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

Percentage Accurate: 70.5% → 77.0%

Time: 25.0s

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: 70.5% 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: 77.0% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 71.3%

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

   1. associate-*l* 71.3%

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

   2. fma-neg 71.3%

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

   3. sub-neg 71.3%

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

   4. +-commutative 71.3%

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

   5. associate-*l/ 71.2%

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

   6. *-commutative 71.2%

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

   7. distribute-rgt-neg-in 71.2%

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

   8. fma-def 71.2%

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

   9. distribute-frac-neg 71.2%

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

   10. neg-mul-1 71.2%

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

   11. associate-/l* 71.1%

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

   12. associate-/r/ 71.3%

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

   13. metadata-eval 71.3%

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

   14. distribute-neg-frac 71.3%

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

   15. associate-/l/ 71.7%

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

   16. neg-mul-1 71.7%

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

   17. associate-/l* 71.6%

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

3. Simplified 71.6%

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

4. Taylor expanded in t around 0 79.7%

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

5. Final simplification 79.7%

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

Alternative 2: 72.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{a}{b \cdot 3}\\ t_2 := 2 \cdot \sqrt{x}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{-58}:\\ \;\;\;\;t_2 - \frac{a \cdot 0.3333333333333333}{b}\\ \mathbf{elif}\;t_1 \leq 5 \cdot 10^{-110}:\\ \;\;\;\;\sqrt{x} \cdot \left(2 \cdot \cos y\right)\\ \mathbf{else}:\\ \;\;\;\;t_2 - t_1\\ \end{array} \end{array} \]

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 -2e-58)
     (- t_2 (/ (* a 0.3333333333333333) b))
     (if (<= t_1 5e-110) (* (sqrt x) (* 2.0 (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 <= -2e-58) {
		tmp = t_2 - ((a * 0.3333333333333333) / b);
	} else if (t_1 <= 5e-110) {
		tmp = sqrt(x) * (2.0 * 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 <= (-2d-58)) then
        tmp = t_2 - ((a * 0.3333333333333333d0) / b)
    else if (t_1 <= 5d-110) then
        tmp = sqrt(x) * (2.0d0 * 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 <= -2e-58) {
		tmp = t_2 - ((a * 0.3333333333333333) / b);
	} else if (t_1 <= 5e-110) {
		tmp = Math.sqrt(x) * (2.0 * 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 <= -2e-58:
		tmp = t_2 - ((a * 0.3333333333333333) / b)
	elif t_1 <= 5e-110:
		tmp = math.sqrt(x) * (2.0 * 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 <= -2e-58)
		tmp = Float64(t_2 - Float64(Float64(a * 0.3333333333333333) / b));
	elseif (t_1 <= 5e-110)
		tmp = Float64(sqrt(x) * Float64(2.0 * 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 <= -2e-58)
		tmp = t_2 - ((a * 0.3333333333333333) / b);
	elseif (t_1 <= 5e-110)
		tmp = sqrt(x) * (2.0 * 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, -2e-58], N[(t$95$2 - N[(N[(a * 0.3333333333333333), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e-110], N[(N[Sqrt[x], $MachinePrecision] * N[(2.0 * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$2 - t$95$1), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 a (*.f64 b 3)) < -2.0000000000000001e-58

   1. Initial program 85.5%

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

   2. Taylor expanded in z around 0 94.5%

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

      1. associate-*r* 94.5%

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

   4. Simplified 94.5%

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

   5. Taylor expanded in y around 0 93.1%

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

      1. associate-*r/ 93.1%

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

   7. Applied egg-rr 93.1%

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

   if -2.0000000000000001e-58 < (/.f64 a (*.f64 b 3)) < 5e-110

   1. Initial program 58.1%

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

      1. associate-*l* 58.1%

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

      2. fma-neg 58.1%

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

      3. sub-neg 58.1%

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

      4. +-commutative 58.1%

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

      5. associate-*l/ 58.1%

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

      6. *-commutative 58.1%

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

      7. distribute-rgt-neg-in 58.1%

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

      8. fma-def 58.3%

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

      9. distribute-frac-neg 58.3%

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

      10. neg-mul-1 58.3%

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

      11. associate-/l* 58.3%

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

      12. associate-/r/ 58.1%

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

      13. metadata-eval 58.1%

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

      14. distribute-neg-frac 58.1%

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

      15. associate-/l/ 59.2%

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

      16. neg-mul-1 59.2%

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

      17. associate-/l* 59.2%

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

   3. Simplified 59.2%

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

   4. Taylor expanded in t around 0 60.5%

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

   5. Taylor expanded in a around 0 58.7%

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

      1. associate-*r* 58.7%

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

      2. *-commutative 58.7%

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

      3. *-commutative 58.7%

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

      4. *-commutative 58.7%

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

   7. Simplified 58.7%

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

   if 5e-110 < (/.f64 a (*.f64 b 3))

   1. Initial program 72.0%

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

   2. Taylor expanded in z around 0 86.2%

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

      1. associate-*r* 86.2%

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

   4. Simplified 86.2%

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

   5. Taylor expanded in y around 0 83.6%

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

      1. *-commutative 83.6%

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

   7. Simplified 83.6%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{a}{b \cdot 3} \leq -2 \cdot 10^{-58}:\\ \;\;\;\;2 \cdot \sqrt{x} - \frac{a \cdot 0.3333333333333333}{b}\\ \mathbf{elif}\;\frac{a}{b \cdot 3} \leq 5 \cdot 10^{-110}:\\ \;\;\;\;\sqrt{x} \cdot \left(2 \cdot \cos y\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{x} - \frac{a}{b \cdot 3}\\ \end{array} \]

Alternative 3: 77.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 71.3%

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

   1. associate-*l* 71.3%

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

   2. fma-neg 71.3%

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

   3. sub-neg 71.3%

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

   4. +-commutative 71.3%

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

   5. associate-*l/ 71.2%

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

   6. *-commutative 71.2%

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

   7. distribute-rgt-neg-in 71.2%

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

   8. fma-def 71.2%

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

   9. distribute-frac-neg 71.2%

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

   10. neg-mul-1 71.2%

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

   11. associate-/l* 71.1%

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

   12. associate-/r/ 71.3%

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

   13. metadata-eval 71.3%

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

   14. distribute-neg-frac 71.3%

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

   15. associate-/l/ 71.7%

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

   16. neg-mul-1 71.7%

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

   17. associate-/l* 71.6%

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

3. Simplified 71.6%

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

4. Taylor expanded in t around 0 79.7%

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

   1. fma-udef 79.7%

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

   2. *-commutative 79.7%

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

   3. associate-*l* 79.7%

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

   4. *-commutative 79.7%

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

   5. *-commutative 79.7%

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

   6. associate-/l* 79.6%

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

6. Applied egg-rr 79.6%

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

7. Final simplification 79.6%

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

Alternative 4: 65.5% accurate, 2.0× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 71.3%

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

2. Taylor expanded in z around 0 79.3%

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

   1. associate-*r* 79.3%

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

4. Simplified 79.3%

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

5. Taylor expanded in y around 0 67.4%

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

6. Final simplification 67.4%

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

Alternative 5: 65.6% 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 71.3%

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

2. Taylor expanded in z around 0 79.3%

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

   1. associate-*r* 79.3%

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

4. Simplified 79.3%

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

5. Taylor expanded in y around 0 67.4%

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

   1. associate-*r/ 67.5%

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

7. Applied egg-rr 67.5%

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

8. Final simplification 67.5%

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

Alternative 6: 53.8% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6 \cdot 10^{+187} \lor \neg \left(b \leq 5 \cdot 10^{+191}\right):\\ \;\;\;\;2 \cdot \sqrt{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{-0.3333333333333333 \cdot a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -6e+187) (not (<= b 5e+191)))
   (* 2.0 (sqrt x))
   (/ (* -0.3333333333333333 a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -6e+187) || !(b <= 5e+191)) {
		tmp = 2.0 * sqrt(x);
	} else {
		tmp = (-0.3333333333333333 * a) / 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) :: tmp
    if ((b <= (-6d+187)) .or. (.not. (b <= 5d+191))) then
        tmp = 2.0d0 * sqrt(x)
    else
        tmp = ((-0.3333333333333333d0) * a) / 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 tmp;
	if ((b <= -6e+187) || !(b <= 5e+191)) {
		tmp = 2.0 * Math.sqrt(x);
	} else {
		tmp = (-0.3333333333333333 * a) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -6e+187) or not (b <= 5e+191):
		tmp = 2.0 * math.sqrt(x)
	else:
		tmp = (-0.3333333333333333 * a) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -6e+187) || !(b <= 5e+191))
		tmp = Float64(2.0 * sqrt(x));
	else
		tmp = Float64(Float64(-0.3333333333333333 * a) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -6e+187) || ~((b <= 5e+191)))
		tmp = 2.0 * sqrt(x);
	else
		tmp = (-0.3333333333333333 * a) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -6e+187], N[Not[LessEqual[b, 5e+191]], $MachinePrecision]], N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision], N[(N[(-0.3333333333333333 * a), $MachinePrecision] / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -5.9999999999999998e187 or 5.0000000000000002e191 < b

   1. Initial program 62.6%

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

   2. Taylor expanded in z around 0 64.6%

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

      1. associate-*r* 64.6%

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

   4. Simplified 64.6%

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

   5. Taylor expanded in y around 0 48.4%

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

   6. Taylor expanded in a around 0 36.8%

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

   if -5.9999999999999998e187 < b < 5.0000000000000002e191

   1. Initial program 73.8%

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

      1. associate-*l* 73.8%

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

      2. fma-neg 73.8%

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

      3. sub-neg 73.8%

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

      4. +-commutative 73.8%

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

      5. associate-*l/ 73.6%

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

      6. *-commutative 73.6%

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

      7. distribute-rgt-neg-in 73.6%

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

      8. fma-def 73.6%

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

      9. distribute-frac-neg 73.6%

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

      10. neg-mul-1 73.6%

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

      11. associate-/l* 73.4%

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

      12. associate-/r/ 73.8%

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

      13. metadata-eval 73.8%

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

      14. distribute-neg-frac 73.8%

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

      15. associate-/l/ 73.8%

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

      16. neg-mul-1 73.8%

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

      17. associate-/l* 73.8%

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

   3. Simplified 73.7%

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

   4. Taylor expanded in t around 0 83.6%

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

   5. Taylor expanded in y around inf 83.5%

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

      1. associate-*r* 83.5%

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

      2. *-commutative 83.5%

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

      3. *-commutative 83.5%

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

      4. fma-def 83.5%

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

      5. *-commutative 83.5%

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

   7. Simplified 83.5%

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

   8. Taylor expanded in x around 0 63.2%

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

      1. associate-*r/ 63.3%

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

   10. Applied egg-rr 63.3%

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

4. Final simplification 57.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6 \cdot 10^{+187} \lor \neg \left(b \leq 5 \cdot 10^{+191}\right):\\ \;\;\;\;2 \cdot \sqrt{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{-0.3333333333333333 \cdot a}{b}\\ \end{array} \]

Alternative 7: 53.9% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -9.5 \cdot 10^{+181} \lor \neg \left(b \leq 5.5 \cdot 10^{+191}\right):\\ \;\;\;\;2 \cdot \sqrt{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{-a}{b \cdot 3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -9.5e+181) (not (<= b 5.5e+191)))
   (* 2.0 (sqrt x))
   (/ (- a) (* b 3.0))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -9.5e+181) || !(b <= 5.5e+191)) {
		tmp = 2.0 * sqrt(x);
	} else {
		tmp = -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) :: tmp
    if ((b <= (-9.5d+181)) .or. (.not. (b <= 5.5d+191))) then
        tmp = 2.0d0 * sqrt(x)
    else
        tmp = -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 tmp;
	if ((b <= -9.5e+181) || !(b <= 5.5e+191)) {
		tmp = 2.0 * Math.sqrt(x);
	} else {
		tmp = -a / (b * 3.0);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -9.5e+181) or not (b <= 5.5e+191):
		tmp = 2.0 * math.sqrt(x)
	else:
		tmp = -a / (b * 3.0)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -9.5e+181) || !(b <= 5.5e+191))
		tmp = Float64(2.0 * sqrt(x));
	else
		tmp = Float64(Float64(-a) / Float64(b * 3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -9.5e+181) || ~((b <= 5.5e+191)))
		tmp = 2.0 * sqrt(x);
	else
		tmp = -a / (b * 3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -9.5e+181], N[Not[LessEqual[b, 5.5e+191]], $MachinePrecision]], N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision], N[((-a) / N[(b * 3.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -9.50000000000000032e181 or 5.5000000000000002e191 < b

   1. Initial program 62.6%

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

   2. Taylor expanded in z around 0 64.6%

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

      1. associate-*r* 64.6%

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

   4. Simplified 64.6%

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

   5. Taylor expanded in y around 0 48.4%

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

   6. Taylor expanded in a around 0 36.8%

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

   if -9.50000000000000032e181 < b < 5.5000000000000002e191

   1. Initial program 73.8%

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

      1. associate-*l* 73.8%

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

      2. fma-neg 73.8%

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

      3. remove-double-neg 73.8%

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

      4. fma-neg 73.8%

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

      5. remove-double-neg 73.8%

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

      6. associate-*l/ 73.6%

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

      7. *-commutative 73.6%

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

   3. Simplified 73.6%

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

      1. log1p-expm1-u 46.7%

         \[\leadsto 2 \cdot \color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\sqrt{x} \cdot \cos \left(y - \frac{z}{3} \cdot t\right)\right)\right)} - \frac{a}{3 \cdot b} \]

      2. log1p-udef 39.5%

         \[\leadsto 2 \cdot \color{blue}{\log \left(1 + \mathsf{expm1}\left(\sqrt{x} \cdot \cos \left(y - \frac{z}{3} \cdot t\right)\right)\right)} - \frac{a}{3 \cdot b} \]

      3. *-commutative 39.5%

         \[\leadsto 2 \cdot \log \left(1 + \mathsf{expm1}\left(\sqrt{x} \cdot \cos \left(y - \color{blue}{t \cdot \frac{z}{3}}\right)\right)\right) - \frac{a}{3 \cdot b} \]

      4. div-inv 39.6%

         \[\leadsto 2 \cdot \log \left(1 + \mathsf{expm1}\left(\sqrt{x} \cdot \cos \left(y - t \cdot \color{blue}{\left(z \cdot \frac{1}{3}\right)}\right)\right)\right) - \frac{a}{3 \cdot b} \]

      5. metadata-eval 39.6%

         \[\leadsto 2 \cdot \log \left(1 + \mathsf{expm1}\left(\sqrt{x} \cdot \cos \left(y - t \cdot \left(z \cdot \color{blue}{0.3333333333333333}\right)\right)\right)\right) - \frac{a}{3 \cdot b} \]

   5. Applied egg-rr 39.6%

      \[\leadsto 2 \cdot \color{blue}{\log \left(1 + \mathsf{expm1}\left(\sqrt{x} \cdot \cos \left(y - t \cdot \left(z \cdot 0.3333333333333333\right)\right)\right)\right)} - \frac{a}{3 \cdot b} \]

   6. Taylor expanded in x around 0 63.3%

      \[\leadsto 2 \cdot \log \color{blue}{1} - \frac{a}{3 \cdot b} \]
3. Recombined 2 regimes into one program.

4. Final simplification 57.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9.5 \cdot 10^{+181} \lor \neg \left(b \leq 5.5 \cdot 10^{+191}\right):\\ \;\;\;\;2 \cdot \sqrt{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{-a}{b \cdot 3}\\ \end{array} \]

Alternative 8: 50.6% 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 71.3%

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

   1. associate-*l* 71.3%

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

   2. fma-neg 71.3%

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

   3. sub-neg 71.3%

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

   4. +-commutative 71.3%

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

   5. associate-*l/ 71.2%

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

   6. *-commutative 71.2%

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

   7. distribute-rgt-neg-in 71.2%

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

   8. fma-def 71.2%

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

   9. distribute-frac-neg 71.2%

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

   10. neg-mul-1 71.2%

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

   11. associate-/l* 71.1%

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

   12. associate-/r/ 71.3%

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

   13. metadata-eval 71.3%

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

   14. distribute-neg-frac 71.3%

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

   15. associate-/l/ 71.7%

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

   16. neg-mul-1 71.7%

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

   17. associate-/l* 71.6%

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

3. Simplified 71.6%

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

4. Taylor expanded in t around 0 79.7%

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

5. Taylor expanded in y around inf 79.6%

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

   1. associate-*r* 79.6%

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

   2. *-commutative 79.6%

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

   3. *-commutative 79.6%

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

   4. fma-def 79.6%

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

   5. *-commutative 79.6%

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

7. Simplified 79.6%

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

8. Taylor expanded in x around 0 52.2%

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

9. Final simplification 52.2%

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

Alternative 9: 50.7% 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 71.3%

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

   1. associate-*l* 71.3%

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

   2. fma-neg 71.3%

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

   3. sub-neg 71.3%

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

   4. +-commutative 71.3%

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

   5. associate-*l/ 71.2%

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

   6. *-commutative 71.2%

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

   7. distribute-rgt-neg-in 71.2%

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

   8. fma-def 71.2%

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

   9. distribute-frac-neg 71.2%

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

   10. neg-mul-1 71.2%

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

   11. associate-/l* 71.1%

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

   12. associate-/r/ 71.3%

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

   13. metadata-eval 71.3%

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

   14. distribute-neg-frac 71.3%

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

   15. associate-/l/ 71.7%

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

   16. neg-mul-1 71.7%

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

   17. associate-/l* 71.6%

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

3. Simplified 71.6%

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

4. Taylor expanded in t around 0 79.7%

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

5. Taylor expanded in y around inf 79.6%

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

   1. associate-*r* 79.6%

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

   2. *-commutative 79.6%

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

   3. *-commutative 79.6%

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

   4. fma-def 79.6%

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

   5. *-commutative 79.6%

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

7. Simplified 79.6%

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

8. Taylor expanded in x around 0 52.2%

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

   1. expm1-log1p-u 30.5%

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

   2. expm1-udef 25.7%

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

   3. associate-*r/ 25.7%

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

10. Applied egg-rr 25.7%

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

    1. expm1-def 30.5%

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

    2. expm1-log1p 52.3%

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

    3. associate-/l* 52.2%

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

12. Simplified 52.2%

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

13. Final simplification 52.2%

    \[\leadsto \frac{-0.3333333333333333}{\frac{b}{a}} \]

Alternative 10: 50.7% accurate, 43.4× speedup

Math

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

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

Derivation

1. Initial program 71.3%

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

   1. associate-*l* 71.3%

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

   2. fma-neg 71.3%

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

   3. sub-neg 71.3%

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

   4. +-commutative 71.3%

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

   5. associate-*l/ 71.2%

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

   6. *-commutative 71.2%

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

   7. distribute-rgt-neg-in 71.2%

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

   8. fma-def 71.2%

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

   9. distribute-frac-neg 71.2%

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

   10. neg-mul-1 71.2%

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

   11. associate-/l* 71.1%

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

   12. associate-/r/ 71.3%

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

   13. metadata-eval 71.3%

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

   14. distribute-neg-frac 71.3%

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

   15. associate-/l/ 71.7%

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

   16. neg-mul-1 71.7%

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

   17. associate-/l* 71.6%

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

3. Simplified 71.6%

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

4. Taylor expanded in t around 0 79.7%

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

5. Taylor expanded in y around inf 79.6%

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

   1. associate-*r* 79.6%

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

   2. *-commutative 79.6%

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

   3. *-commutative 79.6%

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

   4. fma-def 79.6%

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

   5. *-commutative 79.6%

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

7. Simplified 79.6%

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

8. Taylor expanded in x around 0 52.2%

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

   1. associate-*r/ 52.3%

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

10. Applied egg-rr 52.3%

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

11. Final simplification 52.3%

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

Developer target: 74.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023200 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, K"
  :precision binary64

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

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