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

Percentage Accurate: 70.3% → 76.5%

Time: 17.5s

Alternatives: 10

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: 70.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 76.5% 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 71.7%

   \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
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 79.7%

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

5. Simplified 79.7%

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

Alternative 2: 71.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a}{b \cdot 3}\\ t_2 := 2 \cdot \sqrt{x}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-86}:\\ \;\;\;\;a \cdot \left(2 \cdot \frac{\sqrt{x}}{a} + \frac{-0.3333333333333333}{b}\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-197}:\\ \;\;\;\;t\_2 \cdot \cos \left(\left(0.3333333333333333 \cdot z\right) \cdot t - y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2 + \frac{a \cdot -0.3333333333333333}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ a (* b 3.0))) (t_2 (* 2.0 (sqrt x))))
   (if (<= t_1 -5e-86)
     (* a (+ (* 2.0 (/ (sqrt x) a)) (/ -0.3333333333333333 b)))
     (if (<= t_1 5e-197)
       (* t_2 (cos (- (* (* 0.3333333333333333 z) t) y)))
       (+ t_2 (/ (* a -0.3333333333333333) b))))))

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 tmp;
	if (t_1 <= -5e-86) {
		tmp = a * ((2.0 * (sqrt(x) / a)) + (-0.3333333333333333 / b));
	} else if (t_1 <= 5e-197) {
		tmp = t_2 * cos((((0.3333333333333333 * z) * t) - y));
	} else {
		tmp = t_2 + ((a * -0.3333333333333333) / b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a / (b * 3.0d0)
    t_2 = 2.0d0 * sqrt(x)
    if (t_1 <= (-5d-86)) then
        tmp = a * ((2.0d0 * (sqrt(x) / a)) + ((-0.3333333333333333d0) / b))
    else if (t_1 <= 5d-197) then
        tmp = t_2 * cos((((0.3333333333333333d0 * z) * t) - y))
    else
        tmp = t_2 + ((a * (-0.3333333333333333d0)) / b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a / (b * 3.0);
	double t_2 = 2.0 * Math.sqrt(x);
	double tmp;
	if (t_1 <= -5e-86) {
		tmp = a * ((2.0 * (Math.sqrt(x) / a)) + (-0.3333333333333333 / b));
	} else if (t_1 <= 5e-197) {
		tmp = t_2 * Math.cos((((0.3333333333333333 * z) * t) - y));
	} else {
		tmp = t_2 + ((a * -0.3333333333333333) / b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a / (b * 3.0)
	t_2 = 2.0 * math.sqrt(x)
	tmp = 0
	if t_1 <= -5e-86:
		tmp = a * ((2.0 * (math.sqrt(x) / a)) + (-0.3333333333333333 / b))
	elif t_1 <= 5e-197:
		tmp = t_2 * math.cos((((0.3333333333333333 * z) * t) - y))
	else:
		tmp = t_2 + ((a * -0.3333333333333333) / b)
	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))
	tmp = 0.0
	if (t_1 <= -5e-86)
		tmp = Float64(a * Float64(Float64(2.0 * Float64(sqrt(x) / a)) + Float64(-0.3333333333333333 / b)));
	elseif (t_1 <= 5e-197)
		tmp = Float64(t_2 * cos(Float64(Float64(Float64(0.3333333333333333 * z) * t) - y)));
	else
		tmp = Float64(t_2 + Float64(Float64(a * -0.3333333333333333) / b));
	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);
	tmp = 0.0;
	if (t_1 <= -5e-86)
		tmp = a * ((2.0 * (sqrt(x) / a)) + (-0.3333333333333333 / b));
	elseif (t_1 <= 5e-197)
		tmp = t_2 * cos((((0.3333333333333333 * z) * t) - y));
	else
		tmp = t_2 + ((a * -0.3333333333333333) / b);
	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]}, If[LessEqual[t$95$1, -5e-86], N[(a * N[(N[(2.0 * N[(N[Sqrt[x], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] + N[(-0.3333333333333333 / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e-197], N[(t$95$2 * N[Cos[N[(N[(N[(0.3333333333333333 * z), $MachinePrecision] * t), $MachinePrecision] - y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(t$95$2 + N[(N[(a * -0.3333333333333333), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 a (*.f64 b #s(literal 3 binary64))) < -4.9999999999999999e-86

   1. Initial program 75.9%

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

   3. Taylor expanded in a around inf

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

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

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(2 \cdot \left(\frac{\cos \left(y - \frac{1}{3} \cdot \left(t \cdot z\right)\right)}{a} \cdot \sqrt{x}\right) - \frac{1}{3} \cdot \frac{1}{b}\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(2 \cdot \left(\frac{\cos \left(y - \frac{1}{3} \cdot \left(t \cdot z\right)\right)}{a} \cdot \sqrt{x}\right) + \color{blue}{\left(\mathsf{neg}\left(\frac{1}{3} \cdot \frac{1}{b}\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(\left(2 \cdot \left(\frac{\cos \left(y - \frac{1}{3} \cdot \left(t \cdot z\right)\right)}{a} \cdot \sqrt{x}\right)\right), \color{blue}{\left(\mathsf{neg}\left(\frac{1}{3} \cdot \frac{1}{b}\right)\right)}\right)\right) \]

   5. Simplified 75.0%

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

   6. Taylor expanded in t around 0

      \[\leadsto \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\color{blue}{\cos \left(\mathsf{neg}\left(y\right)\right)}, \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), a\right)\right), \mathsf{/.f64}\left(\frac{-1}{3}, b\right)\right)\right) \]
   7. Step-by-step derivation

      1. cos-neg N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\cos y, \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), a\right)\right), \mathsf{/.f64}\left(\frac{-1}{3}, b\right)\right)\right) \]

      2. cos-lowering-cos.f64 88.0%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{cos.f64}\left(y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), a\right)\right), \mathsf{/.f64}\left(\frac{-1}{3}, b\right)\right)\right) \]

   8. Simplified 88.0%

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

   9. Taylor expanded in y around 0

      \[\leadsto \color{blue}{a \cdot \left(2 \cdot \left(\frac{1}{a} \cdot \sqrt{x}\right) - \frac{1}{3} \cdot \frac{1}{b}\right)} \]
   10. Step-by-step derivation

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

          \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(2 \cdot \left(\frac{1}{a} \cdot \sqrt{x}\right) - \frac{1}{3} \cdot \frac{1}{b}\right)}\right) \]

       2. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(a, \left(2 \cdot \left(\frac{1}{a} \cdot \sqrt{x}\right) + \color{blue}{\left(\mathsf{neg}\left(\frac{1}{3} \cdot \frac{1}{b}\right)\right)}\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(\left(2 \cdot \left(\frac{1}{a} \cdot \sqrt{x}\right)\right), \color{blue}{\left(\mathsf{neg}\left(\frac{1}{3} \cdot \frac{1}{b}\right)\right)}\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \left(\frac{1}{a} \cdot \sqrt{x}\right)\right), \left(\mathsf{neg}\left(\color{blue}{\frac{1}{3} \cdot \frac{1}{b}}\right)\right)\right)\right) \]

       5. associate-*l/ N/A

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \left(\frac{1 \cdot \sqrt{x}}{a}\right)\right), \left(\mathsf{neg}\left(\frac{1}{3} \cdot \color{blue}{\frac{1}{b}}\right)\right)\right)\right) \]

       6. *-lft-identity N/A

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \left(\frac{\sqrt{x}}{a}\right)\right), \left(\mathsf{neg}\left(\frac{1}{3} \cdot \frac{\color{blue}{1}}{b}\right)\right)\right)\right) \]

       7. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{/.f64}\left(\left(\sqrt{x}\right), a\right)\right), \left(\mathsf{neg}\left(\frac{1}{3} \cdot \color{blue}{\frac{1}{b}}\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{/.f64}\left(\mathsf{sqrt.f64}\left(x\right), a\right)\right), \left(\mathsf{neg}\left(\frac{1}{3} \cdot \frac{\color{blue}{1}}{b}\right)\right)\right)\right) \]

       9. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{/.f64}\left(\mathsf{sqrt.f64}\left(x\right), a\right)\right), \left(\mathsf{neg}\left(\frac{\frac{1}{3} \cdot 1}{b}\right)\right)\right)\right) \]

       10. metadata-eval N/A

           \[\leadsto \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{/.f64}\left(\mathsf{sqrt.f64}\left(x\right), a\right)\right), \left(\mathsf{neg}\left(\frac{\frac{1}{3}}{b}\right)\right)\right)\right) \]

       11. distribute-neg-frac N/A

           \[\leadsto \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{/.f64}\left(\mathsf{sqrt.f64}\left(x\right), a\right)\right), \left(\frac{\mathsf{neg}\left(\frac{1}{3}\right)}{\color{blue}{b}}\right)\right)\right) \]

       12. metadata-eval N/A

           \[\leadsto \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{/.f64}\left(\mathsf{sqrt.f64}\left(x\right), a\right)\right), \left(\frac{\frac{-1}{3}}{b}\right)\right)\right) \]

       13. /-lowering-/.f64 84.7%

           \[\leadsto \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{/.f64}\left(\mathsf{sqrt.f64}\left(x\right), a\right)\right), \mathsf{/.f64}\left(\frac{-1}{3}, \color{blue}{b}\right)\right)\right) \]

   11. Simplified 84.7%

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

   if -4.9999999999999999e-86 < (/.f64 a (*.f64 b #s(literal 3 binary64))) < 5.0000000000000002e-197

   1. Initial program 62.5%

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

   3. Taylor expanded in x around inf

      \[\leadsto \color{blue}{2 \cdot \left(\sqrt{x} \cdot \cos \left(y - \frac{1}{3} \cdot \left(t \cdot z\right)\right)\right)} \]
   4. Step-by-step derivation

      1. associate-*r* N/A

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

      2. *-commutative N/A

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

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

         \[\leadsto \mathsf{*.f64}\left(\cos \left(y - \frac{1}{3} \cdot \left(t \cdot z\right)\right), \color{blue}{\left(2 \cdot \sqrt{x}\right)}\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\cos \left(y + \left(\mathsf{neg}\left(\frac{1}{3} \cdot \left(t \cdot z\right)\right)\right)\right), \left(2 \cdot \sqrt{x}\right)\right) \]

      5. remove-double-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\cos \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(y\right)\right)\right)\right) + \left(\mathsf{neg}\left(\frac{1}{3} \cdot \left(t \cdot z\right)\right)\right)\right), \left(2 \cdot \sqrt{x}\right)\right) \]

      6. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\cos \left(\left(\mathsf{neg}\left(-1 \cdot y\right)\right) + \left(\mathsf{neg}\left(\frac{1}{3} \cdot \left(t \cdot z\right)\right)\right)\right), \left(2 \cdot \sqrt{x}\right)\right) \]

      7. distribute-neg-in N/A

         \[\leadsto \mathsf{*.f64}\left(\cos \left(\mathsf{neg}\left(\left(-1 \cdot y + \frac{1}{3} \cdot \left(t \cdot z\right)\right)\right)\right), \left(2 \cdot \sqrt{x}\right)\right) \]

      8. cos-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\cos \left(-1 \cdot y + \frac{1}{3} \cdot \left(t \cdot z\right)\right), \left(\color{blue}{2} \cdot \sqrt{x}\right)\right) \]

      9. cos-lowering-cos.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{cos.f64}\left(\left(-1 \cdot y + \frac{1}{3} \cdot \left(t \cdot z\right)\right)\right), \left(\color{blue}{2} \cdot \sqrt{x}\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{cos.f64}\left(\left(\frac{1}{3} \cdot \left(t \cdot z\right) + -1 \cdot y\right)\right), \left(2 \cdot \sqrt{x}\right)\right) \]

      11. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{cos.f64}\left(\left(\frac{1}{3} \cdot \left(t \cdot z\right) + \left(\mathsf{neg}\left(y\right)\right)\right)\right), \left(2 \cdot \sqrt{x}\right)\right) \]

      12. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{cos.f64}\left(\left(\frac{1}{3} \cdot \left(t \cdot z\right) - y\right)\right), \left(2 \cdot \sqrt{x}\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{cos.f64}\left(\mathsf{\_.f64}\left(\left(\frac{1}{3} \cdot \left(t \cdot z\right)\right), y\right)\right), \left(2 \cdot \sqrt{x}\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{cos.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\frac{1}{3}, \left(t \cdot z\right)\right), y\right)\right), \left(2 \cdot \sqrt{x}\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{cos.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\frac{1}{3}, \mathsf{*.f64}\left(t, z\right)\right), y\right)\right), \left(2 \cdot \sqrt{x}\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{cos.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\frac{1}{3}, \mathsf{*.f64}\left(t, z\right)\right), y\right)\right), \mathsf{*.f64}\left(2, \color{blue}{\left(\sqrt{x}\right)}\right)\right) \]

      17. sqrt-lowering-sqrt.f64 60.9%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{cos.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\frac{1}{3}, \mathsf{*.f64}\left(t, z\right)\right), y\right)\right), \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right)\right) \]

   5. Simplified 60.9%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{cos.f64}\left(\mathsf{\_.f64}\left(\left(\frac{1}{3} \cdot \left(z \cdot t\right)\right), y\right)\right), \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right)\right) \]

      2. associate-*r* N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{cos.f64}\left(\mathsf{\_.f64}\left(\left(\left(\frac{1}{3} \cdot z\right) \cdot t\right), y\right)\right), \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(\mathsf{cos.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\left(\frac{1}{3} \cdot z\right), t\right), y\right)\right), \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right)\right) \]

      4. *-lowering-*.f64 61.4%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{cos.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{3}, z\right), t\right), y\right)\right), \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right)\right) \]

   7. Applied egg-rr 61.4%

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

   if 5.0000000000000002e-197 < (/.f64 a (*.f64 b #s(literal 3 binary64)))

   1. Initial program 75.2%

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

   3. Taylor expanded in z around 0

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

      1. cos-lowering-cos.f64 85.5%

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

   5. Simplified 85.5%

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

   6. Taylor expanded in y around 0

      \[\leadsto \color{blue}{2 \cdot \sqrt{x} - \frac{1}{3} \cdot \frac{a}{b}} \]
   7. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto 2 \cdot \sqrt{x} + \color{blue}{\left(\mathsf{neg}\left(\frac{1}{3} \cdot \frac{a}{b}\right)\right)} \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(2 \cdot \sqrt{x}\right), \color{blue}{\left(\mathsf{neg}\left(\frac{1}{3} \cdot \frac{a}{b}\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \left(\sqrt{x}\right)\right), \left(\mathsf{neg}\left(\color{blue}{\frac{1}{3} \cdot \frac{a}{b}}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \left(\mathsf{neg}\left(\frac{1}{3} \cdot \color{blue}{\frac{a}{b}}\right)\right)\right) \]

      5. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \left(\mathsf{neg}\left(\frac{\frac{1}{3} \cdot a}{b}\right)\right)\right) \]

      6. distribute-neg-frac N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \left(\frac{\mathsf{neg}\left(\frac{1}{3} \cdot a\right)}{\color{blue}{b}}\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{/.f64}\left(\left(\mathsf{neg}\left(\frac{1}{3} \cdot a\right)\right), \color{blue}{b}\right)\right) \]

      8. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{/.f64}\left(\left(\left(\mathsf{neg}\left(\frac{1}{3}\right)\right) \cdot a\right), b\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{/.f64}\left(\left(\frac{-1}{3} \cdot a\right), b\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{/.f64}\left(\left(a \cdot \frac{-1}{3}\right), b\right)\right) \]

      11. *-lowering-*.f64 81.4%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \frac{-1}{3}\right), b\right)\right) \]

   8. Simplified 81.4%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{a}{b \cdot 3} \leq -5 \cdot 10^{-86}:\\ \;\;\;\;a \cdot \left(2 \cdot \frac{\sqrt{x}}{a} + \frac{-0.3333333333333333}{b}\right)\\ \mathbf{elif}\;\frac{a}{b \cdot 3} \leq 5 \cdot 10^{-197}:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(\left(0.3333333333333333 \cdot z\right) \cdot t - y\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{x} + \frac{a \cdot -0.3333333333333333}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 71.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a}{b \cdot 3}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-86}:\\ \;\;\;\;a \cdot \left(2 \cdot \frac{\sqrt{x}}{a} + \frac{-0.3333333333333333}{b}\right)\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-197}:\\ \;\;\;\;2 \cdot \left(\sqrt{x} \cdot \cos \left(z \cdot \left(0.3333333333333333 \cdot t\right) - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{x} + \frac{a \cdot -0.3333333333333333}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ a (* b 3.0))))
   (if (<= t_1 -5e-86)
     (* a (+ (* 2.0 (/ (sqrt x) a)) (/ -0.3333333333333333 b)))
     (if (<= t_1 5e-197)
       (* 2.0 (* (sqrt x) (cos (- (* z (* 0.3333333333333333 t)) y))))
       (+ (* 2.0 (sqrt x)) (/ (* a -0.3333333333333333) b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a / (b * 3.0);
	double tmp;
	if (t_1 <= -5e-86) {
		tmp = a * ((2.0 * (sqrt(x) / a)) + (-0.3333333333333333 / b));
	} else if (t_1 <= 5e-197) {
		tmp = 2.0 * (sqrt(x) * cos(((z * (0.3333333333333333 * t)) - y)));
	} else {
		tmp = (2.0 * sqrt(x)) + ((a * -0.3333333333333333) / b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a / (b * 3.0d0)
    if (t_1 <= (-5d-86)) then
        tmp = a * ((2.0d0 * (sqrt(x) / a)) + ((-0.3333333333333333d0) / b))
    else if (t_1 <= 5d-197) then
        tmp = 2.0d0 * (sqrt(x) * cos(((z * (0.3333333333333333d0 * t)) - y)))
    else
        tmp = (2.0d0 * sqrt(x)) + ((a * (-0.3333333333333333d0)) / b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a / (b * 3.0);
	double tmp;
	if (t_1 <= -5e-86) {
		tmp = a * ((2.0 * (Math.sqrt(x) / a)) + (-0.3333333333333333 / b));
	} else if (t_1 <= 5e-197) {
		tmp = 2.0 * (Math.sqrt(x) * Math.cos(((z * (0.3333333333333333 * t)) - y)));
	} else {
		tmp = (2.0 * Math.sqrt(x)) + ((a * -0.3333333333333333) / b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a / (b * 3.0)
	tmp = 0
	if t_1 <= -5e-86:
		tmp = a * ((2.0 * (math.sqrt(x) / a)) + (-0.3333333333333333 / b))
	elif t_1 <= 5e-197:
		tmp = 2.0 * (math.sqrt(x) * math.cos(((z * (0.3333333333333333 * t)) - y)))
	else:
		tmp = (2.0 * math.sqrt(x)) + ((a * -0.3333333333333333) / b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a / Float64(b * 3.0))
	tmp = 0.0
	if (t_1 <= -5e-86)
		tmp = Float64(a * Float64(Float64(2.0 * Float64(sqrt(x) / a)) + Float64(-0.3333333333333333 / b)));
	elseif (t_1 <= 5e-197)
		tmp = Float64(2.0 * Float64(sqrt(x) * cos(Float64(Float64(z * Float64(0.3333333333333333 * t)) - y))));
	else
		tmp = Float64(Float64(2.0 * sqrt(x)) + Float64(Float64(a * -0.3333333333333333) / b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a / (b * 3.0);
	tmp = 0.0;
	if (t_1 <= -5e-86)
		tmp = a * ((2.0 * (sqrt(x) / a)) + (-0.3333333333333333 / b));
	elseif (t_1 <= 5e-197)
		tmp = 2.0 * (sqrt(x) * cos(((z * (0.3333333333333333 * t)) - y)));
	else
		tmp = (2.0 * sqrt(x)) + ((a * -0.3333333333333333) / b);
	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]}, If[LessEqual[t$95$1, -5e-86], N[(a * N[(N[(2.0 * N[(N[Sqrt[x], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] + N[(-0.3333333333333333 / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e-197], N[(2.0 * N[(N[Sqrt[x], $MachinePrecision] * N[Cos[N[(N[(z * N[(0.3333333333333333 * t), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] + N[(N[(a * -0.3333333333333333), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 a (*.f64 b #s(literal 3 binary64))) < -4.9999999999999999e-86

   1. Initial program 75.9%

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

   3. Taylor expanded in a around inf

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

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

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(2 \cdot \left(\frac{\cos \left(y - \frac{1}{3} \cdot \left(t \cdot z\right)\right)}{a} \cdot \sqrt{x}\right) - \frac{1}{3} \cdot \frac{1}{b}\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(2 \cdot \left(\frac{\cos \left(y - \frac{1}{3} \cdot \left(t \cdot z\right)\right)}{a} \cdot \sqrt{x}\right) + \color{blue}{\left(\mathsf{neg}\left(\frac{1}{3} \cdot \frac{1}{b}\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(\left(2 \cdot \left(\frac{\cos \left(y - \frac{1}{3} \cdot \left(t \cdot z\right)\right)}{a} \cdot \sqrt{x}\right)\right), \color{blue}{\left(\mathsf{neg}\left(\frac{1}{3} \cdot \frac{1}{b}\right)\right)}\right)\right) \]

   5. Simplified 75.0%

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

   6. Taylor expanded in t around 0

      \[\leadsto \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\color{blue}{\cos \left(\mathsf{neg}\left(y\right)\right)}, \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), a\right)\right), \mathsf{/.f64}\left(\frac{-1}{3}, b\right)\right)\right) \]
   7. Step-by-step derivation

      1. cos-neg N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\cos y, \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), a\right)\right), \mathsf{/.f64}\left(\frac{-1}{3}, b\right)\right)\right) \]

      2. cos-lowering-cos.f64 88.0%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{cos.f64}\left(y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), a\right)\right), \mathsf{/.f64}\left(\frac{-1}{3}, b\right)\right)\right) \]

   8. Simplified 88.0%

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

   9. Taylor expanded in y around 0

      \[\leadsto \color{blue}{a \cdot \left(2 \cdot \left(\frac{1}{a} \cdot \sqrt{x}\right) - \frac{1}{3} \cdot \frac{1}{b}\right)} \]
   10. Step-by-step derivation

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

          \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(2 \cdot \left(\frac{1}{a} \cdot \sqrt{x}\right) - \frac{1}{3} \cdot \frac{1}{b}\right)}\right) \]

       2. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(a, \left(2 \cdot \left(\frac{1}{a} \cdot \sqrt{x}\right) + \color{blue}{\left(\mathsf{neg}\left(\frac{1}{3} \cdot \frac{1}{b}\right)\right)}\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(\left(2 \cdot \left(\frac{1}{a} \cdot \sqrt{x}\right)\right), \color{blue}{\left(\mathsf{neg}\left(\frac{1}{3} \cdot \frac{1}{b}\right)\right)}\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \left(\frac{1}{a} \cdot \sqrt{x}\right)\right), \left(\mathsf{neg}\left(\color{blue}{\frac{1}{3} \cdot \frac{1}{b}}\right)\right)\right)\right) \]

       5. associate-*l/ N/A

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \left(\frac{1 \cdot \sqrt{x}}{a}\right)\right), \left(\mathsf{neg}\left(\frac{1}{3} \cdot \color{blue}{\frac{1}{b}}\right)\right)\right)\right) \]

       6. *-lft-identity N/A

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \left(\frac{\sqrt{x}}{a}\right)\right), \left(\mathsf{neg}\left(\frac{1}{3} \cdot \frac{\color{blue}{1}}{b}\right)\right)\right)\right) \]

       7. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{/.f64}\left(\left(\sqrt{x}\right), a\right)\right), \left(\mathsf{neg}\left(\frac{1}{3} \cdot \color{blue}{\frac{1}{b}}\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{/.f64}\left(\mathsf{sqrt.f64}\left(x\right), a\right)\right), \left(\mathsf{neg}\left(\frac{1}{3} \cdot \frac{\color{blue}{1}}{b}\right)\right)\right)\right) \]

       9. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{/.f64}\left(\mathsf{sqrt.f64}\left(x\right), a\right)\right), \left(\mathsf{neg}\left(\frac{\frac{1}{3} \cdot 1}{b}\right)\right)\right)\right) \]

       10. metadata-eval N/A

           \[\leadsto \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{/.f64}\left(\mathsf{sqrt.f64}\left(x\right), a\right)\right), \left(\mathsf{neg}\left(\frac{\frac{1}{3}}{b}\right)\right)\right)\right) \]

       11. distribute-neg-frac N/A

           \[\leadsto \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{/.f64}\left(\mathsf{sqrt.f64}\left(x\right), a\right)\right), \left(\frac{\mathsf{neg}\left(\frac{1}{3}\right)}{\color{blue}{b}}\right)\right)\right) \]

       12. metadata-eval N/A

           \[\leadsto \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{/.f64}\left(\mathsf{sqrt.f64}\left(x\right), a\right)\right), \left(\frac{\frac{-1}{3}}{b}\right)\right)\right) \]

       13. /-lowering-/.f64 84.7%

           \[\leadsto \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{/.f64}\left(\mathsf{sqrt.f64}\left(x\right), a\right)\right), \mathsf{/.f64}\left(\frac{-1}{3}, \color{blue}{b}\right)\right)\right) \]

   11. Simplified 84.7%

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

   if -4.9999999999999999e-86 < (/.f64 a (*.f64 b #s(literal 3 binary64))) < 5.0000000000000002e-197

   1. Initial program 62.5%

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

      1. pow1/2 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \left({x}^{\frac{1}{2}}\right)\right), \mathsf{cos.f64}\left(\mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 3\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      2. sqr-pow N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \left({x}^{\left(\frac{\frac{1}{2}}{2}\right)} \cdot {x}^{\left(\frac{\frac{1}{2}}{2}\right)}\right)\right), \mathsf{cos.f64}\left(\mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 3\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      3. pow2 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \left({\left({x}^{\left(\frac{\frac{1}{2}}{2}\right)}\right)}^{2}\right)\right), \mathsf{cos.f64}\left(\mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 3\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

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

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\left({x}^{\left(\frac{\frac{1}{2}}{2}\right)}\right), 2\right)\right), \mathsf{cos.f64}\left(\mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 3\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      5. pow-lowering-pow.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\mathsf{pow.f64}\left(x, \left(\frac{\frac{1}{2}}{2}\right)\right), 2\right)\right), \mathsf{cos.f64}\left(\mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 3\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      6. metadata-eval 62.2%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\mathsf{pow.f64}\left(x, \frac{1}{4}\right), 2\right)\right), \mathsf{cos.f64}\left(\mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, t\right), 3\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

   4. Applied egg-rr 62.2%

      \[\leadsto \left(2 \cdot \color{blue}{{\left({x}^{0.25}\right)}^{2}}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{2 \cdot \left(\sqrt{x} \cdot \cos \left(y - \frac{1}{3} \cdot \left(t \cdot z\right)\right)\right)} \]
   6. Step-by-step derivation

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

         \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{\left(\sqrt{x} \cdot \cos \left(y - \frac{1}{3} \cdot \left(t \cdot z\right)\right)\right)}\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\left(\sqrt{x}\right), \color{blue}{\cos \left(y - \frac{1}{3} \cdot \left(t \cdot z\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \cos \color{blue}{\left(y - \frac{1}{3} \cdot \left(t \cdot z\right)\right)}\right)\right) \]

      4. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \cos \left(y + \left(\mathsf{neg}\left(\frac{1}{3} \cdot \left(t \cdot z\right)\right)\right)\right)\right)\right) \]

      5. remove-double-neg N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \cos \left(\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(y\right)\right)\right)\right) + \left(\mathsf{neg}\left(\frac{1}{3} \cdot \left(t \cdot z\right)\right)\right)\right)\right)\right) \]

      6. neg-mul-1 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \cos \left(\left(\mathsf{neg}\left(-1 \cdot y\right)\right) + \left(\mathsf{neg}\left(\frac{1}{3} \cdot \left(t \cdot z\right)\right)\right)\right)\right)\right) \]

      7. distribute-neg-in N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \cos \left(\mathsf{neg}\left(\left(-1 \cdot y + \frac{1}{3} \cdot \left(t \cdot z\right)\right)\right)\right)\right)\right) \]

      8. cos-neg N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \cos \left(-1 \cdot y + \frac{1}{3} \cdot \left(t \cdot z\right)\right)\right)\right) \]

      9. cos-lowering-cos.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{cos.f64}\left(\left(-1 \cdot y + \frac{1}{3} \cdot \left(t \cdot z\right)\right)\right)\right)\right) \]

      10. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{cos.f64}\left(\left(\frac{1}{3} \cdot \left(t \cdot z\right) + -1 \cdot y\right)\right)\right)\right) \]

      11. neg-mul-1 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{cos.f64}\left(\left(\frac{1}{3} \cdot \left(t \cdot z\right) + \left(\mathsf{neg}\left(y\right)\right)\right)\right)\right)\right) \]

      12. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{cos.f64}\left(\left(\frac{1}{3} \cdot \left(t \cdot z\right) - y\right)\right)\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{cos.f64}\left(\mathsf{\_.f64}\left(\left(\frac{1}{3} \cdot \left(t \cdot z\right)\right), y\right)\right)\right)\right) \]

      14. associate-*r* N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{cos.f64}\left(\mathsf{\_.f64}\left(\left(\left(\frac{1}{3} \cdot t\right) \cdot z\right), y\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{cos.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\left(\frac{1}{3} \cdot t\right), z\right), y\right)\right)\right)\right) \]

      16. *-lowering-*.f64 61.1%

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{cos.f64}\left(\mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(\frac{1}{3}, t\right), z\right), y\right)\right)\right)\right) \]

   7. Simplified 61.1%

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

   if 5.0000000000000002e-197 < (/.f64 a (*.f64 b #s(literal 3 binary64)))

   1. Initial program 75.2%

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

   3. Taylor expanded in z around 0

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

      1. cos-lowering-cos.f64 85.5%

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

   5. Simplified 85.5%

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

   6. Taylor expanded in y around 0

      \[\leadsto \color{blue}{2 \cdot \sqrt{x} - \frac{1}{3} \cdot \frac{a}{b}} \]
   7. Step-by-step derivation

      1. sub-neg N/A

         \[\leadsto 2 \cdot \sqrt{x} + \color{blue}{\left(\mathsf{neg}\left(\frac{1}{3} \cdot \frac{a}{b}\right)\right)} \]

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

         \[\leadsto \mathsf{+.f64}\left(\left(2 \cdot \sqrt{x}\right), \color{blue}{\left(\mathsf{neg}\left(\frac{1}{3} \cdot \frac{a}{b}\right)\right)}\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \left(\sqrt{x}\right)\right), \left(\mathsf{neg}\left(\color{blue}{\frac{1}{3} \cdot \frac{a}{b}}\right)\right)\right) \]

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

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \left(\mathsf{neg}\left(\frac{1}{3} \cdot \color{blue}{\frac{a}{b}}\right)\right)\right) \]

      5. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \left(\mathsf{neg}\left(\frac{\frac{1}{3} \cdot a}{b}\right)\right)\right) \]

      6. distribute-neg-frac N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \left(\frac{\mathsf{neg}\left(\frac{1}{3} \cdot a\right)}{\color{blue}{b}}\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{/.f64}\left(\left(\mathsf{neg}\left(\frac{1}{3} \cdot a\right)\right), \color{blue}{b}\right)\right) \]

      8. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{/.f64}\left(\left(\left(\mathsf{neg}\left(\frac{1}{3}\right)\right) \cdot a\right), b\right)\right) \]

      9. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{/.f64}\left(\left(\frac{-1}{3} \cdot a\right), b\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{/.f64}\left(\left(a \cdot \frac{-1}{3}\right), b\right)\right) \]

      11. *-lowering-*.f64 81.4%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \frac{-1}{3}\right), b\right)\right) \]

   8. Simplified 81.4%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{a}{b \cdot 3} \leq -5 \cdot 10^{-86}:\\ \;\;\;\;a \cdot \left(2 \cdot \frac{\sqrt{x}}{a} + \frac{-0.3333333333333333}{b}\right)\\ \mathbf{elif}\;\frac{a}{b \cdot 3} \leq 5 \cdot 10^{-197}:\\ \;\;\;\;2 \cdot \left(\sqrt{x} \cdot \cos \left(z \cdot \left(0.3333333333333333 \cdot t\right) - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{x} + \frac{a \cdot -0.3333333333333333}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 71.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a}{b \cdot 3}\\ t_2 := 2 \cdot \sqrt{x}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-94}:\\ \;\;\;\;a \cdot \left(2 \cdot \frac{\sqrt{x}}{a} + \frac{-0.3333333333333333}{b}\right)\\ \mathbf{elif}\;t\_1 \leq 10^{-79}:\\ \;\;\;\;t\_2 \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;t\_2 - t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ a (* b 3.0))) (t_2 (* 2.0 (sqrt x))))
   (if (<= t_1 -1e-94)
     (* a (+ (* 2.0 (/ (sqrt x) a)) (/ -0.3333333333333333 b)))
     (if (<= t_1 1e-79) (* t_2 (cos y)) (- t_2 t_1)))))

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 tmp;
	if (t_1 <= -1e-94) {
		tmp = a * ((2.0 * (sqrt(x) / a)) + (-0.3333333333333333 / b));
	} else if (t_1 <= 1e-79) {
		tmp = t_2 * cos(y);
	} else {
		tmp = t_2 - t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a / (b * 3.0d0)
    t_2 = 2.0d0 * sqrt(x)
    if (t_1 <= (-1d-94)) then
        tmp = a * ((2.0d0 * (sqrt(x) / a)) + ((-0.3333333333333333d0) / b))
    else if (t_1 <= 1d-79) then
        tmp = t_2 * cos(y)
    else
        tmp = t_2 - t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a / (b * 3.0);
	double t_2 = 2.0 * Math.sqrt(x);
	double tmp;
	if (t_1 <= -1e-94) {
		tmp = a * ((2.0 * (Math.sqrt(x) / a)) + (-0.3333333333333333 / b));
	} else if (t_1 <= 1e-79) {
		tmp = t_2 * Math.cos(y);
	} else {
		tmp = t_2 - t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a / (b * 3.0)
	t_2 = 2.0 * math.sqrt(x)
	tmp = 0
	if t_1 <= -1e-94:
		tmp = a * ((2.0 * (math.sqrt(x) / a)) + (-0.3333333333333333 / b))
	elif t_1 <= 1e-79:
		tmp = t_2 * math.cos(y)
	else:
		tmp = t_2 - t_1
	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))
	tmp = 0.0
	if (t_1 <= -1e-94)
		tmp = Float64(a * Float64(Float64(2.0 * Float64(sqrt(x) / a)) + Float64(-0.3333333333333333 / b)));
	elseif (t_1 <= 1e-79)
		tmp = Float64(t_2 * cos(y));
	else
		tmp = Float64(t_2 - t_1);
	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);
	tmp = 0.0;
	if (t_1 <= -1e-94)
		tmp = a * ((2.0 * (sqrt(x) / a)) + (-0.3333333333333333 / b));
	elseif (t_1 <= 1e-79)
		tmp = t_2 * cos(y);
	else
		tmp = t_2 - t_1;
	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]}, If[LessEqual[t$95$1, -1e-94], N[(a * N[(N[(2.0 * N[(N[Sqrt[x], $MachinePrecision] / a), $MachinePrecision]), $MachinePrecision] + N[(-0.3333333333333333 / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e-79], N[(t$95$2 * N[Cos[y], $MachinePrecision]), $MachinePrecision], N[(t$95$2 - t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 a (*.f64 b #s(literal 3 binary64))) < -9.9999999999999996e-95

   1. Initial program 75.0%

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

   3. Taylor expanded in a around inf

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

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

         \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(2 \cdot \left(\frac{\cos \left(y - \frac{1}{3} \cdot \left(t \cdot z\right)\right)}{a} \cdot \sqrt{x}\right) - \frac{1}{3} \cdot \frac{1}{b}\right)}\right) \]

      2. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(a, \left(2 \cdot \left(\frac{\cos \left(y - \frac{1}{3} \cdot \left(t \cdot z\right)\right)}{a} \cdot \sqrt{x}\right) + \color{blue}{\left(\mathsf{neg}\left(\frac{1}{3} \cdot \frac{1}{b}\right)\right)}\right)\right) \]

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

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(\left(2 \cdot \left(\frac{\cos \left(y - \frac{1}{3} \cdot \left(t \cdot z\right)\right)}{a} \cdot \sqrt{x}\right)\right), \color{blue}{\left(\mathsf{neg}\left(\frac{1}{3} \cdot \frac{1}{b}\right)\right)}\right)\right) \]

   5. Simplified 74.2%

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

   6. Taylor expanded in t around 0

      \[\leadsto \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\color{blue}{\cos \left(\mathsf{neg}\left(y\right)\right)}, \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), a\right)\right), \mathsf{/.f64}\left(\frac{-1}{3}, b\right)\right)\right) \]
   7. Step-by-step derivation

      1. cos-neg N/A

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\cos y, \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), a\right)\right), \mathsf{/.f64}\left(\frac{-1}{3}, b\right)\right)\right) \]

      2. cos-lowering-cos.f64 87.0%

         \[\leadsto \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{cos.f64}\left(y\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), a\right)\right), \mathsf{/.f64}\left(\frac{-1}{3}, b\right)\right)\right) \]

   8. Simplified 87.0%

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

   9. Taylor expanded in y around 0

      \[\leadsto \color{blue}{a \cdot \left(2 \cdot \left(\frac{1}{a} \cdot \sqrt{x}\right) - \frac{1}{3} \cdot \frac{1}{b}\right)} \]
   10. Step-by-step derivation

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

          \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(2 \cdot \left(\frac{1}{a} \cdot \sqrt{x}\right) - \frac{1}{3} \cdot \frac{1}{b}\right)}\right) \]

       2. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(a, \left(2 \cdot \left(\frac{1}{a} \cdot \sqrt{x}\right) + \color{blue}{\left(\mathsf{neg}\left(\frac{1}{3} \cdot \frac{1}{b}\right)\right)}\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(\left(2 \cdot \left(\frac{1}{a} \cdot \sqrt{x}\right)\right), \color{blue}{\left(\mathsf{neg}\left(\frac{1}{3} \cdot \frac{1}{b}\right)\right)}\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \left(\frac{1}{a} \cdot \sqrt{x}\right)\right), \left(\mathsf{neg}\left(\color{blue}{\frac{1}{3} \cdot \frac{1}{b}}\right)\right)\right)\right) \]

       5. associate-*l/ N/A

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \left(\frac{1 \cdot \sqrt{x}}{a}\right)\right), \left(\mathsf{neg}\left(\frac{1}{3} \cdot \color{blue}{\frac{1}{b}}\right)\right)\right)\right) \]

       6. *-lft-identity N/A

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \left(\frac{\sqrt{x}}{a}\right)\right), \left(\mathsf{neg}\left(\frac{1}{3} \cdot \frac{\color{blue}{1}}{b}\right)\right)\right)\right) \]

       7. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{/.f64}\left(\left(\sqrt{x}\right), a\right)\right), \left(\mathsf{neg}\left(\frac{1}{3} \cdot \color{blue}{\frac{1}{b}}\right)\right)\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{/.f64}\left(\mathsf{sqrt.f64}\left(x\right), a\right)\right), \left(\mathsf{neg}\left(\frac{1}{3} \cdot \frac{\color{blue}{1}}{b}\right)\right)\right)\right) \]

       9. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{/.f64}\left(\mathsf{sqrt.f64}\left(x\right), a\right)\right), \left(\mathsf{neg}\left(\frac{\frac{1}{3} \cdot 1}{b}\right)\right)\right)\right) \]

       10. metadata-eval N/A

           \[\leadsto \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{/.f64}\left(\mathsf{sqrt.f64}\left(x\right), a\right)\right), \left(\mathsf{neg}\left(\frac{\frac{1}{3}}{b}\right)\right)\right)\right) \]

       11. distribute-neg-frac N/A

           \[\leadsto \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{/.f64}\left(\mathsf{sqrt.f64}\left(x\right), a\right)\right), \left(\frac{\mathsf{neg}\left(\frac{1}{3}\right)}{\color{blue}{b}}\right)\right)\right) \]

       12. metadata-eval N/A

           \[\leadsto \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{/.f64}\left(\mathsf{sqrt.f64}\left(x\right), a\right)\right), \left(\frac{\frac{-1}{3}}{b}\right)\right)\right) \]

       13. /-lowering-/.f64 83.8%

           \[\leadsto \mathsf{*.f64}\left(a, \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{/.f64}\left(\mathsf{sqrt.f64}\left(x\right), a\right)\right), \mathsf{/.f64}\left(\frac{-1}{3}, \color{blue}{b}\right)\right)\right) \]

   11. Simplified 83.8%

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

   if -9.9999999999999996e-95 < (/.f64 a (*.f64 b #s(literal 3 binary64))) < 1e-79

   1. Initial program 62.5%

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

   3. Taylor expanded in z around 0

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

      1. cos-lowering-cos.f64 62.0%

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

   5. Simplified 62.0%

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

   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 59.5%

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

   8. Simplified 59.5%

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

   if 1e-79 < (/.f64 a (*.f64 b #s(literal 3 binary64)))

   1. Initial program 78.5%

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

   3. Taylor expanded in z around 0

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

      1. cos-lowering-cos.f64 90.5%

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

   5. Simplified 90.5%

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

   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 87.4%

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

   8. Simplified 87.4%

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

Alternative 5: 76.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 71.7%

   \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
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 79.7%

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

5. Simplified 79.7%

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

   1. clear-num N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{cos.f64}\left(y\right)\right), \left(\frac{1}{\color{blue}{\frac{b \cdot 3}{a}}}\right)\right) \]

   2. associate-/r/ N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{cos.f64}\left(y\right)\right), \left(\frac{1}{b \cdot 3} \cdot \color{blue}{a}\right)\right) \]

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

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{*.f64}\left(\left(\frac{1}{b \cdot 3}\right), \color{blue}{a}\right)\right) \]

   4. *-commutative N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{*.f64}\left(\left(\frac{1}{3 \cdot b}\right), a\right)\right) \]

   5. associate-/r* N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{*.f64}\left(\left(\frac{\frac{1}{3}}{b}\right), a\right)\right) \]

   6. metadata-eval N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{*.f64}\left(\left(\frac{\frac{1}{3}}{b}\right), a\right)\right) \]

   7. /-lowering-/.f64 79.7%

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{1}{3}, b\right), a\right)\right) \]

7. Applied egg-rr 79.7%

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

8. Final simplification 79.7%

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

Alternative 6: 65.3% accurate, 2.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 71.7%

   \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
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 79.7%

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

5. Simplified 79.7%

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

6. Taylor expanded in y around 0

   \[\leadsto \color{blue}{2 \cdot \sqrt{x} - \frac{1}{3} \cdot \frac{a}{b}} \]
7. Step-by-step derivation

   1. sub-neg N/A

      \[\leadsto 2 \cdot \sqrt{x} + \color{blue}{\left(\mathsf{neg}\left(\frac{1}{3} \cdot \frac{a}{b}\right)\right)} \]

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

      \[\leadsto \mathsf{+.f64}\left(\left(2 \cdot \sqrt{x}\right), \color{blue}{\left(\mathsf{neg}\left(\frac{1}{3} \cdot \frac{a}{b}\right)\right)}\right) \]

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

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \left(\sqrt{x}\right)\right), \left(\mathsf{neg}\left(\color{blue}{\frac{1}{3} \cdot \frac{a}{b}}\right)\right)\right) \]

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

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \left(\mathsf{neg}\left(\frac{1}{3} \cdot \color{blue}{\frac{a}{b}}\right)\right)\right) \]

   5. associate-*r/ N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \left(\mathsf{neg}\left(\frac{\frac{1}{3} \cdot a}{b}\right)\right)\right) \]

   6. distribute-neg-frac N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \left(\frac{\mathsf{neg}\left(\frac{1}{3} \cdot a\right)}{\color{blue}{b}}\right)\right) \]

   7. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{/.f64}\left(\left(\mathsf{neg}\left(\frac{1}{3} \cdot a\right)\right), \color{blue}{b}\right)\right) \]

   8. distribute-lft-neg-in N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{/.f64}\left(\left(\left(\mathsf{neg}\left(\frac{1}{3}\right)\right) \cdot a\right), b\right)\right) \]

   9. metadata-eval N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{/.f64}\left(\left(\frac{-1}{3} \cdot a\right), b\right)\right) \]

   10. *-commutative N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{/.f64}\left(\left(a \cdot \frac{-1}{3}\right), b\right)\right) \]

   11. *-lowering-*.f64 70.3%

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(a, \frac{-1}{3}\right), b\right)\right) \]

8. Simplified 70.3%

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

Alternative 7: 50.6% 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 71.7%

   \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
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 54.0%

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

5. Simplified 54.0%

   \[\leadsto \color{blue}{\frac{a \cdot -0.3333333333333333}{b}} \]
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 54.0%

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

7. Applied egg-rr 54.0%

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

Alternative 8: 50.5% accurate, 43.4× speedup

Math

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

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(Float64(a * -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[(N[(a * -0.3333333333333333), $MachinePrecision] / b), $MachinePrecision]

Derivation

1. Initial program 71.7%

   \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
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 54.0%

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

5. Simplified 54.0%

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

Alternative 9: 50.5% 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 71.7%

   \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
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 54.0%

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

5. Simplified 54.0%

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

   1. *-commutative N/A

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

   2. associate-*l/ N/A

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

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

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

   4. /-lowering-/.f64 54.0%

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

7. Applied egg-rr 54.0%

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

8. Final simplification 54.0%

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

Alternative 10: 50.5% 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 71.7%

   \[\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{b \cdot 3} \]
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 54.0%

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

5. Simplified 54.0%

   \[\leadsto \color{blue}{\frac{a \cdot -0.3333333333333333}{b}} \]
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 54.0%

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

7. Applied egg-rr 54.0%

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

Developer Target 1: 74.3% 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 2024145 
(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))))