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

Percentage Accurate: 69.3% → 75.6%

Time: 20.3s

Alternatives: 7

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 69.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 75.6% accurate, 1.0× speedup

Math

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

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

Derivation

1. Initial program 69.9%

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

   1. *-commutative 69.9%

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

   2. *-commutative 69.9%

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

   3. *-commutative 69.9%

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

   4. *-commutative 69.9%

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

   5. associate-/l* 69.9%

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

   6. *-commutative 69.9%

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

3. Simplified 69.9%

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

5. Taylor expanded in z around 0 77.2%

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

6. Final simplification 77.2%

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

Alternative 2: 65.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \sqrt{x}\\ \mathbf{if}\;b \leq 4.8 \cdot 10^{+211}:\\ \;\;\;\;t\_1 - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;t\_1 \cdot \cos y - a \cdot \frac{-0.3333333333333333}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* 2.0 (sqrt x))))
   (if (<= b 4.8e+211)
     (- t_1 (/ a (* 3.0 b)))
     (- (* t_1 (cos y)) (* a (/ -0.3333333333333333 b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 2.0 * sqrt(x);
	double tmp;
	if (b <= 4.8e+211) {
		tmp = t_1 - (a / (3.0 * b));
	} else {
		tmp = (t_1 * cos(y)) - (a * (-0.3333333333333333 / b));
	}
	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 = 2.0d0 * sqrt(x)
    if (b <= 4.8d+211) then
        tmp = t_1 - (a / (3.0d0 * b))
    else
        tmp = (t_1 * cos(y)) - (a * ((-0.3333333333333333d0) / b))
    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 tmp;
	if (b <= 4.8e+211) {
		tmp = t_1 - (a / (3.0 * b));
	} else {
		tmp = (t_1 * Math.cos(y)) - (a * (-0.3333333333333333 / b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = 2.0 * math.sqrt(x)
	tmp = 0
	if b <= 4.8e+211:
		tmp = t_1 - (a / (3.0 * b))
	else:
		tmp = (t_1 * math.cos(y)) - (a * (-0.3333333333333333 / b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(2.0 * sqrt(x))
	tmp = 0.0
	if (b <= 4.8e+211)
		tmp = Float64(t_1 - Float64(a / Float64(3.0 * b)));
	else
		tmp = Float64(Float64(t_1 * cos(y)) - Float64(a * Float64(-0.3333333333333333 / b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 2.0 * sqrt(x);
	tmp = 0.0;
	if (b <= 4.8e+211)
		tmp = t_1 - (a / (3.0 * b));
	else
		tmp = (t_1 * cos(y)) - (a * (-0.3333333333333333 / b));
	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]}, If[LessEqual[b, 4.8e+211], N[(t$95$1 - N[(a / N[(3.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t$95$1 * N[Cos[y], $MachinePrecision]), $MachinePrecision] - N[(a * N[(-0.3333333333333333 / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if b < 4.80000000000000035e211

   1. Initial program 71.4%

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

      1. *-commutative 71.4%

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

      2. *-commutative 71.4%

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

      3. *-commutative 71.4%

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

      4. *-commutative 71.4%

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

      5. associate-/l* 71.2%

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

      6. *-commutative 71.2%

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

   3. Simplified 71.2%

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

   5. Taylor expanded in z around 0 79.2%

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

   6. Taylor expanded in y around 0 71.5%

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

   if 4.80000000000000035e211 < b

   1. Initial program 56.9%

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

      1. *-commutative 56.9%

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

      2. *-commutative 56.9%

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

      3. *-commutative 56.9%

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

      4. *-commutative 56.9%

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

      5. associate-/l* 57.9%

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

      6. *-commutative 57.9%

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

   3. Simplified 57.9%

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

   5. Taylor expanded in z around 0 58.5%

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

   6. Taylor expanded in a around 0 58.6%

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

      1. *-commutative 34.9%

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

      2. rem-square-sqrt 21.3%

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

      3. fabs-sqr 21.3%

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

      4. rem-square-sqrt 30.9%

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

      5. associate-*l/ 30.9%

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

      6. associate-*r/ 30.9%

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

      7. *-commutative 30.9%

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

      8. metadata-eval 30.9%

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

      9. associate-/r* 30.9%

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

      10. associate-/r/ 30.9%

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

      11. associate-*r/ 30.9%

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

      12. associate-/r* 30.9%

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

      13. metadata-eval 30.9%

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

      14. fabs-div 30.9%

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

      15. metadata-eval 30.9%

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

      16. metadata-eval 30.9%

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

      17. fabs-div 30.9%

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

      18. rem-square-sqrt 22.0%

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

      19. fabs-sqr 22.0%

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

      20. rem-square-sqrt 30.9%

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

      21. associate-/r/ 30.9%

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

      22. *-commutative 30.9%

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

   8. Simplified 54.6%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 4.8 \cdot 10^{+211}:\\ \;\;\;\;2 \cdot \sqrt{x} - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \cos y - a \cdot \frac{-0.3333333333333333}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((2.0 * sqrt(x)) * cos(y)) - (a * (0.3333333333333333 / 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 * (0.3333333333333333d0 / 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 * (0.3333333333333333 / b));
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 69.9%

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

   1. *-commutative 69.9%

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

   2. *-commutative 69.9%

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

   3. *-commutative 69.9%

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

   4. *-commutative 69.9%

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

   5. associate-/l* 69.9%

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

   6. *-commutative 69.9%

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

3. Simplified 69.9%

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

5. Taylor expanded in z around 0 77.2%

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

6. Taylor expanded in a around 0 77.1%

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

   1. associate-*r/ 67.9%

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

   2. associate-*l/ 67.8%

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

   3. *-commutative 67.8%

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

8. Simplified 77.1%

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

9. Final simplification 77.1%

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

Alternative 4: 16.9% accurate, 2.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b) {
	return (2.0 * sqrt(x)) - (a * (-0.3333333333333333 / 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 * ((-0.3333333333333333d0) / 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 * (-0.3333333333333333 / b));
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 69.9%

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

   1. *-commutative 69.9%

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

   2. *-commutative 69.9%

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

   3. *-commutative 69.9%

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

   4. *-commutative 69.9%

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

   5. associate-/l* 69.9%

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

   6. *-commutative 69.9%

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

3. Simplified 69.9%

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

5. Taylor expanded in z around 0 77.2%

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

6. Taylor expanded in y around 0 67.9%

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

7. Taylor expanded in a around 0 67.9%

   \[\leadsto 2 \cdot \sqrt{x} - \color{blue}{0.3333333333333333 \cdot \frac{a}{b}} \]
8. Step-by-step derivation

   1. *-commutative 67.9%

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

   2. rem-square-sqrt 35.2%

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

   3. fabs-sqr 35.2%

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

   4. rem-square-sqrt 41.3%

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

   5. associate-*l/ 41.3%

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

   6. associate-*r/ 41.3%

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

   7. *-commutative 41.3%

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

   8. metadata-eval 41.3%

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

   9. associate-/r* 41.3%

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

   10. associate-/r/ 41.3%

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

   11. associate-*r/ 41.3%

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

   12. associate-/r* 41.3%

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

   13. metadata-eval 41.3%

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

   14. fabs-div 41.3%

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

   15. metadata-eval 41.3%

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

   16. metadata-eval 41.3%

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

   17. fabs-div 41.3%

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

   18. rem-square-sqrt 9.4%

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

   19. fabs-sqr 9.4%

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

   20. rem-square-sqrt 16.5%

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

   21. associate-/r/ 16.5%

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

   22. *-commutative 16.5%

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

9. Simplified 16.5%

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

10. Final simplification 16.5%

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

Alternative 5: 64.8% accurate, 2.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b) {
	return (2.0 * sqrt(x)) - (a * (0.3333333333333333 / 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 * (0.3333333333333333d0 / 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 * (0.3333333333333333 / b));
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 69.9%

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

   1. *-commutative 69.9%

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

   2. *-commutative 69.9%

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

   3. *-commutative 69.9%

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

   4. *-commutative 69.9%

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

   5. associate-/l* 69.9%

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

   6. *-commutative 69.9%

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

3. Simplified 69.9%

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

5. Taylor expanded in z around 0 77.2%

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

6. Taylor expanded in y around 0 67.9%

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

7. Taylor expanded in a around 0 67.9%

   \[\leadsto 2 \cdot \sqrt{x} - \color{blue}{0.3333333333333333 \cdot \frac{a}{b}} \]
8. Step-by-step derivation

   1. associate-*r/ 67.9%

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

   2. associate-*l/ 67.8%

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

   3. *-commutative 67.8%

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

9. Simplified 67.8%

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

10. Final simplification 67.8%

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

Alternative 6: 64.9% 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 69.9%

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

   1. *-commutative 69.9%

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

   2. *-commutative 69.9%

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

   3. *-commutative 69.9%

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

   4. *-commutative 69.9%

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

   5. associate-/l* 69.9%

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

   6. *-commutative 69.9%

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

3. Simplified 69.9%

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

5. Taylor expanded in z around 0 77.2%

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

6. Taylor expanded in y around 0 67.9%

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

7. Final simplification 67.9%

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

Alternative 7: 2.2% 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 69.9%

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

   1. *-commutative 69.9%

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

   2. *-commutative 69.9%

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

   3. *-commutative 69.9%

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

   4. *-commutative 69.9%

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

   5. associate-/l* 69.9%

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

   6. *-commutative 69.9%

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

3. Simplified 69.9%

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

5. Taylor expanded in z around 0 77.2%

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

6. Taylor expanded in y around 0 67.9%

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

7. Taylor expanded in a around 0 67.9%

   \[\leadsto 2 \cdot \sqrt{x} - \color{blue}{0.3333333333333333 \cdot \frac{a}{b}} \]
8. Step-by-step derivation

   1. *-commutative 67.9%

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

   2. rem-square-sqrt 35.2%

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

   3. fabs-sqr 35.2%

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

   4. rem-square-sqrt 41.3%

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

   5. associate-*l/ 41.3%

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

   6. associate-*r/ 41.3%

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

   7. *-commutative 41.3%

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

   8. metadata-eval 41.3%

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

   9. associate-/r* 41.3%

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

   10. associate-/r/ 41.3%

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

   11. associate-*r/ 41.3%

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

   12. associate-/r* 41.3%

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

   13. metadata-eval 41.3%

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

   14. fabs-div 41.3%

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

   15. metadata-eval 41.3%

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

   16. metadata-eval 41.3%

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

   17. fabs-div 41.3%

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

   18. rem-square-sqrt 9.4%

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

   19. fabs-sqr 9.4%

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

   20. rem-square-sqrt 16.5%

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

   21. associate-/r/ 16.5%

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

   22. *-commutative 16.5%

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

9. Simplified 16.5%

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

10. Taylor expanded in x around 0 2.1%

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

11. Final simplification 2.1%

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

Developer target: 73.5% 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 2024044 
(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))))