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

Percentage Accurate: 69.4% → 77.0%

Time: 24.5s

Alternatives: 12

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 69.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 77.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := \sin \left(-0.3333333333333333 \cdot \left(z \cdot t\right)\right)\\ t_2 := 2 \cdot \sqrt{x}\\ t_3 := \cos \left(z \cdot \left(t \cdot 0.3333333333333333\right)\right)\\ t_4 := \frac{a}{3 \cdot b}\\ \mathbf{if}\;t_2 \cdot \cos \left(y - \frac{z \cdot t}{3}\right) \leq 10^{+72}:\\ \;\;\;\;t_2 \cdot \frac{t_3 \cdot \left(t_3 \cdot {\cos y}^{2}\right) - {\sin y}^{2} \cdot {t_1}^{2}}{\mathsf{fma}\left(\cos y, t_3, \sin y \cdot t_1\right)} - t_4\\ \mathbf{else}:\\ \;\;\;\;t_2 \cdot \cos y - t_4\\ \end{array} \end{array} \]

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 (sin (* -0.3333333333333333 (* z t))))
        (t_2 (* 2.0 (sqrt x)))
        (t_3 (cos (* z (* t 0.3333333333333333))))
        (t_4 (/ a (* 3.0 b))))
   (if (<= (* t_2 (cos (- y (/ (* z t) 3.0)))) 1e+72)
     (-
      (*
       t_2
       (/
        (-
         (* t_3 (* t_3 (pow (cos y) 2.0)))
         (* (pow (sin y) 2.0) (pow t_1 2.0)))
        (fma (cos y) t_3 (* (sin y) t_1))))
      t_4)
     (- (* t_2 (cos y)) t_4))))

C

assert(z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = sin((-0.3333333333333333 * (z * t)));
	double t_2 = 2.0 * sqrt(x);
	double t_3 = cos((z * (t * 0.3333333333333333)));
	double t_4 = a / (3.0 * b);
	double tmp;
	if ((t_2 * cos((y - ((z * t) / 3.0)))) <= 1e+72) {
		tmp = (t_2 * (((t_3 * (t_3 * pow(cos(y), 2.0))) - (pow(sin(y), 2.0) * pow(t_1, 2.0))) / fma(cos(y), t_3, (sin(y) * t_1)))) - t_4;
	} else {
		tmp = (t_2 * cos(y)) - t_4;
	}
	return tmp;
}

Julia

z, t = sort([z, t])
function code(x, y, z, t, a, b)
	t_1 = sin(Float64(-0.3333333333333333 * Float64(z * t)))
	t_2 = Float64(2.0 * sqrt(x))
	t_3 = cos(Float64(z * Float64(t * 0.3333333333333333)))
	t_4 = Float64(a / Float64(3.0 * b))
	tmp = 0.0
	if (Float64(t_2 * cos(Float64(y - Float64(Float64(z * t) / 3.0)))) <= 1e+72)
		tmp = Float64(Float64(t_2 * Float64(Float64(Float64(t_3 * Float64(t_3 * (cos(y) ^ 2.0))) - Float64((sin(y) ^ 2.0) * (t_1 ^ 2.0))) / fma(cos(y), t_3, Float64(sin(y) * t_1)))) - t_4);
	else
		tmp = Float64(Float64(t_2 * cos(y)) - t_4);
	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[Sin[N[(-0.3333333333333333 * N[(z * t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[Cos[N[(z * N[(t * 0.3333333333333333), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$4 = N[(a / N[(3.0 * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$2 * N[Cos[N[(y - N[(N[(z * t), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 1e+72], N[(N[(t$95$2 * N[(N[(N[(t$95$3 * N[(t$95$3 * N[Power[N[Cos[y], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[Power[N[Sin[y], $MachinePrecision], 2.0], $MachinePrecision] * N[Power[t$95$1, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[Cos[y], $MachinePrecision] * t$95$3 + N[(N[Sin[y], $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$4), $MachinePrecision], N[(N[(t$95$2 * N[Cos[y], $MachinePrecision]), $MachinePrecision] - t$95$4), $MachinePrecision]]]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3)))) < 9.99999999999999944e71

   1. Initial program 80.9%

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

      1. *-commutative 80.9%

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

      2. *-commutative 80.9%

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

      3. associate-/l* 81.1%

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

      4. *-commutative 81.1%

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

   3. Simplified 81.1%

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

      1. associate-/l* 80.9%

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

      2. add-sqr-sqrt 48.8%

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

      3. pow2 48.8%

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

      4. associate-/l* 49.4%

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

      5. div-inv 48.4%

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

      6. clear-num 48.4%

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

      7. div-inv 48.9%

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

      8. metadata-eval 48.9%

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

   5. Applied egg-rr 48.9%

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

      1. unpow2 48.9%

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

      2. add-sqr-sqrt 81.0%

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

      3. cos-diff 81.9%

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

      4. flip-+ 81.9%

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

   7. Applied egg-rr 81.9%

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

   9. Simplified 82.2%

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

   if 9.99999999999999944e71 < (*.f64 (*.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3))))

   1. Initial program 48.6%

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

      1. *-commutative 48.6%

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

      2. *-commutative 48.6%

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

      3. associate-/l* 48.0%

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

      4. *-commutative 48.0%

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

   3. Simplified 48.0%

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

   4. Taylor expanded in z around 0 73.4%

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

      1. associate-*r* 73.4%

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

      2. *-commutative 73.4%

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

   6. Simplified 73.4%

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

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) \leq 10^{+72}:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \frac{\cos \left(z \cdot \left(t \cdot 0.3333333333333333\right)\right) \cdot \left(\cos \left(z \cdot \left(t \cdot 0.3333333333333333\right)\right) \cdot {\cos y}^{2}\right) - {\sin y}^{2} \cdot {\sin \left(-0.3333333333333333 \cdot \left(z \cdot t\right)\right)}^{2}}{\mathsf{fma}\left(\cos y, \cos \left(z \cdot \left(t \cdot 0.3333333333333333\right)\right), \sin y \cdot \sin \left(-0.3333333333333333 \cdot \left(z \cdot t\right)\right)\right)} - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \cos y - \frac{a}{3 \cdot b}\\ \end{array} \]

Alternative 2: 77.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := \frac{a}{3 \cdot b}\\ t_2 := 2 \cdot \sqrt{x}\\ t_3 := z \cdot \left(t \cdot 0.3333333333333333\right)\\ \mathbf{if}\;t_2 \cdot \cos \left(y - \frac{z \cdot t}{3}\right) \leq 10^{+72}:\\ \;\;\;\;t_2 \cdot \left(\cos t_3 \cdot \cos y + \sin y \cdot \sin t_3\right) - t_1\\ \mathbf{else}:\\ \;\;\;\;t_2 \cdot \cos y - t_1\\ \end{array} \end{array} \]

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)))
        (t_3 (* z (* t 0.3333333333333333))))
   (if (<= (* t_2 (cos (- y (/ (* z t) 3.0)))) 1e+72)
     (- (* t_2 (+ (* (cos t_3) (cos y)) (* (sin y) (sin t_3)))) t_1)
     (- (* t_2 (cos y)) t_1))))

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 t_3 = z * (t * 0.3333333333333333);
	double tmp;
	if ((t_2 * cos((y - ((z * t) / 3.0)))) <= 1e+72) {
		tmp = (t_2 * ((cos(t_3) * cos(y)) + (sin(y) * sin(t_3)))) - t_1;
	} else {
		tmp = (t_2 * cos(y)) - t_1;
	}
	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 = a / (3.0d0 * b)
    t_2 = 2.0d0 * sqrt(x)
    t_3 = z * (t * 0.3333333333333333d0)
    if ((t_2 * cos((y - ((z * t) / 3.0d0)))) <= 1d+72) then
        tmp = (t_2 * ((cos(t_3) * cos(y)) + (sin(y) * sin(t_3)))) - t_1
    else
        tmp = (t_2 * cos(y)) - t_1
    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 t_3 = z * (t * 0.3333333333333333);
	double tmp;
	if ((t_2 * Math.cos((y - ((z * t) / 3.0)))) <= 1e+72) {
		tmp = (t_2 * ((Math.cos(t_3) * Math.cos(y)) + (Math.sin(y) * Math.sin(t_3)))) - t_1;
	} else {
		tmp = (t_2 * Math.cos(y)) - t_1;
	}
	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)
	t_3 = z * (t * 0.3333333333333333)
	tmp = 0
	if (t_2 * math.cos((y - ((z * t) / 3.0)))) <= 1e+72:
		tmp = (t_2 * ((math.cos(t_3) * math.cos(y)) + (math.sin(y) * math.sin(t_3)))) - t_1
	else:
		tmp = (t_2 * math.cos(y)) - t_1
	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))
	t_3 = Float64(z * Float64(t * 0.3333333333333333))
	tmp = 0.0
	if (Float64(t_2 * cos(Float64(y - Float64(Float64(z * t) / 3.0)))) <= 1e+72)
		tmp = Float64(Float64(t_2 * Float64(Float64(cos(t_3) * cos(y)) + Float64(sin(y) * sin(t_3)))) - t_1);
	else
		tmp = Float64(Float64(t_2 * cos(y)) - t_1);
	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);
	t_3 = z * (t * 0.3333333333333333);
	tmp = 0.0;
	if ((t_2 * cos((y - ((z * t) / 3.0)))) <= 1e+72)
		tmp = (t_2 * ((cos(t_3) * cos(y)) + (sin(y) * sin(t_3)))) - t_1;
	else
		tmp = (t_2 * cos(y)) - t_1;
	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]}, Block[{t$95$3 = N[(z * N[(t * 0.3333333333333333), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$2 * N[Cos[N[(y - N[(N[(z * t), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 1e+72], N[(N[(t$95$2 * N[(N[(N[Cos[t$95$3], $MachinePrecision] * N[Cos[y], $MachinePrecision]), $MachinePrecision] + N[(N[Sin[y], $MachinePrecision] * N[Sin[t$95$3], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(t$95$2 * N[Cos[y], $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3)))) < 9.99999999999999944e71

   1. Initial program 80.9%

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

      1. *-commutative 80.9%

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

      2. *-commutative 80.9%

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

      3. associate-/l* 81.1%

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

      4. *-commutative 81.1%

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

   3. Simplified 81.1%

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

      1. associate-/l* 80.9%

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

      2. cos-diff 82.0%

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

      3. associate-/l* 82.1%

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

      4. div-inv 81.9%

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

      5. clear-num 82.3%

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

      6. div-inv 82.0%

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

      7. metadata-eval 82.0%

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

      8. associate-/l* 82.0%

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

      9. div-inv 81.9%

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

      10. clear-num 81.8%

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

      11. div-inv 81.9%

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

      12. metadata-eval 81.9%

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

   5. Applied egg-rr 81.9%

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

   if 9.99999999999999944e71 < (*.f64 (*.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3))))

   1. Initial program 48.6%

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

      1. *-commutative 48.6%

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

      2. *-commutative 48.6%

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

      3. associate-/l* 48.0%

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

      4. *-commutative 48.0%

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

   3. Simplified 48.0%

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

   4. Taylor expanded in z around 0 73.4%

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

      1. associate-*r* 73.4%

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

      2. *-commutative 73.4%

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

   6. Simplified 73.4%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) \leq 10^{+72}:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \left(\cos \left(z \cdot \left(t \cdot 0.3333333333333333\right)\right) \cdot \cos y + \sin y \cdot \sin \left(z \cdot \left(t \cdot 0.3333333333333333\right)\right)\right) - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \cos y - \frac{a}{3 \cdot b}\\ \end{array} \]

Alternative 3: 76.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{log1p}\left(\mathsf{expm1}\left(\cos y\right)\right) - \frac{a}{3 \cdot b} \end{array} \]

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)) (log1p (expm1 (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)) * log1p(expm1(cos(y)))) - (a / (3.0 * b));
}

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.log1p(Math.expm1(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.log1p(math.expm1(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)) * log1p(expm1(cos(y)))) - Float64(a / Float64(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[Log[1 + N[(Exp[N[Cos[y], $MachinePrecision]] - 1), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - N[(a / N[(3.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 72.8%

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

   1. *-commutative 72.8%

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

   2. *-commutative 72.8%

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

   3. associate-/l* 72.8%

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

   4. *-commutative 72.8%

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

3. Simplified 72.8%

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

   1. associate-/l* 72.8%

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

   2. sub-neg 72.8%

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

   3. sub-neg 72.8%

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

   4. log1p-expm1-u 72.8%

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\cos \left(y - \frac{z \cdot t}{3}\right)\right)\right)} - \frac{a}{3 \cdot b} \]

   5. associate-/l* 72.8%

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{log1p}\left(\mathsf{expm1}\left(\cos \left(y - \color{blue}{\frac{z}{\frac{3}{t}}}\right)\right)\right) - \frac{a}{3 \cdot b} \]

   6. div-inv 72.7%

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{log1p}\left(\mathsf{expm1}\left(\cos \left(y - \color{blue}{z \cdot \frac{1}{\frac{3}{t}}}\right)\right)\right) - \frac{a}{3 \cdot b} \]

   7. clear-num 72.8%

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{log1p}\left(\mathsf{expm1}\left(\cos \left(y - z \cdot \color{blue}{\frac{t}{3}}\right)\right)\right) - \frac{a}{3 \cdot b} \]

   8. div-inv 72.9%

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{log1p}\left(\mathsf{expm1}\left(\cos \left(y - z \cdot \color{blue}{\left(t \cdot \frac{1}{3}\right)}\right)\right)\right) - \frac{a}{3 \cdot b} \]

   9. metadata-eval 72.9%

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{log1p}\left(\mathsf{expm1}\left(\cos \left(y - z \cdot \left(t \cdot \color{blue}{0.3333333333333333}\right)\right)\right)\right) - \frac{a}{3 \cdot b} \]

5. Applied egg-rr 72.9%

   \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\cos \left(y - z \cdot \left(t \cdot 0.3333333333333333\right)\right)\right)\right)} - \frac{a}{3 \cdot b} \]

6. Taylor expanded in z around 0 78.1%

   \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{log1p}\left(\color{blue}{e^{\cos y} - 1}\right) - \frac{a}{3 \cdot b} \]
7. Step-by-step derivation

   1. expm1-def 78.2%

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{log1p}\left(\color{blue}{\mathsf{expm1}\left(\cos y\right)}\right) - \frac{a}{3 \cdot b} \]

8. Simplified 78.2%

   \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{log1p}\left(\color{blue}{\mathsf{expm1}\left(\cos y\right)}\right) - \frac{a}{3 \cdot b} \]

9. Final simplification 78.2%

   \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \mathsf{log1p}\left(\mathsf{expm1}\left(\cos y\right)\right) - \frac{a}{3 \cdot b} \]

Alternative 4: 66.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq 4.6 \cdot 10^{+178}:\\ \;\;\;\;2 \cdot \sqrt{x} - 0.3333333333333333 \cdot \frac{a}{b}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt{x} \cdot \cos \left(y + -0.3333333333333333 \cdot \left(z \cdot t\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 4.6e+178)
   (- (* 2.0 (sqrt x)) (* 0.3333333333333333 (/ a b)))
   (* 2.0 (* (sqrt x) (cos (+ y (* -0.3333333333333333 (* z t))))))))

C

assert(z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 4.6e+178) {
		tmp = (2.0 * sqrt(x)) - (0.3333333333333333 * (a / b));
	} else {
		tmp = 2.0 * (sqrt(x) * cos((y + (-0.3333333333333333 * (z * t)))));
	}
	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 (b <= 4.6d+178) then
        tmp = (2.0d0 * sqrt(x)) - (0.3333333333333333d0 * (a / b))
    else
        tmp = 2.0d0 * (sqrt(x) * cos((y + ((-0.3333333333333333d0) * (z * t)))))
    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 (b <= 4.6e+178) {
		tmp = (2.0 * Math.sqrt(x)) - (0.3333333333333333 * (a / b));
	} else {
		tmp = 2.0 * (Math.sqrt(x) * Math.cos((y + (-0.3333333333333333 * (z * t)))));
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 4.6e+178:
		tmp = (2.0 * math.sqrt(x)) - (0.3333333333333333 * (a / b))
	else:
		tmp = 2.0 * (math.sqrt(x) * math.cos((y + (-0.3333333333333333 * (z * t)))))
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 4.6e+178)
		tmp = Float64(Float64(2.0 * sqrt(x)) - Float64(0.3333333333333333 * Float64(a / b)));
	else
		tmp = Float64(2.0 * Float64(sqrt(x) * cos(Float64(y + Float64(-0.3333333333333333 * Float64(z * t))))));
	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 (b <= 4.6e+178)
		tmp = (2.0 * sqrt(x)) - (0.3333333333333333 * (a / b));
	else
		tmp = 2.0 * (sqrt(x) * cos((y + (-0.3333333333333333 * (z * t)))));
	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[LessEqual[b, 4.6e+178], N[(N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] - N[(0.3333333333333333 * N[(a / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[Sqrt[x], $MachinePrecision] * N[Cos[N[(y + N[(-0.3333333333333333 * N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 4.6000000000000002e178

   1. Initial program 73.6%

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

      1. *-commutative 73.6%

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

      2. *-commutative 73.6%

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

      3. associate-/l* 73.6%

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

      4. *-commutative 73.6%

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

   3. Simplified 73.6%

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

   4. Taylor expanded in z around 0 79.2%

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

      1. associate-*r* 79.2%

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

      2. *-commutative 79.2%

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

   6. Simplified 79.2%

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

   7. Taylor expanded in y around 0 69.6%

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

   if 4.6000000000000002e178 < b

   1. Initial program 65.3%

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

      1. *-commutative 65.3%

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

      2. *-commutative 65.3%

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

      3. *-commutative 65.3%

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

      4. associate-*l* 65.3%

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

      5. fma-neg 65.3%

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

   3. Simplified 65.7%

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

   4. Taylor expanded in a around 0 61.7%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 4.6 \cdot 10^{+178}:\\ \;\;\;\;2 \cdot \sqrt{x} - 0.3333333333333333 \cdot \frac{a}{b}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt{x} \cdot \cos \left(y + -0.3333333333333333 \cdot \left(z \cdot t\right)\right)\right)\\ \end{array} \]

Alternative 5: 76.2% accurate, 1.0× speedup

Math

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

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)) (* 2.0 (* (sqrt x) (cos y)))))

C

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

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)) + (2.0d0 * (sqrt(x) * cos(y)))
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)) + (2.0 * (Math.sqrt(x) * Math.cos(y)));
}

Python

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

Julia

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

MATLAB

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

Derivation

1. Initial program 72.8%

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

   1. fma-neg 72.8%

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

   2. *-commutative 72.8%

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

   3. associate-*l/ 72.8%

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

   4. distribute-frac-neg 72.8%

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

   5. neg-mul-1 72.8%

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

   6. *-commutative 72.8%

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

   7. times-frac 72.8%

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

   8. metadata-eval 72.8%

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

3. Simplified 72.8%

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

4. Taylor expanded in t around 0 78.1%

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

5. Final simplification 78.1%

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

Alternative 6: 76.3% 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 72.8%

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

   1. *-commutative 72.8%

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

   2. *-commutative 72.8%

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

   3. associate-/l* 72.8%

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

   4. *-commutative 72.8%

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

3. Simplified 72.8%

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

4. Taylor expanded in z around 0 78.2%

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

   1. associate-*r* 78.2%

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

   2. *-commutative 78.2%

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

6. Simplified 78.2%

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

7. Final simplification 78.2%

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

Alternative 7: 66.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq 4.2 \cdot 10^{+180}:\\ \;\;\;\;2 \cdot \sqrt{x} - 0.3333333333333333 \cdot \frac{a}{b}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt{x} \cdot \cos y\right)\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 4.2e+180)
   (- (* 2.0 (sqrt x)) (* 0.3333333333333333 (/ a 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 tmp;
	if (b <= 4.2e+180) {
		tmp = (2.0 * sqrt(x)) - (0.3333333333333333 * (a / b));
	} else {
		tmp = 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) :: tmp
    if (b <= 4.2d+180) then
        tmp = (2.0d0 * sqrt(x)) - (0.3333333333333333d0 * (a / b))
    else
        tmp = 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 tmp;
	if (b <= 4.2e+180) {
		tmp = (2.0 * Math.sqrt(x)) - (0.3333333333333333 * (a / b));
	} else {
		tmp = 2.0 * (Math.sqrt(x) * Math.cos(y));
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 4.2e+180:
		tmp = (2.0 * math.sqrt(x)) - (0.3333333333333333 * (a / b))
	else:
		tmp = 2.0 * (math.sqrt(x) * math.cos(y))
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 4.2e+180)
		tmp = Float64(Float64(2.0 * sqrt(x)) - Float64(0.3333333333333333 * Float64(a / b)));
	else
		tmp = 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)
	tmp = 0.0;
	if (b <= 4.2e+180)
		tmp = (2.0 * sqrt(x)) - (0.3333333333333333 * (a / b));
	else
		tmp = 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_] := If[LessEqual[b, 4.2e+180], N[(N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] - N[(0.3333333333333333 * N[(a / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[Sqrt[x], $MachinePrecision] * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 4.1999999999999999e180

   1. Initial program 73.6%

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

      1. *-commutative 73.6%

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

      2. *-commutative 73.6%

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

      3. associate-/l* 73.6%

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

      4. *-commutative 73.6%

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

   3. Simplified 73.6%

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

   4. Taylor expanded in z around 0 79.2%

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

      1. associate-*r* 79.2%

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

      2. *-commutative 79.2%

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

   6. Simplified 79.2%

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

   7. Taylor expanded in y around 0 69.6%

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

   if 4.1999999999999999e180 < b

   1. Initial program 65.3%

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

      1. *-commutative 65.3%

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

      2. *-commutative 65.3%

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

      3. *-commutative 65.3%

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

      4. associate-*l* 65.3%

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

      5. fma-neg 65.3%

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

   3. Simplified 65.7%

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

   4. Taylor expanded in a around 0 61.7%

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

   5. Taylor expanded in t around 0 60.9%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 4.2 \cdot 10^{+180}:\\ \;\;\;\;2 \cdot \sqrt{x} - 0.3333333333333333 \cdot \frac{a}{b}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt{x} \cdot \cos y\right)\\ \end{array} \]

Alternative 8: 65.8% accurate, 2.0× speedup

Math

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

FPCore

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

C

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

Fortran

NOTE: 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)) - (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 (2.0 * Math.sqrt(x)) - (0.3333333333333333 * (a / b));
}

Python

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

Julia

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

MATLAB

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

Derivation

1. Initial program 72.8%

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

   1. *-commutative 72.8%

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

   2. *-commutative 72.8%

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

   3. associate-/l* 72.8%

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

   4. *-commutative 72.8%

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

3. Simplified 72.8%

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

4. Taylor expanded in z around 0 78.2%

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

   1. associate-*r* 78.2%

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

   2. *-commutative 78.2%

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

6. Simplified 78.2%

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

7. Taylor expanded in y around 0 66.1%

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

8. Final simplification 66.1%

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

Alternative 9: 50.7% accurate, 36.2× speedup

Math

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

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

Derivation

1. Initial program 72.8%

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

   1. *-commutative 72.8%

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

   2. *-commutative 72.8%

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

   3. associate-/l* 72.8%

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

   4. *-commutative 72.8%

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

3. Simplified 72.8%

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

4. Taylor expanded in z around 0 78.2%

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

   1. associate-*r* 78.2%

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

   2. *-commutative 78.2%

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

6. Simplified 78.2%

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

7. Taylor expanded in x around 0 53.0%

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

   1. *-commutative 53.0%

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

9. Simplified 53.0%

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

    1. *-commutative 53.0%

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

    2. metadata-eval 53.0%

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

    3. distribute-lft-neg-in 53.0%

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

    4. clear-num 53.0%

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

    5. div-inv 53.0%

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

    6. clear-num 53.0%

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

    7. distribute-neg-frac 53.0%

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

    8. metadata-eval 53.0%

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

    9. div-inv 53.0%

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

    10. metadata-eval 53.0%

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

11. Applied egg-rr 53.0%

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

    1. associate-/r* 53.0%

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

    2. metadata-eval 53.0%

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

    3. distribute-neg-frac 53.0%

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

    4. associate-/l* 53.1%

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

    5. *-lft-identity 53.1%

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

    6. distribute-neg-frac 53.1%

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

13. Simplified 53.1%

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

14. Final simplification 53.1%

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

Alternative 10: 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 72.8%

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

   1. *-commutative 72.8%

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

   2. *-commutative 72.8%

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

   3. associate-/l* 72.8%

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

   4. *-commutative 72.8%

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

3. Simplified 72.8%

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

4. Taylor expanded in z around 0 78.2%

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

   1. associate-*r* 78.2%

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

   2. *-commutative 78.2%

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

6. Simplified 78.2%

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

7. Taylor expanded in x around 0 53.0%

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

   1. metadata-eval 53.0%

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

   2. distribute-lft-neg-in 53.0%

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

   3. metadata-eval 53.0%

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

   4. times-frac 53.1%

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

   5. associate-*l/ 53.0%

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

   6. *-commutative 53.0%

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

   7. distribute-rgt-neg-in 53.0%

      \[\leadsto \color{blue}{a \cdot \left(-\frac{1}{3 \cdot b}\right)} \]

   8. associate-/r* 53.0%

      \[\leadsto a \cdot \left(-\color{blue}{\frac{\frac{1}{3}}{b}}\right) \]

   9. metadata-eval 53.0%

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

   10. distribute-neg-frac 53.0%

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

   11. metadata-eval 53.0%

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

9. Simplified 53.0%

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

10. Final simplification 53.0%

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

Alternative 11: 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 72.8%

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

   1. *-commutative 72.8%

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

   2. *-commutative 72.8%

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

   3. associate-/l* 72.8%

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

   4. *-commutative 72.8%

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

3. Simplified 72.8%

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

4. Taylor expanded in z around 0 78.2%

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

   1. associate-*r* 78.2%

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

   2. *-commutative 78.2%

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

6. Simplified 78.2%

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

7. Taylor expanded in x around 0 53.0%

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

   1. *-commutative 53.0%

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

9. Simplified 53.0%

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

10. Final simplification 53.0%

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

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 72.8%

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

   1. *-commutative 72.8%

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

   2. *-commutative 72.8%

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

   3. associate-/l* 72.8%

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

   4. *-commutative 72.8%

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

3. Simplified 72.8%

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

4. Taylor expanded in z around 0 78.2%

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

   1. associate-*r* 78.2%

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

   2. *-commutative 78.2%

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

6. Simplified 78.2%

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

7. Taylor expanded in x around 0 53.0%

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

   1. metadata-eval 53.0%

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

   2. distribute-lft-neg-in 53.0%

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

   3. metadata-eval 53.0%

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

   4. times-frac 53.1%

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

   5. associate-*l/ 53.0%

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

   6. *-commutative 53.0%

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

   7. distribute-rgt-neg-in 53.0%

      \[\leadsto \color{blue}{a \cdot \left(-\frac{1}{3 \cdot b}\right)} \]

   8. associate-/r* 53.0%

      \[\leadsto a \cdot \left(-\color{blue}{\frac{\frac{1}{3}}{b}}\right) \]

   9. metadata-eval 53.0%

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

   10. distribute-neg-frac 53.0%

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

   11. metadata-eval 53.0%

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

9. Simplified 53.0%

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

    1. associate-*r/ 53.0%

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

    2. metadata-eval 53.0%

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

    3. div-inv 53.1%

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

    4. associate-/l/ 53.1%

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

11. Applied egg-rr 53.1%

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

12. Final simplification 53.1%

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

Developer target: 73.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023308 
(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))))