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

Percentage Accurate: 70.5% → 78.2%

Time: 29.8s

Alternatives: 12

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 70.5% 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: 78.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := \frac{a}{3 \cdot b}\\ t_2 := 2 \cdot \sqrt{x}\\ \mathbf{if}\;t_2 \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - t_1 \leq 2 \cdot 10^{+187}:\\ \;\;\;\;t_2 \cdot \mathsf{fma}\left(\cos y, \log \left(e^{\cos \left(t \cdot \left(z \cdot -0.3333333333333333\right)\right)}\right), \sin y \cdot \sin \left(0.3333333333333333 \cdot \left(z \cdot t\right)\right)\right) - t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{-\frac{a}{3}}{b} - 2 \cdot \left(\sqrt{x} \cdot \cos y\right)\\ \end{array} \end{array} \]

FPCore

NOTE: z and t 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) 2e+187)
     (-
      (*
       t_2
       (fma
        (cos y)
        (log (exp (cos (* t (* z -0.3333333333333333)))))
        (* (sin y) (sin (* 0.3333333333333333 (* z t))))))
      t_1)
     (- (/ (- (/ a 3.0)) b) (* 2.0 (* (sqrt x) (cos y)))))))

C

assert(z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a / (3.0 * b);
	double t_2 = 2.0 * sqrt(x);
	double tmp;
	if (((t_2 * cos((y - ((z * t) / 3.0)))) - t_1) <= 2e+187) {
		tmp = (t_2 * fma(cos(y), log(exp(cos((t * (z * -0.3333333333333333))))), (sin(y) * sin((0.3333333333333333 * (z * t)))))) - t_1;
	} else {
		tmp = (-(a / 3.0) / b) - (2.0 * (sqrt(x) * cos(y)));
	}
	return tmp;
}

Julia

z, t = sort([z, t])
function code(x, y, z, t, a, b)
	t_1 = Float64(a / Float64(3.0 * b))
	t_2 = Float64(2.0 * sqrt(x))
	tmp = 0.0
	if (Float64(Float64(t_2 * cos(Float64(y - Float64(Float64(z * t) / 3.0)))) - t_1) <= 2e+187)
		tmp = Float64(Float64(t_2 * fma(cos(y), log(exp(cos(Float64(t * Float64(z * -0.3333333333333333))))), Float64(sin(y) * sin(Float64(0.3333333333333333 * Float64(z * t)))))) - t_1);
	else
		tmp = Float64(Float64(Float64(-Float64(a / 3.0)) / b) - Float64(2.0 * Float64(sqrt(x) * cos(y))));
	end
	return tmp
end

Wolfram

NOTE: z and t 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], 2e+187], N[(N[(t$95$2 * N[(N[Cos[y], $MachinePrecision] * N[Log[N[Exp[N[Cos[N[(t * N[(z * -0.3333333333333333), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision]], $MachinePrecision] + N[(N[Sin[y], $MachinePrecision] * N[Sin[N[(0.3333333333333333 * N[(z * t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[((-N[(a / 3.0), $MachinePrecision]) / b), $MachinePrecision] - N[(2.0 * N[(N[Sqrt[x], $MachinePrecision] * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 (*.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3)))) (/.f64 a (*.f64 b 3))) < 1.99999999999999981e187

   1. Initial program 75.3%

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

      1. *-commutative 75.3%

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

      2. *-commutative 75.3%

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

      3. associate-/l* 75.3%

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

      4. *-commutative 75.3%

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

   3. Simplified 75.3%

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

      1. *-un-lft-identity 75.3%

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

      2. add-cube-cbrt 75.1%

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

      3. times-frac 74.9%

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

      4. pow2 75.0%

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

   5. Applied egg-rr 75.0%

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

      1. cos-diff 76.0%

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

      2. div-inv 75.8%

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

      3. associate-*r* 75.9%

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

      4. /-rgt-identity 75.9%

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

      5. unpow2 75.8%

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

      6. add-cube-cbrt 75.8%

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

      7. associate-/r/ 76.0%

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

      8. metadata-eval 76.0%

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

      9. *-commutative 76.0%

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

      10. div-inv 75.8%

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

   7. Applied egg-rr 76.0%

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

      1. fma-def 76.0%

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

      2. cos-neg 76.0%

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

      3. associate-*r* 75.9%

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

      4. *-commutative 75.9%

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

      5. *-commutative 75.9%

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

      6. *-commutative 75.9%

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

      7. distribute-rgt-neg-in 75.9%

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

      8. metadata-eval 75.9%

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

      9. associate-*r* 76.1%

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

      10. *-commutative 76.1%

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

      11. associate-*r* 76.3%

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

      12. *-commutative 76.3%

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

      13. *-commutative 76.3%

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

   9. Simplified 76.3%

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

       1. add-log-exp 76.3%

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

   11. Applied egg-rr 76.3%

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

   if 1.99999999999999981e187 < (-.f64 (*.f64 (*.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3)))) (/.f64 a (*.f64 b 3)))

   1. Initial program 49.9%

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

      1. *-commutative 49.9%

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

      2. *-commutative 49.9%

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

      3. associate-/l* 49.9%

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

      4. *-commutative 49.9%

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

   3. Simplified 49.9%

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

   4. Taylor expanded in z around 0 69.4%

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

      1. associate-*r* 69.4%

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

      2. *-commutative 69.4%

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

      3. *-commutative 69.4%

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

      4. *-commutative 69.4%

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

   6. Simplified 69.4%

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

      1. *-un-lft-identity 69.4%

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

      2. *-commutative 69.4%

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

   8. Applied egg-rr 69.4%

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

      1. *-rgt-identity 69.4%

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

      2. associate-*r* 69.4%

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

      3. associate-/r* 69.5%

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

   10. Simplified 69.5%

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

       1. associate-*r* 69.5%

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

       2. add-cube-cbrt 69.5%

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

       3. pow3 69.5%

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

   12. Applied egg-rr 69.5%

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

   13. Taylor expanded in x around -inf 0.0%

       \[\leadsto \color{blue}{2 \cdot \left({1}^{0.16666666666666666} \cdot \left(\sqrt{x} \cdot \left(\cos y \cdot {\left(\sqrt{-1}\right)}^{2}\right)\right)\right)} - \frac{\frac{a}{3}}{b} \]
   14. Step-by-step derivation

       1. pow-base-1 0.0%

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

       2. *-lft-identity 0.0%

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

       3. unpow2 0.0%

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

       4. rem-square-sqrt 71.1%

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

   15. Simplified 71.1%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{3 \cdot b} \leq 2 \cdot 10^{+187}:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos y, \log \left(e^{\cos \left(t \cdot \left(z \cdot -0.3333333333333333\right)\right)}\right), \sin y \cdot \sin \left(0.3333333333333333 \cdot \left(z \cdot t\right)\right)\right) - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\frac{a}{3}}{b} - 2 \cdot \left(\sqrt{x} \cdot \cos y\right)\\ \end{array} \]

Alternative 2: 78.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := \frac{a}{3 \cdot b}\\ t_2 := 2 \cdot \sqrt{x}\\ \mathbf{if}\;t_2 \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - t_1 \leq 2 \cdot 10^{+187}:\\ \;\;\;\;t_2 \cdot \mathsf{fma}\left(\cos y, \cos \left(t \cdot \left(z \cdot -0.3333333333333333\right)\right), \sin y \cdot \sin \left(0.3333333333333333 \cdot \left(z \cdot t\right)\right)\right) - t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{-\frac{a}{3}}{b} - 2 \cdot \left(\sqrt{x} \cdot \cos y\right)\\ \end{array} \end{array} \]

FPCore

NOTE: z and t 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) 2e+187)
     (-
      (*
       t_2
       (fma
        (cos y)
        (cos (* t (* z -0.3333333333333333)))
        (* (sin y) (sin (* 0.3333333333333333 (* z t))))))
      t_1)
     (- (/ (- (/ a 3.0)) b) (* 2.0 (* (sqrt x) (cos y)))))))

C

assert(z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a / (3.0 * b);
	double t_2 = 2.0 * sqrt(x);
	double tmp;
	if (((t_2 * cos((y - ((z * t) / 3.0)))) - t_1) <= 2e+187) {
		tmp = (t_2 * fma(cos(y), cos((t * (z * -0.3333333333333333))), (sin(y) * sin((0.3333333333333333 * (z * t)))))) - t_1;
	} else {
		tmp = (-(a / 3.0) / b) - (2.0 * (sqrt(x) * cos(y)));
	}
	return tmp;
}

Julia

z, t = sort([z, t])
function code(x, y, z, t, a, b)
	t_1 = Float64(a / Float64(3.0 * b))
	t_2 = Float64(2.0 * sqrt(x))
	tmp = 0.0
	if (Float64(Float64(t_2 * cos(Float64(y - Float64(Float64(z * t) / 3.0)))) - t_1) <= 2e+187)
		tmp = Float64(Float64(t_2 * fma(cos(y), cos(Float64(t * Float64(z * -0.3333333333333333))), Float64(sin(y) * sin(Float64(0.3333333333333333 * Float64(z * t)))))) - t_1);
	else
		tmp = Float64(Float64(Float64(-Float64(a / 3.0)) / b) - Float64(2.0 * Float64(sqrt(x) * cos(y))));
	end
	return tmp
end

Wolfram

NOTE: z and t 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], 2e+187], N[(N[(t$95$2 * N[(N[Cos[y], $MachinePrecision] * N[Cos[N[(t * N[(z * -0.3333333333333333), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] + N[(N[Sin[y], $MachinePrecision] * N[Sin[N[(0.3333333333333333 * N[(z * t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[((-N[(a / 3.0), $MachinePrecision]) / b), $MachinePrecision] - N[(2.0 * N[(N[Sqrt[x], $MachinePrecision] * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 (*.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3)))) (/.f64 a (*.f64 b 3))) < 1.99999999999999981e187

   1. Initial program 75.3%

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

      1. *-commutative 75.3%

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

      2. *-commutative 75.3%

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

      3. associate-/l* 75.3%

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

      4. *-commutative 75.3%

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

   3. Simplified 75.3%

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

      1. *-un-lft-identity 75.3%

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

      2. add-cube-cbrt 75.1%

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

      3. times-frac 74.9%

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

      4. pow2 75.0%

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

   5. Applied egg-rr 75.0%

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

      1. cos-diff 76.0%

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

      2. div-inv 75.8%

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

      3. associate-*r* 75.9%

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

      4. /-rgt-identity 75.9%

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

      5. unpow2 75.8%

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

      6. add-cube-cbrt 75.8%

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

      7. associate-/r/ 76.0%

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

      8. metadata-eval 76.0%

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

      9. *-commutative 76.0%

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

      10. div-inv 75.8%

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

   7. Applied egg-rr 76.0%

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

      1. fma-def 76.0%

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

      2. cos-neg 76.0%

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

      3. associate-*r* 75.9%

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

      4. *-commutative 75.9%

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

      5. *-commutative 75.9%

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

      6. *-commutative 75.9%

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

      7. distribute-rgt-neg-in 75.9%

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

      8. metadata-eval 75.9%

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

      9. associate-*r* 76.1%

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

      10. *-commutative 76.1%

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

      11. associate-*r* 76.3%

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

      12. *-commutative 76.3%

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

      13. *-commutative 76.3%

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

   9. Simplified 76.3%

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

   if 1.99999999999999981e187 < (-.f64 (*.f64 (*.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3)))) (/.f64 a (*.f64 b 3)))

   1. Initial program 49.9%

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

      1. *-commutative 49.9%

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

      2. *-commutative 49.9%

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

      3. associate-/l* 49.9%

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

      4. *-commutative 49.9%

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

   3. Simplified 49.9%

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

   4. Taylor expanded in z around 0 69.4%

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

      1. associate-*r* 69.4%

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

      2. *-commutative 69.4%

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

      3. *-commutative 69.4%

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

      4. *-commutative 69.4%

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

   6. Simplified 69.4%

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

      1. *-un-lft-identity 69.4%

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

      2. *-commutative 69.4%

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

   8. Applied egg-rr 69.4%

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

      1. *-rgt-identity 69.4%

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

      2. associate-*r* 69.4%

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

      3. associate-/r* 69.5%

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

   10. Simplified 69.5%

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

       1. associate-*r* 69.5%

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

       2. add-cube-cbrt 69.5%

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

       3. pow3 69.5%

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

   12. Applied egg-rr 69.5%

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

   13. Taylor expanded in x around -inf 0.0%

       \[\leadsto \color{blue}{2 \cdot \left({1}^{0.16666666666666666} \cdot \left(\sqrt{x} \cdot \left(\cos y \cdot {\left(\sqrt{-1}\right)}^{2}\right)\right)\right)} - \frac{\frac{a}{3}}{b} \]
   14. Step-by-step derivation

       1. pow-base-1 0.0%

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

       2. *-lft-identity 0.0%

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

       3. unpow2 0.0%

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

       4. rem-square-sqrt 71.1%

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

   15. Simplified 71.1%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{3 \cdot b} \leq 2 \cdot 10^{+187}:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \mathsf{fma}\left(\cos y, \cos \left(t \cdot \left(z \cdot -0.3333333333333333\right)\right), \sin y \cdot \sin \left(0.3333333333333333 \cdot \left(z \cdot t\right)\right)\right) - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\frac{a}{3}}{b} - 2 \cdot \left(\sqrt{x} \cdot \cos y\right)\\ \end{array} \]

Alternative 3: 78.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := z \cdot \left(t \cdot 0.3333333333333333\right)\\ t_2 := \frac{a}{3 \cdot b}\\ t_3 := 2 \cdot \sqrt{x}\\ \mathbf{if}\;t_3 \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - t_2 \leq 2 \cdot 10^{+187}:\\ \;\;\;\;t_3 \cdot \left(\sin y \cdot \sin t_1 + \cos y \cdot \cos t_1\right) - t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{-\frac{a}{3}}{b} - 2 \cdot \left(\sqrt{x} \cdot \cos y\right)\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (* t 0.3333333333333333)))
        (t_2 (/ a (* 3.0 b)))
        (t_3 (* 2.0 (sqrt x))))
   (if (<= (- (* t_3 (cos (- y (/ (* z t) 3.0)))) t_2) 2e+187)
     (- (* t_3 (+ (* (sin y) (sin t_1)) (* (cos y) (cos t_1)))) t_2)
     (- (/ (- (/ a 3.0)) b) (* 2.0 (* (sqrt x) (cos y)))))))

C

assert(z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (t * 0.3333333333333333);
	double t_2 = a / (3.0 * b);
	double t_3 = 2.0 * sqrt(x);
	double tmp;
	if (((t_3 * cos((y - ((z * t) / 3.0)))) - t_2) <= 2e+187) {
		tmp = (t_3 * ((sin(y) * sin(t_1)) + (cos(y) * cos(t_1)))) - t_2;
	} else {
		tmp = (-(a / 3.0) / b) - (2.0 * (sqrt(x) * cos(y)));
	}
	return tmp;
}

Fortran

NOTE: z and t 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 = z * (t * 0.3333333333333333d0)
    t_2 = a / (3.0d0 * b)
    t_3 = 2.0d0 * sqrt(x)
    if (((t_3 * cos((y - ((z * t) / 3.0d0)))) - t_2) <= 2d+187) then
        tmp = (t_3 * ((sin(y) * sin(t_1)) + (cos(y) * cos(t_1)))) - t_2
    else
        tmp = (-(a / 3.0d0) / b) - (2.0d0 * (sqrt(x) * cos(y)))
    end if
    code = tmp
end function

Java

assert z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (t * 0.3333333333333333);
	double t_2 = a / (3.0 * b);
	double t_3 = 2.0 * Math.sqrt(x);
	double tmp;
	if (((t_3 * Math.cos((y - ((z * t) / 3.0)))) - t_2) <= 2e+187) {
		tmp = (t_3 * ((Math.sin(y) * Math.sin(t_1)) + (Math.cos(y) * Math.cos(t_1)))) - t_2;
	} else {
		tmp = (-(a / 3.0) / b) - (2.0 * (Math.sqrt(x) * Math.cos(y)));
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t, a, b):
	t_1 = z * (t * 0.3333333333333333)
	t_2 = a / (3.0 * b)
	t_3 = 2.0 * math.sqrt(x)
	tmp = 0
	if ((t_3 * math.cos((y - ((z * t) / 3.0)))) - t_2) <= 2e+187:
		tmp = (t_3 * ((math.sin(y) * math.sin(t_1)) + (math.cos(y) * math.cos(t_1)))) - t_2
	else:
		tmp = (-(a / 3.0) / b) - (2.0 * (math.sqrt(x) * math.cos(y)))
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(t * 0.3333333333333333))
	t_2 = Float64(a / Float64(3.0 * b))
	t_3 = Float64(2.0 * sqrt(x))
	tmp = 0.0
	if (Float64(Float64(t_3 * cos(Float64(y - Float64(Float64(z * t) / 3.0)))) - t_2) <= 2e+187)
		tmp = Float64(Float64(t_3 * Float64(Float64(sin(y) * sin(t_1)) + Float64(cos(y) * cos(t_1)))) - t_2);
	else
		tmp = Float64(Float64(Float64(-Float64(a / 3.0)) / b) - Float64(2.0 * Float64(sqrt(x) * cos(y))));
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (t * 0.3333333333333333);
	t_2 = a / (3.0 * b);
	t_3 = 2.0 * sqrt(x);
	tmp = 0.0;
	if (((t_3 * cos((y - ((z * t) / 3.0)))) - t_2) <= 2e+187)
		tmp = (t_3 * ((sin(y) * sin(t_1)) + (cos(y) * cos(t_1)))) - t_2;
	else
		tmp = (-(a / 3.0) / b) - (2.0 * (sqrt(x) * cos(y)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(t * 0.3333333333333333), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a / N[(3.0 * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(t$95$3 * N[Cos[N[(y - N[(N[(z * t), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], 2e+187], N[(N[(t$95$3 * N[(N[(N[Sin[y], $MachinePrecision] * N[Sin[t$95$1], $MachinePrecision]), $MachinePrecision] + N[(N[Cos[y], $MachinePrecision] * N[Cos[t$95$1], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], N[(N[((-N[(a / 3.0), $MachinePrecision]) / b), $MachinePrecision] - N[(2.0 * N[(N[Sqrt[x], $MachinePrecision] * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 (*.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3)))) (/.f64 a (*.f64 b 3))) < 1.99999999999999981e187

   1. Initial program 75.3%

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

      1. *-commutative 75.3%

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

      2. *-commutative 75.3%

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

      3. associate-/l* 75.3%

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

      4. *-commutative 75.3%

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

   3. Simplified 75.3%

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

      1. *-un-lft-identity 75.3%

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

      2. add-cube-cbrt 75.1%

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

      3. times-frac 74.9%

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

      4. pow2 75.0%

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

   5. Applied egg-rr 75.0%

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

      1. cos-diff 76.0%

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

      2. +-commutative 76.0%

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

      3. div-inv 75.8%

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

      4. associate-*r* 75.8%

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

      5. /-rgt-identity 75.8%

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

      6. unpow2 75.8%

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

      7. add-cube-cbrt 75.7%

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

      8. associate-/r/ 75.8%

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

      9. metadata-eval 75.8%

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

      10. *-commutative 75.8%

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

   7. Applied egg-rr 76.0%

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

   if 1.99999999999999981e187 < (-.f64 (*.f64 (*.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3)))) (/.f64 a (*.f64 b 3)))

   1. Initial program 49.9%

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

      1. *-commutative 49.9%

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

      2. *-commutative 49.9%

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

      3. associate-/l* 49.9%

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

      4. *-commutative 49.9%

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

   3. Simplified 49.9%

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

   4. Taylor expanded in z around 0 69.4%

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

      1. associate-*r* 69.4%

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

      2. *-commutative 69.4%

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

      3. *-commutative 69.4%

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

      4. *-commutative 69.4%

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

   6. Simplified 69.4%

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

      1. *-un-lft-identity 69.4%

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

      2. *-commutative 69.4%

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

   8. Applied egg-rr 69.4%

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

      1. *-rgt-identity 69.4%

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

      2. associate-*r* 69.4%

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

      3. associate-/r* 69.5%

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

   10. Simplified 69.5%

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

       1. associate-*r* 69.5%

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

       2. add-cube-cbrt 69.5%

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

       3. pow3 69.5%

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

   12. Applied egg-rr 69.5%

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

   13. Taylor expanded in x around -inf 0.0%

       \[\leadsto \color{blue}{2 \cdot \left({1}^{0.16666666666666666} \cdot \left(\sqrt{x} \cdot \left(\cos y \cdot {\left(\sqrt{-1}\right)}^{2}\right)\right)\right)} - \frac{\frac{a}{3}}{b} \]
   14. Step-by-step derivation

       1. pow-base-1 0.0%

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

       2. *-lft-identity 0.0%

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

       3. unpow2 0.0%

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

       4. rem-square-sqrt 71.1%

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

   15. Simplified 71.1%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{3 \cdot b} \leq 2 \cdot 10^{+187}:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \left(\sin y \cdot \sin \left(z \cdot \left(t \cdot 0.3333333333333333\right)\right) + \cos y \cdot \cos \left(z \cdot \left(t \cdot 0.3333333333333333\right)\right)\right) - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\frac{a}{3}}{b} - 2 \cdot \left(\sqrt{x} \cdot \cos y\right)\\ \end{array} \]

Alternative 4: 77.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := \frac{a}{3 \cdot b}\\ t_2 := 2 \cdot \sqrt{x}\\ \mathbf{if}\;t_2 \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - t_1 \leq 2 \cdot 10^{+187}:\\ \;\;\;\;t_2 \cdot \cos \left(y - {\left(\sqrt[3]{t \cdot \left(z \cdot -0.3333333333333333\right)}\right)}^{3}\right) - t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{-\frac{a}{3}}{b} - 2 \cdot \left(\sqrt{x} \cdot \cos y\right)\\ \end{array} \end{array} \]

FPCore

NOTE: z and t 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) 2e+187)
     (-
      (* t_2 (cos (- y (pow (cbrt (* t (* z -0.3333333333333333))) 3.0))))
      t_1)
     (- (/ (- (/ a 3.0)) b) (* 2.0 (* (sqrt x) (cos y)))))))

C

assert(z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a / (3.0 * b);
	double t_2 = 2.0 * sqrt(x);
	double tmp;
	if (((t_2 * cos((y - ((z * t) / 3.0)))) - t_1) <= 2e+187) {
		tmp = (t_2 * cos((y - pow(cbrt((t * (z * -0.3333333333333333))), 3.0)))) - t_1;
	} else {
		tmp = (-(a / 3.0) / b) - (2.0 * (sqrt(x) * cos(y)));
	}
	return tmp;
}

Java

assert z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a / (3.0 * b);
	double t_2 = 2.0 * Math.sqrt(x);
	double tmp;
	if (((t_2 * Math.cos((y - ((z * t) / 3.0)))) - t_1) <= 2e+187) {
		tmp = (t_2 * Math.cos((y - Math.pow(Math.cbrt((t * (z * -0.3333333333333333))), 3.0)))) - t_1;
	} else {
		tmp = (-(a / 3.0) / b) - (2.0 * (Math.sqrt(x) * Math.cos(y)));
	}
	return tmp;
}

Julia

z, t = sort([z, t])
function code(x, y, z, t, a, b)
	t_1 = Float64(a / Float64(3.0 * b))
	t_2 = Float64(2.0 * sqrt(x))
	tmp = 0.0
	if (Float64(Float64(t_2 * cos(Float64(y - Float64(Float64(z * t) / 3.0)))) - t_1) <= 2e+187)
		tmp = Float64(Float64(t_2 * cos(Float64(y - (cbrt(Float64(t * Float64(z * -0.3333333333333333))) ^ 3.0)))) - t_1);
	else
		tmp = Float64(Float64(Float64(-Float64(a / 3.0)) / b) - Float64(2.0 * Float64(sqrt(x) * cos(y))));
	end
	return tmp
end

Wolfram

NOTE: z and t 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], 2e+187], N[(N[(t$95$2 * N[Cos[N[(y - N[Power[N[Power[N[(t * N[(z * -0.3333333333333333), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision], 3.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[((-N[(a / 3.0), $MachinePrecision]) / b), $MachinePrecision] - N[(2.0 * N[(N[Sqrt[x], $MachinePrecision] * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 (*.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3)))) (/.f64 a (*.f64 b 3))) < 1.99999999999999981e187

   1. Initial program 75.3%

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

      1. *-commutative 75.3%

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

      2. *-commutative 75.3%

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

      3. associate-/l* 75.3%

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

      4. *-commutative 75.3%

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

   3. Simplified 75.3%

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

      1. add-cube-cbrt 75.4%

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

      2. pow3 75.3%

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

      3. add-sqr-sqrt 40.3%

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

      4. sqrt-unprod 65.9%

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

      5. frac-times 65.3%

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

      6. metadata-eval 65.3%

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - {\left(\sqrt[3]{\frac{z}{\sqrt{\frac{\color{blue}{9}}{t \cdot t}}}}\right)}^{3}\right) - \frac{a}{3 \cdot b} \]

      7. metadata-eval 65.3%

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

      8. frac-times 65.9%

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

      9. sqrt-unprod 34.9%

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

      10. add-sqr-sqrt 75.4%

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

      11. associate-/r/ 75.2%

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

      12. *-commutative 75.2%

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

      13. div-inv 75.6%

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

      14. metadata-eval 75.6%

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

      15. *-commutative 75.6%

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

   5. Applied egg-rr 75.6%

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

   if 1.99999999999999981e187 < (-.f64 (*.f64 (*.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3)))) (/.f64 a (*.f64 b 3)))

   1. Initial program 49.9%

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

      1. *-commutative 49.9%

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

      2. *-commutative 49.9%

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

      3. associate-/l* 49.9%

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

      4. *-commutative 49.9%

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

   3. Simplified 49.9%

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

   4. Taylor expanded in z around 0 69.4%

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

      1. associate-*r* 69.4%

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

      2. *-commutative 69.4%

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

      3. *-commutative 69.4%

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

      4. *-commutative 69.4%

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

   6. Simplified 69.4%

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

      1. *-un-lft-identity 69.4%

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

      2. *-commutative 69.4%

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

   8. Applied egg-rr 69.4%

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

      1. *-rgt-identity 69.4%

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

      2. associate-*r* 69.4%

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

      3. associate-/r* 69.5%

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

   10. Simplified 69.5%

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

       1. associate-*r* 69.5%

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

       2. add-cube-cbrt 69.5%

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

       3. pow3 69.5%

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

   12. Applied egg-rr 69.5%

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

   13. Taylor expanded in x around -inf 0.0%

       \[\leadsto \color{blue}{2 \cdot \left({1}^{0.16666666666666666} \cdot \left(\sqrt{x} \cdot \left(\cos y \cdot {\left(\sqrt{-1}\right)}^{2}\right)\right)\right)} - \frac{\frac{a}{3}}{b} \]
   14. Step-by-step derivation

       1. pow-base-1 0.0%

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

       2. *-lft-identity 0.0%

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

       3. unpow2 0.0%

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

       4. rem-square-sqrt 71.1%

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

   15. Simplified 71.1%

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

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{3 \cdot b} \leq 2 \cdot 10^{+187}:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - {\left(\sqrt[3]{t \cdot \left(z \cdot -0.3333333333333333\right)}\right)}^{3}\right) - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\frac{a}{3}}{b} - 2 \cdot \left(\sqrt{x} \cdot \cos y\right)\\ \end{array} \]

Alternative 5: 77.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := \frac{a}{3 \cdot b}\\ t_2 := 2 \cdot \sqrt{x}\\ \mathbf{if}\;t_2 \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - t_1 \leq 2 \cdot 10^{+187}:\\ \;\;\;\;t_2 \cdot \cos \left(y - {\left(\frac{\frac{3}{t}}{z}\right)}^{-1}\right) - t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{-\frac{a}{3}}{b} - 2 \cdot \left(\sqrt{x} \cdot \cos y\right)\\ \end{array} \end{array} \]

FPCore

NOTE: z and t 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) 2e+187)
     (- (* t_2 (cos (- y (pow (/ (/ 3.0 t) z) -1.0)))) t_1)
     (- (/ (- (/ a 3.0)) b) (* 2.0 (* (sqrt x) (cos y)))))))

C

assert(z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a / (3.0 * b);
	double t_2 = 2.0 * sqrt(x);
	double tmp;
	if (((t_2 * cos((y - ((z * t) / 3.0)))) - t_1) <= 2e+187) {
		tmp = (t_2 * cos((y - pow(((3.0 / t) / z), -1.0)))) - t_1;
	} else {
		tmp = (-(a / 3.0) / b) - (2.0 * (sqrt(x) * cos(y)));
	}
	return tmp;
}

Fortran

NOTE: z and t 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)
    if (((t_2 * cos((y - ((z * t) / 3.0d0)))) - t_1) <= 2d+187) then
        tmp = (t_2 * cos((y - (((3.0d0 / t) / z) ** (-1.0d0))))) - t_1
    else
        tmp = (-(a / 3.0d0) / b) - (2.0d0 * (sqrt(x) * cos(y)))
    end if
    code = tmp
end function

Java

assert z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a / (3.0 * b);
	double t_2 = 2.0 * Math.sqrt(x);
	double tmp;
	if (((t_2 * Math.cos((y - ((z * t) / 3.0)))) - t_1) <= 2e+187) {
		tmp = (t_2 * Math.cos((y - Math.pow(((3.0 / t) / z), -1.0)))) - t_1;
	} else {
		tmp = (-(a / 3.0) / b) - (2.0 * (Math.sqrt(x) * Math.cos(y)));
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t, a, b):
	t_1 = a / (3.0 * b)
	t_2 = 2.0 * math.sqrt(x)
	tmp = 0
	if ((t_2 * math.cos((y - ((z * t) / 3.0)))) - t_1) <= 2e+187:
		tmp = (t_2 * math.cos((y - math.pow(((3.0 / t) / z), -1.0)))) - t_1
	else:
		tmp = (-(a / 3.0) / b) - (2.0 * (math.sqrt(x) * math.cos(y)))
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t, a, b)
	t_1 = Float64(a / Float64(3.0 * b))
	t_2 = Float64(2.0 * sqrt(x))
	tmp = 0.0
	if (Float64(Float64(t_2 * cos(Float64(y - Float64(Float64(z * t) / 3.0)))) - t_1) <= 2e+187)
		tmp = Float64(Float64(t_2 * cos(Float64(y - (Float64(Float64(3.0 / t) / z) ^ -1.0)))) - t_1);
	else
		tmp = Float64(Float64(Float64(-Float64(a / 3.0)) / b) - Float64(2.0 * Float64(sqrt(x) * cos(y))));
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a / (3.0 * b);
	t_2 = 2.0 * sqrt(x);
	tmp = 0.0;
	if (((t_2 * cos((y - ((z * t) / 3.0)))) - t_1) <= 2e+187)
		tmp = (t_2 * cos((y - (((3.0 / t) / z) ^ -1.0)))) - t_1;
	else
		tmp = (-(a / 3.0) / b) - (2.0 * (sqrt(x) * cos(y)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z and t 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], 2e+187], N[(N[(t$95$2 * N[Cos[N[(y - N[Power[N[(N[(3.0 / t), $MachinePrecision] / z), $MachinePrecision], -1.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[((-N[(a / 3.0), $MachinePrecision]) / b), $MachinePrecision] - N[(2.0 * N[(N[Sqrt[x], $MachinePrecision] * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 (*.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3)))) (/.f64 a (*.f64 b 3))) < 1.99999999999999981e187

   1. Initial program 75.3%

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

      1. *-commutative 75.3%

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

      2. *-commutative 75.3%

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

      3. associate-/l* 75.3%

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

      4. *-commutative 75.3%

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

   3. Simplified 75.3%

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

      1. associate-/l* 75.3%

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

      2. clear-num 75.4%

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

      3. inv-pow 75.4%

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

      4. associate-/l/ 75.5%

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

   5. Applied egg-rr 75.5%

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

   if 1.99999999999999981e187 < (-.f64 (*.f64 (*.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3)))) (/.f64 a (*.f64 b 3)))

   1. Initial program 49.9%

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

      1. *-commutative 49.9%

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

      2. *-commutative 49.9%

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

      3. associate-/l* 49.9%

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

      4. *-commutative 49.9%

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

   3. Simplified 49.9%

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

   4. Taylor expanded in z around 0 69.4%

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

      1. associate-*r* 69.4%

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

      2. *-commutative 69.4%

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

      3. *-commutative 69.4%

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

      4. *-commutative 69.4%

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

   6. Simplified 69.4%

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

      1. *-un-lft-identity 69.4%

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

      2. *-commutative 69.4%

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

   8. Applied egg-rr 69.4%

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

      1. *-rgt-identity 69.4%

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

      2. associate-*r* 69.4%

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

      3. associate-/r* 69.5%

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

   10. Simplified 69.5%

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

       1. associate-*r* 69.5%

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

       2. add-cube-cbrt 69.5%

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

       3. pow3 69.5%

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

   12. Applied egg-rr 69.5%

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

   13. Taylor expanded in x around -inf 0.0%

       \[\leadsto \color{blue}{2 \cdot \left({1}^{0.16666666666666666} \cdot \left(\sqrt{x} \cdot \left(\cos y \cdot {\left(\sqrt{-1}\right)}^{2}\right)\right)\right)} - \frac{\frac{a}{3}}{b} \]
   14. Step-by-step derivation

       1. pow-base-1 0.0%

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

       2. *-lft-identity 0.0%

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

       3. unpow2 0.0%

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

       4. rem-square-sqrt 71.1%

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

   15. Simplified 71.1%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{3 \cdot b} \leq 2 \cdot 10^{+187}:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - {\left(\frac{\frac{3}{t}}{z}\right)}^{-1}\right) - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\frac{a}{3}}{b} - 2 \cdot \left(\sqrt{x} \cdot \cos y\right)\\ \end{array} \]

Alternative 6: 77.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := \frac{a}{3 \cdot b}\\ t_2 := 2 \cdot \sqrt{x}\\ \mathbf{if}\;t_2 \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - t_1 \leq 2 \cdot 10^{+187}:\\ \;\;\;\;t_2 \cdot \cos \left(y - t \cdot \left(z \cdot -0.3333333333333333\right)\right) - t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{-\frac{a}{3}}{b} - 2 \cdot \left(\sqrt{x} \cdot \cos y\right)\\ \end{array} \end{array} \]

FPCore

NOTE: z and t 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) 2e+187)
     (- (* t_2 (cos (- y (* t (* z -0.3333333333333333))))) t_1)
     (- (/ (- (/ a 3.0)) b) (* 2.0 (* (sqrt x) (cos y)))))))

C

assert(z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a / (3.0 * b);
	double t_2 = 2.0 * sqrt(x);
	double tmp;
	if (((t_2 * cos((y - ((z * t) / 3.0)))) - t_1) <= 2e+187) {
		tmp = (t_2 * cos((y - (t * (z * -0.3333333333333333))))) - t_1;
	} else {
		tmp = (-(a / 3.0) / b) - (2.0 * (sqrt(x) * cos(y)));
	}
	return tmp;
}

Fortran

NOTE: z and t 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)
    if (((t_2 * cos((y - ((z * t) / 3.0d0)))) - t_1) <= 2d+187) then
        tmp = (t_2 * cos((y - (t * (z * (-0.3333333333333333d0)))))) - t_1
    else
        tmp = (-(a / 3.0d0) / b) - (2.0d0 * (sqrt(x) * cos(y)))
    end if
    code = tmp
end function

Java

assert z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a / (3.0 * b);
	double t_2 = 2.0 * Math.sqrt(x);
	double tmp;
	if (((t_2 * Math.cos((y - ((z * t) / 3.0)))) - t_1) <= 2e+187) {
		tmp = (t_2 * Math.cos((y - (t * (z * -0.3333333333333333))))) - t_1;
	} else {
		tmp = (-(a / 3.0) / b) - (2.0 * (Math.sqrt(x) * Math.cos(y)));
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t, a, b):
	t_1 = a / (3.0 * b)
	t_2 = 2.0 * math.sqrt(x)
	tmp = 0
	if ((t_2 * math.cos((y - ((z * t) / 3.0)))) - t_1) <= 2e+187:
		tmp = (t_2 * math.cos((y - (t * (z * -0.3333333333333333))))) - t_1
	else:
		tmp = (-(a / 3.0) / b) - (2.0 * (math.sqrt(x) * math.cos(y)))
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t, a, b)
	t_1 = Float64(a / Float64(3.0 * b))
	t_2 = Float64(2.0 * sqrt(x))
	tmp = 0.0
	if (Float64(Float64(t_2 * cos(Float64(y - Float64(Float64(z * t) / 3.0)))) - t_1) <= 2e+187)
		tmp = Float64(Float64(t_2 * cos(Float64(y - Float64(t * Float64(z * -0.3333333333333333))))) - t_1);
	else
		tmp = Float64(Float64(Float64(-Float64(a / 3.0)) / b) - Float64(2.0 * Float64(sqrt(x) * cos(y))));
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a / (3.0 * b);
	t_2 = 2.0 * sqrt(x);
	tmp = 0.0;
	if (((t_2 * cos((y - ((z * t) / 3.0)))) - t_1) <= 2e+187)
		tmp = (t_2 * cos((y - (t * (z * -0.3333333333333333))))) - t_1;
	else
		tmp = (-(a / 3.0) / b) - (2.0 * (sqrt(x) * cos(y)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z and t 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], 2e+187], N[(N[(t$95$2 * N[Cos[N[(y - N[(t * N[(z * -0.3333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[((-N[(a / 3.0), $MachinePrecision]) / b), $MachinePrecision] - N[(2.0 * N[(N[Sqrt[x], $MachinePrecision] * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 (*.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3)))) (/.f64 a (*.f64 b 3))) < 1.99999999999999981e187

   1. Initial program 75.3%

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

      1. *-commutative 75.3%

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

      2. *-commutative 75.3%

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

      3. associate-/l* 75.3%

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

      4. *-commutative 75.3%

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

   3. Simplified 75.3%

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

      1. add-sqr-sqrt 40.0%

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

      2. sqrt-unprod 65.8%

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

      3. frac-times 65.1%

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

      4. metadata-eval 65.1%

         \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z}{\sqrt{\frac{\color{blue}{9}}{t \cdot t}}}\right) - \frac{a}{3 \cdot b} \]

      5. metadata-eval 65.1%

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

      6. frac-times 65.8%

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

      7. sqrt-unprod 35.0%

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

      8. add-sqr-sqrt 75.2%

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

      9. associate-/r/ 75.2%

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

      10. div-inv 75.3%

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

      11. metadata-eval 75.3%

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

      12. *-commutative 75.3%

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

   5. Applied egg-rr 75.3%

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

   if 1.99999999999999981e187 < (-.f64 (*.f64 (*.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3)))) (/.f64 a (*.f64 b 3)))

   1. Initial program 49.9%

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

      1. *-commutative 49.9%

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

      2. *-commutative 49.9%

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

      3. associate-/l* 49.9%

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

      4. *-commutative 49.9%

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

   3. Simplified 49.9%

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

   4. Taylor expanded in z around 0 69.4%

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

      1. associate-*r* 69.4%

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

      2. *-commutative 69.4%

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

      3. *-commutative 69.4%

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

      4. *-commutative 69.4%

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

   6. Simplified 69.4%

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

      1. *-un-lft-identity 69.4%

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

      2. *-commutative 69.4%

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

   8. Applied egg-rr 69.4%

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

      1. *-rgt-identity 69.4%

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

      2. associate-*r* 69.4%

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

      3. associate-/r* 69.5%

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

   10. Simplified 69.5%

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

       1. associate-*r* 69.5%

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

       2. add-cube-cbrt 69.5%

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

       3. pow3 69.5%

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

   12. Applied egg-rr 69.5%

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

   13. Taylor expanded in x around -inf 0.0%

       \[\leadsto \color{blue}{2 \cdot \left({1}^{0.16666666666666666} \cdot \left(\sqrt{x} \cdot \left(\cos y \cdot {\left(\sqrt{-1}\right)}^{2}\right)\right)\right)} - \frac{\frac{a}{3}}{b} \]
   14. Step-by-step derivation

       1. pow-base-1 0.0%

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

       2. *-lft-identity 0.0%

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

       3. unpow2 0.0%

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

       4. rem-square-sqrt 71.1%

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

   15. Simplified 71.1%

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

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{3 \cdot b} \leq 2 \cdot 10^{+187}:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - t \cdot \left(z \cdot -0.3333333333333333\right)\right) - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\frac{-\frac{a}{3}}{b} - 2 \cdot \left(\sqrt{x} \cdot \cos y\right)\\ \end{array} \]

Alternative 7: 77.2% accurate, 1.0× speedup

Math

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

FPCore

NOTE: z and t 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(z < t);
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: z and t 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 z < t;
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

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

Julia

z, t = sort([z, t])
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

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

Wolfram

NOTE: z and t 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 69.7%

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

   1. *-commutative 69.7%

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

   2. *-commutative 69.7%

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

   3. associate-/l* 69.7%

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

   4. *-commutative 69.7%

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

3. Simplified 69.7%

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

4. Taylor expanded in z around 0 72.1%

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

   1. associate-*r* 72.1%

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

   2. *-commutative 72.1%

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

   3. *-commutative 72.1%

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

   4. *-commutative 72.1%

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

6. Simplified 72.1%

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

7. Final simplification 72.1%

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

Alternative 8: 65.7% accurate, 2.0× speedup

Math

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

FPCore

NOTE: z and t 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(z < t);
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: z and t 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 z < t;
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

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

Julia

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

MATLAB

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

Wolfram

NOTE: z and t 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 69.7%

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

   1. *-commutative 69.7%

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

   2. *-commutative 69.7%

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

   3. associate-/l* 69.7%

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

   4. *-commutative 69.7%

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

3. Simplified 69.7%

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

4. Taylor expanded in z around 0 72.1%

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

   1. associate-*r* 72.1%

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

   2. *-commutative 72.1%

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

   3. *-commutative 72.1%

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

   4. *-commutative 72.1%

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

6. Simplified 72.1%

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

7. Taylor expanded in y around 0 63.8%

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

8. Final simplification 63.8%

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

Alternative 9: 52.8% accurate, 2.0× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -6.5 \cdot 10^{-79} \lor \neg \left(a \leq 6.1 \cdot 10^{-174}\right):\\ \;\;\;\;\frac{a}{b \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{x}\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= a -6.5e-79) (not (<= a 6.1e-174)))
   (/ a (* b -3.0))
   (* 2.0 (sqrt x))))

C

assert(z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -6.5e-79) || !(a <= 6.1e-174)) {
		tmp = a / (b * -3.0);
	} else {
		tmp = 2.0 * sqrt(x);
	}
	return tmp;
}

Fortran

NOTE: z and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((a <= (-6.5d-79)) .or. (.not. (a <= 6.1d-174))) then
        tmp = a / (b * (-3.0d0))
    else
        tmp = 2.0d0 * sqrt(x)
    end if
    code = tmp
end function

Java

assert z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((a <= -6.5e-79) || !(a <= 6.1e-174)) {
		tmp = a / (b * -3.0);
	} else {
		tmp = 2.0 * Math.sqrt(x);
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t, a, b):
	tmp = 0
	if (a <= -6.5e-79) or not (a <= 6.1e-174):
		tmp = a / (b * -3.0)
	else:
		tmp = 2.0 * math.sqrt(x)
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((a <= -6.5e-79) || !(a <= 6.1e-174))
		tmp = Float64(a / Float64(b * -3.0));
	else
		tmp = Float64(2.0 * sqrt(x));
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((a <= -6.5e-79) || ~((a <= 6.1e-174)))
		tmp = a / (b * -3.0);
	else
		tmp = 2.0 * sqrt(x);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[a, -6.5e-79], N[Not[LessEqual[a, 6.1e-174]], $MachinePrecision]], N[(a / N[(b * -3.0), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -6.5000000000000003e-79 or 6.09999999999999964e-174 < a

   1. Initial program 75.4%

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

      1. fma-neg 75.4%

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

      2. *-commutative 75.4%

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

      3. associate-*r/ 75.4%

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

      4. cancel-sign-sub-inv 75.4%

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

      5. *-commutative 75.4%

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

      6. associate-/r/ 75.5%

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

      7. neg-mul-1 75.5%

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

      8. associate-/r* 75.5%

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

      9. metadata-eval 75.5%

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

      10. neg-mul-1 75.5%

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

      11. associate-*r/ 75.5%

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

      12. *-commutative 75.5%

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

      13. times-frac 75.3%

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

      14. metadata-eval 75.3%

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

   3. Simplified 75.3%

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

   4. Taylor expanded in x around 0 61.7%

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

      1. *-commutative 61.7%

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

      2. associate-*l/ 61.8%

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

      3. associate-/l* 61.8%

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

      4. div-inv 61.9%

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

      5. metadata-eval 61.9%

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

   6. Applied egg-rr 61.9%

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

   if -6.5000000000000003e-79 < a < 6.09999999999999964e-174

   1. Initial program 57.5%

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

      1. associate-*l* 57.5%

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

      2. fma-neg 57.5%

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

   3. Simplified 58.2%

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

   4. Taylor expanded in t around 0 53.2%

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

   5. Taylor expanded in a around 0 47.6%

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

   6. Taylor expanded in y around 0 36.6%

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

4. Final simplification 53.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.5 \cdot 10^{-79} \lor \neg \left(a \leq 6.1 \cdot 10^{-174}\right):\\ \;\;\;\;\frac{a}{b \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{x}\\ \end{array} \]

Alternative 10: 50.6% accurate, 43.4× speedup

Math

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

FPCore

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

C

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

Fortran

NOTE: z and t 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 = (-0.3333333333333333d0) * (a / b)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 69.7%

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

   1. fma-neg 69.7%

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

   2. *-commutative 69.7%

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

   3. associate-*r/ 69.7%

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

   4. cancel-sign-sub-inv 69.7%

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

   5. *-commutative 69.7%

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

   6. associate-/r/ 69.7%

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

   7. neg-mul-1 69.7%

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

   8. associate-/r* 69.7%

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

   9. metadata-eval 69.7%

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

   10. neg-mul-1 69.7%

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

   11. associate-*r/ 69.7%

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

   12. *-commutative 69.7%

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

   13. times-frac 69.6%

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

   14. metadata-eval 69.6%

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

3. Simplified 69.6%

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

4. Taylor expanded in x around 0 46.4%

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

5. Final simplification 46.4%

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

Alternative 11: 50.6% accurate, 43.4× speedup

Math

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

FPCore

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

Fortran

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

Python

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

Julia

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

MATLAB

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

Wolfram

NOTE: z and t 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 69.7%

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

   1. fma-neg 69.7%

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

   2. *-commutative 69.7%

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

   3. associate-*r/ 69.7%

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

   4. cancel-sign-sub-inv 69.7%

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

   5. *-commutative 69.7%

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

   6. associate-/r/ 69.7%

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

   7. neg-mul-1 69.7%

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

   8. associate-/r* 69.7%

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

   9. metadata-eval 69.7%

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

   10. neg-mul-1 69.7%

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

   11. associate-*r/ 69.7%

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

   12. *-commutative 69.7%

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

   13. times-frac 69.6%

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

   14. metadata-eval 69.6%

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

3. Simplified 69.6%

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

4. Taylor expanded in x around 0 46.4%

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

   1. associate-*r/ 46.5%

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

   2. *-commutative 46.5%

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

   3. associate-*r/ 46.5%

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

6. Simplified 46.5%

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

7. Final simplification 46.5%

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

Alternative 12: 50.7% accurate, 43.4× speedup

Math

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

FPCore

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

Fortran

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

Python

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

Julia

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

MATLAB

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

Wolfram

NOTE: z and t 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 69.7%

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

   1. fma-neg 69.7%

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

   2. *-commutative 69.7%

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

   3. associate-*r/ 69.7%

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

   4. cancel-sign-sub-inv 69.7%

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

   5. *-commutative 69.7%

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

   6. associate-/r/ 69.7%

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

   7. neg-mul-1 69.7%

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

   8. associate-/r* 69.7%

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

   9. metadata-eval 69.7%

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

   10. neg-mul-1 69.7%

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

   11. associate-*r/ 69.7%

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

   12. *-commutative 69.7%

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

   13. times-frac 69.6%

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

   14. metadata-eval 69.6%

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

3. Simplified 69.6%

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

4. Taylor expanded in x around 0 46.4%

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

   1. *-commutative 46.4%

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

   2. associate-*l/ 46.5%

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

   3. associate-/l* 46.5%

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

   4. div-inv 46.6%

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

   5. metadata-eval 46.6%

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

6. Applied egg-rr 46.6%

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

7. Final simplification 46.6%

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

Developer target: 74.3% 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 2023301 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, K"
  :precision binary64

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

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