Codec.Picture.Jpg.FastDct:referenceDct from JuicyPixels-3.2.6.1

Percentage Accurate: 27.0% → 31.6%

Time: 23.9s

Alternatives: 6

Speedup: 225.0×

Specification

Math

\[\begin{array}{l} \\ \left(x \cdot \cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right)\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right) \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (*
  (* x (cos (/ (* (* (+ (* y 2.0) 1.0) z) t) 16.0)))
  (cos (/ (* (* (+ (* a 2.0) 1.0) b) t) 16.0))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return (x * cos((((((y * 2.0) + 1.0) * z) * t) / 16.0))) * cos((((((a * 2.0) + 1.0) * b) * t) / 16.0));
}

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 = (x * cos((((((y * 2.0d0) + 1.0d0) * z) * t) / 16.0d0))) * cos((((((a * 2.0d0) + 1.0d0) * b) * t) / 16.0d0))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return (x * Math.cos((((((y * 2.0) + 1.0) * z) * t) / 16.0))) * Math.cos((((((a * 2.0) + 1.0) * b) * t) / 16.0));
}

Python

def code(x, y, z, t, a, b):
	return (x * math.cos((((((y * 2.0) + 1.0) * z) * t) / 16.0))) * math.cos((((((a * 2.0) + 1.0) * b) * t) / 16.0))

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(x * cos(Float64(Float64(Float64(Float64(Float64(y * 2.0) + 1.0) * z) * t) / 16.0))) * cos(Float64(Float64(Float64(Float64(Float64(a * 2.0) + 1.0) * b) * t) / 16.0)))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = (x * cos((((((y * 2.0) + 1.0) * z) * t) / 16.0))) * cos((((((a * 2.0) + 1.0) * b) * t) / 16.0));
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(x * N[Cos[N[(N[(N[(N[(N[(y * 2.0), $MachinePrecision] + 1.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision] / 16.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[Cos[N[(N[(N[(N[(N[(a * 2.0), $MachinePrecision] + 1.0), $MachinePrecision] * b), $MachinePrecision] * t), $MachinePrecision] / 16.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Initial Program: 27.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x \cdot \cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right)\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right) \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (*
  (* x (cos (/ (* (* (+ (* y 2.0) 1.0) z) t) 16.0)))
  (cos (/ (* (* (+ (* a 2.0) 1.0) b) t) 16.0))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return (x * cos((((((y * 2.0) + 1.0) * z) * t) / 16.0))) * cos((((((a * 2.0) + 1.0) * b) * t) / 16.0));
}

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 = (x * cos((((((y * 2.0d0) + 1.0d0) * z) * t) / 16.0d0))) * cos((((((a * 2.0d0) + 1.0d0) * b) * t) / 16.0d0))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return (x * Math.cos((((((y * 2.0) + 1.0) * z) * t) / 16.0))) * Math.cos((((((a * 2.0) + 1.0) * b) * t) / 16.0));
}

Python

def code(x, y, z, t, a, b):
	return (x * math.cos((((((y * 2.0) + 1.0) * z) * t) / 16.0))) * math.cos((((((a * 2.0) + 1.0) * b) * t) / 16.0))

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(x * cos(Float64(Float64(Float64(Float64(Float64(y * 2.0) + 1.0) * z) * t) / 16.0))) * cos(Float64(Float64(Float64(Float64(Float64(a * 2.0) + 1.0) * b) * t) / 16.0)))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = (x * cos((((((y * 2.0) + 1.0) * z) * t) / 16.0))) * cos((((((a * 2.0) + 1.0) * b) * t) / 16.0));
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(x * N[Cos[N[(N[(N[(N[(N[(y * 2.0), $MachinePrecision] + 1.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision] / 16.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[Cos[N[(N[(N[(N[(N[(a * 2.0), $MachinePrecision] + 1.0), $MachinePrecision] * b), $MachinePrecision] * t), $MachinePrecision] / 16.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Alternative 1: 31.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \sqrt[3]{\left(z \cdot \mathsf{fma}\left(y, 2, 1\right)\right) \cdot \left(t \cdot 0.0625\right)}\\ \mathbf{if}\;\left(x \cdot \cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right)\right) \cdot \cos \left(\frac{t \cdot \left(\left(1 + 2 \cdot a\right) \cdot b\right)}{16}\right) \leq 5 \cdot 10^{+301}:\\ \;\;\;\;x \cdot \left(\cos \left({\left({\left({t\_1}^{2}\right)}^{0.3333333333333333} \cdot \sqrt[3]{t\_1}\right)}^{3}\right) \cdot \cos \left(t \cdot \frac{b \cdot \mathsf{fma}\left(2, a, 1\right)}{16}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (cbrt (* (* z (fma y 2.0 1.0)) (* t 0.0625)))))
   (if (<=
        (*
         (* x (cos (/ (* (* (+ (* y 2.0) 1.0) z) t) 16.0)))
         (cos (/ (* t (* (+ 1.0 (* 2.0 a)) b)) 16.0)))
        5e+301)
     (*
      x
      (*
       (cos (pow (* (pow (pow t_1 2.0) 0.3333333333333333) (cbrt t_1)) 3.0))
       (cos (* t (/ (* b (fma 2.0 a 1.0)) 16.0)))))
     x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = cbrt(((z * fma(y, 2.0, 1.0)) * (t * 0.0625)));
	double tmp;
	if (((x * cos((((((y * 2.0) + 1.0) * z) * t) / 16.0))) * cos(((t * ((1.0 + (2.0 * a)) * b)) / 16.0))) <= 5e+301) {
		tmp = x * (cos(pow((pow(pow(t_1, 2.0), 0.3333333333333333) * cbrt(t_1)), 3.0)) * cos((t * ((b * fma(2.0, a, 1.0)) / 16.0))));
	} else {
		tmp = x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = cbrt(Float64(Float64(z * fma(y, 2.0, 1.0)) * Float64(t * 0.0625)))
	tmp = 0.0
	if (Float64(Float64(x * cos(Float64(Float64(Float64(Float64(Float64(y * 2.0) + 1.0) * z) * t) / 16.0))) * cos(Float64(Float64(t * Float64(Float64(1.0 + Float64(2.0 * a)) * b)) / 16.0))) <= 5e+301)
		tmp = Float64(x * Float64(cos((Float64(((t_1 ^ 2.0) ^ 0.3333333333333333) * cbrt(t_1)) ^ 3.0)) * cos(Float64(t * Float64(Float64(b * fma(2.0, a, 1.0)) / 16.0)))));
	else
		tmp = x;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[Power[N[(N[(z * N[(y * 2.0 + 1.0), $MachinePrecision]), $MachinePrecision] * N[(t * 0.0625), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision]}, If[LessEqual[N[(N[(x * N[Cos[N[(N[(N[(N[(N[(y * 2.0), $MachinePrecision] + 1.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision] / 16.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[Cos[N[(N[(t * N[(N[(1.0 + N[(2.0 * a), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision] / 16.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 5e+301], N[(x * N[(N[Cos[N[Power[N[(N[Power[N[Power[t$95$1, 2.0], $MachinePrecision], 0.3333333333333333], $MachinePrecision] * N[Power[t$95$1, 1/3], $MachinePrecision]), $MachinePrecision], 3.0], $MachinePrecision]], $MachinePrecision] * N[Cos[N[(t * N[(N[(b * N[(2.0 * a + 1.0), $MachinePrecision]), $MachinePrecision] / 16.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 x (cos.f64 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 y 2) 1) z) t) 16))) (cos.f64 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 a 2) 1) b) t) 16))) < 5.0000000000000004e301

   1. Initial program 43.3%

      \[\left(x \cdot \cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right)\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right) \]
   2. Step-by-step derivation

      1. associate-*l* 43.3%

         \[\leadsto \color{blue}{x \cdot \left(\cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right)} \]

      2. *-commutative 43.3%

         \[\leadsto x \cdot \left(\cos \left(\frac{\color{blue}{\left(z \cdot \left(y \cdot 2 + 1\right)\right)} \cdot t}{16}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right) \]

      3. associate-*r* 42.7%

         \[\leadsto x \cdot \left(\cos \left(\frac{\color{blue}{z \cdot \left(\left(y \cdot 2 + 1\right) \cdot t\right)}}{16}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right) \]

      4. *-commutative 42.7%

         \[\leadsto x \cdot \left(\cos \left(\frac{\color{blue}{\left(\left(y \cdot 2 + 1\right) \cdot t\right) \cdot z}}{16}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right) \]

      5. associate-*l* 43.5%

         \[\leadsto x \cdot \left(\cos \left(\frac{\color{blue}{\left(y \cdot 2 + 1\right) \cdot \left(t \cdot z\right)}}{16}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right) \]

      6. associate-/l* 43.5%

         \[\leadsto x \cdot \left(\cos \color{blue}{\left(\left(y \cdot 2 + 1\right) \cdot \frac{t \cdot z}{16}\right)} \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right) \]

      7. fma-define 43.5%

         \[\leadsto x \cdot \left(\cos \left(\color{blue}{\mathsf{fma}\left(y, 2, 1\right)} \cdot \frac{t \cdot z}{16}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right) \]

      8. *-commutative 43.5%

         \[\leadsto x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \frac{\color{blue}{z \cdot t}}{16}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right) \]

      9. associate-*r/ 43.5%

         \[\leadsto x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \color{blue}{\left(z \cdot \frac{t}{16}\right)}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right) \]

      10. *-commutative 43.5%

          \[\leadsto x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(z \cdot \frac{t}{16}\right)\right) \cdot \cos \left(\frac{\color{blue}{\left(b \cdot \left(a \cdot 2 + 1\right)\right)} \cdot t}{16}\right)\right) \]

      11. associate-*r* 42.7%

          \[\leadsto x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(z \cdot \frac{t}{16}\right)\right) \cdot \cos \left(\frac{\color{blue}{b \cdot \left(\left(a \cdot 2 + 1\right) \cdot t\right)}}{16}\right)\right) \]

      12. *-commutative 42.7%

          \[\leadsto x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(z \cdot \frac{t}{16}\right)\right) \cdot \cos \left(\frac{\color{blue}{\left(\left(a \cdot 2 + 1\right) \cdot t\right) \cdot b}}{16}\right)\right) \]

   3. Simplified 43.5%

      \[\leadsto \color{blue}{x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(z \cdot \frac{t}{16}\right)\right) \cdot \cos \left(t \cdot \frac{\mathsf{fma}\left(2, a, 1\right) \cdot b}{16}\right)\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. add-cube-cbrt 42.7%

         \[\leadsto x \cdot \left(\cos \color{blue}{\left(\left(\sqrt[3]{\mathsf{fma}\left(y, 2, 1\right) \cdot \left(z \cdot \frac{t}{16}\right)} \cdot \sqrt[3]{\mathsf{fma}\left(y, 2, 1\right) \cdot \left(z \cdot \frac{t}{16}\right)}\right) \cdot \sqrt[3]{\mathsf{fma}\left(y, 2, 1\right) \cdot \left(z \cdot \frac{t}{16}\right)}\right)} \cdot \cos \left(t \cdot \frac{\mathsf{fma}\left(2, a, 1\right) \cdot b}{16}\right)\right) \]

      2. pow3 42.5%

         \[\leadsto x \cdot \left(\cos \color{blue}{\left({\left(\sqrt[3]{\mathsf{fma}\left(y, 2, 1\right) \cdot \left(z \cdot \frac{t}{16}\right)}\right)}^{3}\right)} \cdot \cos \left(t \cdot \frac{\mathsf{fma}\left(2, a, 1\right) \cdot b}{16}\right)\right) \]

      3. associate-*r* 42.7%

         \[\leadsto x \cdot \left(\cos \left({\left(\sqrt[3]{\color{blue}{\left(\mathsf{fma}\left(y, 2, 1\right) \cdot z\right) \cdot \frac{t}{16}}}\right)}^{3}\right) \cdot \cos \left(t \cdot \frac{\mathsf{fma}\left(2, a, 1\right) \cdot b}{16}\right)\right) \]

      4. *-commutative 42.7%

         \[\leadsto x \cdot \left(\cos \left({\left(\sqrt[3]{\color{blue}{\left(z \cdot \mathsf{fma}\left(y, 2, 1\right)\right)} \cdot \frac{t}{16}}\right)}^{3}\right) \cdot \cos \left(t \cdot \frac{\mathsf{fma}\left(2, a, 1\right) \cdot b}{16}\right)\right) \]

      5. associate-*l* 42.0%

         \[\leadsto x \cdot \left(\cos \left({\left(\sqrt[3]{\color{blue}{z \cdot \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \frac{t}{16}\right)}}\right)}^{3}\right) \cdot \cos \left(t \cdot \frac{\mathsf{fma}\left(2, a, 1\right) \cdot b}{16}\right)\right) \]

      6. div-inv 42.0%

         \[\leadsto x \cdot \left(\cos \left({\left(\sqrt[3]{z \cdot \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \color{blue}{\left(t \cdot \frac{1}{16}\right)}\right)}\right)}^{3}\right) \cdot \cos \left(t \cdot \frac{\mathsf{fma}\left(2, a, 1\right) \cdot b}{16}\right)\right) \]

      7. metadata-eval 42.0%

         \[\leadsto x \cdot \left(\cos \left({\left(\sqrt[3]{z \cdot \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(t \cdot \color{blue}{0.0625}\right)\right)}\right)}^{3}\right) \cdot \cos \left(t \cdot \frac{\mathsf{fma}\left(2, a, 1\right) \cdot b}{16}\right)\right) \]

   6. Applied egg-rr 42.0%

      \[\leadsto x \cdot \left(\cos \color{blue}{\left({\left(\sqrt[3]{z \cdot \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(t \cdot 0.0625\right)\right)}\right)}^{3}\right)} \cdot \cos \left(t \cdot \frac{\mathsf{fma}\left(2, a, 1\right) \cdot b}{16}\right)\right) \]
   7. Step-by-step derivation

      1. pow1/3 27.3%

         \[\leadsto x \cdot \left(\cos \left({\color{blue}{\left({\left(z \cdot \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(t \cdot 0.0625\right)\right)\right)}^{0.3333333333333333}\right)}}^{3}\right) \cdot \cos \left(t \cdot \frac{\mathsf{fma}\left(2, a, 1\right) \cdot b}{16}\right)\right) \]

      2. add-cube-cbrt 27.7%

         \[\leadsto x \cdot \left(\cos \left({\left({\color{blue}{\left(\left(\sqrt[3]{z \cdot \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(t \cdot 0.0625\right)\right)} \cdot \sqrt[3]{z \cdot \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(t \cdot 0.0625\right)\right)}\right) \cdot \sqrt[3]{z \cdot \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(t \cdot 0.0625\right)\right)}\right)}}^{0.3333333333333333}\right)}^{3}\right) \cdot \cos \left(t \cdot \frac{\mathsf{fma}\left(2, a, 1\right) \cdot b}{16}\right)\right) \]

      3. unpow-prod-down 27.1%

         \[\leadsto x \cdot \left(\cos \left({\color{blue}{\left({\left(\sqrt[3]{z \cdot \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(t \cdot 0.0625\right)\right)} \cdot \sqrt[3]{z \cdot \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(t \cdot 0.0625\right)\right)}\right)}^{0.3333333333333333} \cdot {\left(\sqrt[3]{z \cdot \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(t \cdot 0.0625\right)\right)}\right)}^{0.3333333333333333}\right)}}^{3}\right) \cdot \cos \left(t \cdot \frac{\mathsf{fma}\left(2, a, 1\right) \cdot b}{16}\right)\right) \]

      4. pow2 27.1%

         \[\leadsto x \cdot \left(\cos \left({\left({\color{blue}{\left({\left(\sqrt[3]{z \cdot \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(t \cdot 0.0625\right)\right)}\right)}^{2}\right)}}^{0.3333333333333333} \cdot {\left(\sqrt[3]{z \cdot \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(t \cdot 0.0625\right)\right)}\right)}^{0.3333333333333333}\right)}^{3}\right) \cdot \cos \left(t \cdot \frac{\mathsf{fma}\left(2, a, 1\right) \cdot b}{16}\right)\right) \]

      5. associate-*r* 27.3%

         \[\leadsto x \cdot \left(\cos \left({\left({\left({\left(\sqrt[3]{\color{blue}{\left(z \cdot \mathsf{fma}\left(y, 2, 1\right)\right) \cdot \left(t \cdot 0.0625\right)}}\right)}^{2}\right)}^{0.3333333333333333} \cdot {\left(\sqrt[3]{z \cdot \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(t \cdot 0.0625\right)\right)}\right)}^{0.3333333333333333}\right)}^{3}\right) \cdot \cos \left(t \cdot \frac{\mathsf{fma}\left(2, a, 1\right) \cdot b}{16}\right)\right) \]

      6. pow1/3 43.9%

         \[\leadsto x \cdot \left(\cos \left({\left({\left({\left(\sqrt[3]{\left(z \cdot \mathsf{fma}\left(y, 2, 1\right)\right) \cdot \left(t \cdot 0.0625\right)}\right)}^{2}\right)}^{0.3333333333333333} \cdot \color{blue}{\sqrt[3]{\sqrt[3]{z \cdot \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(t \cdot 0.0625\right)\right)}}}\right)}^{3}\right) \cdot \cos \left(t \cdot \frac{\mathsf{fma}\left(2, a, 1\right) \cdot b}{16}\right)\right) \]

      7. associate-*r* 44.7%

         \[\leadsto x \cdot \left(\cos \left({\left({\left({\left(\sqrt[3]{\left(z \cdot \mathsf{fma}\left(y, 2, 1\right)\right) \cdot \left(t \cdot 0.0625\right)}\right)}^{2}\right)}^{0.3333333333333333} \cdot \sqrt[3]{\sqrt[3]{\color{blue}{\left(z \cdot \mathsf{fma}\left(y, 2, 1\right)\right) \cdot \left(t \cdot 0.0625\right)}}}\right)}^{3}\right) \cdot \cos \left(t \cdot \frac{\mathsf{fma}\left(2, a, 1\right) \cdot b}{16}\right)\right) \]

   8. Applied egg-rr 44.7%

      \[\leadsto x \cdot \left(\cos \left({\color{blue}{\left({\left({\left(\sqrt[3]{\left(z \cdot \mathsf{fma}\left(y, 2, 1\right)\right) \cdot \left(t \cdot 0.0625\right)}\right)}^{2}\right)}^{0.3333333333333333} \cdot \sqrt[3]{\sqrt[3]{\left(z \cdot \mathsf{fma}\left(y, 2, 1\right)\right) \cdot \left(t \cdot 0.0625\right)}}\right)}}^{3}\right) \cdot \cos \left(t \cdot \frac{\mathsf{fma}\left(2, a, 1\right) \cdot b}{16}\right)\right) \]

   if 5.0000000000000004e301 < (*.f64 (*.f64 x (cos.f64 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 y 2) 1) z) t) 16))) (cos.f64 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 a 2) 1) b) t) 16)))

   1. Initial program 0.0%

      \[\left(x \cdot \cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right)\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right) \]
   2. Step-by-step derivation

      1. associate-*l* 0.0%

         \[\leadsto \color{blue}{x \cdot \left(\cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right)} \]

      2. *-commutative 0.0%

         \[\leadsto x \cdot \left(\cos \left(\frac{\color{blue}{\left(z \cdot \left(y \cdot 2 + 1\right)\right)} \cdot t}{16}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right) \]

      3. associate-*r* 1.0%

         \[\leadsto x \cdot \left(\cos \left(\frac{\color{blue}{z \cdot \left(\left(y \cdot 2 + 1\right) \cdot t\right)}}{16}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right) \]

      4. *-commutative 1.0%

         \[\leadsto x \cdot \left(\cos \left(\frac{\color{blue}{\left(\left(y \cdot 2 + 1\right) \cdot t\right) \cdot z}}{16}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right) \]

      5. associate-*l* 1.1%

         \[\leadsto x \cdot \left(\cos \left(\frac{\color{blue}{\left(y \cdot 2 + 1\right) \cdot \left(t \cdot z\right)}}{16}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right) \]

      6. associate-/l* 1.3%

         \[\leadsto x \cdot \left(\cos \color{blue}{\left(\left(y \cdot 2 + 1\right) \cdot \frac{t \cdot z}{16}\right)} \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right) \]

      7. fma-define 1.3%

         \[\leadsto x \cdot \left(\cos \left(\color{blue}{\mathsf{fma}\left(y, 2, 1\right)} \cdot \frac{t \cdot z}{16}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right) \]

      8. *-commutative 1.3%

         \[\leadsto x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \frac{\color{blue}{z \cdot t}}{16}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right) \]

      9. associate-*r/ 1.3%

         \[\leadsto x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \color{blue}{\left(z \cdot \frac{t}{16}\right)}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right) \]

      10. *-commutative 1.3%

          \[\leadsto x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(z \cdot \frac{t}{16}\right)\right) \cdot \cos \left(\frac{\color{blue}{\left(b \cdot \left(a \cdot 2 + 1\right)\right)} \cdot t}{16}\right)\right) \]

      11. associate-*r* 2.1%

          \[\leadsto x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(z \cdot \frac{t}{16}\right)\right) \cdot \cos \left(\frac{\color{blue}{b \cdot \left(\left(a \cdot 2 + 1\right) \cdot t\right)}}{16}\right)\right) \]

      12. *-commutative 2.1%

          \[\leadsto x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(z \cdot \frac{t}{16}\right)\right) \cdot \cos \left(\frac{\color{blue}{\left(\left(a \cdot 2 + 1\right) \cdot t\right) \cdot b}}{16}\right)\right) \]

   3. Simplified 1.3%

      \[\leadsto \color{blue}{x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(z \cdot \frac{t}{16}\right)\right) \cdot \cos \left(t \cdot \frac{\mathsf{fma}\left(2, a, 1\right) \cdot b}{16}\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 4.8%

      \[\leadsto x \cdot \left(\color{blue}{1} \cdot \cos \left(t \cdot \frac{\mathsf{fma}\left(2, a, 1\right) \cdot b}{16}\right)\right) \]

   6. Taylor expanded in t around 0 11.1%

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

4. Final simplification 30.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot \cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right)\right) \cdot \cos \left(\frac{t \cdot \left(\left(1 + 2 \cdot a\right) \cdot b\right)}{16}\right) \leq 5 \cdot 10^{+301}:\\ \;\;\;\;x \cdot \left(\cos \left({\left({\left({\left(\sqrt[3]{\left(z \cdot \mathsf{fma}\left(y, 2, 1\right)\right) \cdot \left(t \cdot 0.0625\right)}\right)}^{2}\right)}^{0.3333333333333333} \cdot \sqrt[3]{\sqrt[3]{\left(z \cdot \mathsf{fma}\left(y, 2, 1\right)\right) \cdot \left(t \cdot 0.0625\right)}}\right)}^{3}\right) \cdot \cos \left(t \cdot \frac{b \cdot \mathsf{fma}\left(2, a, 1\right)}{16}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 31.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(x \cdot \cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right)\right) \cdot \cos \left(\frac{t \cdot \left(\left(1 + 2 \cdot a\right) \cdot b\right)}{16}\right) \leq 5 \cdot 10^{+301}:\\ \;\;\;\;x \cdot \left(\mathsf{log1p}\left(\mathsf{expm1}\left(\cos \left(\left(z \cdot \mathsf{fma}\left(y, 2, 1\right)\right) \cdot \left(t \cdot 0.0625\right)\right)\right)\right) \cdot \cos \left({\left(\sqrt[3]{t \cdot \left(\mathsf{fma}\left(2, a, 1\right) \cdot \left(b \cdot 0.0625\right)\right)}\right)}^{3}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<=
      (*
       (* x (cos (/ (* (* (+ (* y 2.0) 1.0) z) t) 16.0)))
       (cos (/ (* t (* (+ 1.0 (* 2.0 a)) b)) 16.0)))
      5e+301)
   (*
    x
    (*
     (log1p (expm1 (cos (* (* z (fma y 2.0 1.0)) (* t 0.0625)))))
     (cos (pow (cbrt (* t (* (fma 2.0 a 1.0) (* b 0.0625)))) 3.0))))
   x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((x * cos((((((y * 2.0) + 1.0) * z) * t) / 16.0))) * cos(((t * ((1.0 + (2.0 * a)) * b)) / 16.0))) <= 5e+301) {
		tmp = x * (log1p(expm1(cos(((z * fma(y, 2.0, 1.0)) * (t * 0.0625))))) * cos(pow(cbrt((t * (fma(2.0, a, 1.0) * (b * 0.0625)))), 3.0)));
	} else {
		tmp = x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(Float64(x * cos(Float64(Float64(Float64(Float64(Float64(y * 2.0) + 1.0) * z) * t) / 16.0))) * cos(Float64(Float64(t * Float64(Float64(1.0 + Float64(2.0 * a)) * b)) / 16.0))) <= 5e+301)
		tmp = Float64(x * Float64(log1p(expm1(cos(Float64(Float64(z * fma(y, 2.0, 1.0)) * Float64(t * 0.0625))))) * cos((cbrt(Float64(t * Float64(fma(2.0, a, 1.0) * Float64(b * 0.0625)))) ^ 3.0))));
	else
		tmp = x;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(N[(x * N[Cos[N[(N[(N[(N[(N[(y * 2.0), $MachinePrecision] + 1.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision] / 16.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[Cos[N[(N[(t * N[(N[(1.0 + N[(2.0 * a), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision] / 16.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 5e+301], N[(x * N[(N[Log[1 + N[(Exp[N[Cos[N[(N[(z * N[(y * 2.0 + 1.0), $MachinePrecision]), $MachinePrecision] * N[(t * 0.0625), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]] - 1), $MachinePrecision]], $MachinePrecision] * N[Cos[N[Power[N[Power[N[(t * N[(N[(2.0 * a + 1.0), $MachinePrecision] * N[(b * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision], 3.0], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 x (cos.f64 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 y 2) 1) z) t) 16))) (cos.f64 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 a 2) 1) b) t) 16))) < 5.0000000000000004e301

   1. Initial program 43.3%

      \[\left(x \cdot \cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right)\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right) \]
   2. Step-by-step derivation

      1. associate-*l* 43.3%

         \[\leadsto \color{blue}{x \cdot \left(\cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right)} \]

      2. *-commutative 43.3%

         \[\leadsto x \cdot \left(\cos \left(\frac{\color{blue}{\left(z \cdot \left(y \cdot 2 + 1\right)\right)} \cdot t}{16}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right) \]

      3. associate-*r* 42.7%

         \[\leadsto x \cdot \left(\cos \left(\frac{\color{blue}{z \cdot \left(\left(y \cdot 2 + 1\right) \cdot t\right)}}{16}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right) \]

      4. *-commutative 42.7%

         \[\leadsto x \cdot \left(\cos \left(\frac{\color{blue}{\left(\left(y \cdot 2 + 1\right) \cdot t\right) \cdot z}}{16}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right) \]

      5. associate-*l* 43.5%

         \[\leadsto x \cdot \left(\cos \left(\frac{\color{blue}{\left(y \cdot 2 + 1\right) \cdot \left(t \cdot z\right)}}{16}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right) \]

      6. associate-/l* 43.5%

         \[\leadsto x \cdot \left(\cos \color{blue}{\left(\left(y \cdot 2 + 1\right) \cdot \frac{t \cdot z}{16}\right)} \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right) \]

      7. fma-define 43.5%

         \[\leadsto x \cdot \left(\cos \left(\color{blue}{\mathsf{fma}\left(y, 2, 1\right)} \cdot \frac{t \cdot z}{16}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right) \]

      8. *-commutative 43.5%

         \[\leadsto x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \frac{\color{blue}{z \cdot t}}{16}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right) \]

      9. associate-*r/ 43.5%

         \[\leadsto x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \color{blue}{\left(z \cdot \frac{t}{16}\right)}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right) \]

      10. *-commutative 43.5%

          \[\leadsto x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(z \cdot \frac{t}{16}\right)\right) \cdot \cos \left(\frac{\color{blue}{\left(b \cdot \left(a \cdot 2 + 1\right)\right)} \cdot t}{16}\right)\right) \]

      11. associate-*r* 42.7%

          \[\leadsto x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(z \cdot \frac{t}{16}\right)\right) \cdot \cos \left(\frac{\color{blue}{b \cdot \left(\left(a \cdot 2 + 1\right) \cdot t\right)}}{16}\right)\right) \]

      12. *-commutative 42.7%

          \[\leadsto x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(z \cdot \frac{t}{16}\right)\right) \cdot \cos \left(\frac{\color{blue}{\left(\left(a \cdot 2 + 1\right) \cdot t\right) \cdot b}}{16}\right)\right) \]

   3. Simplified 43.5%

      \[\leadsto \color{blue}{x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(z \cdot \frac{t}{16}\right)\right) \cdot \cos \left(t \cdot \frac{\mathsf{fma}\left(2, a, 1\right) \cdot b}{16}\right)\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. add-cube-cbrt 42.7%

         \[\leadsto x \cdot \left(\cos \color{blue}{\left(\left(\sqrt[3]{\mathsf{fma}\left(y, 2, 1\right) \cdot \left(z \cdot \frac{t}{16}\right)} \cdot \sqrt[3]{\mathsf{fma}\left(y, 2, 1\right) \cdot \left(z \cdot \frac{t}{16}\right)}\right) \cdot \sqrt[3]{\mathsf{fma}\left(y, 2, 1\right) \cdot \left(z \cdot \frac{t}{16}\right)}\right)} \cdot \cos \left(t \cdot \frac{\mathsf{fma}\left(2, a, 1\right) \cdot b}{16}\right)\right) \]

      2. pow3 42.5%

         \[\leadsto x \cdot \left(\cos \color{blue}{\left({\left(\sqrt[3]{\mathsf{fma}\left(y, 2, 1\right) \cdot \left(z \cdot \frac{t}{16}\right)}\right)}^{3}\right)} \cdot \cos \left(t \cdot \frac{\mathsf{fma}\left(2, a, 1\right) \cdot b}{16}\right)\right) \]

      3. associate-*r* 42.7%

         \[\leadsto x \cdot \left(\cos \left({\left(\sqrt[3]{\color{blue}{\left(\mathsf{fma}\left(y, 2, 1\right) \cdot z\right) \cdot \frac{t}{16}}}\right)}^{3}\right) \cdot \cos \left(t \cdot \frac{\mathsf{fma}\left(2, a, 1\right) \cdot b}{16}\right)\right) \]

      4. *-commutative 42.7%

         \[\leadsto x \cdot \left(\cos \left({\left(\sqrt[3]{\color{blue}{\left(z \cdot \mathsf{fma}\left(y, 2, 1\right)\right)} \cdot \frac{t}{16}}\right)}^{3}\right) \cdot \cos \left(t \cdot \frac{\mathsf{fma}\left(2, a, 1\right) \cdot b}{16}\right)\right) \]

      5. associate-*l* 42.0%

         \[\leadsto x \cdot \left(\cos \left({\left(\sqrt[3]{\color{blue}{z \cdot \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \frac{t}{16}\right)}}\right)}^{3}\right) \cdot \cos \left(t \cdot \frac{\mathsf{fma}\left(2, a, 1\right) \cdot b}{16}\right)\right) \]

      6. div-inv 42.0%

         \[\leadsto x \cdot \left(\cos \left({\left(\sqrt[3]{z \cdot \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \color{blue}{\left(t \cdot \frac{1}{16}\right)}\right)}\right)}^{3}\right) \cdot \cos \left(t \cdot \frac{\mathsf{fma}\left(2, a, 1\right) \cdot b}{16}\right)\right) \]

      7. metadata-eval 42.0%

         \[\leadsto x \cdot \left(\cos \left({\left(\sqrt[3]{z \cdot \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(t \cdot \color{blue}{0.0625}\right)\right)}\right)}^{3}\right) \cdot \cos \left(t \cdot \frac{\mathsf{fma}\left(2, a, 1\right) \cdot b}{16}\right)\right) \]

   6. Applied egg-rr 42.0%

      \[\leadsto x \cdot \left(\cos \color{blue}{\left({\left(\sqrt[3]{z \cdot \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(t \cdot 0.0625\right)\right)}\right)}^{3}\right)} \cdot \cos \left(t \cdot \frac{\mathsf{fma}\left(2, a, 1\right) \cdot b}{16}\right)\right) \]
   7. Step-by-step derivation

      1. log1p-expm1-u 42.0%

         \[\leadsto x \cdot \left(\color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\cos \left({\left(\sqrt[3]{z \cdot \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(t \cdot 0.0625\right)\right)}\right)}^{3}\right)\right)\right)} \cdot \cos \left(t \cdot \frac{\mathsf{fma}\left(2, a, 1\right) \cdot b}{16}\right)\right) \]

      2. rem-cube-cbrt 42.7%

         \[\leadsto x \cdot \left(\mathsf{log1p}\left(\mathsf{expm1}\left(\cos \color{blue}{\left(z \cdot \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(t \cdot 0.0625\right)\right)\right)}\right)\right) \cdot \cos \left(t \cdot \frac{\mathsf{fma}\left(2, a, 1\right) \cdot b}{16}\right)\right) \]

      3. associate-*r* 43.3%

         \[\leadsto x \cdot \left(\mathsf{log1p}\left(\mathsf{expm1}\left(\cos \color{blue}{\left(\left(z \cdot \mathsf{fma}\left(y, 2, 1\right)\right) \cdot \left(t \cdot 0.0625\right)\right)}\right)\right) \cdot \cos \left(t \cdot \frac{\mathsf{fma}\left(2, a, 1\right) \cdot b}{16}\right)\right) \]

   8. Applied egg-rr 43.3%

      \[\leadsto x \cdot \left(\color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\cos \left(\left(z \cdot \mathsf{fma}\left(y, 2, 1\right)\right) \cdot \left(t \cdot 0.0625\right)\right)\right)\right)} \cdot \cos \left(t \cdot \frac{\mathsf{fma}\left(2, a, 1\right) \cdot b}{16}\right)\right) \]
   9. Step-by-step derivation

      1. associate-*r/ 43.5%

         \[\leadsto x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(z \cdot \frac{t}{16}\right)\right) \cdot \cos \color{blue}{\left(\frac{t \cdot \left(\mathsf{fma}\left(2, a, 1\right) \cdot b\right)}{16}\right)}\right) \]

      2. fma-undefine 43.5%

         \[\leadsto x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(z \cdot \frac{t}{16}\right)\right) \cdot \cos \left(\frac{t \cdot \left(\color{blue}{\left(2 \cdot a + 1\right)} \cdot b\right)}{16}\right)\right) \]

      3. *-commutative 43.5%

         \[\leadsto x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(z \cdot \frac{t}{16}\right)\right) \cdot \cos \left(\frac{t \cdot \left(\left(\color{blue}{a \cdot 2} + 1\right) \cdot b\right)}{16}\right)\right) \]

      4. *-commutative 43.5%

         \[\leadsto x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(z \cdot \frac{t}{16}\right)\right) \cdot \cos \left(\frac{\color{blue}{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}}{16}\right)\right) \]

      5. add-cube-cbrt 43.5%

         \[\leadsto x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(z \cdot \frac{t}{16}\right)\right) \cdot \cos \color{blue}{\left(\left(\sqrt[3]{\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}} \cdot \sqrt[3]{\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}}\right) \cdot \sqrt[3]{\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}}\right)}\right) \]

      6. pow3 43.9%

         \[\leadsto x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(z \cdot \frac{t}{16}\right)\right) \cdot \cos \color{blue}{\left({\left(\sqrt[3]{\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}}\right)}^{3}\right)}\right) \]

      7. *-commutative 43.9%

         \[\leadsto x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(z \cdot \frac{t}{16}\right)\right) \cdot \cos \left({\left(\sqrt[3]{\frac{\color{blue}{t \cdot \left(\left(a \cdot 2 + 1\right) \cdot b\right)}}{16}}\right)}^{3}\right)\right) \]

      8. *-commutative 43.9%

         \[\leadsto x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(z \cdot \frac{t}{16}\right)\right) \cdot \cos \left({\left(\sqrt[3]{\frac{t \cdot \left(\left(\color{blue}{2 \cdot a} + 1\right) \cdot b\right)}{16}}\right)}^{3}\right)\right) \]

      9. fma-undefine 43.9%

         \[\leadsto x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(z \cdot \frac{t}{16}\right)\right) \cdot \cos \left({\left(\sqrt[3]{\frac{t \cdot \left(\color{blue}{\mathsf{fma}\left(2, a, 1\right)} \cdot b\right)}{16}}\right)}^{3}\right)\right) \]

      10. associate-*r/ 43.9%

          \[\leadsto x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(z \cdot \frac{t}{16}\right)\right) \cdot \cos \left({\left(\sqrt[3]{\color{blue}{t \cdot \frac{\mathsf{fma}\left(2, a, 1\right) \cdot b}{16}}}\right)}^{3}\right)\right) \]

      11. associate-/l* 43.9%

          \[\leadsto x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(z \cdot \frac{t}{16}\right)\right) \cdot \cos \left({\left(\sqrt[3]{t \cdot \color{blue}{\left(\mathsf{fma}\left(2, a, 1\right) \cdot \frac{b}{16}\right)}}\right)}^{3}\right)\right) \]

      12. div-inv 43.9%

          \[\leadsto x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(z \cdot \frac{t}{16}\right)\right) \cdot \cos \left({\left(\sqrt[3]{t \cdot \left(\mathsf{fma}\left(2, a, 1\right) \cdot \color{blue}{\left(b \cdot \frac{1}{16}\right)}\right)}\right)}^{3}\right)\right) \]

      13. metadata-eval 43.9%

          \[\leadsto x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(z \cdot \frac{t}{16}\right)\right) \cdot \cos \left({\left(\sqrt[3]{t \cdot \left(\mathsf{fma}\left(2, a, 1\right) \cdot \left(b \cdot \color{blue}{0.0625}\right)\right)}\right)}^{3}\right)\right) \]

   10. Applied egg-rr 43.9%

       \[\leadsto x \cdot \left(\mathsf{log1p}\left(\mathsf{expm1}\left(\cos \left(\left(z \cdot \mathsf{fma}\left(y, 2, 1\right)\right) \cdot \left(t \cdot 0.0625\right)\right)\right)\right) \cdot \cos \color{blue}{\left({\left(\sqrt[3]{t \cdot \left(\mathsf{fma}\left(2, a, 1\right) \cdot \left(b \cdot 0.0625\right)\right)}\right)}^{3}\right)}\right) \]

   if 5.0000000000000004e301 < (*.f64 (*.f64 x (cos.f64 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 y 2) 1) z) t) 16))) (cos.f64 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 a 2) 1) b) t) 16)))

   1. Initial program 0.0%

      \[\left(x \cdot \cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right)\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right) \]
   2. Step-by-step derivation

      1. associate-*l* 0.0%

         \[\leadsto \color{blue}{x \cdot \left(\cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right)} \]

      2. *-commutative 0.0%

         \[\leadsto x \cdot \left(\cos \left(\frac{\color{blue}{\left(z \cdot \left(y \cdot 2 + 1\right)\right)} \cdot t}{16}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right) \]

      3. associate-*r* 1.0%

         \[\leadsto x \cdot \left(\cos \left(\frac{\color{blue}{z \cdot \left(\left(y \cdot 2 + 1\right) \cdot t\right)}}{16}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right) \]

      4. *-commutative 1.0%

         \[\leadsto x \cdot \left(\cos \left(\frac{\color{blue}{\left(\left(y \cdot 2 + 1\right) \cdot t\right) \cdot z}}{16}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right) \]

      5. associate-*l* 1.1%

         \[\leadsto x \cdot \left(\cos \left(\frac{\color{blue}{\left(y \cdot 2 + 1\right) \cdot \left(t \cdot z\right)}}{16}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right) \]

      6. associate-/l* 1.3%

         \[\leadsto x \cdot \left(\cos \color{blue}{\left(\left(y \cdot 2 + 1\right) \cdot \frac{t \cdot z}{16}\right)} \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right) \]

      7. fma-define 1.3%

         \[\leadsto x \cdot \left(\cos \left(\color{blue}{\mathsf{fma}\left(y, 2, 1\right)} \cdot \frac{t \cdot z}{16}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right) \]

      8. *-commutative 1.3%

         \[\leadsto x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \frac{\color{blue}{z \cdot t}}{16}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right) \]

      9. associate-*r/ 1.3%

         \[\leadsto x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \color{blue}{\left(z \cdot \frac{t}{16}\right)}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right) \]

      10. *-commutative 1.3%

          \[\leadsto x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(z \cdot \frac{t}{16}\right)\right) \cdot \cos \left(\frac{\color{blue}{\left(b \cdot \left(a \cdot 2 + 1\right)\right)} \cdot t}{16}\right)\right) \]

      11. associate-*r* 2.1%

          \[\leadsto x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(z \cdot \frac{t}{16}\right)\right) \cdot \cos \left(\frac{\color{blue}{b \cdot \left(\left(a \cdot 2 + 1\right) \cdot t\right)}}{16}\right)\right) \]

      12. *-commutative 2.1%

          \[\leadsto x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(z \cdot \frac{t}{16}\right)\right) \cdot \cos \left(\frac{\color{blue}{\left(\left(a \cdot 2 + 1\right) \cdot t\right) \cdot b}}{16}\right)\right) \]

   3. Simplified 1.3%

      \[\leadsto \color{blue}{x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(z \cdot \frac{t}{16}\right)\right) \cdot \cos \left(t \cdot \frac{\mathsf{fma}\left(2, a, 1\right) \cdot b}{16}\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 4.8%

      \[\leadsto x \cdot \left(\color{blue}{1} \cdot \cos \left(t \cdot \frac{\mathsf{fma}\left(2, a, 1\right) \cdot b}{16}\right)\right) \]

   6. Taylor expanded in t around 0 11.1%

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

4. Final simplification 29.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot \cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right)\right) \cdot \cos \left(\frac{t \cdot \left(\left(1 + 2 \cdot a\right) \cdot b\right)}{16}\right) \leq 5 \cdot 10^{+301}:\\ \;\;\;\;x \cdot \left(\mathsf{log1p}\left(\mathsf{expm1}\left(\cos \left(\left(z \cdot \mathsf{fma}\left(y, 2, 1\right)\right) \cdot \left(t \cdot 0.0625\right)\right)\right)\right) \cdot \cos \left({\left(\sqrt[3]{t \cdot \left(\mathsf{fma}\left(2, a, 1\right) \cdot \left(b \cdot 0.0625\right)\right)}\right)}^{3}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 31.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(x \cdot \cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right)\right) \cdot \cos \left(\frac{t \cdot \left(\left(1 + 2 \cdot a\right) \cdot b\right)}{16}\right) \leq 5 \cdot 10^{+301}:\\ \;\;\;\;x \cdot \left(\cos \left({\left(\sqrt[3]{t \cdot \left(\mathsf{fma}\left(2, a, 1\right) \cdot \left(b \cdot 0.0625\right)\right)}\right)}^{3}\right) \cdot \cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(z \cdot \frac{t}{16}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<=
      (*
       (* x (cos (/ (* (* (+ (* y 2.0) 1.0) z) t) 16.0)))
       (cos (/ (* t (* (+ 1.0 (* 2.0 a)) b)) 16.0)))
      5e+301)
   (*
    x
    (*
     (cos (pow (cbrt (* t (* (fma 2.0 a 1.0) (* b 0.0625)))) 3.0))
     (cos (* (fma y 2.0 1.0) (* z (/ t 16.0))))))
   x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((x * cos((((((y * 2.0) + 1.0) * z) * t) / 16.0))) * cos(((t * ((1.0 + (2.0 * a)) * b)) / 16.0))) <= 5e+301) {
		tmp = x * (cos(pow(cbrt((t * (fma(2.0, a, 1.0) * (b * 0.0625)))), 3.0)) * cos((fma(y, 2.0, 1.0) * (z * (t / 16.0)))));
	} else {
		tmp = x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(Float64(x * cos(Float64(Float64(Float64(Float64(Float64(y * 2.0) + 1.0) * z) * t) / 16.0))) * cos(Float64(Float64(t * Float64(Float64(1.0 + Float64(2.0 * a)) * b)) / 16.0))) <= 5e+301)
		tmp = Float64(x * Float64(cos((cbrt(Float64(t * Float64(fma(2.0, a, 1.0) * Float64(b * 0.0625)))) ^ 3.0)) * cos(Float64(fma(y, 2.0, 1.0) * Float64(z * Float64(t / 16.0))))));
	else
		tmp = x;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(N[(x * N[Cos[N[(N[(N[(N[(N[(y * 2.0), $MachinePrecision] + 1.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision] / 16.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[Cos[N[(N[(t * N[(N[(1.0 + N[(2.0 * a), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision] / 16.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 5e+301], N[(x * N[(N[Cos[N[Power[N[Power[N[(t * N[(N[(2.0 * a + 1.0), $MachinePrecision] * N[(b * 0.0625), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision], 3.0], $MachinePrecision]], $MachinePrecision] * N[Cos[N[(N[(y * 2.0 + 1.0), $MachinePrecision] * N[(z * N[(t / 16.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 x (cos.f64 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 y 2) 1) z) t) 16))) (cos.f64 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 a 2) 1) b) t) 16))) < 5.0000000000000004e301

   1. Initial program 43.3%

      \[\left(x \cdot \cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right)\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right) \]
   2. Step-by-step derivation

      1. associate-*l* 43.3%

         \[\leadsto \color{blue}{x \cdot \left(\cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right)} \]

      2. *-commutative 43.3%

         \[\leadsto x \cdot \left(\cos \left(\frac{\color{blue}{\left(z \cdot \left(y \cdot 2 + 1\right)\right)} \cdot t}{16}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right) \]

      3. associate-*r* 42.7%

         \[\leadsto x \cdot \left(\cos \left(\frac{\color{blue}{z \cdot \left(\left(y \cdot 2 + 1\right) \cdot t\right)}}{16}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right) \]

      4. *-commutative 42.7%

         \[\leadsto x \cdot \left(\cos \left(\frac{\color{blue}{\left(\left(y \cdot 2 + 1\right) \cdot t\right) \cdot z}}{16}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right) \]

      5. associate-*l* 43.5%

         \[\leadsto x \cdot \left(\cos \left(\frac{\color{blue}{\left(y \cdot 2 + 1\right) \cdot \left(t \cdot z\right)}}{16}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right) \]

      6. associate-/l* 43.5%

         \[\leadsto x \cdot \left(\cos \color{blue}{\left(\left(y \cdot 2 + 1\right) \cdot \frac{t \cdot z}{16}\right)} \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right) \]

      7. fma-define 43.5%

         \[\leadsto x \cdot \left(\cos \left(\color{blue}{\mathsf{fma}\left(y, 2, 1\right)} \cdot \frac{t \cdot z}{16}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right) \]

      8. *-commutative 43.5%

         \[\leadsto x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \frac{\color{blue}{z \cdot t}}{16}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right) \]

      9. associate-*r/ 43.5%

         \[\leadsto x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \color{blue}{\left(z \cdot \frac{t}{16}\right)}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right) \]

      10. *-commutative 43.5%

          \[\leadsto x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(z \cdot \frac{t}{16}\right)\right) \cdot \cos \left(\frac{\color{blue}{\left(b \cdot \left(a \cdot 2 + 1\right)\right)} \cdot t}{16}\right)\right) \]

      11. associate-*r* 42.7%

          \[\leadsto x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(z \cdot \frac{t}{16}\right)\right) \cdot \cos \left(\frac{\color{blue}{b \cdot \left(\left(a \cdot 2 + 1\right) \cdot t\right)}}{16}\right)\right) \]

      12. *-commutative 42.7%

          \[\leadsto x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(z \cdot \frac{t}{16}\right)\right) \cdot \cos \left(\frac{\color{blue}{\left(\left(a \cdot 2 + 1\right) \cdot t\right) \cdot b}}{16}\right)\right) \]

   3. Simplified 43.5%

      \[\leadsto \color{blue}{x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(z \cdot \frac{t}{16}\right)\right) \cdot \cos \left(t \cdot \frac{\mathsf{fma}\left(2, a, 1\right) \cdot b}{16}\right)\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-*r/ 43.5%

         \[\leadsto x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(z \cdot \frac{t}{16}\right)\right) \cdot \cos \color{blue}{\left(\frac{t \cdot \left(\mathsf{fma}\left(2, a, 1\right) \cdot b\right)}{16}\right)}\right) \]

      2. fma-undefine 43.5%

         \[\leadsto x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(z \cdot \frac{t}{16}\right)\right) \cdot \cos \left(\frac{t \cdot \left(\color{blue}{\left(2 \cdot a + 1\right)} \cdot b\right)}{16}\right)\right) \]

      3. *-commutative 43.5%

         \[\leadsto x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(z \cdot \frac{t}{16}\right)\right) \cdot \cos \left(\frac{t \cdot \left(\left(\color{blue}{a \cdot 2} + 1\right) \cdot b\right)}{16}\right)\right) \]

      4. *-commutative 43.5%

         \[\leadsto x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(z \cdot \frac{t}{16}\right)\right) \cdot \cos \left(\frac{\color{blue}{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}}{16}\right)\right) \]

      5. add-cube-cbrt 43.5%

         \[\leadsto x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(z \cdot \frac{t}{16}\right)\right) \cdot \cos \color{blue}{\left(\left(\sqrt[3]{\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}} \cdot \sqrt[3]{\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}}\right) \cdot \sqrt[3]{\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}}\right)}\right) \]

      6. pow3 43.9%

         \[\leadsto x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(z \cdot \frac{t}{16}\right)\right) \cdot \cos \color{blue}{\left({\left(\sqrt[3]{\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}}\right)}^{3}\right)}\right) \]

      7. *-commutative 43.9%

         \[\leadsto x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(z \cdot \frac{t}{16}\right)\right) \cdot \cos \left({\left(\sqrt[3]{\frac{\color{blue}{t \cdot \left(\left(a \cdot 2 + 1\right) \cdot b\right)}}{16}}\right)}^{3}\right)\right) \]

      8. *-commutative 43.9%

         \[\leadsto x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(z \cdot \frac{t}{16}\right)\right) \cdot \cos \left({\left(\sqrt[3]{\frac{t \cdot \left(\left(\color{blue}{2 \cdot a} + 1\right) \cdot b\right)}{16}}\right)}^{3}\right)\right) \]

      9. fma-undefine 43.9%

         \[\leadsto x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(z \cdot \frac{t}{16}\right)\right) \cdot \cos \left({\left(\sqrt[3]{\frac{t \cdot \left(\color{blue}{\mathsf{fma}\left(2, a, 1\right)} \cdot b\right)}{16}}\right)}^{3}\right)\right) \]

      10. associate-*r/ 43.9%

          \[\leadsto x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(z \cdot \frac{t}{16}\right)\right) \cdot \cos \left({\left(\sqrt[3]{\color{blue}{t \cdot \frac{\mathsf{fma}\left(2, a, 1\right) \cdot b}{16}}}\right)}^{3}\right)\right) \]

      11. associate-/l* 43.9%

          \[\leadsto x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(z \cdot \frac{t}{16}\right)\right) \cdot \cos \left({\left(\sqrt[3]{t \cdot \color{blue}{\left(\mathsf{fma}\left(2, a, 1\right) \cdot \frac{b}{16}\right)}}\right)}^{3}\right)\right) \]

      12. div-inv 43.9%

          \[\leadsto x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(z \cdot \frac{t}{16}\right)\right) \cdot \cos \left({\left(\sqrt[3]{t \cdot \left(\mathsf{fma}\left(2, a, 1\right) \cdot \color{blue}{\left(b \cdot \frac{1}{16}\right)}\right)}\right)}^{3}\right)\right) \]

      13. metadata-eval 43.9%

          \[\leadsto x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(z \cdot \frac{t}{16}\right)\right) \cdot \cos \left({\left(\sqrt[3]{t \cdot \left(\mathsf{fma}\left(2, a, 1\right) \cdot \left(b \cdot \color{blue}{0.0625}\right)\right)}\right)}^{3}\right)\right) \]

   6. Applied egg-rr 43.9%

      \[\leadsto x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(z \cdot \frac{t}{16}\right)\right) \cdot \cos \color{blue}{\left({\left(\sqrt[3]{t \cdot \left(\mathsf{fma}\left(2, a, 1\right) \cdot \left(b \cdot 0.0625\right)\right)}\right)}^{3}\right)}\right) \]

   if 5.0000000000000004e301 < (*.f64 (*.f64 x (cos.f64 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 y 2) 1) z) t) 16))) (cos.f64 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 a 2) 1) b) t) 16)))

   1. Initial program 0.0%

      \[\left(x \cdot \cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right)\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right) \]
   2. Step-by-step derivation

      1. associate-*l* 0.0%

         \[\leadsto \color{blue}{x \cdot \left(\cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right)} \]

      2. *-commutative 0.0%

         \[\leadsto x \cdot \left(\cos \left(\frac{\color{blue}{\left(z \cdot \left(y \cdot 2 + 1\right)\right)} \cdot t}{16}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right) \]

      3. associate-*r* 1.0%

         \[\leadsto x \cdot \left(\cos \left(\frac{\color{blue}{z \cdot \left(\left(y \cdot 2 + 1\right) \cdot t\right)}}{16}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right) \]

      4. *-commutative 1.0%

         \[\leadsto x \cdot \left(\cos \left(\frac{\color{blue}{\left(\left(y \cdot 2 + 1\right) \cdot t\right) \cdot z}}{16}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right) \]

      5. associate-*l* 1.1%

         \[\leadsto x \cdot \left(\cos \left(\frac{\color{blue}{\left(y \cdot 2 + 1\right) \cdot \left(t \cdot z\right)}}{16}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right) \]

      6. associate-/l* 1.3%

         \[\leadsto x \cdot \left(\cos \color{blue}{\left(\left(y \cdot 2 + 1\right) \cdot \frac{t \cdot z}{16}\right)} \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right) \]

      7. fma-define 1.3%

         \[\leadsto x \cdot \left(\cos \left(\color{blue}{\mathsf{fma}\left(y, 2, 1\right)} \cdot \frac{t \cdot z}{16}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right) \]

      8. *-commutative 1.3%

         \[\leadsto x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \frac{\color{blue}{z \cdot t}}{16}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right) \]

      9. associate-*r/ 1.3%

         \[\leadsto x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \color{blue}{\left(z \cdot \frac{t}{16}\right)}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right) \]

      10. *-commutative 1.3%

          \[\leadsto x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(z \cdot \frac{t}{16}\right)\right) \cdot \cos \left(\frac{\color{blue}{\left(b \cdot \left(a \cdot 2 + 1\right)\right)} \cdot t}{16}\right)\right) \]

      11. associate-*r* 2.1%

          \[\leadsto x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(z \cdot \frac{t}{16}\right)\right) \cdot \cos \left(\frac{\color{blue}{b \cdot \left(\left(a \cdot 2 + 1\right) \cdot t\right)}}{16}\right)\right) \]

      12. *-commutative 2.1%

          \[\leadsto x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(z \cdot \frac{t}{16}\right)\right) \cdot \cos \left(\frac{\color{blue}{\left(\left(a \cdot 2 + 1\right) \cdot t\right) \cdot b}}{16}\right)\right) \]

   3. Simplified 1.3%

      \[\leadsto \color{blue}{x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(z \cdot \frac{t}{16}\right)\right) \cdot \cos \left(t \cdot \frac{\mathsf{fma}\left(2, a, 1\right) \cdot b}{16}\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 4.8%

      \[\leadsto x \cdot \left(\color{blue}{1} \cdot \cos \left(t \cdot \frac{\mathsf{fma}\left(2, a, 1\right) \cdot b}{16}\right)\right) \]

   6. Taylor expanded in t around 0 11.1%

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

4. Final simplification 29.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot \cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right)\right) \cdot \cos \left(\frac{t \cdot \left(\left(1 + 2 \cdot a\right) \cdot b\right)}{16}\right) \leq 5 \cdot 10^{+301}:\\ \;\;\;\;x \cdot \left(\cos \left({\left(\sqrt[3]{t \cdot \left(\mathsf{fma}\left(2, a, 1\right) \cdot \left(b \cdot 0.0625\right)\right)}\right)}^{3}\right) \cdot \cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(z \cdot \frac{t}{16}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 31.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(x \cdot \cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right)\right) \cdot \cos \left(\frac{t \cdot \left(\left(1 + 2 \cdot a\right) \cdot b\right)}{16}\right) \leq 5 \cdot 10^{+301}:\\ \;\;\;\;x \cdot \left(\cos \left(t \cdot \frac{b \cdot \mathsf{fma}\left(2, a, 1\right)}{16}\right) \cdot \cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(z \cdot \frac{t}{16}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<=
      (*
       (* x (cos (/ (* (* (+ (* y 2.0) 1.0) z) t) 16.0)))
       (cos (/ (* t (* (+ 1.0 (* 2.0 a)) b)) 16.0)))
      5e+301)
   (*
    x
    (*
     (cos (* t (/ (* b (fma 2.0 a 1.0)) 16.0)))
     (cos (* (fma y 2.0 1.0) (* z (/ t 16.0))))))
   x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((x * cos((((((y * 2.0) + 1.0) * z) * t) / 16.0))) * cos(((t * ((1.0 + (2.0 * a)) * b)) / 16.0))) <= 5e+301) {
		tmp = x * (cos((t * ((b * fma(2.0, a, 1.0)) / 16.0))) * cos((fma(y, 2.0, 1.0) * (z * (t / 16.0)))));
	} else {
		tmp = x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(Float64(x * cos(Float64(Float64(Float64(Float64(Float64(y * 2.0) + 1.0) * z) * t) / 16.0))) * cos(Float64(Float64(t * Float64(Float64(1.0 + Float64(2.0 * a)) * b)) / 16.0))) <= 5e+301)
		tmp = Float64(x * Float64(cos(Float64(t * Float64(Float64(b * fma(2.0, a, 1.0)) / 16.0))) * cos(Float64(fma(y, 2.0, 1.0) * Float64(z * Float64(t / 16.0))))));
	else
		tmp = x;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(N[(x * N[Cos[N[(N[(N[(N[(N[(y * 2.0), $MachinePrecision] + 1.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision] / 16.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[Cos[N[(N[(t * N[(N[(1.0 + N[(2.0 * a), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision] / 16.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 5e+301], N[(x * N[(N[Cos[N[(t * N[(N[(b * N[(2.0 * a + 1.0), $MachinePrecision]), $MachinePrecision] / 16.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[Cos[N[(N[(y * 2.0 + 1.0), $MachinePrecision] * N[(z * N[(t / 16.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 x (cos.f64 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 y 2) 1) z) t) 16))) (cos.f64 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 a 2) 1) b) t) 16))) < 5.0000000000000004e301

   1. Initial program 43.3%

      \[\left(x \cdot \cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right)\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right) \]
   2. Step-by-step derivation

      1. associate-*l* 43.3%

         \[\leadsto \color{blue}{x \cdot \left(\cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right)} \]

      2. *-commutative 43.3%

         \[\leadsto x \cdot \left(\cos \left(\frac{\color{blue}{\left(z \cdot \left(y \cdot 2 + 1\right)\right)} \cdot t}{16}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right) \]

      3. associate-*r* 42.7%

         \[\leadsto x \cdot \left(\cos \left(\frac{\color{blue}{z \cdot \left(\left(y \cdot 2 + 1\right) \cdot t\right)}}{16}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right) \]

      4. *-commutative 42.7%

         \[\leadsto x \cdot \left(\cos \left(\frac{\color{blue}{\left(\left(y \cdot 2 + 1\right) \cdot t\right) \cdot z}}{16}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right) \]

      5. associate-*l* 43.5%

         \[\leadsto x \cdot \left(\cos \left(\frac{\color{blue}{\left(y \cdot 2 + 1\right) \cdot \left(t \cdot z\right)}}{16}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right) \]

      6. associate-/l* 43.5%

         \[\leadsto x \cdot \left(\cos \color{blue}{\left(\left(y \cdot 2 + 1\right) \cdot \frac{t \cdot z}{16}\right)} \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right) \]

      7. fma-define 43.5%

         \[\leadsto x \cdot \left(\cos \left(\color{blue}{\mathsf{fma}\left(y, 2, 1\right)} \cdot \frac{t \cdot z}{16}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right) \]

      8. *-commutative 43.5%

         \[\leadsto x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \frac{\color{blue}{z \cdot t}}{16}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right) \]

      9. associate-*r/ 43.5%

         \[\leadsto x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \color{blue}{\left(z \cdot \frac{t}{16}\right)}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right) \]

      10. *-commutative 43.5%

          \[\leadsto x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(z \cdot \frac{t}{16}\right)\right) \cdot \cos \left(\frac{\color{blue}{\left(b \cdot \left(a \cdot 2 + 1\right)\right)} \cdot t}{16}\right)\right) \]

      11. associate-*r* 42.7%

          \[\leadsto x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(z \cdot \frac{t}{16}\right)\right) \cdot \cos \left(\frac{\color{blue}{b \cdot \left(\left(a \cdot 2 + 1\right) \cdot t\right)}}{16}\right)\right) \]

      12. *-commutative 42.7%

          \[\leadsto x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(z \cdot \frac{t}{16}\right)\right) \cdot \cos \left(\frac{\color{blue}{\left(\left(a \cdot 2 + 1\right) \cdot t\right) \cdot b}}{16}\right)\right) \]

   3. Simplified 43.5%

      \[\leadsto \color{blue}{x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(z \cdot \frac{t}{16}\right)\right) \cdot \cos \left(t \cdot \frac{\mathsf{fma}\left(2, a, 1\right) \cdot b}{16}\right)\right)} \]
   4. Add Preprocessing

   if 5.0000000000000004e301 < (*.f64 (*.f64 x (cos.f64 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 y 2) 1) z) t) 16))) (cos.f64 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 a 2) 1) b) t) 16)))

   1. Initial program 0.0%

      \[\left(x \cdot \cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right)\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right) \]
   2. Step-by-step derivation

      1. associate-*l* 0.0%

         \[\leadsto \color{blue}{x \cdot \left(\cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right)} \]

      2. *-commutative 0.0%

         \[\leadsto x \cdot \left(\cos \left(\frac{\color{blue}{\left(z \cdot \left(y \cdot 2 + 1\right)\right)} \cdot t}{16}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right) \]

      3. associate-*r* 1.0%

         \[\leadsto x \cdot \left(\cos \left(\frac{\color{blue}{z \cdot \left(\left(y \cdot 2 + 1\right) \cdot t\right)}}{16}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right) \]

      4. *-commutative 1.0%

         \[\leadsto x \cdot \left(\cos \left(\frac{\color{blue}{\left(\left(y \cdot 2 + 1\right) \cdot t\right) \cdot z}}{16}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right) \]

      5. associate-*l* 1.1%

         \[\leadsto x \cdot \left(\cos \left(\frac{\color{blue}{\left(y \cdot 2 + 1\right) \cdot \left(t \cdot z\right)}}{16}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right) \]

      6. associate-/l* 1.3%

         \[\leadsto x \cdot \left(\cos \color{blue}{\left(\left(y \cdot 2 + 1\right) \cdot \frac{t \cdot z}{16}\right)} \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right) \]

      7. fma-define 1.3%

         \[\leadsto x \cdot \left(\cos \left(\color{blue}{\mathsf{fma}\left(y, 2, 1\right)} \cdot \frac{t \cdot z}{16}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right) \]

      8. *-commutative 1.3%

         \[\leadsto x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \frac{\color{blue}{z \cdot t}}{16}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right) \]

      9. associate-*r/ 1.3%

         \[\leadsto x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \color{blue}{\left(z \cdot \frac{t}{16}\right)}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right) \]

      10. *-commutative 1.3%

          \[\leadsto x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(z \cdot \frac{t}{16}\right)\right) \cdot \cos \left(\frac{\color{blue}{\left(b \cdot \left(a \cdot 2 + 1\right)\right)} \cdot t}{16}\right)\right) \]

      11. associate-*r* 2.1%

          \[\leadsto x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(z \cdot \frac{t}{16}\right)\right) \cdot \cos \left(\frac{\color{blue}{b \cdot \left(\left(a \cdot 2 + 1\right) \cdot t\right)}}{16}\right)\right) \]

      12. *-commutative 2.1%

          \[\leadsto x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(z \cdot \frac{t}{16}\right)\right) \cdot \cos \left(\frac{\color{blue}{\left(\left(a \cdot 2 + 1\right) \cdot t\right) \cdot b}}{16}\right)\right) \]

   3. Simplified 1.3%

      \[\leadsto \color{blue}{x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(z \cdot \frac{t}{16}\right)\right) \cdot \cos \left(t \cdot \frac{\mathsf{fma}\left(2, a, 1\right) \cdot b}{16}\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 4.8%

      \[\leadsto x \cdot \left(\color{blue}{1} \cdot \cos \left(t \cdot \frac{\mathsf{fma}\left(2, a, 1\right) \cdot b}{16}\right)\right) \]

   6. Taylor expanded in t around 0 11.1%

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

4. Final simplification 29.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot \cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right)\right) \cdot \cos \left(\frac{t \cdot \left(\left(1 + 2 \cdot a\right) \cdot b\right)}{16}\right) \leq 5 \cdot 10^{+301}:\\ \;\;\;\;x \cdot \left(\cos \left(t \cdot \frac{b \cdot \mathsf{fma}\left(2, a, 1\right)}{16}\right) \cdot \cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(z \cdot \frac{t}{16}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 31.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(x \cdot \cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right)\right) \cdot \cos \left(\frac{t \cdot \left(\left(1 + 2 \cdot a\right) \cdot b\right)}{16}\right) \leq 5 \cdot 10^{+230}:\\ \;\;\;\;x \cdot \left(\cos \left(t \cdot \frac{b \cdot \mathsf{fma}\left(2, a, 1\right)}{16}\right) \cdot \cos \left(\frac{z \cdot \mathsf{fma}\left(y, 2, 1\right)}{\frac{16}{t}}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<=
      (*
       (* x (cos (/ (* (* (+ (* y 2.0) 1.0) z) t) 16.0)))
       (cos (/ (* t (* (+ 1.0 (* 2.0 a)) b)) 16.0)))
      5e+230)
   (*
    x
    (*
     (cos (* t (/ (* b (fma 2.0 a 1.0)) 16.0)))
     (cos (/ (* z (fma y 2.0 1.0)) (/ 16.0 t)))))
   x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((x * cos((((((y * 2.0) + 1.0) * z) * t) / 16.0))) * cos(((t * ((1.0 + (2.0 * a)) * b)) / 16.0))) <= 5e+230) {
		tmp = x * (cos((t * ((b * fma(2.0, a, 1.0)) / 16.0))) * cos(((z * fma(y, 2.0, 1.0)) / (16.0 / t))));
	} else {
		tmp = x;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (Float64(Float64(x * cos(Float64(Float64(Float64(Float64(Float64(y * 2.0) + 1.0) * z) * t) / 16.0))) * cos(Float64(Float64(t * Float64(Float64(1.0 + Float64(2.0 * a)) * b)) / 16.0))) <= 5e+230)
		tmp = Float64(x * Float64(cos(Float64(t * Float64(Float64(b * fma(2.0, a, 1.0)) / 16.0))) * cos(Float64(Float64(z * fma(y, 2.0, 1.0)) / Float64(16.0 / t)))));
	else
		tmp = x;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[N[(N[(x * N[Cos[N[(N[(N[(N[(N[(y * 2.0), $MachinePrecision] + 1.0), $MachinePrecision] * z), $MachinePrecision] * t), $MachinePrecision] / 16.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[Cos[N[(N[(t * N[(N[(1.0 + N[(2.0 * a), $MachinePrecision]), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision] / 16.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 5e+230], N[(x * N[(N[Cos[N[(t * N[(N[(b * N[(2.0 * a + 1.0), $MachinePrecision]), $MachinePrecision] / 16.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[Cos[N[(N[(z * N[(y * 2.0 + 1.0), $MachinePrecision]), $MachinePrecision] / N[(16.0 / t), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 x (cos.f64 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 y 2) 1) z) t) 16))) (cos.f64 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 a 2) 1) b) t) 16))) < 5.0000000000000003e230

   1. Initial program 43.5%

      \[\left(x \cdot \cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right)\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right) \]
   2. Step-by-step derivation

      1. associate-*l* 43.5%

         \[\leadsto \color{blue}{x \cdot \left(\cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right)} \]

      2. *-commutative 43.5%

         \[\leadsto x \cdot \left(\cos \left(\frac{\color{blue}{\left(z \cdot \left(y \cdot 2 + 1\right)\right)} \cdot t}{16}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right) \]

      3. associate-*r* 42.9%

         \[\leadsto x \cdot \left(\cos \left(\frac{\color{blue}{z \cdot \left(\left(y \cdot 2 + 1\right) \cdot t\right)}}{16}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right) \]

      4. *-commutative 42.9%

         \[\leadsto x \cdot \left(\cos \left(\frac{\color{blue}{\left(\left(y \cdot 2 + 1\right) \cdot t\right) \cdot z}}{16}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right) \]

      5. associate-*l* 43.8%

         \[\leadsto x \cdot \left(\cos \left(\frac{\color{blue}{\left(y \cdot 2 + 1\right) \cdot \left(t \cdot z\right)}}{16}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right) \]

      6. associate-/l* 43.8%

         \[\leadsto x \cdot \left(\cos \color{blue}{\left(\left(y \cdot 2 + 1\right) \cdot \frac{t \cdot z}{16}\right)} \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right) \]

      7. fma-define 43.8%

         \[\leadsto x \cdot \left(\cos \left(\color{blue}{\mathsf{fma}\left(y, 2, 1\right)} \cdot \frac{t \cdot z}{16}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right) \]

      8. *-commutative 43.8%

         \[\leadsto x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \frac{\color{blue}{z \cdot t}}{16}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right) \]

      9. associate-*r/ 43.8%

         \[\leadsto x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \color{blue}{\left(z \cdot \frac{t}{16}\right)}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right) \]

      10. *-commutative 43.8%

          \[\leadsto x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(z \cdot \frac{t}{16}\right)\right) \cdot \cos \left(\frac{\color{blue}{\left(b \cdot \left(a \cdot 2 + 1\right)\right)} \cdot t}{16}\right)\right) \]

      11. associate-*r* 42.8%

          \[\leadsto x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(z \cdot \frac{t}{16}\right)\right) \cdot \cos \left(\frac{\color{blue}{b \cdot \left(\left(a \cdot 2 + 1\right) \cdot t\right)}}{16}\right)\right) \]

      12. *-commutative 42.8%

          \[\leadsto x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(z \cdot \frac{t}{16}\right)\right) \cdot \cos \left(\frac{\color{blue}{\left(\left(a \cdot 2 + 1\right) \cdot t\right) \cdot b}}{16}\right)\right) \]

   3. Simplified 43.8%

      \[\leadsto \color{blue}{x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(z \cdot \frac{t}{16}\right)\right) \cdot \cos \left(t \cdot \frac{\mathsf{fma}\left(2, a, 1\right) \cdot b}{16}\right)\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. associate-*r* 43.5%

         \[\leadsto x \cdot \left(\cos \color{blue}{\left(\left(\mathsf{fma}\left(y, 2, 1\right) \cdot z\right) \cdot \frac{t}{16}\right)} \cdot \cos \left(t \cdot \frac{\mathsf{fma}\left(2, a, 1\right) \cdot b}{16}\right)\right) \]

      2. clear-num 43.4%

         \[\leadsto x \cdot \left(\cos \left(\left(\mathsf{fma}\left(y, 2, 1\right) \cdot z\right) \cdot \color{blue}{\frac{1}{\frac{16}{t}}}\right) \cdot \cos \left(t \cdot \frac{\mathsf{fma}\left(2, a, 1\right) \cdot b}{16}\right)\right) \]

      3. un-div-inv 43.8%

         \[\leadsto x \cdot \left(\cos \color{blue}{\left(\frac{\mathsf{fma}\left(y, 2, 1\right) \cdot z}{\frac{16}{t}}\right)} \cdot \cos \left(t \cdot \frac{\mathsf{fma}\left(2, a, 1\right) \cdot b}{16}\right)\right) \]

   6. Applied egg-rr 43.8%

      \[\leadsto x \cdot \left(\cos \color{blue}{\left(\frac{\mathsf{fma}\left(y, 2, 1\right) \cdot z}{\frac{16}{t}}\right)} \cdot \cos \left(t \cdot \frac{\mathsf{fma}\left(2, a, 1\right) \cdot b}{16}\right)\right) \]

   if 5.0000000000000003e230 < (*.f64 (*.f64 x (cos.f64 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 y 2) 1) z) t) 16))) (cos.f64 (/.f64 (*.f64 (*.f64 (+.f64 (*.f64 a 2) 1) b) t) 16)))

   1. Initial program 2.3%

      \[\left(x \cdot \cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right)\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right) \]
   2. Step-by-step derivation

      1. associate-*l* 2.3%

         \[\leadsto \color{blue}{x \cdot \left(\cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right)} \]

      2. *-commutative 2.3%

         \[\leadsto x \cdot \left(\cos \left(\frac{\color{blue}{\left(z \cdot \left(y \cdot 2 + 1\right)\right)} \cdot t}{16}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right) \]

      3. associate-*r* 3.2%

         \[\leadsto x \cdot \left(\cos \left(\frac{\color{blue}{z \cdot \left(\left(y \cdot 2 + 1\right) \cdot t\right)}}{16}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right) \]

      4. *-commutative 3.2%

         \[\leadsto x \cdot \left(\cos \left(\frac{\color{blue}{\left(\left(y \cdot 2 + 1\right) \cdot t\right) \cdot z}}{16}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right) \]

      5. associate-*l* 3.3%

         \[\leadsto x \cdot \left(\cos \left(\frac{\color{blue}{\left(y \cdot 2 + 1\right) \cdot \left(t \cdot z\right)}}{16}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right) \]

      6. associate-/l* 3.5%

         \[\leadsto x \cdot \left(\cos \color{blue}{\left(\left(y \cdot 2 + 1\right) \cdot \frac{t \cdot z}{16}\right)} \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right) \]

      7. fma-define 3.5%

         \[\leadsto x \cdot \left(\cos \left(\color{blue}{\mathsf{fma}\left(y, 2, 1\right)} \cdot \frac{t \cdot z}{16}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right) \]

      8. *-commutative 3.5%

         \[\leadsto x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \frac{\color{blue}{z \cdot t}}{16}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right) \]

      9. associate-*r/ 3.5%

         \[\leadsto x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \color{blue}{\left(z \cdot \frac{t}{16}\right)}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right) \]

      10. *-commutative 3.5%

          \[\leadsto x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(z \cdot \frac{t}{16}\right)\right) \cdot \cos \left(\frac{\color{blue}{\left(b \cdot \left(a \cdot 2 + 1\right)\right)} \cdot t}{16}\right)\right) \]

      11. associate-*r* 4.4%

          \[\leadsto x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(z \cdot \frac{t}{16}\right)\right) \cdot \cos \left(\frac{\color{blue}{b \cdot \left(\left(a \cdot 2 + 1\right) \cdot t\right)}}{16}\right)\right) \]

      12. *-commutative 4.4%

          \[\leadsto x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(z \cdot \frac{t}{16}\right)\right) \cdot \cos \left(\frac{\color{blue}{\left(\left(a \cdot 2 + 1\right) \cdot t\right) \cdot b}}{16}\right)\right) \]

   3. Simplified 3.5%

      \[\leadsto \color{blue}{x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(z \cdot \frac{t}{16}\right)\right) \cdot \cos \left(t \cdot \frac{\mathsf{fma}\left(2, a, 1\right) \cdot b}{16}\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 6.7%

      \[\leadsto x \cdot \left(\color{blue}{1} \cdot \cos \left(t \cdot \frac{\mathsf{fma}\left(2, a, 1\right) \cdot b}{16}\right)\right) \]

   6. Taylor expanded in t around 0 12.3%

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

4. Final simplification 29.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot \cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right)\right) \cdot \cos \left(\frac{t \cdot \left(\left(1 + 2 \cdot a\right) \cdot b\right)}{16}\right) \leq 5 \cdot 10^{+230}:\\ \;\;\;\;x \cdot \left(\cos \left(t \cdot \frac{b \cdot \mathsf{fma}\left(2, a, 1\right)}{16}\right) \cdot \cos \left(\frac{z \cdot \mathsf{fma}\left(y, 2, 1\right)}{\frac{16}{t}}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 30.1% accurate, 225.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 x)

C

double code(double x, double y, double z, double t, double a, double b) {
	return x;
}

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 = x
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x;
}

Python

def code(x, y, z, t, a, b):
	return x

Julia

function code(x, y, z, t, a, b)
	return x
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := x

Derivation

1. Initial program 24.5%

   \[\left(x \cdot \cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right)\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right) \]
2. Step-by-step derivation

   1. associate-*l* 24.5%

      \[\leadsto \color{blue}{x \cdot \left(\cos \left(\frac{\left(\left(y \cdot 2 + 1\right) \cdot z\right) \cdot t}{16}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right)} \]

   2. *-commutative 24.5%

      \[\leadsto x \cdot \left(\cos \left(\frac{\color{blue}{\left(z \cdot \left(y \cdot 2 + 1\right)\right)} \cdot t}{16}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right) \]

   3. associate-*r* 24.6%

      \[\leadsto x \cdot \left(\cos \left(\frac{\color{blue}{z \cdot \left(\left(y \cdot 2 + 1\right) \cdot t\right)}}{16}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right) \]

   4. *-commutative 24.6%

      \[\leadsto x \cdot \left(\cos \left(\frac{\color{blue}{\left(\left(y \cdot 2 + 1\right) \cdot t\right) \cdot z}}{16}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right) \]

   5. associate-*l* 25.1%

      \[\leadsto x \cdot \left(\cos \left(\frac{\color{blue}{\left(y \cdot 2 + 1\right) \cdot \left(t \cdot z\right)}}{16}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right) \]

   6. associate-/l* 25.2%

      \[\leadsto x \cdot \left(\cos \color{blue}{\left(\left(y \cdot 2 + 1\right) \cdot \frac{t \cdot z}{16}\right)} \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right) \]

   7. fma-define 25.2%

      \[\leadsto x \cdot \left(\cos \left(\color{blue}{\mathsf{fma}\left(y, 2, 1\right)} \cdot \frac{t \cdot z}{16}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right) \]

   8. *-commutative 25.2%

      \[\leadsto x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \frac{\color{blue}{z \cdot t}}{16}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right) \]

   9. associate-*r/ 25.2%

      \[\leadsto x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \color{blue}{\left(z \cdot \frac{t}{16}\right)}\right) \cdot \cos \left(\frac{\left(\left(a \cdot 2 + 1\right) \cdot b\right) \cdot t}{16}\right)\right) \]

   10. *-commutative 25.2%

       \[\leadsto x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(z \cdot \frac{t}{16}\right)\right) \cdot \cos \left(\frac{\color{blue}{\left(b \cdot \left(a \cdot 2 + 1\right)\right)} \cdot t}{16}\right)\right) \]

   11. associate-*r* 25.1%

       \[\leadsto x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(z \cdot \frac{t}{16}\right)\right) \cdot \cos \left(\frac{\color{blue}{b \cdot \left(\left(a \cdot 2 + 1\right) \cdot t\right)}}{16}\right)\right) \]

   12. *-commutative 25.1%

       \[\leadsto x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(z \cdot \frac{t}{16}\right)\right) \cdot \cos \left(\frac{\color{blue}{\left(\left(a \cdot 2 + 1\right) \cdot t\right) \cdot b}}{16}\right)\right) \]

3. Simplified 25.2%

   \[\leadsto \color{blue}{x \cdot \left(\cos \left(\mathsf{fma}\left(y, 2, 1\right) \cdot \left(z \cdot \frac{t}{16}\right)\right) \cdot \cos \left(t \cdot \frac{\mathsf{fma}\left(2, a, 1\right) \cdot b}{16}\right)\right)} \]
4. Add Preprocessing

5. Taylor expanded in z around 0 26.1%

   \[\leadsto x \cdot \left(\color{blue}{1} \cdot \cos \left(t \cdot \frac{\mathsf{fma}\left(2, a, 1\right) \cdot b}{16}\right)\right) \]

6. Taylor expanded in t around 0 27.9%

   \[\leadsto \color{blue}{x} \]

7. Final simplification 27.9%

   \[\leadsto x \]
8. Add Preprocessing

Developer target: 29.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \cos \left(\frac{b}{16} \cdot \frac{t}{\left(1 - a \cdot 2\right) + {\left(a \cdot 2\right)}^{2}}\right) \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (* x (cos (* (/ b 16.0) (/ t (+ (- 1.0 (* a 2.0)) (pow (* a 2.0) 2.0)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return x * cos(((b / 16.0) * (t / ((1.0 - (a * 2.0)) + pow((a * 2.0), 2.0)))));
}

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 = x * cos(((b / 16.0d0) * (t / ((1.0d0 - (a * 2.0d0)) + ((a * 2.0d0) ** 2.0d0)))))
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return x * Math.cos(((b / 16.0) * (t / ((1.0 - (a * 2.0)) + Math.pow((a * 2.0), 2.0)))));
}

Python

def code(x, y, z, t, a, b):
	return x * math.cos(((b / 16.0) * (t / ((1.0 - (a * 2.0)) + math.pow((a * 2.0), 2.0)))))

Julia

function code(x, y, z, t, a, b)
	return Float64(x * cos(Float64(Float64(b / 16.0) * Float64(t / Float64(Float64(1.0 - Float64(a * 2.0)) + (Float64(a * 2.0) ^ 2.0))))))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = x * cos(((b / 16.0) * (t / ((1.0 - (a * 2.0)) + ((a * 2.0) ^ 2.0)))));
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(x * N[Cos[N[(N[(b / 16.0), $MachinePrecision] * N[(t / N[(N[(1.0 - N[(a * 2.0), $MachinePrecision]), $MachinePrecision] + N[Power[N[(a * 2.0), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024046 
(FPCore (x y z t a b)
  :name "Codec.Picture.Jpg.FastDct:referenceDct from JuicyPixels-3.2.6.1"
  :precision binary64

  :alt
  (* x (cos (* (/ b 16.0) (/ t (+ (- 1.0 (* a 2.0)) (pow (* a 2.0) 2.0))))))

  (* (* x (cos (/ (* (* (+ (* y 2.0) 1.0) z) t) 16.0))) (cos (/ (* (* (+ (* a 2.0) 1.0) b) t) 16.0))))