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

Percentage Accurate: 70.9% → 77.7%

Time: 21.6s

Alternatives: 8

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 70.9% 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: 77.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := 2 \cdot \sqrt{x}\\ \mathbf{if}\;t_1 \cdot \cos \left(y - \frac{z \cdot t}{3}\right) \leq 2 \cdot 10^{+92}:\\ \;\;\;\;t_1 \cdot \left(\cos y \cdot \cos \left(\left(z \cdot t\right) \cdot 0.3333333333333333\right) + \sin y \cdot \sin \left(t \cdot \left(z \cdot 0.3333333333333333\right)\right)\right) - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;t_1 \cdot \cos y + \frac{a}{3} \cdot \frac{-1}{b}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* 2.0 (sqrt x))))
   (if (<= (* t_1 (cos (- y (/ (* z t) 3.0)))) 2e+92)
     (-
      (*
       t_1
       (+
        (* (cos y) (cos (* (* z t) 0.3333333333333333)))
        (* (sin y) (sin (* t (* z 0.3333333333333333))))))
      (/ a (* 3.0 b)))
     (+ (* t_1 (cos y)) (* (/ a 3.0) (/ -1.0 b))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 2.0 * sqrt(x);
	double tmp;
	if ((t_1 * cos((y - ((z * t) / 3.0)))) <= 2e+92) {
		tmp = (t_1 * ((cos(y) * cos(((z * t) * 0.3333333333333333))) + (sin(y) * sin((t * (z * 0.3333333333333333)))))) - (a / (3.0 * b));
	} else {
		tmp = (t_1 * cos(y)) + ((a / 3.0) * (-1.0 / b));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * sqrt(x)
    if ((t_1 * cos((y - ((z * t) / 3.0d0)))) <= 2d+92) then
        tmp = (t_1 * ((cos(y) * cos(((z * t) * 0.3333333333333333d0))) + (sin(y) * sin((t * (z * 0.3333333333333333d0)))))) - (a / (3.0d0 * b))
    else
        tmp = (t_1 * cos(y)) + ((a / 3.0d0) * ((-1.0d0) / b))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
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 tmp;
	if ((t_1 * Math.cos((y - ((z * t) / 3.0)))) <= 2e+92) {
		tmp = (t_1 * ((Math.cos(y) * Math.cos(((z * t) * 0.3333333333333333))) + (Math.sin(y) * Math.sin((t * (z * 0.3333333333333333)))))) - (a / (3.0 * b));
	} else {
		tmp = (t_1 * Math.cos(y)) + ((a / 3.0) * (-1.0 / b));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = 2.0 * math.sqrt(x)
	tmp = 0
	if (t_1 * math.cos((y - ((z * t) / 3.0)))) <= 2e+92:
		tmp = (t_1 * ((math.cos(y) * math.cos(((z * t) * 0.3333333333333333))) + (math.sin(y) * math.sin((t * (z * 0.3333333333333333)))))) - (a / (3.0 * b))
	else:
		tmp = (t_1 * math.cos(y)) + ((a / 3.0) * (-1.0 / b))
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(2.0 * sqrt(x))
	tmp = 0.0
	if (Float64(t_1 * cos(Float64(y - Float64(Float64(z * t) / 3.0)))) <= 2e+92)
		tmp = Float64(Float64(t_1 * Float64(Float64(cos(y) * cos(Float64(Float64(z * t) * 0.3333333333333333))) + Float64(sin(y) * sin(Float64(t * Float64(z * 0.3333333333333333)))))) - Float64(a / Float64(3.0 * b)));
	else
		tmp = Float64(Float64(t_1 * cos(y)) + Float64(Float64(a / 3.0) * Float64(-1.0 / b)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 2.0 * sqrt(x);
	tmp = 0.0;
	if ((t_1 * cos((y - ((z * t) / 3.0)))) <= 2e+92)
		tmp = (t_1 * ((cos(y) * cos(((z * t) * 0.3333333333333333))) + (sin(y) * sin((t * (z * 0.3333333333333333)))))) - (a / (3.0 * b));
	else
		tmp = (t_1 * cos(y)) + ((a / 3.0) * (-1.0 / b));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$1 * N[Cos[N[(y - N[(N[(z * t), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2e+92], N[(N[(t$95$1 * N[(N[(N[Cos[y], $MachinePrecision] * N[Cos[N[(N[(z * t), $MachinePrecision] * 0.3333333333333333), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] + N[(N[Sin[y], $MachinePrecision] * N[Sin[N[(t * N[(z * 0.3333333333333333), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a / N[(3.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$1 * N[Cos[y], $MachinePrecision]), $MachinePrecision] + N[(N[(a / 3.0), $MachinePrecision] * N[(-1.0 / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3)))) < 2.0000000000000001e92

   1. Initial program 79.6%

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

      1. cos-diff 80.4%

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

      2. div-inv 80.4%

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

      3. metadata-eval 80.4%

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

      4. div-inv 80.4%

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

      5. metadata-eval 80.4%

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

   4. Applied egg-rr 80.4%

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

   5. Taylor expanded in z around 0 80.4%

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

      1. *-commutative 80.4%

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

      2. metadata-eval 80.4%

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

      3. distribute-rgt-neg-in 80.4%

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

      4. associate-*r* 80.4%

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

      5. distribute-rgt-neg-in 80.4%

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

      6. distribute-rgt-neg-in 80.4%

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

      7. metadata-eval 80.4%

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

   7. Simplified 80.4%

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

   if 2.0000000000000001e92 < (*.f64 (*.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3))))

   1. Initial program 38.1%

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

   3. Taylor expanded in z around 0 71.7%

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

      1. *-un-lft-identity 71.7%

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

      2. times-frac 71.7%

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

   5. Applied egg-rr 71.7%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) \leq 2 \cdot 10^{+92}:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \left(\cos y \cdot \cos \left(\left(z \cdot t\right) \cdot 0.3333333333333333\right) + \sin y \cdot \sin \left(t \cdot \left(z \cdot 0.3333333333333333\right)\right)\right) - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \cos y + \frac{a}{3} \cdot \frac{-1}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 71.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \frac{a}{3 \cdot b}\\ t_2 := 2 \cdot \sqrt{x}\\ \mathbf{if}\;t_1 \leq -5 \cdot 10^{-184}:\\ \;\;\;\;t_2 - t_1\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{-159}:\\ \;\;\;\;\sqrt{x} \cdot \left(2 \cdot \cos y\right)\\ \mathbf{else}:\\ \;\;\;\;t_2 - 0.3333333333333333 \cdot \frac{a}{b}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ a (* 3.0 b))) (t_2 (* 2.0 (sqrt x))))
   (if (<= t_1 -5e-184)
     (- t_2 t_1)
     (if (<= t_1 5e-159)
       (* (sqrt x) (* 2.0 (cos y)))
       (- t_2 (* 0.3333333333333333 (/ a b)))))))

C

assert(x < y && y < z && z < t && t < a && a < b);
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_1 <= -5e-184) {
		tmp = t_2 - t_1;
	} else if (t_1 <= 5e-159) {
		tmp = sqrt(x) * (2.0 * cos(y));
	} else {
		tmp = t_2 - (0.3333333333333333 * (a / b));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a / (3.0d0 * b)
    t_2 = 2.0d0 * sqrt(x)
    if (t_1 <= (-5d-184)) then
        tmp = t_2 - t_1
    else if (t_1 <= 5d-159) then
        tmp = sqrt(x) * (2.0d0 * cos(y))
    else
        tmp = t_2 - (0.3333333333333333d0 * (a / b))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
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_1 <= -5e-184) {
		tmp = t_2 - t_1;
	} else if (t_1 <= 5e-159) {
		tmp = Math.sqrt(x) * (2.0 * Math.cos(y));
	} else {
		tmp = t_2 - (0.3333333333333333 * (a / b));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = a / (3.0 * b)
	t_2 = 2.0 * math.sqrt(x)
	tmp = 0
	if t_1 <= -5e-184:
		tmp = t_2 - t_1
	elif t_1 <= 5e-159:
		tmp = math.sqrt(x) * (2.0 * math.cos(y))
	else:
		tmp = t_2 - (0.3333333333333333 * (a / b))
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
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 (t_1 <= -5e-184)
		tmp = Float64(t_2 - t_1);
	elseif (t_1 <= 5e-159)
		tmp = Float64(sqrt(x) * Float64(2.0 * cos(y)));
	else
		tmp = Float64(t_2 - Float64(0.3333333333333333 * Float64(a / b)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a / (3.0 * b);
	t_2 = 2.0 * sqrt(x);
	tmp = 0.0;
	if (t_1 <= -5e-184)
		tmp = t_2 - t_1;
	elseif (t_1 <= 5e-159)
		tmp = sqrt(x) * (2.0 * cos(y));
	else
		tmp = t_2 - (0.3333333333333333 * (a / b));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a / N[(3.0 * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e-184], N[(t$95$2 - t$95$1), $MachinePrecision], If[LessEqual[t$95$1, 5e-159], N[(N[Sqrt[x], $MachinePrecision] * N[(2.0 * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$2 - N[(0.3333333333333333 * N[(a / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 a (*.f64 b 3)) < -5.00000000000000003e-184

   1. Initial program 74.9%

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

   3. Taylor expanded in z around 0 80.6%

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

   4. Taylor expanded in y around 0 76.3%

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

   if -5.00000000000000003e-184 < (/.f64 a (*.f64 b 3)) < 5.00000000000000032e-159

   1. Initial program 54.6%

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

   3. Taylor expanded in z around 0 52.9%

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

   4. Taylor expanded in a around 0 52.9%

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

   5. Taylor expanded in a around 0 52.9%

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

      1. *-commutative 52.9%

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

      2. associate-*l* 52.9%

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

   7. Simplified 52.9%

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

   if 5.00000000000000032e-159 < (/.f64 a (*.f64 b 3))

   1. Initial program 73.6%

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

   3. Taylor expanded in z around 0 87.8%

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

   4. Taylor expanded in a around 0 87.8%

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

   5. Taylor expanded in y around 0 83.0%

      \[\leadsto \color{blue}{2 \cdot \sqrt{x} - 0.3333333333333333 \cdot \frac{a}{b}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 73.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{a}{3 \cdot b} \leq -5 \cdot 10^{-184}:\\ \;\;\;\;2 \cdot \sqrt{x} - \frac{a}{3 \cdot b}\\ \mathbf{elif}\;\frac{a}{3 \cdot b} \leq 5 \cdot 10^{-159}:\\ \;\;\;\;\sqrt{x} \cdot \left(2 \cdot \cos y\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{x} - 0.3333333333333333 \cdot \frac{a}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 76.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = ((2.0d0 * sqrt(x)) * cos(y)) - (0.3333333333333333d0 * (a / b))
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
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

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

Julia

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

MATLAB

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

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] * N[Cos[y], $MachinePrecision]), $MachinePrecision] - N[(0.3333333333333333 * N[(a / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 69.4%

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

3. Taylor expanded in z around 0 76.6%

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

4. Taylor expanded in a around 0 76.6%

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

5. Final simplification 76.6%

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

Alternative 4: 76.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = ((2.0d0 * sqrt(x)) * cos(y)) - (0.3333333333333333d0 / (b / a))
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
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 / (b / a));
}

Python

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

Julia

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

MATLAB

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

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] * N[Cos[y], $MachinePrecision]), $MachinePrecision] - N[(0.3333333333333333 / N[(b / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 69.4%

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

3. Taylor expanded in z around 0 76.6%

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

4. Taylor expanded in a around 0 76.6%

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

   1. expm1-log1p-u 52.8%

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

   2. expm1-udef 47.6%

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

6. Applied egg-rr 47.6%

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

   1. expm1-def 52.8%

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

   2. expm1-log1p 76.6%

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

   3. associate-*r/ 76.6%

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

   4. associate-/l* 76.6%

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

8. Simplified 76.6%

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

9. Final simplification 76.6%

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

Alternative 5: 53.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq -9.8 \cdot 10^{+81} \lor \neg \left(b \leq 3.4 \cdot 10^{+231}\right):\\ \;\;\;\;2 \cdot \sqrt{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{b} \cdot -0.3333333333333333\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -9.8e+81) (not (<= b 3.4e+231)))
   (* 2.0 (sqrt x))
   (* (/ a b) -0.3333333333333333)))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -9.8e+81) || !(b <= 3.4e+231)) {
		tmp = 2.0 * sqrt(x);
	} else {
		tmp = (a / b) * -0.3333333333333333;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-9.8d+81)) .or. (.not. (b <= 3.4d+231))) then
        tmp = 2.0d0 * sqrt(x)
    else
        tmp = (a / b) * (-0.3333333333333333d0)
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -9.8e+81) || !(b <= 3.4e+231)) {
		tmp = 2.0 * Math.sqrt(x);
	} else {
		tmp = (a / b) * -0.3333333333333333;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -9.8e+81) or not (b <= 3.4e+231):
		tmp = 2.0 * math.sqrt(x)
	else:
		tmp = (a / b) * -0.3333333333333333
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -9.8e+81) || !(b <= 3.4e+231))
		tmp = Float64(2.0 * sqrt(x));
	else
		tmp = Float64(Float64(a / b) * -0.3333333333333333);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -9.8e+81) || ~((b <= 3.4e+231)))
		tmp = 2.0 * sqrt(x);
	else
		tmp = (a / b) * -0.3333333333333333;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -9.8e+81], N[Not[LessEqual[b, 3.4e+231]], $MachinePrecision]], N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision], N[(N[(a / b), $MachinePrecision] * -0.3333333333333333), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -9.80000000000000045e81 or 3.4e231 < b

   1. Initial program 55.8%

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

   3. Taylor expanded in z around 0 56.0%

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

   4. Taylor expanded in y around 0 33.1%

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

   5. Taylor expanded in a around 0 26.3%

      \[\leadsto \color{blue}{2 \cdot \sqrt{x}} \]

   if -9.80000000000000045e81 < b < 3.4e231

   1. Initial program 73.3%

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

   3. Taylor expanded in z around 0 82.5%

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

   4. Taylor expanded in a around 0 82.5%

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

   5. Taylor expanded in x around 0 69.8%

      \[\leadsto \color{blue}{-0.3333333333333333 \cdot \frac{a}{b}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 60.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9.8 \cdot 10^{+81} \lor \neg \left(b \leq 3.4 \cdot 10^{+231}\right):\\ \;\;\;\;2 \cdot \sqrt{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{b} \cdot -0.3333333333333333\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 65.8% accurate, 2.0× speedup

Math

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

FPCore

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

C

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

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = (2.0d0 * sqrt(x)) - (0.3333333333333333d0 * (a / b))
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
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

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

Julia

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

MATLAB

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

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := N[(N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] - N[(0.3333333333333333 * N[(a / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 69.4%

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

3. Taylor expanded in z around 0 76.6%

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

4. Taylor expanded in a around 0 76.6%

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

5. Taylor expanded in y around 0 67.2%

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

6. Final simplification 67.2%

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

Alternative 7: 65.8% accurate, 2.0× speedup

Math

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

FPCore

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

C

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

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = (2.0d0 * sqrt(x)) - (0.3333333333333333d0 / (b / a))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := N[(N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] - N[(0.3333333333333333 / N[(b / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 69.4%

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

3. Taylor expanded in z around 0 76.6%

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

4. Taylor expanded in a around 0 76.6%

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

   1. expm1-log1p-u 52.8%

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

   2. expm1-udef 47.6%

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

6. Applied egg-rr 47.6%

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

   1. expm1-def 52.8%

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

   2. expm1-log1p 76.6%

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

   3. associate-*r/ 76.6%

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

   4. associate-/l* 76.6%

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

8. Simplified 76.6%

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

9. Taylor expanded in y around 0 67.2%

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

10. Final simplification 67.2%

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

Alternative 8: 50.8% accurate, 43.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 69.4%

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

3. Taylor expanded in z around 0 76.6%

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

4. Taylor expanded in a around 0 76.6%

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

5. Taylor expanded in x around 0 56.4%

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

6. Final simplification 56.4%

   \[\leadsto \frac{a}{b} \cdot -0.3333333333333333 \]
7. Add Preprocessing

Developer target: 74.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024024 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, K"
  :precision binary64

  :herbie-target
  (if (< z -1.3793337487235141e+129) (- (* (* 2.0 (sqrt x)) (cos (- (/ 1.0 y) (/ (/ 0.3333333333333333 z) t)))) (/ (/ a 3.0) b)) (if (< z 3.516290613555987e+106) (- (* (* (sqrt x) 2.0) (cos (- y (* (/ t 3.0) z)))) (/ (/ a 3.0) b)) (- (* (cos (- y (/ (/ 0.3333333333333333 z) t))) (* 2.0 (sqrt x))) (/ (/ a b) 3.0))))

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