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

Percentage Accurate: 70.6% → 77.9%

Time: 19.4s

Alternatives: 13

Speedup: 1.0×

• Could not converge on a ground truth

  1. x = 4.702424381459981e-198
  2. y = 7.350129497717928e+128
  3. z = -2.968229211574817e+48
  4. t = -4.586657050341055e+23
  5. a = 2.0302448087869313e-91
  6. b = -1.5400610426852703e-262

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 70.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 77.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a}{3 \cdot b}\\ t_2 := 2 \cdot \sqrt{x}\\ t_3 := z \cdot \left(t \cdot 0.3333333333333333\right)\\ \mathbf{if}\;t\_2 \cdot \cos \left(y - \frac{z \cdot t}{3}\right) \leq 2 \cdot 10^{+64}:\\ \;\;\;\;t\_2 \cdot \left(\cos y \cdot \cos t\_3 + \sin y \cdot \sin t\_3\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt{x} \cdot \sqrt{{\cos y}^{2}}\right) - t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ a (* 3.0 b)))
        (t_2 (* 2.0 (sqrt x)))
        (t_3 (* z (* t 0.3333333333333333))))
   (if (<= (* t_2 (cos (- y (/ (* z t) 3.0)))) 2e+64)
     (- (* t_2 (+ (* (cos y) (cos t_3)) (* (sin y) (sin t_3)))) t_1)
     (- (* 2.0 (* (sqrt x) (sqrt (pow (cos y) 2.0)))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a / (3.0 * b);
	double t_2 = 2.0 * sqrt(x);
	double t_3 = z * (t * 0.3333333333333333);
	double tmp;
	if ((t_2 * cos((y - ((z * t) / 3.0)))) <= 2e+64) {
		tmp = (t_2 * ((cos(y) * cos(t_3)) + (sin(y) * sin(t_3)))) - t_1;
	} else {
		tmp = (2.0 * (sqrt(x) * sqrt(pow(cos(y), 2.0)))) - t_1;
	}
	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 = a / (3.0d0 * b)
    t_2 = 2.0d0 * sqrt(x)
    t_3 = z * (t * 0.3333333333333333d0)
    if ((t_2 * cos((y - ((z * t) / 3.0d0)))) <= 2d+64) then
        tmp = (t_2 * ((cos(y) * cos(t_3)) + (sin(y) * sin(t_3)))) - t_1
    else
        tmp = (2.0d0 * (sqrt(x) * sqrt((cos(y) ** 2.0d0)))) - t_1
    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 = a / (3.0 * b);
	double t_2 = 2.0 * Math.sqrt(x);
	double t_3 = z * (t * 0.3333333333333333);
	double tmp;
	if ((t_2 * Math.cos((y - ((z * t) / 3.0)))) <= 2e+64) {
		tmp = (t_2 * ((Math.cos(y) * Math.cos(t_3)) + (Math.sin(y) * Math.sin(t_3)))) - t_1;
	} else {
		tmp = (2.0 * (Math.sqrt(x) * Math.sqrt(Math.pow(Math.cos(y), 2.0)))) - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a / (3.0 * b)
	t_2 = 2.0 * math.sqrt(x)
	t_3 = z * (t * 0.3333333333333333)
	tmp = 0
	if (t_2 * math.cos((y - ((z * t) / 3.0)))) <= 2e+64:
		tmp = (t_2 * ((math.cos(y) * math.cos(t_3)) + (math.sin(y) * math.sin(t_3)))) - t_1
	else:
		tmp = (2.0 * (math.sqrt(x) * math.sqrt(math.pow(math.cos(y), 2.0)))) - t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a / Float64(3.0 * b))
	t_2 = Float64(2.0 * sqrt(x))
	t_3 = Float64(z * Float64(t * 0.3333333333333333))
	tmp = 0.0
	if (Float64(t_2 * cos(Float64(y - Float64(Float64(z * t) / 3.0)))) <= 2e+64)
		tmp = Float64(Float64(t_2 * Float64(Float64(cos(y) * cos(t_3)) + Float64(sin(y) * sin(t_3)))) - t_1);
	else
		tmp = Float64(Float64(2.0 * Float64(sqrt(x) * sqrt((cos(y) ^ 2.0)))) - t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a / (3.0 * b);
	t_2 = 2.0 * sqrt(x);
	t_3 = z * (t * 0.3333333333333333);
	tmp = 0.0;
	if ((t_2 * cos((y - ((z * t) / 3.0)))) <= 2e+64)
		tmp = (t_2 * ((cos(y) * cos(t_3)) + (sin(y) * sin(t_3)))) - t_1;
	else
		tmp = (2.0 * (sqrt(x) * sqrt((cos(y) ^ 2.0)))) - t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a / N[(3.0 * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(t * 0.3333333333333333), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$2 * N[Cos[N[(y - N[(N[(z * t), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2e+64], N[(N[(t$95$2 * N[(N[(N[Cos[y], $MachinePrecision] * N[Cos[t$95$3], $MachinePrecision]), $MachinePrecision] + N[(N[Sin[y], $MachinePrecision] * N[Sin[t$95$3], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(2.0 * N[(N[Sqrt[x], $MachinePrecision] * N[Sqrt[N[Power[N[Cos[y], $MachinePrecision], 2.0], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64))))) < 2.00000000000000004e64

   1. Initial program 83.7%

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

      1. associate-*r/ 83.6%

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

      2. add-sqr-sqrt 47.2%

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

      3. sqrt-unprod 76.5%

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

      4. associate-*r/ 76.5%

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

      5. associate-*r/ 76.4%

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

      6. frac-times 76.3%

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

      7. metadata-eval 76.3%

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

      8. metadata-eval 76.3%

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

      9. frac-times 76.4%

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

      10. sqrt-unprod 48.2%

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

      11. expm1-log1p-u 47.9%

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

      12. add-sqr-sqrt 69.0%

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

      13. expm1-undefine 69.0%

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

      14. associate-/l* 69.0%

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

      15. div-inv 69.0%

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

      16. metadata-eval 69.0%

          \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \left(e^{\mathsf{log1p}\left(z \cdot \left(t \cdot \color{blue}{-0.3333333333333333}\right)\right)} - 1\right)\right) - \frac{a}{b \cdot 3} \]

   4. Applied egg-rr 69.0%

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \color{blue}{\left(e^{\mathsf{log1p}\left(z \cdot \left(t \cdot -0.3333333333333333\right)\right)} - 1\right)}\right) - \frac{a}{b \cdot 3} \]
   5. Step-by-step derivation

      1. expm1-define 69.0%

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

      2. rem-square-sqrt 47.9%

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

      3. fabs-sqr 47.9%

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

      4. rem-square-sqrt 83.7%

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

      5. associate-*r* 83.7%

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

      6. fabs-mul 83.7%

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

      7. rem-square-sqrt 47.1%

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

      8. fabs-sqr 47.1%

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

      9. rem-square-sqrt 71.9%

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

      10. metadata-eval 71.9%

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

      11. *-commutative 71.9%

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

      12. *-commutative 71.9%

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

   6. Simplified 71.9%

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

      1. cos-diff 72.5%

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

      2. expm1-log1p-u 72.2%

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

      3. associate-*r* 72.4%

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

      4. expm1-log1p-u 84.5%

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

      5. associate-*r* 84.8%

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

   8. Applied egg-rr 84.8%

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

   if 2.00000000000000004e64 < (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64)))))

   1. Initial program 49.9%

      \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 80.5%

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

      1. add-log-exp 80.5%

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

   5. Applied egg-rr 80.5%

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

      1. rem-log-exp 80.5%

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

      2. add-sqr-sqrt 68.5%

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

      3. sqrt-unprod 80.9%

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

      4. pow2 80.9%

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

   7. Applied egg-rr 80.9%

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

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) \leq 2 \cdot 10^{+64}:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \left(\cos y \cdot \cos \left(z \cdot \left(t \cdot 0.3333333333333333\right)\right) + \sin y \cdot \sin \left(z \cdot \left(t \cdot 0.3333333333333333\right)\right)\right) - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt{x} \cdot \sqrt{{\cos y}^{2}}\right) - \frac{a}{3 \cdot b}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 77.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a}{3 \cdot b}\\ t_2 := 2 \cdot \sqrt{x}\\ \mathbf{if}\;t\_2 \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - t\_1 \leq 2 \cdot 10^{+152}:\\ \;\;\;\;t\_2 \cdot \cos \left(y - \frac{{\left(\sqrt[3]{z \cdot t}\right)}^{3}}{3}\right) - t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2 - t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ a (* 3.0 b))) (t_2 (* 2.0 (sqrt x))))
   (if (<= (- (* t_2 (cos (- y (/ (* z t) 3.0)))) t_1) 2e+152)
     (- (* t_2 (cos (- y (/ (pow (cbrt (* z t)) 3.0) 3.0)))) t_1)
     (- t_2 t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a / (3.0 * b);
	double t_2 = 2.0 * sqrt(x);
	double tmp;
	if (((t_2 * cos((y - ((z * t) / 3.0)))) - t_1) <= 2e+152) {
		tmp = (t_2 * cos((y - (pow(cbrt((z * t)), 3.0) / 3.0)))) - t_1;
	} else {
		tmp = t_2 - t_1;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a / (3.0 * b);
	double t_2 = 2.0 * Math.sqrt(x);
	double tmp;
	if (((t_2 * Math.cos((y - ((z * t) / 3.0)))) - t_1) <= 2e+152) {
		tmp = (t_2 * Math.cos((y - (Math.pow(Math.cbrt((z * t)), 3.0) / 3.0)))) - t_1;
	} else {
		tmp = t_2 - t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a / Float64(3.0 * b))
	t_2 = Float64(2.0 * sqrt(x))
	tmp = 0.0
	if (Float64(Float64(t_2 * cos(Float64(y - Float64(Float64(z * t) / 3.0)))) - t_1) <= 2e+152)
		tmp = Float64(Float64(t_2 * cos(Float64(y - Float64((cbrt(Float64(z * t)) ^ 3.0) / 3.0)))) - t_1);
	else
		tmp = Float64(t_2 - t_1);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a / N[(3.0 * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(t$95$2 * N[Cos[N[(y - N[(N[(z * t), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], 2e+152], N[(N[(t$95$2 * N[Cos[N[(y - N[(N[Power[N[Power[N[(z * t), $MachinePrecision], 1/3], $MachinePrecision], 3.0], $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(t$95$2 - t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64))))) (/.f64 a (*.f64 b #s(literal 3 binary64)))) < 2.0000000000000001e152

   1. Initial program 81.8%

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

      1. add-cube-cbrt 82.0%

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

      2. pow3 82.2%

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

   4. Applied egg-rr 82.2%

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

   if 2.0000000000000001e152 < (-.f64 (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64))))) (/.f64 a (*.f64 b #s(literal 3 binary64))))

   1. Initial program 50.8%

      \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 86.1%

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

   4. Taylor expanded in y around 0 86.3%

      \[\leadsto \color{blue}{2 \cdot \sqrt{x}} - \frac{a}{b \cdot 3} \]
   5. Step-by-step derivation

      1. *-commutative 86.3%

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

   6. Simplified 86.3%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{3 \cdot b} \leq 2 \cdot 10^{+152}:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{{\left(\sqrt[3]{z \cdot t}\right)}^{3}}{3}\right) - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{x} - \frac{a}{3 \cdot b}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 77.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \sqrt{x}\\ t_2 := \frac{a}{3 \cdot b}\\ \mathbf{if}\;t\_1 \cdot \cos \left(y - \frac{z \cdot t}{3}\right) \leq 2 \cdot 10^{-73}:\\ \;\;\;\;t\_1 \cdot \cos \left(y + \frac{-1}{\frac{3}{z \cdot t}}\right) - t\_2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt{x} \cdot \sqrt{{\cos y}^{2}}\right) - t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* 2.0 (sqrt x))) (t_2 (/ a (* 3.0 b))))
   (if (<= (* t_1 (cos (- y (/ (* z t) 3.0)))) 2e-73)
     (- (* t_1 (cos (+ y (/ -1.0 (/ 3.0 (* z t)))))) t_2)
     (- (* 2.0 (* (sqrt x) (sqrt (pow (cos y) 2.0)))) t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 2.0 * sqrt(x);
	double t_2 = a / (3.0 * b);
	double tmp;
	if ((t_1 * cos((y - ((z * t) / 3.0)))) <= 2e-73) {
		tmp = (t_1 * cos((y + (-1.0 / (3.0 / (z * t)))))) - t_2;
	} else {
		tmp = (2.0 * (sqrt(x) * sqrt(pow(cos(y), 2.0)))) - t_2;
	}
	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) :: tmp
    t_1 = 2.0d0 * sqrt(x)
    t_2 = a / (3.0d0 * b)
    if ((t_1 * cos((y - ((z * t) / 3.0d0)))) <= 2d-73) then
        tmp = (t_1 * cos((y + ((-1.0d0) / (3.0d0 / (z * t)))))) - t_2
    else
        tmp = (2.0d0 * (sqrt(x) * sqrt((cos(y) ** 2.0d0)))) - t_2
    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 = 2.0 * Math.sqrt(x);
	double t_2 = a / (3.0 * b);
	double tmp;
	if ((t_1 * Math.cos((y - ((z * t) / 3.0)))) <= 2e-73) {
		tmp = (t_1 * Math.cos((y + (-1.0 / (3.0 / (z * t)))))) - t_2;
	} else {
		tmp = (2.0 * (Math.sqrt(x) * Math.sqrt(Math.pow(Math.cos(y), 2.0)))) - t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = 2.0 * math.sqrt(x)
	t_2 = a / (3.0 * b)
	tmp = 0
	if (t_1 * math.cos((y - ((z * t) / 3.0)))) <= 2e-73:
		tmp = (t_1 * math.cos((y + (-1.0 / (3.0 / (z * t)))))) - t_2
	else:
		tmp = (2.0 * (math.sqrt(x) * math.sqrt(math.pow(math.cos(y), 2.0)))) - t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(2.0 * sqrt(x))
	t_2 = Float64(a / Float64(3.0 * b))
	tmp = 0.0
	if (Float64(t_1 * cos(Float64(y - Float64(Float64(z * t) / 3.0)))) <= 2e-73)
		tmp = Float64(Float64(t_1 * cos(Float64(y + Float64(-1.0 / Float64(3.0 / Float64(z * t)))))) - t_2);
	else
		tmp = Float64(Float64(2.0 * Float64(sqrt(x) * sqrt((cos(y) ^ 2.0)))) - t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 2.0 * sqrt(x);
	t_2 = a / (3.0 * b);
	tmp = 0.0;
	if ((t_1 * cos((y - ((z * t) / 3.0)))) <= 2e-73)
		tmp = (t_1 * cos((y + (-1.0 / (3.0 / (z * t)))))) - t_2;
	else
		tmp = (2.0 * (sqrt(x) * sqrt((cos(y) ^ 2.0)))) - t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a / N[(3.0 * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$1 * N[Cos[N[(y - N[(N[(z * t), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2e-73], N[(N[(t$95$1 * N[Cos[N[(y + N[(-1.0 / N[(3.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], N[(N[(2.0 * N[(N[Sqrt[x], $MachinePrecision] * N[Sqrt[N[Power[N[Cos[y], $MachinePrecision], 2.0], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64))))) < 1.99999999999999999e-73

   1. Initial program 81.0%

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

      1. *-commutative 81.0%

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

      2. *-commutative 81.0%

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

      3. *-commutative 81.0%

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

      4. *-commutative 81.0%

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

      5. associate-/l* 81.0%

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

      6. *-commutative 81.0%

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

   3. Simplified 81.0%

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

      1. associate-*r/ 81.0%

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

      2. clear-num 81.3%

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

   6. Applied egg-rr 81.3%

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

   if 1.99999999999999999e-73 < (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64)))))

   1. Initial program 68.0%

      \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 84.3%

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

      1. add-log-exp 84.3%

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

   5. Applied egg-rr 84.3%

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

      1. rem-log-exp 84.3%

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

      2. add-sqr-sqrt 77.5%

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

      3. sqrt-unprod 84.6%

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

      4. pow2 84.6%

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

   7. Applied egg-rr 84.6%

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

4. Final simplification 83.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) \leq 2 \cdot 10^{-73}:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y + \frac{-1}{\frac{3}{z \cdot t}}\right) - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt{x} \cdot \sqrt{{\cos y}^{2}}\right) - \frac{a}{3 \cdot b}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 77.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \sqrt{x}\\ t_2 := \frac{a}{3 \cdot b}\\ \mathbf{if}\;t\_1 \cdot \cos \left(y - \frac{z \cdot t}{3}\right) \leq 2 \cdot 10^{+152}:\\ \;\;\;\;t\_1 \cdot \cos \left(y - \frac{z \cdot t}{-3}\right) - t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1 - t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* 2.0 (sqrt x))) (t_2 (/ a (* 3.0 b))))
   (if (<= (* t_1 (cos (- y (/ (* z t) 3.0)))) 2e+152)
     (- (* t_1 (cos (- y (/ (* z t) -3.0)))) t_2)
     (- t_1 t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 2.0 * sqrt(x);
	double t_2 = a / (3.0 * b);
	double tmp;
	if ((t_1 * cos((y - ((z * t) / 3.0)))) <= 2e+152) {
		tmp = (t_1 * cos((y - ((z * t) / -3.0)))) - t_2;
	} else {
		tmp = t_1 - t_2;
	}
	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) :: tmp
    t_1 = 2.0d0 * sqrt(x)
    t_2 = a / (3.0d0 * b)
    if ((t_1 * cos((y - ((z * t) / 3.0d0)))) <= 2d+152) then
        tmp = (t_1 * cos((y - ((z * t) / (-3.0d0))))) - t_2
    else
        tmp = t_1 - t_2
    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 = 2.0 * Math.sqrt(x);
	double t_2 = a / (3.0 * b);
	double tmp;
	if ((t_1 * Math.cos((y - ((z * t) / 3.0)))) <= 2e+152) {
		tmp = (t_1 * Math.cos((y - ((z * t) / -3.0)))) - t_2;
	} else {
		tmp = t_1 - t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = 2.0 * math.sqrt(x)
	t_2 = a / (3.0 * b)
	tmp = 0
	if (t_1 * math.cos((y - ((z * t) / 3.0)))) <= 2e+152:
		tmp = (t_1 * math.cos((y - ((z * t) / -3.0)))) - t_2
	else:
		tmp = t_1 - t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(2.0 * sqrt(x))
	t_2 = Float64(a / Float64(3.0 * b))
	tmp = 0.0
	if (Float64(t_1 * cos(Float64(y - Float64(Float64(z * t) / 3.0)))) <= 2e+152)
		tmp = Float64(Float64(t_1 * cos(Float64(y - Float64(Float64(z * t) / -3.0)))) - t_2);
	else
		tmp = Float64(t_1 - t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 2.0 * sqrt(x);
	t_2 = a / (3.0 * b);
	tmp = 0.0;
	if ((t_1 * cos((y - ((z * t) / 3.0)))) <= 2e+152)
		tmp = (t_1 * cos((y - ((z * t) / -3.0)))) - t_2;
	else
		tmp = t_1 - t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a / N[(3.0 * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$1 * N[Cos[N[(y - N[(N[(z * t), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2e+152], N[(N[(t$95$1 * N[Cos[N[(y - N[(N[(z * t), $MachinePrecision] / -3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], N[(t$95$1 - t$95$2), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64))))) < 2.0000000000000001e152

   1. Initial program 84.4%

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

      1. *-commutative 84.4%

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

      2. *-commutative 84.4%

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

      3. *-commutative 84.4%

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

      4. *-commutative 84.4%

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

      5. associate-/l* 84.0%

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

      6. *-commutative 84.0%

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

   3. Simplified 84.0%

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

      1. add-sqr-sqrt 50.3%

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

      2. sqrt-unprod 76.8%

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

      3. associate-*r/ 76.9%

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

      4. associate-*r/ 76.8%

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

      5. frac-times 76.7%

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

      6. metadata-eval 76.7%

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

      7. metadata-eval 76.7%

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

      8. frac-times 76.8%

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

      9. sqrt-unprod 48.5%

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

      10. add-sqr-sqrt 84.5%

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

   6. Applied egg-rr 84.5%

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

   if 2.0000000000000001e152 < (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64)))))

   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. Add Preprocessing

   3. Taylor expanded in z around 0 71.7%

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

   4. Taylor expanded in y around 0 72.2%

      \[\leadsto \color{blue}{2 \cdot \sqrt{x}} - \frac{a}{b \cdot 3} \]
   5. Step-by-step derivation

      1. *-commutative 72.2%

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

   6. Simplified 72.2%

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

4. Final simplification 83.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) \leq 2 \cdot 10^{+152}:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{-3}\right) - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{x} - \frac{a}{3 \cdot b}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 71.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a}{3 \cdot b}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-165} \lor \neg \left(t\_1 \leq 10^{-91}\right):\\ \;\;\;\;2 \cdot \sqrt{x} - t\_1\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt{x} \cdot \cos \left(y + \left(z \cdot t\right) \cdot -0.3333333333333333\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ a (* 3.0 b))))
   (if (or (<= t_1 -5e-165) (not (<= t_1 1e-91)))
     (- (* 2.0 (sqrt x)) t_1)
     (* 2.0 (* (sqrt x) (cos (+ y (* (* z t) -0.3333333333333333))))))))

C

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 <= -5e-165) || !(t_1 <= 1e-91)) {
		tmp = (2.0 * sqrt(x)) - t_1;
	} else {
		tmp = 2.0 * (sqrt(x) * cos((y + ((z * t) * -0.3333333333333333))));
	}
	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) :: tmp
    t_1 = a / (3.0d0 * b)
    if ((t_1 <= (-5d-165)) .or. (.not. (t_1 <= 1d-91))) then
        tmp = (2.0d0 * sqrt(x)) - t_1
    else
        tmp = 2.0d0 * (sqrt(x) * cos((y + ((z * t) * (-0.3333333333333333d0)))))
    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 = a / (3.0 * b);
	double tmp;
	if ((t_1 <= -5e-165) || !(t_1 <= 1e-91)) {
		tmp = (2.0 * Math.sqrt(x)) - t_1;
	} else {
		tmp = 2.0 * (Math.sqrt(x) * Math.cos((y + ((z * t) * -0.3333333333333333))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a / (3.0 * b)
	tmp = 0
	if (t_1 <= -5e-165) or not (t_1 <= 1e-91):
		tmp = (2.0 * math.sqrt(x)) - t_1
	else:
		tmp = 2.0 * (math.sqrt(x) * math.cos((y + ((z * t) * -0.3333333333333333))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a / Float64(3.0 * b))
	tmp = 0.0
	if ((t_1 <= -5e-165) || !(t_1 <= 1e-91))
		tmp = Float64(Float64(2.0 * sqrt(x)) - t_1);
	else
		tmp = Float64(2.0 * Float64(sqrt(x) * cos(Float64(y + Float64(Float64(z * t) * -0.3333333333333333)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a / (3.0 * b);
	tmp = 0.0;
	if ((t_1 <= -5e-165) || ~((t_1 <= 1e-91)))
		tmp = (2.0 * sqrt(x)) - t_1;
	else
		tmp = 2.0 * (sqrt(x) * cos((y + ((z * t) * -0.3333333333333333))));
	end
	tmp_2 = tmp;
end

Wolfram

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, -5e-165], N[Not[LessEqual[t$95$1, 1e-91]], $MachinePrecision]], N[(N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(2.0 * N[(N[Sqrt[x], $MachinePrecision] * N[Cos[N[(y + N[(N[(z * t), $MachinePrecision] * -0.3333333333333333), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 a (*.f64 b #s(literal 3 binary64))) < -4.99999999999999981e-165 or 1.00000000000000002e-91 < (/.f64 a (*.f64 b #s(literal 3 binary64)))

   1. Initial program 78.9%

      \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 89.1%

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

   4. Taylor expanded in y around 0 85.3%

      \[\leadsto \color{blue}{2 \cdot \sqrt{x}} - \frac{a}{b \cdot 3} \]
   5. Step-by-step derivation

      1. *-commutative 85.3%

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

   6. Simplified 85.3%

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

   if -4.99999999999999981e-165 < (/.f64 a (*.f64 b #s(literal 3 binary64))) < 1.00000000000000002e-91

   1. Initial program 61.5%

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

   3. Simplified 61.2%

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

   5. Taylor expanded in x around inf 61.1%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{a}{3 \cdot b} \leq -5 \cdot 10^{-165} \lor \neg \left(\frac{a}{3 \cdot b} \leq 10^{-91}\right):\\ \;\;\;\;2 \cdot \sqrt{x} - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt{x} \cdot \cos \left(y + \left(z \cdot t\right) \cdot -0.3333333333333333\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 72.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a}{3 \cdot b}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-165} \lor \neg \left(t\_1 \leq 5 \cdot 10^{-104}\right):\\ \;\;\;\;2 \cdot \sqrt{x} - t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(\sqrt{x} \cdot \cos y\right) \cdot \left(--2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ a (* 3.0 b))))
   (if (or (<= t_1 -5e-165) (not (<= t_1 5e-104)))
     (- (* 2.0 (sqrt x)) t_1)
     (* (* (sqrt x) (cos y)) (- -2.0)))))

C

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 <= -5e-165) || !(t_1 <= 5e-104)) {
		tmp = (2.0 * sqrt(x)) - t_1;
	} else {
		tmp = (sqrt(x) * cos(y)) * -(-2.0);
	}
	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) :: tmp
    t_1 = a / (3.0d0 * b)
    if ((t_1 <= (-5d-165)) .or. (.not. (t_1 <= 5d-104))) then
        tmp = (2.0d0 * sqrt(x)) - t_1
    else
        tmp = (sqrt(x) * cos(y)) * -(-2.0d0)
    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 = a / (3.0 * b);
	double tmp;
	if ((t_1 <= -5e-165) || !(t_1 <= 5e-104)) {
		tmp = (2.0 * Math.sqrt(x)) - t_1;
	} else {
		tmp = (Math.sqrt(x) * Math.cos(y)) * -(-2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a / (3.0 * b)
	tmp = 0
	if (t_1 <= -5e-165) or not (t_1 <= 5e-104):
		tmp = (2.0 * math.sqrt(x)) - t_1
	else:
		tmp = (math.sqrt(x) * math.cos(y)) * -(-2.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a / Float64(3.0 * b))
	tmp = 0.0
	if ((t_1 <= -5e-165) || !(t_1 <= 5e-104))
		tmp = Float64(Float64(2.0 * sqrt(x)) - t_1);
	else
		tmp = Float64(Float64(sqrt(x) * cos(y)) * Float64(-(-2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a / (3.0 * b);
	tmp = 0.0;
	if ((t_1 <= -5e-165) || ~((t_1 <= 5e-104)))
		tmp = (2.0 * sqrt(x)) - t_1;
	else
		tmp = (sqrt(x) * cos(y)) * -(-2.0);
	end
	tmp_2 = tmp;
end

Wolfram

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, -5e-165], N[Not[LessEqual[t$95$1, 5e-104]], $MachinePrecision]], N[(N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[(N[Sqrt[x], $MachinePrecision] * N[Cos[y], $MachinePrecision]), $MachinePrecision] * (--2.0)), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 a (*.f64 b #s(literal 3 binary64))) < -4.99999999999999981e-165 or 4.99999999999999979e-104 < (/.f64 a (*.f64 b #s(literal 3 binary64)))

   1. Initial program 78.5%

      \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 88.7%

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

   4. Taylor expanded in y around 0 84.9%

      \[\leadsto \color{blue}{2 \cdot \sqrt{x}} - \frac{a}{b \cdot 3} \]
   5. Step-by-step derivation

      1. *-commutative 84.9%

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

   6. Simplified 84.9%

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

   if -4.99999999999999981e-165 < (/.f64 a (*.f64 b #s(literal 3 binary64))) < 4.99999999999999979e-104

   1. Initial program 62.1%

      \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 60.4%

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

      1. associate-/r* 60.4%

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

      2. div-inv 60.4%

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

      3. metadata-eval 60.4%

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

   5. Applied egg-rr 60.4%

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

   6. Taylor expanded in x around -inf 0.0%

      \[\leadsto \color{blue}{-2 \cdot \left(\sqrt{x} \cdot \left(\cos y \cdot {\left(\sqrt{-1}\right)}^{2}\right)\right)} \]
   7. Step-by-step derivation

      1. *-commutative 0.0%

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

      2. unpow2 0.0%

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

      3. rem-square-sqrt 59.9%

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

   8. Simplified 59.9%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{a}{3 \cdot b} \leq -5 \cdot 10^{-165} \lor \neg \left(\frac{a}{3 \cdot b} \leq 5 \cdot 10^{-104}\right):\\ \;\;\;\;2 \cdot \sqrt{x} - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\left(\sqrt{x} \cdot \cos y\right) \cdot \left(--2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 77.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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

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

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

Julia

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

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

Wolfram

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 74.2%

   \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
2. Add Preprocessing

3. Taylor expanded in z around 0 81.2%

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

4. Final simplification 81.2%

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

Alternative 8: 77.1% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (+ (* 2.0 (* (sqrt x) (cos y))) (* -0.3333333333333333 (/ a b))))

C

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

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

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

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

Julia

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

function tmp = code(x, y, z, t, a, b)
	tmp = (2.0 * (sqrt(x) * cos(y))) + (-0.3333333333333333 * (a / b));
end

Wolfram

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 74.2%

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

3. Simplified 73.8%

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

5. Taylor expanded in z around 0 81.1%

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

6. Final simplification 81.1%

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

Alternative 9: 65.5% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ 2 \cdot \sqrt{x} - \frac{a}{3 \cdot b} \end{array} \]

FPCore

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

C

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

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)) - (a / (3.0d0 * b))
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)) - (a / (3.0 * b));
}

Python

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

Julia

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

MATLAB

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

Wolfram

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 74.2%

   \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
2. Add Preprocessing

3. Taylor expanded in z around 0 81.2%

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

4. Taylor expanded in y around 0 72.5%

   \[\leadsto \color{blue}{2 \cdot \sqrt{x}} - \frac{a}{b \cdot 3} \]
5. Step-by-step derivation

   1. *-commutative 72.5%

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

6. Simplified 72.5%

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

7. Final simplification 72.5%

   \[\leadsto 2 \cdot \sqrt{x} - \frac{a}{3 \cdot b} \]
8. Add Preprocessing

Alternative 10: 65.4% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ 2 \cdot \sqrt{x} - 0.3333333333333333 \cdot \frac{a}{b} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (- (* 2.0 (sqrt x)) (* 0.3333333333333333 (/ a b))))

C

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

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)) - (0.3333333333333333d0 * (a / b))
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)) - (0.3333333333333333 * (a / b));
}

Python

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

Julia

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

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = (2.0 * sqrt(x)) - (0.3333333333333333 * (a / b));
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] - N[(0.3333333333333333 * N[(a / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 74.2%

   \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
2. Add Preprocessing

3. Taylor expanded in z around 0 81.2%

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

4. Taylor expanded in y around 0 72.4%

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

Alternative 11: 51.0% accurate, 43.4× speedup

Math

\[\begin{array}{l} \\ \frac{a}{b \cdot -3} \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b) {
	return 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 = a / (b * (-3.0d0))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(a / N[(b * -3.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 74.2%

   \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
2. Add Preprocessing

3. Taylor expanded in z around 0 81.2%

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

4. Taylor expanded in a around inf 57.7%

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

   1. metadata-eval 57.7%

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

   2. distribute-lft-neg-in 57.7%

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

   3. *-commutative 57.7%

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

   4. metadata-eval 57.7%

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

   5. times-frac 57.8%

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

   6. associate-*l/ 57.8%

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

   7. *-rgt-identity 57.8%

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

   8. distribute-neg-frac2 57.8%

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

   9. distribute-rgt-neg-in 57.8%

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

   10. metadata-eval 57.8%

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

6. Simplified 57.8%

   \[\leadsto \color{blue}{\frac{a}{b \cdot -3}} \]
7. Add Preprocessing

Alternative 12: 50.9% accurate, 43.4× speedup

Math

\[\begin{array}{l} \\ \frac{-0.3333333333333333}{\frac{b}{a}} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (/ -0.3333333333333333 (/ b a)))

C

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

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 = (-0.3333333333333333d0) / (b / a)
end function

Java

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

Python

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

Julia

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

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = -0.3333333333333333 / (b / a);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(-0.3333333333333333 / N[(b / a), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 74.2%

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

3. Simplified 73.8%

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

5. Taylor expanded in a around inf 57.7%

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

   1. clear-num 57.7%

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

   2. un-div-inv 57.8%

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

7. Applied egg-rr 57.8%

   \[\leadsto \color{blue}{\frac{-0.3333333333333333}{\frac{b}{a}}} \]
8. Add Preprocessing

Alternative 13: 50.9% accurate, 43.4× speedup

Math

\[\begin{array}{l} \\ -0.3333333333333333 \cdot \frac{a}{b} \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 (* -0.3333333333333333 (/ a b)))

C

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

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 = (-0.3333333333333333d0) * (a / b)
end function

Java

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

Python

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

Julia

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

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = -0.3333333333333333 * (a / b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(-0.3333333333333333 * N[(a / b), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 74.2%

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

3. Simplified 73.8%

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

5. Taylor expanded in a around inf 57.7%

   \[\leadsto \color{blue}{-0.3333333333333333 \cdot \frac{a}{b}} \]
6. Add Preprocessing

Developer Target 1: 74.5% 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 2024165 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, K"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< z -1379333748723514100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (* (* 2 (sqrt x)) (cos (- (/ 1 y) (/ (/ 3333333333333333/10000000000000000 z) t)))) (/ (/ a 3) b)) (if (< z 35162906135559870000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (* (* (sqrt x) 2) (cos (- y (* (/ t 3) z)))) (/ (/ a 3) b)) (- (* (cos (- y (/ (/ 3333333333333333/10000000000000000 z) t))) (* 2 (sqrt x))) (/ (/ a b) 3)))))

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