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

Percentage Accurate: 70.5% → 76.7%

Time: 16.5s

Alternatives: 9

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: 70.5% 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: 76.7% accurate, 1.0× speedup

Math

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

FPCore

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

Python

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

Julia

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

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((2.0 * sqrt(x)) * cos(y)) - ((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[y], $MachinePrecision]), $MachinePrecision] - N[(N[(a / b), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 68.7%

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

3. Taylor expanded in z around 0

   \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \color{blue}{\cos y}\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]
4. Step-by-step derivation

   1. cos-lowering-cos.f64 75.0%

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

5. Simplified 75.0%

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

   1. associate-/r* N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{cos.f64}\left(y\right)\right), \left(\frac{\frac{a}{b}}{\color{blue}{3}}\right)\right) \]

   2. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{/.f64}\left(\left(\frac{a}{b}\right), \color{blue}{3}\right)\right) \]

   3. /-lowering-/.f64 75.1%

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{/.f64}\left(\mathsf{/.f64}\left(a, b\right), 3\right)\right) \]

7. Applied egg-rr 75.1%

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

Alternative 2: 72.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a}{b \cdot 3}\\ t_2 := 2 \cdot \sqrt{x}\\ t_3 := t\_2 - t\_1\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-125}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-101}:\\ \;\;\;\;t\_2 \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ a (* b 3.0))) (t_2 (* 2.0 (sqrt x))) (t_3 (- t_2 t_1)))
   (if (<= t_1 -1e-125) t_3 (if (<= t_1 5e-101) (* t_2 (cos y)) t_3))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a / (b * 3.0);
	double t_2 = 2.0 * sqrt(x);
	double t_3 = t_2 - t_1;
	double tmp;
	if (t_1 <= -1e-125) {
		tmp = t_3;
	} else if (t_1 <= 5e-101) {
		tmp = t_2 * cos(y);
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = a / (b * 3.0d0)
    t_2 = 2.0d0 * sqrt(x)
    t_3 = t_2 - t_1
    if (t_1 <= (-1d-125)) then
        tmp = t_3
    else if (t_1 <= 5d-101) then
        tmp = t_2 * cos(y)
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a / (b * 3.0);
	double t_2 = 2.0 * Math.sqrt(x);
	double t_3 = t_2 - t_1;
	double tmp;
	if (t_1 <= -1e-125) {
		tmp = t_3;
	} else if (t_1 <= 5e-101) {
		tmp = t_2 * Math.cos(y);
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a / (b * 3.0)
	t_2 = 2.0 * math.sqrt(x)
	t_3 = t_2 - t_1
	tmp = 0
	if t_1 <= -1e-125:
		tmp = t_3
	elif t_1 <= 5e-101:
		tmp = t_2 * math.cos(y)
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a / Float64(b * 3.0))
	t_2 = Float64(2.0 * sqrt(x))
	t_3 = Float64(t_2 - t_1)
	tmp = 0.0
	if (t_1 <= -1e-125)
		tmp = t_3;
	elseif (t_1 <= 5e-101)
		tmp = Float64(t_2 * cos(y));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a / (b * 3.0);
	t_2 = 2.0 * sqrt(x);
	t_3 = t_2 - t_1;
	tmp = 0.0;
	if (t_1 <= -1e-125)
		tmp = t_3;
	elseif (t_1 <= 5e-101)
		tmp = t_2 * cos(y);
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a / N[(b * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 - t$95$1), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-125], t$95$3, If[LessEqual[t$95$1, 5e-101], N[(t$95$2 * N[Cos[y], $MachinePrecision]), $MachinePrecision], t$95$3]]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 a (*.f64 b #s(literal 3 binary64))) < -1.00000000000000001e-125 or 5.0000000000000001e-101 < (/.f64 a (*.f64 b #s(literal 3 binary64)))

   1. Initial program 77.8%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \color{blue}{\cos y}\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]
   4. Step-by-step derivation

      1. cos-lowering-cos.f64 86.1%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

   5. Simplified 86.1%

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

   6. Taylor expanded in y around 0

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(2 \cdot \sqrt{x}\right)}, \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(2, \left(\sqrt{x}\right)\right), \mathsf{/.f64}\left(\color{blue}{a}, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      2. sqrt-lowering-sqrt.f64 81.5%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

   8. Simplified 81.5%

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

   if -1.00000000000000001e-125 < (/.f64 a (*.f64 b #s(literal 3 binary64))) < 5.0000000000000001e-101

   1. Initial program 50.7%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \color{blue}{\cos y}\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]
   4. Step-by-step derivation

      1. cos-lowering-cos.f64 53.1%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

   5. Simplified 53.1%

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

   6. Taylor expanded in x around inf

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

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(2 \cdot \sqrt{x}\right), \color{blue}{\cos y}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \left(\sqrt{x}\right)\right), \cos \color{blue}{y}\right) \]

      4. sqrt-lowering-sqrt.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \cos y\right) \]

      5. cos-lowering-cos.f64 53.1%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{cos.f64}\left(y\right)\right) \]

   8. Simplified 53.1%

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

Alternative 3: 76.7% accurate, 1.0× speedup

Math

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

FPCore

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

Python

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

Julia

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

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((2.0 * sqrt(x)) * cos(y)) - (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[y], $MachinePrecision]), $MachinePrecision] - N[(a / N[(b * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 68.7%

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

3. Taylor expanded in z around 0

   \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \color{blue}{\cos y}\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]
4. Step-by-step derivation

   1. cos-lowering-cos.f64 75.0%

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

5. Simplified 75.0%

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

Alternative 4: 52.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \sqrt{x}\\ \mathbf{if}\;b \cdot 3 \leq -1 \cdot 10^{+101}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;b \cdot 3 \leq 10^{+195}:\\ \;\;\;\;\frac{\frac{a}{b}}{-3}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* 2.0 (sqrt x))))
   (if (<= (* b 3.0) -1e+101)
     t_1
     (if (<= (* b 3.0) 1e+195) (/ (/ a b) -3.0) t_1))))

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 * 3.0) <= -1e+101) {
		tmp = t_1;
	} else if ((b * 3.0) <= 1e+195) {
		tmp = (a / b) / -3.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * sqrt(x)
    if ((b * 3.0d0) <= (-1d+101)) then
        tmp = t_1
    else if ((b * 3.0d0) <= 1d+195) then
        tmp = (a / b) / (-3.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 2.0 * Math.sqrt(x);
	double tmp;
	if ((b * 3.0) <= -1e+101) {
		tmp = t_1;
	} else if ((b * 3.0) <= 1e+195) {
		tmp = (a / b) / -3.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = 2.0 * math.sqrt(x)
	tmp = 0
	if (b * 3.0) <= -1e+101:
		tmp = t_1
	elif (b * 3.0) <= 1e+195:
		tmp = (a / b) / -3.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(2.0 * sqrt(x))
	tmp = 0.0
	if (Float64(b * 3.0) <= -1e+101)
		tmp = t_1;
	elseif (Float64(b * 3.0) <= 1e+195)
		tmp = Float64(Float64(a / b) / -3.0);
	else
		tmp = t_1;
	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 * 3.0) <= -1e+101)
		tmp = t_1;
	elseif ((b * 3.0) <= 1e+195)
		tmp = (a / b) / -3.0;
	else
		tmp = t_1;
	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[N[(b * 3.0), $MachinePrecision], -1e+101], t$95$1, If[LessEqual[N[(b * 3.0), $MachinePrecision], 1e+195], N[(N[(a / b), $MachinePrecision] / -3.0), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 b #s(literal 3 binary64)) < -9.9999999999999998e100 or 9.99999999999999977e194 < (*.f64 b #s(literal 3 binary64))

   1. Initial program 64.0%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \color{blue}{\cos y}\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]
   4. Step-by-step derivation

      1. cos-lowering-cos.f64 65.3%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

   5. Simplified 65.3%

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

   6. Taylor expanded in x around inf

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

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(2 \cdot \sqrt{x}\right), \color{blue}{\cos y}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \left(\sqrt{x}\right)\right), \cos \color{blue}{y}\right) \]

      4. sqrt-lowering-sqrt.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \cos y\right) \]

      5. cos-lowering-cos.f64 53.8%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{cos.f64}\left(y\right)\right) \]

   8. Simplified 53.8%

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

   9. Taylor expanded in y around 0

      \[\leadsto \color{blue}{2 \cdot \sqrt{x}} \]
   10. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{\left(\sqrt{x}\right)}\right) \]

       2. sqrt-lowering-sqrt.f64 30.6%

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right) \]

   11. Simplified 30.6%

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

   if -9.9999999999999998e100 < (*.f64 b #s(literal 3 binary64)) < 9.99999999999999977e194

   1. Initial program 70.6%

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

   3. Taylor expanded in a around inf

      \[\leadsto \color{blue}{\frac{-1}{3} \cdot \frac{a}{b}} \]
   4. Step-by-step derivation

      1. associate-*r/ N/A

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

      2. metadata-eval N/A

         \[\leadsto \frac{\left(\mathsf{neg}\left(\frac{1}{3}\right)\right) \cdot a}{b} \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\left(\mathsf{neg}\left(\frac{1}{3}\right)\right) \cdot a\right), \color{blue}{b}\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{-1}{3} \cdot a\right), b\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(a \cdot \frac{-1}{3}\right), b\right) \]

      6. *-lowering-*.f64 61.5%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \frac{-1}{3}\right), b\right) \]

   5. Simplified 61.5%

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

      1. associate-/l* N/A

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

      2. clear-num N/A

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

      3. un-div-inv N/A

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

      4. div-inv N/A

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

      5. metadata-eval N/A

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

      6. metadata-eval N/A

         \[\leadsto \frac{a}{b \cdot \left(\mathsf{neg}\left(3\right)\right)} \]

      7. distribute-rgt-neg-in N/A

         \[\leadsto \frac{a}{\mathsf{neg}\left(b \cdot 3\right)} \]

      8. distribute-neg-frac2 N/A

         \[\leadsto \mathsf{neg}\left(\frac{a}{b \cdot 3}\right) \]

      9. associate-/r* N/A

         \[\leadsto \mathsf{neg}\left(\frac{\frac{a}{b}}{3}\right) \]

      10. distribute-neg-frac2 N/A

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

      11. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(\frac{a}{b}\right), \color{blue}{\left(\mathsf{neg}\left(3\right)\right)}\right) \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(a, b\right), \left(\mathsf{neg}\left(\color{blue}{3}\right)\right)\right) \]

      13. metadata-eval 61.7%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(a, b\right), -3\right) \]

   7. Applied egg-rr 61.7%

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

Alternative 5: 65.6% accurate, 2.0× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 68.7%

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

3. Taylor expanded in z around 0

   \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \color{blue}{\cos y}\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]
4. Step-by-step derivation

   1. cos-lowering-cos.f64 75.0%

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

5. Simplified 75.0%

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

6. Taylor expanded in y around 0

   \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(2 \cdot \sqrt{x}\right)}, \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]
7. Step-by-step derivation

   1. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(2, \left(\sqrt{x}\right)\right), \mathsf{/.f64}\left(\color{blue}{a}, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

   2. sqrt-lowering-sqrt.f64 64.9%

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

8. Simplified 64.9%

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

Alternative 6: 50.5% accurate, 43.4× speedup

Math

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

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(Float64(a / 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[(N[(a / b), $MachinePrecision] / -3.0), $MachinePrecision]

Derivation

1. Initial program 68.7%

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

3. Taylor expanded in a around inf

   \[\leadsto \color{blue}{\frac{-1}{3} \cdot \frac{a}{b}} \]
4. Step-by-step derivation

   1. associate-*r/ N/A

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

   2. metadata-eval N/A

      \[\leadsto \frac{\left(\mathsf{neg}\left(\frac{1}{3}\right)\right) \cdot a}{b} \]

   3. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\left(\left(\mathsf{neg}\left(\frac{1}{3}\right)\right) \cdot a\right), \color{blue}{b}\right) \]

   4. metadata-eval N/A

      \[\leadsto \mathsf{/.f64}\left(\left(\frac{-1}{3} \cdot a\right), b\right) \]

   5. *-commutative N/A

      \[\leadsto \mathsf{/.f64}\left(\left(a \cdot \frac{-1}{3}\right), b\right) \]

   6. *-lowering-*.f64 48.0%

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \frac{-1}{3}\right), b\right) \]

5. Simplified 48.0%

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

   1. associate-/l* N/A

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

   2. clear-num N/A

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

   3. un-div-inv N/A

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

   4. div-inv N/A

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

   5. metadata-eval N/A

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

   6. metadata-eval N/A

      \[\leadsto \frac{a}{b \cdot \left(\mathsf{neg}\left(3\right)\right)} \]

   7. distribute-rgt-neg-in N/A

      \[\leadsto \frac{a}{\mathsf{neg}\left(b \cdot 3\right)} \]

   8. distribute-neg-frac2 N/A

      \[\leadsto \mathsf{neg}\left(\frac{a}{b \cdot 3}\right) \]

   9. associate-/r* N/A

      \[\leadsto \mathsf{neg}\left(\frac{\frac{a}{b}}{3}\right) \]

   10. distribute-neg-frac2 N/A

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

   11. /-lowering-/.f64 N/A

       \[\leadsto \mathsf{/.f64}\left(\left(\frac{a}{b}\right), \color{blue}{\left(\mathsf{neg}\left(3\right)\right)}\right) \]

   12. /-lowering-/.f64 N/A

       \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(a, b\right), \left(\mathsf{neg}\left(\color{blue}{3}\right)\right)\right) \]

   13. metadata-eval 48.1%

       \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(a, b\right), -3\right) \]

7. Applied egg-rr 48.1%

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

Alternative 7: 50.5% 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 68.7%

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

3. Taylor expanded in a around inf

   \[\leadsto \color{blue}{\frac{-1}{3} \cdot \frac{a}{b}} \]
4. Step-by-step derivation

   1. associate-*r/ N/A

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

   2. metadata-eval N/A

      \[\leadsto \frac{\left(\mathsf{neg}\left(\frac{1}{3}\right)\right) \cdot a}{b} \]

   3. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\left(\left(\mathsf{neg}\left(\frac{1}{3}\right)\right) \cdot a\right), \color{blue}{b}\right) \]

   4. metadata-eval N/A

      \[\leadsto \mathsf{/.f64}\left(\left(\frac{-1}{3} \cdot a\right), b\right) \]

   5. *-commutative N/A

      \[\leadsto \mathsf{/.f64}\left(\left(a \cdot \frac{-1}{3}\right), b\right) \]

   6. *-lowering-*.f64 48.0%

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \frac{-1}{3}\right), b\right) \]

5. Simplified 48.0%

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

   1. *-commutative N/A

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

   2. associate-/l* N/A

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

   3. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\frac{-1}{3}, \color{blue}{\left(\frac{a}{b}\right)}\right) \]

   4. /-lowering-/.f64 47.9%

      \[\leadsto \mathsf{*.f64}\left(\frac{-1}{3}, \mathsf{/.f64}\left(a, \color{blue}{b}\right)\right) \]

7. Applied egg-rr 47.9%

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

   1. *-commutative N/A

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

   2. metadata-eval N/A

      \[\leadsto \frac{a}{b} \cdot \left(\mathsf{neg}\left(\frac{1}{3}\right)\right) \]

   3. distribute-rgt-neg-in N/A

      \[\leadsto \mathsf{neg}\left(\frac{a}{b} \cdot \frac{1}{3}\right) \]

   4. metadata-eval N/A

      \[\leadsto \mathsf{neg}\left(\frac{a}{b} \cdot \frac{1}{3}\right) \]

   5. div-inv N/A

      \[\leadsto \mathsf{neg}\left(\frac{\frac{a}{b}}{3}\right) \]

   6. associate-/r* N/A

      \[\leadsto \mathsf{neg}\left(\frac{a}{b \cdot 3}\right) \]

   7. distribute-neg-frac2 N/A

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

   8. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(a, \color{blue}{\left(\mathsf{neg}\left(b \cdot 3\right)\right)}\right) \]

   9. distribute-rgt-neg-in N/A

      \[\leadsto \mathsf{/.f64}\left(a, \left(b \cdot \color{blue}{\left(\mathsf{neg}\left(3\right)\right)}\right)\right) \]

   10. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, \color{blue}{\left(\mathsf{neg}\left(3\right)\right)}\right)\right) \]

   11. metadata-eval 48.1%

       \[\leadsto \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, -3\right)\right) \]

9. Applied egg-rr 48.1%

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

Alternative 8: 50.5% accurate, 43.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 68.7%

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

3. Taylor expanded in a around inf

   \[\leadsto \color{blue}{\frac{-1}{3} \cdot \frac{a}{b}} \]
4. Step-by-step derivation

   1. associate-*r/ N/A

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

   2. metadata-eval N/A

      \[\leadsto \frac{\left(\mathsf{neg}\left(\frac{1}{3}\right)\right) \cdot a}{b} \]

   3. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\left(\left(\mathsf{neg}\left(\frac{1}{3}\right)\right) \cdot a\right), \color{blue}{b}\right) \]

   4. metadata-eval N/A

      \[\leadsto \mathsf{/.f64}\left(\left(\frac{-1}{3} \cdot a\right), b\right) \]

   5. *-commutative N/A

      \[\leadsto \mathsf{/.f64}\left(\left(a \cdot \frac{-1}{3}\right), b\right) \]

   6. *-lowering-*.f64 48.0%

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \frac{-1}{3}\right), b\right) \]

5. Simplified 48.0%

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

   1. *-commutative N/A

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

   2. associate-/l* N/A

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

   3. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\frac{-1}{3}, \color{blue}{\left(\frac{a}{b}\right)}\right) \]

   4. /-lowering-/.f64 47.9%

      \[\leadsto \mathsf{*.f64}\left(\frac{-1}{3}, \mathsf{/.f64}\left(a, \color{blue}{b}\right)\right) \]

7. Applied egg-rr 47.9%

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

   1. clear-num N/A

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

   2. un-div-inv N/A

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

   3. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\frac{-1}{3}, \color{blue}{\left(\frac{b}{a}\right)}\right) \]

   4. /-lowering-/.f64 48.0%

      \[\leadsto \mathsf{/.f64}\left(\frac{-1}{3}, \mathsf{/.f64}\left(b, \color{blue}{a}\right)\right) \]

9. Applied egg-rr 48.0%

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

Alternative 9: 50.5% accurate, 43.4× speedup

Math

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

FPCore

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

C

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

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) * (-0.3333333333333333d0)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 68.7%

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

3. Taylor expanded in a around inf

   \[\leadsto \color{blue}{\frac{-1}{3} \cdot \frac{a}{b}} \]
4. Step-by-step derivation

   1. associate-*r/ N/A

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

   2. metadata-eval N/A

      \[\leadsto \frac{\left(\mathsf{neg}\left(\frac{1}{3}\right)\right) \cdot a}{b} \]

   3. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\left(\left(\mathsf{neg}\left(\frac{1}{3}\right)\right) \cdot a\right), \color{blue}{b}\right) \]

   4. metadata-eval N/A

      \[\leadsto \mathsf{/.f64}\left(\left(\frac{-1}{3} \cdot a\right), b\right) \]

   5. *-commutative N/A

      \[\leadsto \mathsf{/.f64}\left(\left(a \cdot \frac{-1}{3}\right), b\right) \]

   6. *-lowering-*.f64 48.0%

      \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \frac{-1}{3}\right), b\right) \]

5. Simplified 48.0%

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

   1. *-commutative N/A

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

   2. associate-/l* N/A

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

   3. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\frac{-1}{3}, \color{blue}{\left(\frac{a}{b}\right)}\right) \]

   4. /-lowering-/.f64 47.9%

      \[\leadsto \mathsf{*.f64}\left(\frac{-1}{3}, \mathsf{/.f64}\left(a, \color{blue}{b}\right)\right) \]

7. Applied egg-rr 47.9%

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

8. Final simplification 47.9%

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

Developer Target 1: 74.6% 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 2024150 
(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))))