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

Percentage Accurate: 70.7% → 77.0%

Time: 21.3s

Alternatives: 11

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: 70.7% 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: 77.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b) {
	return (cos(y) * (sqrt(x) * 2.0)) - (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 = (cos(y) * (sqrt(x) * 2.0d0)) - (a / (3.0d0 * b))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 72.8%

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

   1. *-commutative 72.8%

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

   2. *-commutative 72.8%

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

   3. *-commutative 72.8%

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

   4. *-commutative 72.8%

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

   5. associate-/l* 72.9%

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

   6. *-commutative 72.9%

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

3. Simplified 72.9%

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

5. Taylor expanded in z around 0 78.2%

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

   1. associate-*r* 78.2%

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

   2. *-commutative 78.2%

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

   3. *-commutative 78.2%

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

7. Simplified 78.2%

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

Alternative 2: 67.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \sqrt{x} \cdot 2\\ \mathbf{if}\;b \leq -1.1 \cdot 10^{+231}:\\ \;\;\;\;\cos y \cdot t\_1\\ \mathbf{elif}\;b \leq 9.2 \cdot 10^{+232}:\\ \;\;\;\;t\_1 - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt{x} \cdot \cos \left(y + -0.3333333333333333 \cdot \left(t \cdot z\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (sqrt x) 2.0)))
   (if (<= b -1.1e+231)
     (* (cos y) t_1)
     (if (<= b 9.2e+232)
       (- t_1 (/ a (* 3.0 b)))
       (* 2.0 (* (sqrt x) (cos (+ y (* -0.3333333333333333 (* t z))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = sqrt(x) * 2.0;
	double tmp;
	if (b <= -1.1e+231) {
		tmp = cos(y) * t_1;
	} else if (b <= 9.2e+232) {
		tmp = t_1 - (a / (3.0 * b));
	} else {
		tmp = 2.0 * (sqrt(x) * cos((y + (-0.3333333333333333 * (t * z)))));
	}
	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 = sqrt(x) * 2.0d0
    if (b <= (-1.1d+231)) then
        tmp = cos(y) * t_1
    else if (b <= 9.2d+232) then
        tmp = t_1 - (a / (3.0d0 * b))
    else
        tmp = 2.0d0 * (sqrt(x) * cos((y + ((-0.3333333333333333d0) * (t * z)))))
    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 = Math.sqrt(x) * 2.0;
	double tmp;
	if (b <= -1.1e+231) {
		tmp = Math.cos(y) * t_1;
	} else if (b <= 9.2e+232) {
		tmp = t_1 - (a / (3.0 * b));
	} else {
		tmp = 2.0 * (Math.sqrt(x) * Math.cos((y + (-0.3333333333333333 * (t * z)))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = math.sqrt(x) * 2.0
	tmp = 0
	if b <= -1.1e+231:
		tmp = math.cos(y) * t_1
	elif b <= 9.2e+232:
		tmp = t_1 - (a / (3.0 * b))
	else:
		tmp = 2.0 * (math.sqrt(x) * math.cos((y + (-0.3333333333333333 * (t * z)))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(sqrt(x) * 2.0)
	tmp = 0.0
	if (b <= -1.1e+231)
		tmp = Float64(cos(y) * t_1);
	elseif (b <= 9.2e+232)
		tmp = Float64(t_1 - Float64(a / Float64(3.0 * b)));
	else
		tmp = Float64(2.0 * Float64(sqrt(x) * cos(Float64(y + Float64(-0.3333333333333333 * Float64(t * z))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = sqrt(x) * 2.0;
	tmp = 0.0;
	if (b <= -1.1e+231)
		tmp = cos(y) * t_1;
	elseif (b <= 9.2e+232)
		tmp = t_1 - (a / (3.0 * b));
	else
		tmp = 2.0 * (sqrt(x) * cos((y + (-0.3333333333333333 * (t * z)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[Sqrt[x], $MachinePrecision] * 2.0), $MachinePrecision]}, If[LessEqual[b, -1.1e+231], N[(N[Cos[y], $MachinePrecision] * t$95$1), $MachinePrecision], If[LessEqual[b, 9.2e+232], N[(t$95$1 - N[(a / N[(3.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[Sqrt[x], $MachinePrecision] * N[Cos[N[(y + N[(-0.3333333333333333 * N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.09999999999999996e231

   1. Initial program 63.7%

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

   3. Simplified 63.1%

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

      1. expm1-log1p-u 43.5%

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

   6. Applied egg-rr 43.5%

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

   7. Taylor expanded in x around inf 30.2%

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

   8. Taylor expanded in t around 0 52.6%

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

      1. associate-*r* 52.6%

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

   10. Simplified 52.6%

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

   if -1.09999999999999996e231 < b < 9.20000000000000024e232

   1. Initial program 74.2%

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

      1. *-commutative 74.2%

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

      2. *-commutative 74.2%

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

      3. *-commutative 74.2%

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

      4. *-commutative 74.2%

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

      5. associate-/l* 74.4%

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

      6. *-commutative 74.4%

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

   3. Simplified 74.4%

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

   5. Taylor expanded in z around 0 80.6%

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

      1. associate-*r* 80.6%

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

      2. *-commutative 80.6%

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

      3. *-commutative 80.6%

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

   7. Simplified 80.6%

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

   8. Taylor expanded in y around 0 75.8%

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

   if 9.20000000000000024e232 < b

   1. Initial program 65.4%

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

   3. Simplified 65.6%

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

   5. Taylor expanded in x around inf 58.7%

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

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.1 \cdot 10^{+231}:\\ \;\;\;\;\cos y \cdot \left(\sqrt{x} \cdot 2\right)\\ \mathbf{elif}\;b \leq 9.2 \cdot 10^{+232}:\\ \;\;\;\;\sqrt{x} \cdot 2 - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt{x} \cdot \cos \left(y + -0.3333333333333333 \cdot \left(t \cdot z\right)\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 67.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \sqrt{x} \cdot 2\\ \mathbf{if}\;b \leq -8 \cdot 10^{+230} \lor \neg \left(b \leq 4 \cdot 10^{+234}\right):\\ \;\;\;\;\cos y \cdot t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_1 - \frac{a}{3 \cdot b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (sqrt x) 2.0)))
   (if (or (<= b -8e+230) (not (<= b 4e+234)))
     (* (cos y) t_1)
     (- t_1 (/ a (* 3.0 b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = sqrt(x) * 2.0;
	double tmp;
	if ((b <= -8e+230) || !(b <= 4e+234)) {
		tmp = cos(y) * t_1;
	} else {
		tmp = t_1 - (a / (3.0 * 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 = sqrt(x) * 2.0d0
    if ((b <= (-8d+230)) .or. (.not. (b <= 4d+234))) then
        tmp = cos(y) * t_1
    else
        tmp = t_1 - (a / (3.0d0 * 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 = Math.sqrt(x) * 2.0;
	double tmp;
	if ((b <= -8e+230) || !(b <= 4e+234)) {
		tmp = Math.cos(y) * t_1;
	} else {
		tmp = t_1 - (a / (3.0 * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = math.sqrt(x) * 2.0
	tmp = 0
	if (b <= -8e+230) or not (b <= 4e+234):
		tmp = math.cos(y) * t_1
	else:
		tmp = t_1 - (a / (3.0 * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(sqrt(x) * 2.0)
	tmp = 0.0
	if ((b <= -8e+230) || !(b <= 4e+234))
		tmp = Float64(cos(y) * t_1);
	else
		tmp = Float64(t_1 - Float64(a / Float64(3.0 * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = sqrt(x) * 2.0;
	tmp = 0.0;
	if ((b <= -8e+230) || ~((b <= 4e+234)))
		tmp = cos(y) * t_1;
	else
		tmp = t_1 - (a / (3.0 * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[Sqrt[x], $MachinePrecision] * 2.0), $MachinePrecision]}, If[Or[LessEqual[b, -8e+230], N[Not[LessEqual[b, 4e+234]], $MachinePrecision]], N[(N[Cos[y], $MachinePrecision] * t$95$1), $MachinePrecision], N[(t$95$1 - N[(a / N[(3.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if b < -8.0000000000000008e230 or 4.00000000000000007e234 < b

   1. Initial program 64.5%

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

   3. Simplified 64.2%

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

      1. expm1-log1p-u 43.6%

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

   6. Applied egg-rr 43.6%

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

   7. Taylor expanded in x around inf 33.7%

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

   8. Taylor expanded in t around 0 54.4%

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

      1. associate-*r* 54.4%

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

   10. Simplified 54.4%

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

   if -8.0000000000000008e230 < b < 4.00000000000000007e234

   1. Initial program 74.2%

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

      1. *-commutative 74.2%

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

      2. *-commutative 74.2%

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

      3. *-commutative 74.2%

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

      4. *-commutative 74.2%

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

      5. associate-/l* 74.4%

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

      6. *-commutative 74.4%

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

   3. Simplified 74.4%

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

   5. Taylor expanded in z around 0 80.6%

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

      1. associate-*r* 80.6%

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

      2. *-commutative 80.6%

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

      3. *-commutative 80.6%

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

   7. Simplified 80.6%

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

   8. Taylor expanded in y around 0 75.8%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8 \cdot 10^{+230} \lor \neg \left(b \leq 4 \cdot 10^{+234}\right):\\ \;\;\;\;\cos y \cdot \left(\sqrt{x} \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot 2 - \frac{a}{3 \cdot b}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 76.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = (a * ((-0.3333333333333333d0) / b)) + (cos(y) * (sqrt(x) * 2.0d0))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 72.8%

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

   1. *-commutative 72.8%

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

   2. *-commutative 72.8%

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

   3. *-commutative 72.8%

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

   4. *-commutative 72.8%

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

   5. associate-/l* 72.9%

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

   6. *-commutative 72.9%

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

3. Simplified 72.9%

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

5. Taylor expanded in z around 0 78.2%

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

   1. associate-*r* 78.2%

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

   2. *-commutative 78.2%

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

   3. *-commutative 78.2%

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

7. Simplified 78.2%

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

   1. sub-neg 78.2%

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

   2. distribute-neg-frac2 78.2%

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

   3. *-commutative 78.2%

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

   4. distribute-rgt-neg-in 78.2%

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

   5. metadata-eval 78.2%

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

   6. metadata-eval 78.2%

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

   7. div-inv 78.1%

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

   8. un-div-inv 78.1%

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

   9. clear-num 78.1%

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

9. Applied egg-rr 78.1%

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

10. Final simplification 78.1%

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

Alternative 5: 76.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = ((-0.3333333333333333d0) * (a / b)) + (2.0d0 * (cos(y) * sqrt(x)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 72.8%

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

3. Simplified 72.6%

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

5. Taylor expanded in z around 0 77.8%

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

6. Final simplification 77.8%

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

Alternative 6: 66.3% accurate, 2.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b) {
	return (sqrt(x) * 2.0) - (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 = (sqrt(x) * 2.0d0) - (a / (3.0d0 * b))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 72.8%

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

   1. *-commutative 72.8%

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

   2. *-commutative 72.8%

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

   3. *-commutative 72.8%

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

   4. *-commutative 72.8%

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

   5. associate-/l* 72.9%

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

   6. *-commutative 72.9%

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

3. Simplified 72.9%

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

5. Taylor expanded in z around 0 78.2%

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

   1. associate-*r* 78.2%

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

   2. *-commutative 78.2%

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

   3. *-commutative 78.2%

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

7. Simplified 78.2%

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

8. Taylor expanded in y around 0 68.3%

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

9. Final simplification 68.3%

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

Alternative 7: 66.3% accurate, 2.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b) {
	return (sqrt(x) * 2.0) + ((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 = (sqrt(x) * 2.0d0) + ((a * (-0.3333333333333333d0)) / b)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 72.8%

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

   1. *-commutative 72.8%

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

   2. *-commutative 72.8%

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

   3. *-commutative 72.8%

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

   4. *-commutative 72.8%

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

   5. associate-/l* 72.9%

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

   6. *-commutative 72.9%

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

3. Simplified 72.9%

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

5. Taylor expanded in z around 0 78.2%

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

   1. associate-*r* 78.2%

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

   2. *-commutative 78.2%

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

   3. *-commutative 78.2%

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

7. Simplified 78.2%

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

8. Taylor expanded in y around 0 68.0%

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

   1. cancel-sign-sub-inv 68.0%

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

   2. metadata-eval 68.0%

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

   3. associate-*r/ 68.3%

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

10. Simplified 68.3%

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

11. Final simplification 68.3%

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

Alternative 8: 66.3% accurate, 2.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = (a * ((-0.3333333333333333d0) / b)) + (sqrt(x) * 2.0d0)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 72.8%

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

   1. *-commutative 72.8%

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

   2. *-commutative 72.8%

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

   3. *-commutative 72.8%

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

   4. *-commutative 72.8%

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

   5. associate-/l* 72.9%

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

   6. *-commutative 72.9%

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

3. Simplified 72.9%

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

5. Taylor expanded in z around 0 78.2%

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

   1. associate-*r* 78.2%

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

   2. *-commutative 78.2%

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

   3. *-commutative 78.2%

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

7. Simplified 78.2%

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

   1. sub-neg 78.2%

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

   2. distribute-neg-frac2 78.2%

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

   3. *-commutative 78.2%

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

   4. distribute-rgt-neg-in 78.2%

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

   5. metadata-eval 78.2%

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

   6. metadata-eval 78.2%

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

   7. div-inv 78.1%

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

   8. un-div-inv 78.1%

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

   9. clear-num 78.1%

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

9. Applied egg-rr 78.1%

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

10. Taylor expanded in y around 0 68.3%

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

11. Final simplification 68.3%

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

Alternative 9: 51.8% accurate, 43.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 72.8%

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

3. Simplified 72.6%

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

5. Taylor expanded in a around inf 53.9%

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

   1. associate-*r/ 54.3%

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

   2. *-commutative 54.3%

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

   3. associate-*r/ 54.2%

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

7. Simplified 54.2%

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

8. Taylor expanded in a around 0 53.9%

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

   1. *-commutative 53.9%

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

   2. metadata-eval 53.9%

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

   3. distribute-rgt-neg-in 53.9%

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

   4. metadata-eval 53.9%

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

   5. times-frac 54.3%

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

   6. *-rgt-identity 54.3%

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

   7. distribute-neg-frac2 54.3%

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

   8. distribute-rgt-neg-in 54.3%

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

   9. metadata-eval 54.3%

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

10. Simplified 54.3%

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

Alternative 10: 51.7% accurate, 43.4× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t, double a, double b) {
	return 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 = a * ((-0.3333333333333333d0) / b)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 72.8%

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

3. Simplified 72.6%

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

5. Taylor expanded in a around inf 53.9%

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

   1. associate-*r/ 54.3%

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

   2. *-commutative 54.3%

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

   3. associate-*r/ 54.2%

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

7. Simplified 54.2%

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

Alternative 11: 51.7% 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 72.8%

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

3. Simplified 72.6%

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

5. Taylor expanded in a around inf 53.9%

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

Developer Target 1: 74.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{0.3333333333333333}{z}}{t}\\ t_2 := \frac{\frac{a}{3}}{b}\\ t_3 := 2 \cdot \sqrt{x}\\ \mathbf{if}\;z < -1.3793337487235141 \cdot 10^{+129}:\\ \;\;\;\;t\_3 \cdot \cos \left(\frac{1}{y} - t\_1\right) - t\_2\\ \mathbf{elif}\;z < 3.516290613555987 \cdot 10^{+106}:\\ \;\;\;\;\left(\sqrt{x} \cdot 2\right) \cdot \cos \left(y - \frac{t}{3} \cdot z\right) - t\_2\\ \mathbf{else}:\\ \;\;\;\;\cos \left(y - t\_1\right) \cdot t\_3 - \frac{\frac{a}{b}}{3}\\ \end{array} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024133 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, K"
  :precision binary64

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

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