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

Percentage Accurate: 69.3% → 76.4%

Time: 23.0s

Alternatives: 12

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 69.3% 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: 76.4% accurate, 0.3× speedup

Math

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

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ a (* 3.0 b))) (t_2 (* t (/ z 3.0))))
   (if (<= (* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0)))) 1e+142)
     (- (* 2.0 (* (sqrt x) (fma (sin y) (sin t_2) (* (cos y) (cos t_2))))) t_1)
     (- (* 2.0 (* (sqrt x) (- (cos y)))) t_1))))

C

assert(z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a / (3.0 * b);
	double t_2 = t * (z / 3.0);
	double tmp;
	if (((2.0 * sqrt(x)) * cos((y - ((z * t) / 3.0)))) <= 1e+142) {
		tmp = (2.0 * (sqrt(x) * fma(sin(y), sin(t_2), (cos(y) * cos(t_2))))) - t_1;
	} else {
		tmp = (2.0 * (sqrt(x) * -cos(y))) - t_1;
	}
	return tmp;
}

Julia

z, t = sort([z, t])
function code(x, y, z, t, a, b)
	t_1 = Float64(a / Float64(3.0 * b))
	t_2 = Float64(t * Float64(z / 3.0))
	tmp = 0.0
	if (Float64(Float64(2.0 * sqrt(x)) * cos(Float64(y - Float64(Float64(z * t) / 3.0)))) <= 1e+142)
		tmp = Float64(Float64(2.0 * Float64(sqrt(x) * fma(sin(y), sin(t_2), Float64(cos(y) * cos(t_2))))) - t_1);
	else
		tmp = Float64(Float64(2.0 * Float64(sqrt(x) * Float64(-cos(y)))) - t_1);
	end
	return tmp
end

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3)))) < 1.00000000000000005e142

   1. Initial program 77.9%

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

      1. associate-*l* 77.9%

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

      2. fma-neg 77.9%

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

      3. remove-double-neg 77.9%

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

      4. fma-neg 77.9%

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

      5. remove-double-neg 77.9%

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

      6. associate-/l* 77.9%

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

      7. *-commutative 77.9%

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

   3. Simplified 77.9%

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

      1. cos-diff 79.8%

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

      2. associate-/r/ 79.3%

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

      3. *-commutative 79.3%

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

      4. div-inv 79.5%

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

      5. metadata-eval 79.5%

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

      6. associate-/r/ 79.6%

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

      7. *-commutative 79.6%

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

      8. div-inv 79.6%

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

      9. metadata-eval 79.6%

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

   5. Applied egg-rr 79.6%

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

      1. +-commutative 79.6%

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

      2. cos-neg 79.6%

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

      3. fma-def 79.6%

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

      4. *-commutative 79.6%

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

      5. associate-*l* 79.4%

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

      6. metadata-eval 79.4%

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

      7. associate-/r/ 79.6%

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

      8. associate-*r/ 79.5%

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

      9. *-rgt-identity 79.5%

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

      10. associate-/r/ 79.6%

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

      11. *-commutative 79.6%

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

      12. *-commutative 79.6%

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

      13. associate-*l* 79.3%

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

      14. *-commutative 79.3%

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

      15. associate-*r* 79.3%

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

      16. distribute-lft-neg-in 79.3%

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

      17. metadata-eval 79.3%

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

   7. Simplified 79.3%

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

   if 1.00000000000000005e142 < (*.f64 (*.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3))))

   1. Initial program 8.4%

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

      1. associate-*l* 8.4%

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

      2. fma-neg 8.4%

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

      3. remove-double-neg 8.4%

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

      4. fma-neg 8.4%

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

      5. remove-double-neg 8.4%

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

      6. associate-/l* 8.4%

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

      7. *-commutative 8.4%

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

   3. Simplified 8.4%

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

   4. Taylor expanded in z around 0 52.6%

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

      1. add-cube-cbrt 52.6%

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

      2. pow3 52.6%

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

   6. Applied egg-rr 52.6%

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

   7. Taylor expanded in x around -inf 0.0%

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

      1. *-commutative 0.0%

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

      2. pow-base-1 0.0%

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

      3. *-lft-identity 0.0%

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

      4. unpow2 0.0%

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

      5. rem-square-sqrt 54.2%

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

      6. neg-mul-1 54.2%

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

   9. Simplified 54.2%

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

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) \leq 10^{+142}:\\ \;\;\;\;2 \cdot \left(\sqrt{x} \cdot \mathsf{fma}\left(\sin y, \sin \left(t \cdot \frac{z}{3}\right), \cos y \cdot \cos \left(t \cdot \frac{z}{3}\right)\right)\right) - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt{x} \cdot \left(-\cos y\right)\right) - \frac{a}{3 \cdot b}\\ \end{array} \]

Alternative 2: 77.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := \frac{a}{3 \cdot b}\\ t_2 := t \cdot \left(z \cdot 0.3333333333333333\right)\\ \mathbf{if}\;\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) \leq 2 \cdot 10^{+154}:\\ \;\;\;\;2 \cdot \left(\sqrt{x} \cdot \mathsf{fma}\left(\cos y, \cos t_2, \sin y \cdot \sin t_2\right)\right) - t_1\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt{x} \cdot \left(-\cos y\right)\right) - t_1\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ a (* 3.0 b))) (t_2 (* t (* z 0.3333333333333333))))
   (if (<= (* (* 2.0 (sqrt x)) (cos (- y (/ (* z t) 3.0)))) 2e+154)
     (- (* 2.0 (* (sqrt x) (fma (cos y) (cos t_2) (* (sin y) (sin t_2))))) t_1)
     (- (* 2.0 (* (sqrt x) (- (cos y)))) t_1))))

C

assert(z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a / (3.0 * b);
	double t_2 = t * (z * 0.3333333333333333);
	double tmp;
	if (((2.0 * sqrt(x)) * cos((y - ((z * t) / 3.0)))) <= 2e+154) {
		tmp = (2.0 * (sqrt(x) * fma(cos(y), cos(t_2), (sin(y) * sin(t_2))))) - t_1;
	} else {
		tmp = (2.0 * (sqrt(x) * -cos(y))) - t_1;
	}
	return tmp;
}

Julia

z, t = sort([z, t])
function code(x, y, z, t, a, b)
	t_1 = Float64(a / Float64(3.0 * b))
	t_2 = Float64(t * Float64(z * 0.3333333333333333))
	tmp = 0.0
	if (Float64(Float64(2.0 * sqrt(x)) * cos(Float64(y - Float64(Float64(z * t) / 3.0)))) <= 2e+154)
		tmp = Float64(Float64(2.0 * Float64(sqrt(x) * fma(cos(y), cos(t_2), Float64(sin(y) * sin(t_2))))) - t_1);
	else
		tmp = Float64(Float64(2.0 * Float64(sqrt(x) * Float64(-cos(y)))) - t_1);
	end
	return tmp
end

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a / N[(3.0 * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(z * 0.3333333333333333), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] * N[Cos[N[(y - N[(N[(z * t), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2e+154], N[(N[(2.0 * N[(N[Sqrt[x], $MachinePrecision] * N[(N[Cos[y], $MachinePrecision] * N[Cos[t$95$2], $MachinePrecision] + N[(N[Sin[y], $MachinePrecision] * N[Sin[t$95$2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(2.0 * N[(N[Sqrt[x], $MachinePrecision] * (-N[Cos[y], $MachinePrecision])), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3)))) < 2.00000000000000007e154

   1. Initial program 77.8%

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

      1. associate-*l* 77.8%

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

      2. fma-neg 77.8%

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

      3. remove-double-neg 77.8%

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

      4. fma-neg 77.8%

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

      5. remove-double-neg 77.8%

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

      6. associate-/l* 77.9%

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

      7. *-commutative 77.9%

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

   3. Simplified 77.9%

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

      1. associate-/r/ 77.8%

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

      2. cos-diff 79.3%

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

      3. fma-def 79.3%

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

      4. *-commutative 79.3%

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

      5. div-inv 79.6%

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

      6. metadata-eval 79.6%

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

      7. associate-/r/ 79.6%

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

      8. associate-/r/ 79.6%

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

      9. *-commutative 79.6%

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

      10. div-inv 79.6%

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

      11. metadata-eval 79.6%

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

   5. Applied egg-rr 79.6%

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

   if 2.00000000000000007e154 < (*.f64 (*.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3))))

   1. Initial program 0.0%

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

      1. associate-*l* 0.0%

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

      2. fma-neg 0.0%

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

      3. remove-double-neg 0.0%

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

      4. fma-neg 0.0%

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

      5. remove-double-neg 0.0%

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

      6. associate-/l* 0.0%

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

      7. *-commutative 0.0%

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

   3. Simplified 0.0%

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

   4. Taylor expanded in z around 0 49.8%

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

      1. add-cube-cbrt 49.8%

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

      2. pow3 49.8%

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

   6. Applied egg-rr 49.8%

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

   7. Taylor expanded in x around -inf 0.0%

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

      1. *-commutative 0.0%

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

      2. pow-base-1 0.0%

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

      3. *-lft-identity 0.0%

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

      4. unpow2 0.0%

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

      5. rem-square-sqrt 50.9%

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

      6. neg-mul-1 50.9%

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

   9. Simplified 50.9%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) \leq 2 \cdot 10^{+154}:\\ \;\;\;\;2 \cdot \left(\sqrt{x} \cdot \mathsf{fma}\left(\cos y, \cos \left(t \cdot \left(z \cdot 0.3333333333333333\right)\right), \sin y \cdot \sin \left(t \cdot \left(z \cdot 0.3333333333333333\right)\right)\right)\right) - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt{x} \cdot \left(-\cos y\right)\right) - \frac{a}{3 \cdot b}\\ \end{array} \]

Alternative 3: 77.4% accurate, 0.3× speedup

Math

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

FPCore

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

C

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

Fortran

NOTE: z and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a / (3.0d0 * b)
    t_2 = t * (z * 0.3333333333333333d0)
    if (cos((y - ((z * t) / 3.0d0))) <= 2.0d0) then
        tmp = (2.0d0 * (sqrt(x) * ((sin(y) * sin(t_2)) + (cos(y) * cos(t_2))))) - t_1
    else
        tmp = (2.0d0 * (sqrt(x) * -cos(y))) - t_1
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3))) < 2

   1. Initial program 77.8%

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

      1. associate-*l* 77.8%

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

      2. fma-neg 77.8%

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

      3. remove-double-neg 77.8%

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

      4. fma-neg 77.8%

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

      5. remove-double-neg 77.8%

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

      6. associate-/l* 77.9%

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

      7. *-commutative 77.9%

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

   3. Simplified 77.9%

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

      1. cos-diff 79.8%

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

      2. associate-/r/ 79.3%

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

      3. *-commutative 79.3%

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

      4. div-inv 79.6%

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

      5. metadata-eval 79.6%

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

      6. associate-/r/ 79.6%

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

      7. *-commutative 79.6%

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

      8. div-inv 79.6%

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

      9. metadata-eval 79.6%

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

   5. Applied egg-rr 79.6%

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

   if 2 < (cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3)))

   1. Initial program 0.0%

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

      1. associate-*l* 0.0%

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

      2. fma-neg 0.0%

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

      3. remove-double-neg 0.0%

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

      4. fma-neg 0.0%

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

      5. remove-double-neg 0.0%

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

      6. associate-/l* 0.0%

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

      7. *-commutative 0.0%

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

   3. Simplified 0.0%

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

   4. Taylor expanded in z around 0 49.8%

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

      1. add-cube-cbrt 49.8%

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

      2. pow3 49.8%

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

   6. Applied egg-rr 49.8%

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

   7. Taylor expanded in x around -inf 0.0%

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

      1. *-commutative 0.0%

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

      2. pow-base-1 0.0%

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

      3. *-lft-identity 0.0%

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

      4. unpow2 0.0%

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

      5. rem-square-sqrt 50.9%

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

      6. neg-mul-1 50.9%

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

   9. Simplified 50.9%

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

4. Final simplification 76.0%

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

Alternative 4: 76.4% accurate, 0.7× speedup

Math

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

FPCore

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

Julia

z, t = sort([z, t])
function code(x, y, z, t, a, b)
	return fma(Float64(2.0 * sqrt(x)), cos(y), Float64(Float64(-Float64(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[Cos[y], $MachinePrecision] + N[((-N[(a / 3.0), $MachinePrecision]) / b), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 68.1%

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

   1. associate-*l* 68.1%

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

   2. fma-neg 68.1%

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

   3. remove-double-neg 68.1%

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

   4. fma-neg 68.1%

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

   5. remove-double-neg 68.1%

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

   6. associate-/l* 68.1%

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

   7. *-commutative 68.1%

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

3. Simplified 68.1%

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

4. Taylor expanded in z around 0 73.3%

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

   1. associate-*r* 73.3%

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

   2. fma-neg 73.3%

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

6. Applied egg-rr 73.3%

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

   1. *-commutative 73.3%

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

   2. associate-/r* 73.3%

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

8. Simplified 73.3%

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

9. Final simplification 73.3%

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

Alternative 5: 71.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := \frac{a}{3 \cdot b}\\ \mathbf{if}\;t_1 \leq -1 \cdot 10^{-63} \lor \neg \left(t_1 \leq 1.5 \cdot 10^{-162}\right):\\ \;\;\;\;2 \cdot \sqrt{x} - t_1\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot \left(2 \cdot \cos y\right)\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ a (* 3.0 b))))
   (if (or (<= t_1 -1e-63) (not (<= t_1 1.5e-162)))
     (- (* 2.0 (sqrt x)) t_1)
     (* (sqrt x) (* 2.0 (cos y))))))

C

assert(z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a / (3.0 * b);
	double tmp;
	if ((t_1 <= -1e-63) || !(t_1 <= 1.5e-162)) {
		tmp = (2.0 * sqrt(x)) - t_1;
	} else {
		tmp = sqrt(x) * (2.0 * cos(y));
	}
	return tmp;
}

Fortran

NOTE: z and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a / (3.0d0 * b)
    if ((t_1 <= (-1d-63)) .or. (.not. (t_1 <= 1.5d-162))) then
        tmp = (2.0d0 * sqrt(x)) - t_1
    else
        tmp = sqrt(x) * (2.0d0 * cos(y))
    end if
    code = tmp
end function

Java

assert z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a / (3.0 * b);
	double tmp;
	if ((t_1 <= -1e-63) || !(t_1 <= 1.5e-162)) {
		tmp = (2.0 * Math.sqrt(x)) - t_1;
	} else {
		tmp = Math.sqrt(x) * (2.0 * Math.cos(y));
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t, a, b):
	t_1 = a / (3.0 * b)
	tmp = 0
	if (t_1 <= -1e-63) or not (t_1 <= 1.5e-162):
		tmp = (2.0 * math.sqrt(x)) - t_1
	else:
		tmp = math.sqrt(x) * (2.0 * math.cos(y))
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t, a, b)
	t_1 = Float64(a / Float64(3.0 * b))
	tmp = 0.0
	if ((t_1 <= -1e-63) || !(t_1 <= 1.5e-162))
		tmp = Float64(Float64(2.0 * sqrt(x)) - t_1);
	else
		tmp = Float64(sqrt(x) * Float64(2.0 * cos(y)));
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a / (3.0 * b);
	tmp = 0.0;
	if ((t_1 <= -1e-63) || ~((t_1 <= 1.5e-162)))
		tmp = (2.0 * sqrt(x)) - t_1;
	else
		tmp = sqrt(x) * (2.0 * cos(y));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a / N[(3.0 * b), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -1e-63], N[Not[LessEqual[t$95$1, 1.5e-162]], $MachinePrecision]], N[(N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[Sqrt[x], $MachinePrecision] * N[(2.0 * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 a (*.f64 b 3)) < -1.00000000000000007e-63 or 1.49999999999999999e-162 < (/.f64 a (*.f64 b 3))

   1. Initial program 78.1%

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

      1. associate-*l* 78.1%

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

      2. fma-neg 78.1%

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

      3. remove-double-neg 78.1%

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

      4. fma-neg 78.1%

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

      5. remove-double-neg 78.1%

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

      6. associate-/l* 78.0%

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

      7. *-commutative 78.0%

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

   3. Simplified 78.0%

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

   4. Taylor expanded in z around 0 86.1%

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

   5. Taylor expanded in y around 0 80.1%

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

   if -1.00000000000000007e-63 < (/.f64 a (*.f64 b 3)) < 1.49999999999999999e-162

   1. Initial program 47.5%

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

      1. associate-*l* 47.5%

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

      2. fma-neg 47.5%

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

      3. remove-double-neg 47.5%

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

      4. fma-neg 47.5%

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

      5. remove-double-neg 47.5%

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

      6. associate-/l* 48.0%

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

      7. *-commutative 48.0%

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

   3. Simplified 48.0%

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

   4. Taylor expanded in z around 0 47.0%

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

   5. Taylor expanded in a around 0 47.0%

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

      1. *-commutative 47.0%

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

      2. *-commutative 47.0%

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

      3. associate-*l* 47.0%

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

   7. Simplified 47.0%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{a}{3 \cdot b} \leq -1 \cdot 10^{-63} \lor \neg \left(\frac{a}{3 \cdot b} \leq 1.5 \cdot 10^{-162}\right):\\ \;\;\;\;2 \cdot \sqrt{x} - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot \left(2 \cdot \cos y\right)\\ \end{array} \]

Alternative 6: 76.3% 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 68.1%

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

   1. associate-*l* 68.1%

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

   2. fma-neg 68.1%

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

   3. remove-double-neg 68.1%

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

   4. fma-neg 68.1%

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

   5. remove-double-neg 68.1%

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

   6. associate-/l* 68.1%

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

   7. *-commutative 68.1%

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

3. Simplified 68.1%

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

4. Taylor expanded in z around 0 73.3%

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

5. Taylor expanded in a around 0 73.2%

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

6. Final simplification 73.2%

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

Alternative 7: 76.4% 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 68.1%

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

   1. associate-*l* 68.1%

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

   2. fma-neg 68.1%

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

   3. remove-double-neg 68.1%

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

   4. fma-neg 68.1%

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

   5. remove-double-neg 68.1%

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

   6. associate-/l* 68.1%

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

   7. *-commutative 68.1%

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

3. Simplified 68.1%

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

4. Taylor expanded in z around 0 73.3%

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

5. Final simplification 73.3%

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

Alternative 8: 65.8% 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 68.1%

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

   1. associate-*l* 68.1%

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

   2. fma-neg 68.1%

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

   3. remove-double-neg 68.1%

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

   4. fma-neg 68.1%

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

   5. remove-double-neg 68.1%

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

   6. associate-/l* 68.1%

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

   7. *-commutative 68.1%

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

3. Simplified 68.1%

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

4. Taylor expanded in z around 0 73.3%

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

5. Taylor expanded in y around 0 62.2%

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

6. Final simplification 62.2%

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

Alternative 9: 50.9% accurate, 43.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 68.1%

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

   1. associate-*l* 68.1%

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

   2. fma-neg 68.1%

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

   3. remove-double-neg 68.1%

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

   4. fma-neg 68.1%

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

   5. remove-double-neg 68.1%

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

   6. associate-/l* 68.1%

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

   7. *-commutative 68.1%

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

3. Simplified 68.1%

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

4. Taylor expanded in z around 0 73.3%

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

5. Taylor expanded in x around 0 51.5%

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

6. Final simplification 51.5%

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

Alternative 10: 51.0% accurate, 43.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 68.1%

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

   1. associate-*l* 68.1%

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

   2. fma-neg 68.1%

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

   3. remove-double-neg 68.1%

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

   4. fma-neg 68.1%

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

   5. remove-double-neg 68.1%

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

   6. associate-/l* 68.1%

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

   7. *-commutative 68.1%

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

3. Simplified 68.1%

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

4. Taylor expanded in z around 0 73.3%

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

   1. associate-*r* 73.3%

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

   2. fma-neg 73.3%

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

6. Applied egg-rr 73.3%

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

   1. *-commutative 73.3%

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

   2. associate-/r* 73.3%

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

8. Simplified 73.3%

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

9. Taylor expanded in x around 0 51.5%

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

    1. associate-*r/ 51.5%

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

    2. *-commutative 51.5%

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

    3. *-rgt-identity 51.5%

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

    4. associate-*r/ 51.4%

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

    5. associate-*l* 51.4%

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

    6. associate-*r/ 51.5%

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

    7. metadata-eval 51.5%

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

11. Simplified 51.5%

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

12. Final simplification 51.5%

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

Alternative 11: 51.0% accurate, 43.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 68.1%

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

   1. associate-*l* 68.1%

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

   2. fma-neg 68.1%

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

   3. remove-double-neg 68.1%

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

   4. fma-neg 68.1%

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

   5. remove-double-neg 68.1%

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

   6. associate-/l* 68.1%

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

   7. *-commutative 68.1%

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

3. Simplified 68.1%

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

4. Taylor expanded in z around 0 73.3%

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

5. Taylor expanded in x around 0 51.5%

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

   1. expm1-log1p-u 27.0%

      \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(-0.3333333333333333 \cdot \frac{a}{b}\right)\right)} \]

   2. expm1-udef 22.2%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(-0.3333333333333333 \cdot \frac{a}{b}\right)} - 1} \]

7. Applied egg-rr 22.2%

   \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(-0.3333333333333333 \cdot \frac{a}{b}\right)} - 1} \]
8. Step-by-step derivation

   1. expm1-def 27.0%

      \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(-0.3333333333333333 \cdot \frac{a}{b}\right)\right)} \]

   2. expm1-log1p 51.5%

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

   3. *-commutative 51.5%

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

   4. associate-/r/ 51.5%

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

9. Simplified 51.5%

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

10. Final simplification 51.5%

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

Alternative 12: 51.0% accurate, 43.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 68.1%

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

   1. associate-*l* 68.1%

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

   2. fma-neg 68.1%

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

   3. remove-double-neg 68.1%

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

   4. fma-neg 68.1%

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

   5. remove-double-neg 68.1%

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

   6. associate-/l* 68.1%

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

   7. *-commutative 68.1%

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

3. Simplified 68.1%

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

4. Taylor expanded in z around 0 73.3%

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

5. Taylor expanded in x around 0 51.5%

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

   1. associate-*r/ 51.5%

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

   2. *-commutative 51.5%

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

7. Applied egg-rr 51.5%

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

8. Final simplification 51.5%

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

Developer target: 73.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023257 
(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))))