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

Percentage Accurate: 71.0% → 77.4%

Time: 28.6s

Alternatives: 13

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: 71.0% 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: 77.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := 2 \cdot \sqrt{x}\\ \mathbf{if}\;t_1 \cdot \cos \left(y - \frac{z \cdot t}{3}\right) \leq 10^{+136}:\\ \;\;\;\;2 \cdot \left(\sqrt{x} \cdot \mathsf{fma}\left(\cos y, \cos \left(z \cdot \left(t \cdot -0.3333333333333333\right)\right), \sin y \cdot \sin \left(0.3333333333333333 \cdot \left(z \cdot t\right)\right)\right)\right) - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;t_1 - \frac{\frac{a}{3}}{b}\\ \end{array} \end{array} \]

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 (* 2.0 (sqrt x))))
   (if (<= (* t_1 (cos (- y (/ (* z t) 3.0)))) 1e+136)
     (-
      (*
       2.0
       (*
        (sqrt x)
        (fma
         (cos y)
         (cos (* z (* t -0.3333333333333333)))
         (* (sin y) (sin (* 0.3333333333333333 (* z t)))))))
      (/ a (* 3.0 b)))
     (- t_1 (/ (/ a 3.0) b)))))

C

assert(z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 2.0 * sqrt(x);
	double tmp;
	if ((t_1 * cos((y - ((z * t) / 3.0)))) <= 1e+136) {
		tmp = (2.0 * (sqrt(x) * fma(cos(y), cos((z * (t * -0.3333333333333333))), (sin(y) * sin((0.3333333333333333 * (z * t))))))) - (a / (3.0 * b));
	} else {
		tmp = t_1 - ((a / 3.0) / b);
	}
	return tmp;
}

Julia

z, t = sort([z, t])
function code(x, y, z, t, a, b)
	t_1 = Float64(2.0 * sqrt(x))
	tmp = 0.0
	if (Float64(t_1 * cos(Float64(y - Float64(Float64(z * t) / 3.0)))) <= 1e+136)
		tmp = Float64(Float64(2.0 * Float64(sqrt(x) * fma(cos(y), cos(Float64(z * Float64(t * -0.3333333333333333))), Float64(sin(y) * sin(Float64(0.3333333333333333 * Float64(z * t))))))) - Float64(a / Float64(3.0 * b)));
	else
		tmp = Float64(t_1 - Float64(Float64(a / 3.0) / b));
	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[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$1 * N[Cos[N[(y - N[(N[(z * t), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 1e+136], N[(N[(2.0 * N[(N[Sqrt[x], $MachinePrecision] * N[(N[Cos[y], $MachinePrecision] * N[Cos[N[(z * N[(t * -0.3333333333333333), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] + N[(N[Sin[y], $MachinePrecision] * N[Sin[N[(0.3333333333333333 * N[(z * t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a / N[(3.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 - N[(N[(a / 3.0), $MachinePrecision] / b), $MachinePrecision]), $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)))) < 1.00000000000000006e136

   1. Initial program 80.0%

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

      1. associate-*l* 80.0%

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

      2. fma-neg 80.0%

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

      3. remove-double-neg 80.0%

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

      4. fma-neg 80.0%

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

      5. remove-double-neg 80.0%

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

      6. associate-/l* 80.1%

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

      7. *-commutative 80.1%

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

   3. Simplified 80.1%

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

      1. cos-diff 81.1%

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

      2. associate-/r/ 81.3%

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

      3. *-commutative 81.3%

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

      4. div-inv 81.3%

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

      5. metadata-eval 81.3%

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

      6. associate-/r/ 81.5%

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

      7. *-commutative 81.5%

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

      8. div-inv 81.5%

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

      9. metadata-eval 81.5%

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

   5. Applied egg-rr 81.5%

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

      1. fma-def 81.5%

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

      2. associate-*r* 81.4%

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

      3. *-commutative 81.4%

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

      4. cos-neg 81.4%

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

      5. distribute-lft-neg-in 81.4%

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

      6. metadata-eval 81.4%

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

      7. *-commutative 81.4%

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

      8. *-commutative 81.4%

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

      9. associate-*r* 81.5%

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

      10. associate-*r* 81.6%

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

      11. *-commutative 81.6%

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

   7. Simplified 81.6%

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

   if 1.00000000000000006e136 < (*.f64 (*.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3))))

   1. Initial program 20.0%

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

      1. associate-*l* 20.0%

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

      2. fma-neg 20.0%

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

      3. remove-double-neg 20.0%

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

      4. fma-neg 20.0%

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

      5. remove-double-neg 20.0%

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

      6. associate-/l* 20.0%

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

      7. *-commutative 20.0%

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

   3. Simplified 20.0%

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

   4. Taylor expanded in z around 0 62.4%

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

      1. *-un-lft-identity 62.4%

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

      2. associate-/r* 62.5%

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

   6. Applied egg-rr 62.5%

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

   7. Taylor expanded in y around 0 63.4%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) \leq 10^{+136}:\\ \;\;\;\;2 \cdot \left(\sqrt{x} \cdot \mathsf{fma}\left(\cos y, \cos \left(z \cdot \left(t \cdot -0.3333333333333333\right)\right), \sin y \cdot \sin \left(0.3333333333333333 \cdot \left(z \cdot t\right)\right)\right)\right) - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{x} - \frac{\frac{a}{3}}{b}\\ \end{array} \]

Alternative 2: 77.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := 2 \cdot \sqrt{x}\\ t_2 := t \cdot \left(z \cdot 0.3333333333333333\right)\\ \mathbf{if}\;t_1 \cdot \cos \left(y - \frac{z \cdot t}{3}\right) \leq 10^{+136}:\\ \;\;\;\;2 \cdot \left(\sqrt{x} \cdot \left(\cos y \cdot \cos t_2 + \sin y \cdot \sin t_2\right)\right) - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;t_1 - \frac{\frac{a}{3}}{b}\\ \end{array} \end{array} \]

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 (* 2.0 (sqrt x))) (t_2 (* t (* z 0.3333333333333333))))
   (if (<= (* t_1 (cos (- y (/ (* z t) 3.0)))) 1e+136)
     (-
      (* 2.0 (* (sqrt x) (+ (* (cos y) (cos t_2)) (* (sin y) (sin t_2)))))
      (/ a (* 3.0 b)))
     (- t_1 (/ (/ a 3.0) b)))))

C

assert(z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 2.0 * sqrt(x);
	double t_2 = t * (z * 0.3333333333333333);
	double tmp;
	if ((t_1 * cos((y - ((z * t) / 3.0)))) <= 1e+136) {
		tmp = (2.0 * (sqrt(x) * ((cos(y) * cos(t_2)) + (sin(y) * sin(t_2))))) - (a / (3.0 * b));
	} else {
		tmp = t_1 - ((a / 3.0) / b);
	}
	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 = 2.0d0 * sqrt(x)
    t_2 = t * (z * 0.3333333333333333d0)
    if ((t_1 * cos((y - ((z * t) / 3.0d0)))) <= 1d+136) then
        tmp = (2.0d0 * (sqrt(x) * ((cos(y) * cos(t_2)) + (sin(y) * sin(t_2))))) - (a / (3.0d0 * b))
    else
        tmp = t_1 - ((a / 3.0d0) / b)
    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 = 2.0 * Math.sqrt(x);
	double t_2 = t * (z * 0.3333333333333333);
	double tmp;
	if ((t_1 * Math.cos((y - ((z * t) / 3.0)))) <= 1e+136) {
		tmp = (2.0 * (Math.sqrt(x) * ((Math.cos(y) * Math.cos(t_2)) + (Math.sin(y) * Math.sin(t_2))))) - (a / (3.0 * b));
	} else {
		tmp = t_1 - ((a / 3.0) / b);
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t, a, b):
	t_1 = 2.0 * math.sqrt(x)
	t_2 = t * (z * 0.3333333333333333)
	tmp = 0
	if (t_1 * math.cos((y - ((z * t) / 3.0)))) <= 1e+136:
		tmp = (2.0 * (math.sqrt(x) * ((math.cos(y) * math.cos(t_2)) + (math.sin(y) * math.sin(t_2))))) - (a / (3.0 * b))
	else:
		tmp = t_1 - ((a / 3.0) / b)
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t, a, b)
	t_1 = Float64(2.0 * sqrt(x))
	t_2 = Float64(t * Float64(z * 0.3333333333333333))
	tmp = 0.0
	if (Float64(t_1 * cos(Float64(y - Float64(Float64(z * t) / 3.0)))) <= 1e+136)
		tmp = Float64(Float64(2.0 * Float64(sqrt(x) * Float64(Float64(cos(y) * cos(t_2)) + Float64(sin(y) * sin(t_2))))) - Float64(a / Float64(3.0 * b)));
	else
		tmp = Float64(t_1 - Float64(Float64(a / 3.0) / b));
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 2.0 * sqrt(x);
	t_2 = t * (z * 0.3333333333333333);
	tmp = 0.0;
	if ((t_1 * cos((y - ((z * t) / 3.0)))) <= 1e+136)
		tmp = (2.0 * (sqrt(x) * ((cos(y) * cos(t_2)) + (sin(y) * sin(t_2))))) - (a / (3.0 * b));
	else
		tmp = t_1 - ((a / 3.0) / b);
	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[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(z * 0.3333333333333333), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$1 * N[Cos[N[(y - N[(N[(z * t), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 1e+136], N[(N[(2.0 * N[(N[Sqrt[x], $MachinePrecision] * N[(N[(N[Cos[y], $MachinePrecision] * N[Cos[t$95$2], $MachinePrecision]), $MachinePrecision] + N[(N[Sin[y], $MachinePrecision] * N[Sin[t$95$2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a / N[(3.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 - N[(N[(a / 3.0), $MachinePrecision] / b), $MachinePrecision]), $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)))) < 1.00000000000000006e136

   1. Initial program 80.0%

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

      1. associate-*l* 80.0%

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

      2. fma-neg 80.0%

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

      3. remove-double-neg 80.0%

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

      4. fma-neg 80.0%

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

      5. remove-double-neg 80.0%

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

      6. associate-/l* 80.1%

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

      7. *-commutative 80.1%

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

   3. Simplified 80.1%

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

      1. cos-diff 81.1%

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

      2. associate-/r/ 81.3%

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

      3. *-commutative 81.3%

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

      4. div-inv 81.3%

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

      5. metadata-eval 81.3%

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

      6. associate-/r/ 81.5%

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

      7. *-commutative 81.5%

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

      8. div-inv 81.5%

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

      9. metadata-eval 81.5%

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

   5. Applied egg-rr 81.5%

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

   if 1.00000000000000006e136 < (*.f64 (*.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3))))

   1. Initial program 20.0%

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

      1. associate-*l* 20.0%

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

      2. fma-neg 20.0%

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

      3. remove-double-neg 20.0%

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

      4. fma-neg 20.0%

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

      5. remove-double-neg 20.0%

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

      6. associate-/l* 20.0%

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

      7. *-commutative 20.0%

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

   3. Simplified 20.0%

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

   4. Taylor expanded in z around 0 62.4%

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

      1. *-un-lft-identity 62.4%

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

      2. associate-/r* 62.5%

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

   6. Applied egg-rr 62.5%

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

   7. Taylor expanded in y around 0 63.4%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) \leq 10^{+136}:\\ \;\;\;\;2 \cdot \left(\sqrt{x} \cdot \left(\cos y \cdot \cos \left(t \cdot \left(z \cdot 0.3333333333333333\right)\right) + \sin y \cdot \sin \left(t \cdot \left(z \cdot 0.3333333333333333\right)\right)\right)\right) - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{x} - \frac{\frac{a}{3}}{b}\\ \end{array} \]

Alternative 3: 77.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := 2 \cdot \sqrt{x}\\ t_2 := z \cdot \left(t \cdot 0.3333333333333333\right)\\ \mathbf{if}\;t_1 \cdot \cos \left(y - \frac{z \cdot t}{3}\right) \leq 10^{+136}:\\ \;\;\;\;2 \cdot \left(\sqrt{x} \cdot \left(\cos y \cdot \cos t_2 + \sin y \cdot \sin t_2\right)\right) - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;t_1 - \frac{\frac{a}{3}}{b}\\ \end{array} \end{array} \]

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 (* 2.0 (sqrt x))) (t_2 (* z (* t 0.3333333333333333))))
   (if (<= (* t_1 (cos (- y (/ (* z t) 3.0)))) 1e+136)
     (-
      (* 2.0 (* (sqrt x) (+ (* (cos y) (cos t_2)) (* (sin y) (sin t_2)))))
      (/ a (* 3.0 b)))
     (- t_1 (/ (/ a 3.0) b)))))

C

assert(z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 2.0 * sqrt(x);
	double t_2 = z * (t * 0.3333333333333333);
	double tmp;
	if ((t_1 * cos((y - ((z * t) / 3.0)))) <= 1e+136) {
		tmp = (2.0 * (sqrt(x) * ((cos(y) * cos(t_2)) + (sin(y) * sin(t_2))))) - (a / (3.0 * b));
	} else {
		tmp = t_1 - ((a / 3.0) / b);
	}
	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 = 2.0d0 * sqrt(x)
    t_2 = z * (t * 0.3333333333333333d0)
    if ((t_1 * cos((y - ((z * t) / 3.0d0)))) <= 1d+136) then
        tmp = (2.0d0 * (sqrt(x) * ((cos(y) * cos(t_2)) + (sin(y) * sin(t_2))))) - (a / (3.0d0 * b))
    else
        tmp = t_1 - ((a / 3.0d0) / b)
    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 = 2.0 * Math.sqrt(x);
	double t_2 = z * (t * 0.3333333333333333);
	double tmp;
	if ((t_1 * Math.cos((y - ((z * t) / 3.0)))) <= 1e+136) {
		tmp = (2.0 * (Math.sqrt(x) * ((Math.cos(y) * Math.cos(t_2)) + (Math.sin(y) * Math.sin(t_2))))) - (a / (3.0 * b));
	} else {
		tmp = t_1 - ((a / 3.0) / b);
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t, a, b):
	t_1 = 2.0 * math.sqrt(x)
	t_2 = z * (t * 0.3333333333333333)
	tmp = 0
	if (t_1 * math.cos((y - ((z * t) / 3.0)))) <= 1e+136:
		tmp = (2.0 * (math.sqrt(x) * ((math.cos(y) * math.cos(t_2)) + (math.sin(y) * math.sin(t_2))))) - (a / (3.0 * b))
	else:
		tmp = t_1 - ((a / 3.0) / b)
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t, a, b)
	t_1 = Float64(2.0 * sqrt(x))
	t_2 = Float64(z * Float64(t * 0.3333333333333333))
	tmp = 0.0
	if (Float64(t_1 * cos(Float64(y - Float64(Float64(z * t) / 3.0)))) <= 1e+136)
		tmp = Float64(Float64(2.0 * Float64(sqrt(x) * Float64(Float64(cos(y) * cos(t_2)) + Float64(sin(y) * sin(t_2))))) - Float64(a / Float64(3.0 * b)));
	else
		tmp = Float64(t_1 - Float64(Float64(a / 3.0) / b));
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 2.0 * sqrt(x);
	t_2 = z * (t * 0.3333333333333333);
	tmp = 0.0;
	if ((t_1 * cos((y - ((z * t) / 3.0)))) <= 1e+136)
		tmp = (2.0 * (sqrt(x) * ((cos(y) * cos(t_2)) + (sin(y) * sin(t_2))))) - (a / (3.0 * b));
	else
		tmp = t_1 - ((a / 3.0) / b);
	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[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(t * 0.3333333333333333), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$1 * N[Cos[N[(y - N[(N[(z * t), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 1e+136], N[(N[(2.0 * N[(N[Sqrt[x], $MachinePrecision] * N[(N[(N[Cos[y], $MachinePrecision] * N[Cos[t$95$2], $MachinePrecision]), $MachinePrecision] + N[(N[Sin[y], $MachinePrecision] * N[Sin[t$95$2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a / N[(3.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 - N[(N[(a / 3.0), $MachinePrecision] / b), $MachinePrecision]), $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)))) < 1.00000000000000006e136

   1. Initial program 80.0%

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

      1. associate-*l* 80.0%

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

      2. fma-neg 80.0%

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

      3. remove-double-neg 80.0%

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

      4. fma-neg 80.0%

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

      5. remove-double-neg 80.0%

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

      6. associate-/l* 80.1%

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

      7. *-commutative 80.1%

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

   3. Simplified 80.1%

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

      1. *-un-lft-identity 80.1%

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

      2. add-sqr-sqrt 38.6%

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

      3. times-frac 38.7%

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

   5. Applied egg-rr 38.7%

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

      1. associate-*l/ 38.8%

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

      2. *-lft-identity 38.8%

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

   7. Simplified 38.8%

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

      1. associate-/l/ 38.6%

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

      2. *-un-lft-identity 38.6%

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

      3. add-sqr-sqrt 80.1%

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

      4. add-cube-cbrt 80.0%

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

      5. times-frac 80.0%

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

      6. pow2 80.0%

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

   9. Applied egg-rr 80.0%

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

       1. cos-diff 81.5%

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

       2. frac-times 81.5%

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

       3. *-un-lft-identity 81.5%

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

       4. unpow2 81.5%

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

       5. add-cube-cbrt 81.0%

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

       6. div-inv 81.0%

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

       7. clear-num 81.3%

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

       8. div-inv 81.3%

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

       9. metadata-eval 81.3%

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

       10. frac-times 81.2%

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

   11. Applied egg-rr 81.4%

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

   if 1.00000000000000006e136 < (*.f64 (*.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3))))

   1. Initial program 20.0%

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

      1. associate-*l* 20.0%

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

      2. fma-neg 20.0%

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

      3. remove-double-neg 20.0%

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

      4. fma-neg 20.0%

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

      5. remove-double-neg 20.0%

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

      6. associate-/l* 20.0%

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

      7. *-commutative 20.0%

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

   3. Simplified 20.0%

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

   4. Taylor expanded in z around 0 62.4%

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

      1. *-un-lft-identity 62.4%

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

      2. associate-/r* 62.5%

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

   6. Applied egg-rr 62.5%

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

   7. Taylor expanded in y around 0 63.4%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) \leq 10^{+136}:\\ \;\;\;\;2 \cdot \left(\sqrt{x} \cdot \left(\cos y \cdot \cos \left(z \cdot \left(t \cdot 0.3333333333333333\right)\right) + \sin y \cdot \sin \left(z \cdot \left(t \cdot 0.3333333333333333\right)\right)\right)\right) - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{x} - \frac{\frac{a}{3}}{b}\\ \end{array} \]

Alternative 4: 76.7% accurate, 1.0× speedup

Math

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

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) (cos y))) (* 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) * cos(y))) - (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) * cos(y))) - (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) * Math.cos(y))) - (0.3333333333333333 * (a / b));
}

Python

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

Julia

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

Derivation

1. Initial program 71.5%

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

   1. associate-*l* 71.5%

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

   2. fma-neg 71.5%

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

   3. remove-double-neg 71.5%

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

   4. fma-neg 71.5%

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

   5. remove-double-neg 71.5%

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

   6. associate-/l* 71.7%

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

   7. *-commutative 71.7%

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

3. Simplified 71.7%

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

4. Taylor expanded in z around 0 76.6%

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

5. Taylor expanded in a around 0 76.6%

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

6. Final simplification 76.6%

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

Alternative 5: 76.8% accurate, 1.0× speedup

Math

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

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) (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(2.0 * Float64(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[(2.0 * N[(N[Sqrt[x], $MachinePrecision] * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a / N[(3.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 71.5%

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

   1. associate-*l* 71.5%

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

   2. fma-neg 71.5%

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

   3. remove-double-neg 71.5%

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

   4. fma-neg 71.5%

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

   5. remove-double-neg 71.5%

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

   6. associate-/l* 71.7%

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

   7. *-commutative 71.7%

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

3. Simplified 71.7%

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

4. Taylor expanded in z around 0 76.6%

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

5. Final simplification 76.6%

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

Alternative 6: 76.8% accurate, 1.0× speedup

Math

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

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(2.0 * Float64(sqrt(x) * cos(y))) - Float64(Float64(a / 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[(2.0 * N[(N[Sqrt[x], $MachinePrecision] * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(a / 3.0), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 71.5%

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

   1. associate-*l* 71.5%

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

   2. fma-neg 71.5%

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

   3. remove-double-neg 71.5%

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

   4. fma-neg 71.5%

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

   5. remove-double-neg 71.5%

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

   6. associate-/l* 71.7%

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

   7. *-commutative 71.7%

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

3. Simplified 71.7%

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

4. Taylor expanded in z around 0 76.6%

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

   1. *-un-lft-identity 76.6%

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

   2. associate-/r* 76.7%

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

6. Applied egg-rr 76.7%

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

7. Final simplification 76.7%

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

Alternative 7: 66.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -2.5 \cdot 10^{+249} \lor \neg \left(b \leq 1.85 \cdot 10^{+230}\right):\\ \;\;\;\;2 \cdot \left(\sqrt{x} \cdot \cos y\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{x} - \frac{\frac{a}{3}}{b}\\ \end{array} \end{array} \]

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 (<= b -2.5e+249) (not (<= b 1.85e+230)))
   (* 2.0 (* (sqrt x) (cos y)))
   (- (* 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) {
	double tmp;
	if ((b <= -2.5e+249) || !(b <= 1.85e+230)) {
		tmp = 2.0 * (sqrt(x) * cos(y));
	} else {
		tmp = (2.0 * sqrt(x)) - ((a / 3.0) / b);
	}
	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 <= (-2.5d+249)) .or. (.not. (b <= 1.85d+230))) then
        tmp = 2.0d0 * (sqrt(x) * cos(y))
    else
        tmp = (2.0d0 * sqrt(x)) - ((a / 3.0d0) / b)
    end if
    code = tmp
end function

Java

assert z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -2.5e+249) || !(b <= 1.85e+230)) {
		tmp = 2.0 * (Math.sqrt(x) * Math.cos(y));
	} else {
		tmp = (2.0 * Math.sqrt(x)) - ((a / 3.0) / b);
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -2.5e+249) or not (b <= 1.85e+230):
		tmp = 2.0 * (math.sqrt(x) * math.cos(y))
	else:
		tmp = (2.0 * math.sqrt(x)) - ((a / 3.0) / b)
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -2.5e+249) || !(b <= 1.85e+230))
		tmp = Float64(2.0 * Float64(sqrt(x) * cos(y)));
	else
		tmp = Float64(Float64(2.0 * sqrt(x)) - Float64(Float64(a / 3.0) / b));
	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 <= -2.5e+249) || ~((b <= 1.85e+230)))
		tmp = 2.0 * (sqrt(x) * cos(y));
	else
		tmp = (2.0 * sqrt(x)) - ((a / 3.0) / b);
	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[b, -2.5e+249], N[Not[LessEqual[b, 1.85e+230]], $MachinePrecision]], N[(2.0 * N[(N[Sqrt[x], $MachinePrecision] * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] - N[(N[(a / 3.0), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -2.4999999999999998e249 or 1.84999999999999996e230 < b

   1. Initial program 58.4%

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

      1. associate-*l* 58.4%

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

      2. fma-neg 58.4%

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

      3. remove-double-neg 58.4%

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

      4. fma-neg 58.4%

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

      5. remove-double-neg 58.4%

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

      6. associate-/l* 58.4%

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

      7. *-commutative 58.4%

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

   3. Simplified 58.4%

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

   4. Taylor expanded in z around 0 56.6%

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

   5. Taylor expanded in a around 0 56.6%

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

   6. Taylor expanded in a around 0 56.6%

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

      1. *-commutative 56.6%

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

   8. Simplified 56.6%

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

   if -2.4999999999999998e249 < b < 1.84999999999999996e230

   1. Initial program 73.1%

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

      1. associate-*l* 73.1%

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

      2. fma-neg 73.1%

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

      3. remove-double-neg 73.1%

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

      4. fma-neg 73.1%

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

      5. remove-double-neg 73.1%

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

      6. associate-/l* 73.2%

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

      7. *-commutative 73.2%

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

   3. Simplified 73.2%

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

   4. Taylor expanded in z around 0 79.0%

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

      1. *-un-lft-identity 79.0%

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

      2. associate-/r* 79.0%

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

   6. Applied egg-rr 79.0%

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

   7. Taylor expanded in y around 0 73.8%

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

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.5 \cdot 10^{+249} \lor \neg \left(b \leq 1.85 \cdot 10^{+230}\right):\\ \;\;\;\;2 \cdot \left(\sqrt{x} \cdot \cos y\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{x} - \frac{\frac{a}{3}}{b}\\ \end{array} \]

Alternative 8: 65.2% 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 71.5%

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

   1. associate-*l* 71.5%

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

   2. fma-neg 71.5%

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

   3. remove-double-neg 71.5%

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

   4. fma-neg 71.5%

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

   5. remove-double-neg 71.5%

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

   6. associate-/l* 71.7%

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

   7. *-commutative 71.7%

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

3. Simplified 71.7%

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

4. Taylor expanded in z around 0 76.6%

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

5. Taylor expanded in y around 0 68.3%

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

6. Taylor expanded in a around 0 68.3%

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

7. Final simplification 68.3%

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

Alternative 9: 65.3% 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 71.5%

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

   1. associate-*l* 71.5%

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

   2. fma-neg 71.5%

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

   3. remove-double-neg 71.5%

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

   4. fma-neg 71.5%

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

   5. remove-double-neg 71.5%

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

   6. associate-/l* 71.7%

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

   7. *-commutative 71.7%

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

3. Simplified 71.7%

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

4. Taylor expanded in z around 0 76.6%

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

5. Taylor expanded in y around 0 68.3%

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

6. Final simplification 68.3%

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

Alternative 10: 65.3% accurate, 2.0× speedup

Math

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

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

Derivation

1. Initial program 71.5%

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

   1. associate-*l* 71.5%

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

   2. fma-neg 71.5%

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

   3. remove-double-neg 71.5%

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

   4. fma-neg 71.5%

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

   5. remove-double-neg 71.5%

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

   6. associate-/l* 71.7%

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

   7. *-commutative 71.7%

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

3. Simplified 71.7%

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

4. Taylor expanded in z around 0 76.6%

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

   1. *-un-lft-identity 76.6%

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

   2. associate-/r* 76.7%

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

6. Applied egg-rr 76.7%

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

7. Taylor expanded in y around 0 68.4%

   \[\leadsto 2 \cdot \color{blue}{\sqrt{x}} - 1 \cdot \frac{\frac{a}{3}}{b} \]

8. Final simplification 68.4%

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

Alternative 11: 52.3% accurate, 2.0× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;a \leq -3 \cdot 10^{-66} \lor \neg \left(a \leq 8 \cdot 10^{-133}\right):\\ \;\;\;\;\frac{-0.3333333333333333}{\frac{b}{a}}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{x}\\ \end{array} \end{array} \]

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 -3e-66) (not (<= a 8e-133)))
   (/ -0.3333333333333333 (/ b a))
   (* 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 <= -3e-66) || !(a <= 8e-133)) {
		tmp = -0.3333333333333333 / (b / a);
	} 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 <= (-3d-66)) .or. (.not. (a <= 8d-133))) then
        tmp = (-0.3333333333333333d0) / (b / a)
    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 <= -3e-66) || !(a <= 8e-133)) {
		tmp = -0.3333333333333333 / (b / a);
	} 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 <= -3e-66) or not (a <= 8e-133):
		tmp = -0.3333333333333333 / (b / a)
	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 <= -3e-66) || !(a <= 8e-133))
		tmp = Float64(-0.3333333333333333 / Float64(b / a));
	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 <= -3e-66) || ~((a <= 8e-133)))
		tmp = -0.3333333333333333 / (b / a);
	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, -3e-66], N[Not[LessEqual[a, 8e-133]], $MachinePrecision]], N[(-0.3333333333333333 / N[(b / a), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -3.0000000000000002e-66 or 8.0000000000000005e-133 < a

   1. Initial program 77.2%

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

      1. associate-*l* 77.2%

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

      2. fma-neg 77.2%

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

      3. remove-double-neg 77.2%

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

      4. fma-neg 77.2%

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

      5. remove-double-neg 77.2%

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

      6. associate-/l* 77.3%

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

      7. *-commutative 77.3%

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

   3. Simplified 77.3%

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

   4. Taylor expanded in z around 0 85.0%

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

   5. Taylor expanded in a around 0 84.9%

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

   6. Taylor expanded in x around 0 69.1%

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

      1. associate-*r/ 69.1%

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

      2. associate-/l* 69.1%

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

   8. Simplified 69.1%

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

   if -3.0000000000000002e-66 < a < 8.0000000000000005e-133

   1. Initial program 56.3%

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

      1. associate-*l* 56.3%

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

      2. fma-neg 56.3%

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

      3. remove-double-neg 56.3%

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

      4. fma-neg 56.3%

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

      5. remove-double-neg 56.3%

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

      6. associate-/l* 56.5%

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

      7. *-commutative 56.5%

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

   3. Simplified 56.5%

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

   4. Taylor expanded in z around 0 54.1%

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

   5. Taylor expanded in y around 0 42.1%

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

   6. Taylor expanded in a around 0 42.0%

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

   7. Taylor expanded in a around 0 33.5%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3 \cdot 10^{-66} \lor \neg \left(a \leq 8 \cdot 10^{-133}\right):\\ \;\;\;\;\frac{-0.3333333333333333}{\frac{b}{a}}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{x}\\ \end{array} \]

Alternative 12: 49.9% 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 71.5%

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

   1. associate-*l* 71.5%

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

   2. fma-neg 71.5%

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

   3. remove-double-neg 71.5%

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

   4. fma-neg 71.5%

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

   5. remove-double-neg 71.5%

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

   6. associate-/l* 71.7%

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

   7. *-commutative 71.7%

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

3. Simplified 71.7%

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

4. Taylor expanded in z around 0 76.6%

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

5. Taylor expanded in a around 0 76.6%

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

6. Taylor expanded in x around 0 53.8%

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

7. Final simplification 53.8%

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

Alternative 13: 49.9% accurate, 43.4× speedup

Math

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

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 (/ b a)))

C

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

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) / (b / a)
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 / (b / a);
}

Python

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

Julia

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

MATLAB

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

Derivation

1. Initial program 71.5%

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

   1. associate-*l* 71.5%

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

   2. fma-neg 71.5%

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

   3. remove-double-neg 71.5%

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

   4. fma-neg 71.5%

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

   5. remove-double-neg 71.5%

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

   6. associate-/l* 71.7%

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

   7. *-commutative 71.7%

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

3. Simplified 71.7%

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

4. Taylor expanded in z around 0 76.6%

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

5. Taylor expanded in a around 0 76.6%

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

6. Taylor expanded in x around 0 53.8%

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

   1. associate-*r/ 53.8%

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

   2. associate-/l* 53.8%

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

8. Simplified 53.8%

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

9. Final simplification 53.8%

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

Developer target: 74.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023255 
(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))))