / b) * -0.3333333333333333)
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) * -0.3333333333333333;
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 / b), $MachinePrecision] * -0.3333333333333333), $MachinePrecision]

Derivation

1. Initial program 68.3%

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

3. Taylor expanded in a around inf

   \[\leadsto \color{blue}{\frac{-1}{3} \cdot \frac{a}{b}} \]
4. Step-by-step derivation

   1. *-commutative N/A

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

   2. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\left(\frac{a}{b}\right), \color{blue}{\frac{-1}{3}}\right) \]

   3. /-lowering-/.f64 45.2%

      \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(a, b\right), \frac{-1}{3}\right) \]

5. Simplified 45.2%

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

Alternative 11: 51.1% accurate, 43.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 68.3%

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

3. Taylor expanded in a around inf

   \[\leadsto \color{blue}{\frac{-1}{3} \cdot \frac{a}{b}} \]
4. Step-by-step derivation

   1. *-commutative N/A

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

   2. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\left(\frac{a}{b}\right), \color{blue}{\frac{-1}{3}}\right) \]

   3. /-lowering-/.f64 45.2%

      \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(a, b\right), \frac{-1}{3}\right) \]

5. Simplified 45.2%

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

   1. associate-*l/ N/A

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

   2. associate-/l* N/A

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

   3. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(\frac{\frac{-1}{3}}{b}\right)}\right) \]

   4. /-lowering-/.f64 45.2%

      \[\leadsto \mathsf{*.f64}\left(a, \mathsf{/.f64}\left(\frac{-1}{3}, \color{blue}{b}\right)\right) \]

7. Applied egg-rr 45.2%

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

Developer Target 1: 74.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{0.3333333333333333}{z}}{t}\\ t_2 := \frac{\frac{a}{3}}{b}\\ t_3 := 2 \cdot \sqrt{x}\\ \mathbf{if}\;z < -1.3793337487235141 \cdot 10^{+129}:\\ \;\;\;\;t\_3 \cdot \cos \left(\frac{1}{y} - t\_1\right) - t\_2\\ \mathbf{elif}\;z < 3.516290613555987 \cdot 10^{+106}:\\ \;\;\;\;\left(\sqrt{x} \cdot 2\right) \cdot \cos \left(y - \frac{t}{3} \cdot z\right) - t\_2\\ \mathbf{else}:\\ \;\;\;\;\cos \left(y - t\_1\right) \cdot t\_3 - \frac{\frac{a}{b}}{3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (/ 0.3333333333333333 z) t))
        (t_2 (/ (/ a 3.0) b))
        (t_3 (* 2.0 (sqrt x))))
   (if (< z -1.3793337487235141e+129)
     (- (* t_3 (cos (- (/ 1.0 y) t_1))) t_2)
     (if (< z 3.516290613555987e+106)
       (- (* (* (sqrt x) 2.0) (cos (- y (* (/ t 3.0) z)))) t_2)
       (- (* (cos (- y t_1)) t_3) (/ (/ a b) 3.0))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (0.3333333333333333 / z) / t;
	double t_2 = (a / 3.0) / b;
	double t_3 = 2.0 * sqrt(x);
	double tmp;
	if (z < -1.3793337487235141e+129) {
		tmp = (t_3 * cos(((1.0 / y) - t_1))) - t_2;
	} else if (z < 3.516290613555987e+106) {
		tmp = ((sqrt(x) * 2.0) * cos((y - ((t / 3.0) * z)))) - t_2;
	} else {
		tmp = (cos((y - t_1)) * t_3) - ((a / b) / 3.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (0.3333333333333333d0 / z) / t
    t_2 = (a / 3.0d0) / b
    t_3 = 2.0d0 * sqrt(x)
    if (z < (-1.3793337487235141d+129)) then
        tmp = (t_3 * cos(((1.0d0 / y) - t_1))) - t_2
    else if (z < 3.516290613555987d+106) then
        tmp = ((sqrt(x) * 2.0d0) * cos((y - ((t / 3.0d0) * z)))) - t_2
    else
        tmp = (cos((y - t_1)) * t_3) - ((a / b) / 3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (0.3333333333333333 / z) / t;
	double t_2 = (a / 3.0) / b;
	double t_3 = 2.0 * Math.sqrt(x);
	double tmp;
	if (z < -1.3793337487235141e+129) {
		tmp = (t_3 * Math.cos(((1.0 / y) - t_1))) - t_2;
	} else if (z < 3.516290613555987e+106) {
		tmp = ((Math.sqrt(x) * 2.0) * Math.cos((y - ((t / 3.0) * z)))) - t_2;
	} else {
		tmp = (Math.cos((y - t_1)) * t_3) - ((a / b) / 3.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (0.3333333333333333 / z) / t
	t_2 = (a / 3.0) / b
	t_3 = 2.0 * math.sqrt(x)
	tmp = 0
	if z < -1.3793337487235141e+129:
		tmp = (t_3 * math.cos(((1.0 / y) - t_1))) - t_2
	elif z < 3.516290613555987e+106:
		tmp = ((math.sqrt(x) * 2.0) * math.cos((y - ((t / 3.0) * z)))) - t_2
	else:
		tmp = (math.cos((y - t_1)) * t_3) - ((a / b) / 3.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(0.3333333333333333 / z) / t)
	t_2 = Float64(Float64(a / 3.0) / b)
	t_3 = Float64(2.0 * sqrt(x))
	tmp = 0.0
	if (z < -1.3793337487235141e+129)
		tmp = Float64(Float64(t_3 * cos(Float64(Float64(1.0 / y) - t_1))) - t_2);
	elseif (z < 3.516290613555987e+106)
		tmp = Float64(Float64(Float64(sqrt(x) * 2.0) * cos(Float64(y - Float64(Float64(t / 3.0) * z)))) - t_2);
	else
		tmp = Float64(Float64(cos(Float64(y - t_1)) * t_3) - Float64(Float64(a / b) / 3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (0.3333333333333333 / z) / t;
	t_2 = (a / 3.0) / b;
	t_3 = 2.0 * sqrt(x);
	tmp = 0.0;
	if (z < -1.3793337487235141e+129)
		tmp = (t_3 * cos(((1.0 / y) - t_1))) - t_2;
	elseif (z < 3.516290613555987e+106)
		tmp = ((sqrt(x) * 2.0) * cos((y - ((t / 3.0) * z)))) - t_2;
	else
		tmp = (cos((y - t_1)) * t_3) - ((a / b) / 3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(0.3333333333333333 / z), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$2 = N[(N[(a / 3.0), $MachinePrecision] / b), $MachinePrecision]}, Block[{t$95$3 = N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]}, If[Less[z, -1.3793337487235141e+129], N[(N[(t$95$3 * N[Cos[N[(N[(1.0 / y), $MachinePrecision] - t$95$1), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], If[Less[z, 3.516290613555987e+106], N[(N[(N[(N[Sqrt[x], $MachinePrecision] * 2.0), $MachinePrecision] * N[Cos[N[(y - N[(N[(t / 3.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], N[(N[(N[Cos[N[(y - t$95$1), $MachinePrecision]], $MachinePrecision] * t$95$3), $MachinePrecision] - N[(N[(a / b), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]]]]]]

Reproduce

herbie shell --seed 2024160 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, K"
  :precision binary64

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

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