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

Percentage Accurate: 70.2% → 77.6%

Time: 30.0s

Alternatives: 13

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: 70.2% 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: 77.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z \cdot t\right) \cdot -0.3333333333333333\\ \mathbf{if}\;\cos \left(y - \frac{z \cdot t}{3}\right) \leq 1:\\ \;\;\;\;2 \cdot \left(\sqrt{x} \cdot \left(\cos y \cdot \cos t\_1 - \sin y \cdot \sin t\_1\right)\right) - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{x} - \frac{\frac{a}{3}}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (* z t) -0.3333333333333333)))
   (if (<= (cos (- y (/ (* z t) 3.0))) 1.0)
     (-
      (* 2.0 (* (sqrt x) (- (* (cos y) (cos t_1)) (* (sin y) (sin t_1)))))
      (/ a (* 3.0 b)))
     (- (* 2.0 (sqrt x)) (/ (/ a 3.0) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * t) * -0.3333333333333333;
	double tmp;
	if (cos((y - ((z * t) / 3.0))) <= 1.0) {
		tmp = (2.0 * (sqrt(x) * ((cos(y) * cos(t_1)) - (sin(y) * sin(t_1))))) - (a / (3.0 * b));
	} else {
		tmp = (2.0 * sqrt(x)) - ((a / 3.0) / b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z * t) * (-0.3333333333333333d0)
    if (cos((y - ((z * t) / 3.0d0))) <= 1.0d0) then
        tmp = (2.0d0 * (sqrt(x) * ((cos(y) * cos(t_1)) - (sin(y) * sin(t_1))))) - (a / (3.0d0 * b))
    else
        tmp = (2.0d0 * sqrt(x)) - ((a / 3.0d0) / b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * t) * -0.3333333333333333;
	double tmp;
	if (Math.cos((y - ((z * t) / 3.0))) <= 1.0) {
		tmp = (2.0 * (Math.sqrt(x) * ((Math.cos(y) * Math.cos(t_1)) - (Math.sin(y) * Math.sin(t_1))))) - (a / (3.0 * b));
	} else {
		tmp = (2.0 * Math.sqrt(x)) - ((a / 3.0) / b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z * t) * -0.3333333333333333
	tmp = 0
	if math.cos((y - ((z * t) / 3.0))) <= 1.0:
		tmp = (2.0 * (math.sqrt(x) * ((math.cos(y) * math.cos(t_1)) - (math.sin(y) * math.sin(t_1))))) - (a / (3.0 * b))
	else:
		tmp = (2.0 * math.sqrt(x)) - ((a / 3.0) / b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z * t) * -0.3333333333333333)
	tmp = 0.0
	if (cos(Float64(y - Float64(Float64(z * t) / 3.0))) <= 1.0)
		tmp = Float64(Float64(2.0 * Float64(sqrt(x) * Float64(Float64(cos(y) * cos(t_1)) - Float64(sin(y) * sin(t_1))))) - Float64(a / Float64(3.0 * b)));
	else
		tmp = Float64(Float64(2.0 * sqrt(x)) - Float64(Float64(a / 3.0) / b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z * t) * -0.3333333333333333;
	tmp = 0.0;
	if (cos((y - ((z * t) / 3.0))) <= 1.0)
		tmp = (2.0 * (sqrt(x) * ((cos(y) * cos(t_1)) - (sin(y) * sin(t_1))))) - (a / (3.0 * b));
	else
		tmp = (2.0 * sqrt(x)) - ((a / 3.0) / b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z * t), $MachinePrecision] * -0.3333333333333333), $MachinePrecision]}, If[LessEqual[N[Cos[N[(y - N[(N[(z * t), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], 1.0], N[(N[(2.0 * N[(N[Sqrt[x], $MachinePrecision] * N[(N[(N[Cos[y], $MachinePrecision] * N[Cos[t$95$1], $MachinePrecision]), $MachinePrecision] - N[(N[Sin[y], $MachinePrecision] * N[Sin[t$95$1], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a / N[(3.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] - N[(N[(a / 3.0), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64)))) < 1

   1. Initial program 81.8%

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

      1. *-commutative 81.8%

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

      2. *-commutative 81.8%

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

      3. *-commutative 81.8%

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

      4. *-commutative 81.8%

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

      5. associate-/l* 81.9%

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

      6. *-commutative 81.9%

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

   3. Simplified 81.9%

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

      1. associate-*r/ 81.8%

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

      2. div-inv 82.1%

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

      3. metadata-eval 82.1%

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

      4. metadata-eval 82.1%

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

      5. cancel-sign-sub-inv 82.1%

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

      6. metadata-eval 82.1%

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

      7. metadata-eval 82.1%

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

      8. div-inv 81.8%

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

      9. metadata-eval 81.8%

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

      10. frac-2neg 81.8%

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

      11. +-commutative 81.8%

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

      12. cos-sum 82.3%

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

      13. div-inv 82.4%

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

      14. metadata-eval 82.4%

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

      15. associate-*r* 82.4%

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

      16. *-commutative 82.4%

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

      17. associate-*r* 82.3%

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

   6. Applied egg-rr 82.3%

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

   7. Taylor expanded in x around 0 82.6%

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

   if 1 < (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64))))

   1. Initial program 0.0%

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

      1. *-commutative 0.0%

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

      2. *-commutative 0.0%

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

      3. *-commutative 0.0%

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

      4. *-commutative 0.0%

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

      5. associate-/l* 0.0%

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

      6. *-commutative 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in z around 0 69.2%

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

   6. Taylor expanded in a around 0 69.0%

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

      1. associate-*r/ 69.1%

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

   8. Simplified 69.1%

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

      1. *-commutative 69.1%

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

      2. metadata-eval 69.1%

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

      3. div-inv 69.1%

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

   10. Applied egg-rr 69.1%

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

   11. Taylor expanded in y around 0 70.0%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\cos \left(y - \frac{z \cdot t}{3}\right) \leq 1:\\ \;\;\;\;2 \cdot \left(\sqrt{x} \cdot \left(\cos y \cdot \cos \left(\left(z \cdot t\right) \cdot -0.3333333333333333\right) - \sin y \cdot \sin \left(\left(z \cdot t\right) \cdot -0.3333333333333333\right)\right)\right) - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{x} - \frac{\frac{a}{3}}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 76.9% accurate, 0.4× speedup

Math

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

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* 2.0 (sqrt x))))
   (if (<= (cos (- y (/ (* z t) 3.0))) 1.0)
     (-
      (* t_1 (log (exp (cos (+ y (* (* z t) -0.3333333333333333))))))
      (/ a (* 3.0 b)))
     (- t_1 (/ (/ a 3.0) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 2.0 * sqrt(x);
	double tmp;
	if (cos((y - ((z * t) / 3.0))) <= 1.0) {
		tmp = (t_1 * log(exp(cos((y + ((z * t) * -0.3333333333333333)))))) - (a / (3.0 * b));
	} else {
		tmp = t_1 - ((a / 3.0) / b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * sqrt(x)
    if (cos((y - ((z * t) / 3.0d0))) <= 1.0d0) then
        tmp = (t_1 * log(exp(cos((y + ((z * t) * (-0.3333333333333333d0))))))) - (a / (3.0d0 * b))
    else
        tmp = t_1 - ((a / 3.0d0) / b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 2.0 * Math.sqrt(x);
	double tmp;
	if (Math.cos((y - ((z * t) / 3.0))) <= 1.0) {
		tmp = (t_1 * Math.log(Math.exp(Math.cos((y + ((z * t) * -0.3333333333333333)))))) - (a / (3.0 * b));
	} else {
		tmp = t_1 - ((a / 3.0) / b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = 2.0 * math.sqrt(x)
	tmp = 0
	if math.cos((y - ((z * t) / 3.0))) <= 1.0:
		tmp = (t_1 * math.log(math.exp(math.cos((y + ((z * t) * -0.3333333333333333)))))) - (a / (3.0 * b))
	else:
		tmp = t_1 - ((a / 3.0) / b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(2.0 * sqrt(x))
	tmp = 0.0
	if (cos(Float64(y - Float64(Float64(z * t) / 3.0))) <= 1.0)
		tmp = Float64(Float64(t_1 * log(exp(cos(Float64(y + Float64(Float64(z * t) * -0.3333333333333333)))))) - Float64(a / Float64(3.0 * b)));
	else
		tmp = Float64(t_1 - Float64(Float64(a / 3.0) / b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 2.0 * sqrt(x);
	tmp = 0.0;
	if (cos((y - ((z * t) / 3.0))) <= 1.0)
		tmp = (t_1 * log(exp(cos((y + ((z * t) * -0.3333333333333333)))))) - (a / (3.0 * b));
	else
		tmp = t_1 - ((a / 3.0) / b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[Cos[N[(y - N[(N[(z * t), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], 1.0], N[(N[(t$95$1 * N[Log[N[Exp[N[Cos[N[(y + N[(N[(z * t), $MachinePrecision] * -0.3333333333333333), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]], $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - N[(a / N[(3.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 - N[(N[(a / 3.0), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64)))) < 1

   1. Initial program 81.8%

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

      1. *-commutative 81.8%

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

      2. *-commutative 81.8%

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

      3. *-commutative 81.8%

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

      4. *-commutative 81.8%

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

      5. associate-/l* 81.9%

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

      6. *-commutative 81.9%

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

   3. Simplified 81.9%

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

      1. associate-*r/ 81.8%

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

      2. div-inv 82.1%

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

      3. metadata-eval 82.1%

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

      4. metadata-eval 82.1%

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

      5. cancel-sign-sub-inv 82.1%

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

      6. metadata-eval 82.1%

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

      7. metadata-eval 82.1%

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

      8. div-inv 81.8%

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

      9. metadata-eval 81.8%

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

      10. frac-2neg 81.8%

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

      11. +-commutative 81.8%

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

      12. associate-/l* 81.9%

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

      13. fma-define 81.8%

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

      14. div-inv 81.7%

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

      15. metadata-eval 81.7%

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

      16. add-log-exp 81.6%

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

   6. Applied egg-rr 81.6%

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

   7. Taylor expanded in z around inf 82.0%

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

   if 1 < (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64))))

   1. Initial program 0.0%

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

      1. *-commutative 0.0%

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

      2. *-commutative 0.0%

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

      3. *-commutative 0.0%

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

      4. *-commutative 0.0%

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

      5. associate-/l* 0.0%

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

      6. *-commutative 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in z around 0 69.2%

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

   6. Taylor expanded in a around 0 69.0%

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

      1. associate-*r/ 69.1%

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

   8. Simplified 69.1%

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

      1. *-commutative 69.1%

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

      2. metadata-eval 69.1%

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

      3. div-inv 69.1%

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

   10. Applied egg-rr 69.1%

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

   11. Taylor expanded in y around 0 70.0%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\cos \left(y - \frac{z \cdot t}{3}\right) \leq 1:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \log \left(e^{\cos \left(y + \left(z \cdot t\right) \cdot -0.3333333333333333\right)}\right) - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{x} - \frac{\frac{a}{3}}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 77.0% accurate, 0.7× speedup

Math

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

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* 2.0 (sqrt x))))
   (if (<= (cos (- y (/ (* z t) 3.0))) 1.0)
     (- (* t_1 (cos (+ y (/ -1.0 (/ 3.0 (* z t)))))) (/ a (* 3.0 b)))
     (- t_1 (/ (/ a 3.0) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 2.0 * sqrt(x);
	double tmp;
	if (cos((y - ((z * t) / 3.0))) <= 1.0) {
		tmp = (t_1 * cos((y + (-1.0 / (3.0 / (z * t)))))) - (a / (3.0 * b));
	} else {
		tmp = t_1 - ((a / 3.0) / b);
	}
	return tmp;
}

Fortran

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

Java

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

Python

def code(x, y, z, t, a, b):
	t_1 = 2.0 * math.sqrt(x)
	tmp = 0
	if math.cos((y - ((z * t) / 3.0))) <= 1.0:
		tmp = (t_1 * math.cos((y + (-1.0 / (3.0 / (z * t)))))) - (a / (3.0 * b))
	else:
		tmp = t_1 - ((a / 3.0) / b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(2.0 * sqrt(x))
	tmp = 0.0
	if (cos(Float64(y - Float64(Float64(z * t) / 3.0))) <= 1.0)
		tmp = Float64(Float64(t_1 * cos(Float64(y + Float64(-1.0 / Float64(3.0 / Float64(z * t)))))) - Float64(a / Float64(3.0 * b)));
	else
		tmp = Float64(t_1 - Float64(Float64(a / 3.0) / b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 2.0 * sqrt(x);
	tmp = 0.0;
	if (cos((y - ((z * t) / 3.0))) <= 1.0)
		tmp = (t_1 * cos((y + (-1.0 / (3.0 / (z * t)))))) - (a / (3.0 * b));
	else
		tmp = t_1 - ((a / 3.0) / b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[Cos[N[(y - N[(N[(z * t), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], 1.0], N[(N[(t$95$1 * N[Cos[N[(y + N[(-1.0 / N[(3.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - N[(a / N[(3.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 - N[(N[(a / 3.0), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64)))) < 1

   1. Initial program 81.8%

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

      1. *-commutative 81.8%

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

      2. *-commutative 81.8%

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

      3. *-commutative 81.8%

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

      4. *-commutative 81.8%

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

      5. associate-/l* 81.9%

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

      6. *-commutative 81.9%

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

   3. Simplified 81.9%

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

      1. associate-*r/ 81.8%

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

      2. clear-num 81.9%

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

   6. Applied egg-rr 81.9%

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

   if 1 < (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64))))

   1. Initial program 0.0%

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

      1. *-commutative 0.0%

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

      2. *-commutative 0.0%

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

      3. *-commutative 0.0%

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

      4. *-commutative 0.0%

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

      5. associate-/l* 0.0%

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

      6. *-commutative 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in z around 0 69.2%

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

   6. Taylor expanded in a around 0 69.0%

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

      1. associate-*r/ 69.1%

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

   8. Simplified 69.1%

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

      1. *-commutative 69.1%

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

      2. metadata-eval 69.1%

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

      3. div-inv 69.1%

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

   10. Applied egg-rr 69.1%

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

   11. Taylor expanded in y around 0 70.0%

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

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\cos \left(y - \frac{z \cdot t}{3}\right) \leq 1:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y + \frac{-1}{\frac{3}{z \cdot t}}\right) - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{x} - \frac{\frac{a}{3}}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 77.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \sqrt{x}\\ \mathbf{if}\;\cos \left(y - \frac{z \cdot t}{3}\right) \leq 1:\\ \;\;\;\;t\_1 \cdot \cos \left(y - \frac{z}{\frac{3}{t}}\right) - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;t\_1 - \frac{\frac{a}{3}}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* 2.0 (sqrt x))))
   (if (<= (cos (- y (/ (* z t) 3.0))) 1.0)
     (- (* t_1 (cos (- y (/ z (/ 3.0 t))))) (/ a (* 3.0 b)))
     (- t_1 (/ (/ a 3.0) b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 2.0 * sqrt(x);
	double tmp;
	if (cos((y - ((z * t) / 3.0))) <= 1.0) {
		tmp = (t_1 * cos((y - (z / (3.0 / t))))) - (a / (3.0 * b));
	} else {
		tmp = t_1 - ((a / 3.0) / b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * sqrt(x)
    if (cos((y - ((z * t) / 3.0d0))) <= 1.0d0) then
        tmp = (t_1 * cos((y - (z / (3.0d0 / t))))) - (a / (3.0d0 * b))
    else
        tmp = t_1 - ((a / 3.0d0) / b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 2.0 * Math.sqrt(x);
	double tmp;
	if (Math.cos((y - ((z * t) / 3.0))) <= 1.0) {
		tmp = (t_1 * Math.cos((y - (z / (3.0 / t))))) - (a / (3.0 * b));
	} else {
		tmp = t_1 - ((a / 3.0) / b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = 2.0 * math.sqrt(x)
	tmp = 0
	if math.cos((y - ((z * t) / 3.0))) <= 1.0:
		tmp = (t_1 * math.cos((y - (z / (3.0 / t))))) - (a / (3.0 * b))
	else:
		tmp = t_1 - ((a / 3.0) / b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(2.0 * sqrt(x))
	tmp = 0.0
	if (cos(Float64(y - Float64(Float64(z * t) / 3.0))) <= 1.0)
		tmp = Float64(Float64(t_1 * cos(Float64(y - Float64(z / Float64(3.0 / t))))) - Float64(a / Float64(3.0 * b)));
	else
		tmp = Float64(t_1 - Float64(Float64(a / 3.0) / b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 2.0 * sqrt(x);
	tmp = 0.0;
	if (cos((y - ((z * t) / 3.0))) <= 1.0)
		tmp = (t_1 * cos((y - (z / (3.0 / t))))) - (a / (3.0 * b));
	else
		tmp = t_1 - ((a / 3.0) / b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[Cos[N[(y - N[(N[(z * t), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], 1.0], N[(N[(t$95$1 * N[Cos[N[(y - N[(z / N[(3.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - N[(a / N[(3.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 - N[(N[(a / 3.0), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64)))) < 1

   1. Initial program 81.8%

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

      1. *-commutative 81.8%

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

      2. *-commutative 81.8%

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

      3. *-commutative 81.8%

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

      4. *-commutative 81.8%

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

      5. associate-/l* 81.9%

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

      6. *-commutative 81.9%

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

   3. Simplified 81.9%

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

   5. Taylor expanded in z around 0 82.1%

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \color{blue}{0.3333333333333333 \cdot \left(t \cdot z\right)}\right) - \frac{a}{3 \cdot b} \]
   6. Step-by-step derivation

      1. associate-*r* 81.7%

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

      2. metadata-eval 81.7%

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

      3. associate-/r/ 81.6%

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

      4. associate-*l/ 81.9%

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

      5. *-lft-identity 81.9%

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

   7. Simplified 81.9%

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

   if 1 < (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64))))

   1. Initial program 0.0%

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

      1. *-commutative 0.0%

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

      2. *-commutative 0.0%

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

      3. *-commutative 0.0%

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

      4. *-commutative 0.0%

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

      5. associate-/l* 0.0%

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

      6. *-commutative 0.0%

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

   3. Simplified 0.0%

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

   5. Taylor expanded in z around 0 69.2%

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

   6. Taylor expanded in a around 0 69.0%

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

      1. associate-*r/ 69.1%

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

   8. Simplified 69.1%

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

      1. *-commutative 69.1%

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

      2. metadata-eval 69.1%

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

      3. div-inv 69.1%

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

   10. Applied egg-rr 69.1%

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

   11. Taylor expanded in y around 0 70.0%

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

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\cos \left(y - \frac{z \cdot t}{3}\right) \leq 1:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z}{\frac{3}{t}}\right) - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{x} - \frac{\frac{a}{3}}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 67.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \sqrt{x}\\ \mathbf{if}\;a \leq -6 \cdot 10^{-242} \lor \neg \left(a \leq 5.8 \cdot 10^{-167}\right):\\ \;\;\;\;t\_1 - \frac{\frac{a}{3}}{b}\\ \mathbf{else}:\\ \;\;\;\;\cos y \cdot t\_1 - a \cdot \frac{-0.3333333333333333}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* 2.0 (sqrt x))))
   (if (or (<= a -6e-242) (not (<= a 5.8e-167)))
     (- t_1 (/ (/ a 3.0) b))
     (- (* (cos y) t_1) (* a (/ -0.3333333333333333 b))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 2.0 * sqrt(x);
	double tmp;
	if ((a <= -6e-242) || !(a <= 5.8e-167)) {
		tmp = t_1 - ((a / 3.0) / b);
	} else {
		tmp = (cos(y) * t_1) - (a * (-0.3333333333333333 / b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 * sqrt(x)
    if ((a <= (-6d-242)) .or. (.not. (a <= 5.8d-167))) then
        tmp = t_1 - ((a / 3.0d0) / b)
    else
        tmp = (cos(y) * t_1) - (a * ((-0.3333333333333333d0) / b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 2.0 * Math.sqrt(x);
	double tmp;
	if ((a <= -6e-242) || !(a <= 5.8e-167)) {
		tmp = t_1 - ((a / 3.0) / b);
	} else {
		tmp = (Math.cos(y) * t_1) - (a * (-0.3333333333333333 / b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = 2.0 * math.sqrt(x)
	tmp = 0
	if (a <= -6e-242) or not (a <= 5.8e-167):
		tmp = t_1 - ((a / 3.0) / b)
	else:
		tmp = (math.cos(y) * t_1) - (a * (-0.3333333333333333 / b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(2.0 * sqrt(x))
	tmp = 0.0
	if ((a <= -6e-242) || !(a <= 5.8e-167))
		tmp = Float64(t_1 - Float64(Float64(a / 3.0) / b));
	else
		tmp = Float64(Float64(cos(y) * t_1) - Float64(a * Float64(-0.3333333333333333 / b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 2.0 * sqrt(x);
	tmp = 0.0;
	if ((a <= -6e-242) || ~((a <= 5.8e-167)))
		tmp = t_1 - ((a / 3.0) / b);
	else
		tmp = (cos(y) * t_1) - (a * (-0.3333333333333333 / b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[a, -6e-242], N[Not[LessEqual[a, 5.8e-167]], $MachinePrecision]], N[(t$95$1 - N[(N[(a / 3.0), $MachinePrecision] / b), $MachinePrecision]), $MachinePrecision], N[(N[(N[Cos[y], $MachinePrecision] * t$95$1), $MachinePrecision] - N[(a * N[(-0.3333333333333333 / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if a < -6e-242 or 5.80000000000000005e-167 < a

   1. Initial program 70.0%

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

      1. *-commutative 70.0%

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

      2. *-commutative 70.0%

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

      3. *-commutative 70.0%

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

      4. *-commutative 70.0%

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

      5. associate-/l* 70.1%

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

      6. *-commutative 70.1%

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

   3. Simplified 70.1%

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

   5. Taylor expanded in z around 0 81.5%

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

   6. Taylor expanded in a around 0 81.3%

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

      1. associate-*r/ 81.4%

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

   8. Simplified 81.4%

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

      1. *-commutative 81.4%

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

      2. metadata-eval 81.4%

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

      3. div-inv 81.5%

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

   10. Applied egg-rr 81.5%

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

   11. Taylor expanded in y around 0 74.4%

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

   if -6e-242 < a < 5.80000000000000005e-167

   1. Initial program 61.7%

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

      1. *-commutative 61.7%

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

      2. *-commutative 61.7%

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

      3. *-commutative 61.7%

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

      4. *-commutative 61.7%

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

      5. associate-/l* 61.5%

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

      6. *-commutative 61.5%

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

   3. Simplified 61.5%

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

   5. Taylor expanded in z around 0 60.2%

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

   6. Taylor expanded in a around 0 60.2%

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

      1. *-commutative 36.7%

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

      2. rem-square-sqrt 32.1%

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

      3. fabs-sqr 32.1%

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

      4. rem-square-sqrt 36.7%

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

      5. *-commutative 36.7%

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

      6. metadata-eval 36.7%

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

      7. times-frac 36.7%

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

      8. associate-*l/ 36.7%

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

      9. associate-/r/ 36.7%

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

      10. associate-*r/ 36.7%

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

      11. associate-/r* 36.7%

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

      12. metadata-eval 36.7%

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

      13. fabs-div 36.7%

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

      14. metadata-eval 36.7%

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

      15. metadata-eval 36.7%

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

      16. fabs-div 36.7%

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

      17. rem-square-sqrt 12.3%

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

      18. fabs-sqr 12.3%

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

      19. rem-square-sqrt 34.2%

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

      20. associate-/r/ 34.2%

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

      21. *-commutative 34.2%

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

   8. Simplified 57.7%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6 \cdot 10^{-242} \lor \neg \left(a \leq 5.8 \cdot 10^{-167}\right):\\ \;\;\;\;2 \cdot \sqrt{x} - \frac{\frac{a}{3}}{b}\\ \mathbf{else}:\\ \;\;\;\;\cos y \cdot \left(2 \cdot \sqrt{x}\right) - a \cdot \frac{-0.3333333333333333}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 76.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 68.7%

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

   1. *-commutative 68.7%

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

   2. *-commutative 68.7%

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

   3. *-commutative 68.7%

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

   4. *-commutative 68.7%

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

   5. associate-/l* 68.8%

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

   6. *-commutative 68.8%

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

3. Simplified 68.8%

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

5. Taylor expanded in z around 0 78.2%

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

6. Taylor expanded in a around 0 78.1%

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

   1. associate-*r/ 78.2%

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

   2. associate-*l/ 78.1%

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

   3. *-commutative 78.1%

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

8. Simplified 78.1%

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

9. Final simplification 78.1%

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

Alternative 7: 76.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 68.7%

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

   1. *-commutative 68.7%

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

   2. *-commutative 68.7%

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

   3. *-commutative 68.7%

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

   4. *-commutative 68.7%

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

   5. associate-/l* 68.8%

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

   6. *-commutative 68.8%

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

3. Simplified 68.8%

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

5. Taylor expanded in z around 0 78.2%

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

6. Final simplification 78.2%

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

Alternative 8: 76.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 68.7%

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

   1. *-commutative 68.7%

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

   2. *-commutative 68.7%

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

   3. *-commutative 68.7%

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

   4. *-commutative 68.7%

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

   5. associate-/l* 68.8%

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

   6. *-commutative 68.8%

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

3. Simplified 68.8%

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

5. Taylor expanded in z around 0 78.2%

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

6. Taylor expanded in a around 0 78.1%

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

   1. associate-*r/ 78.2%

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

8. Simplified 78.2%

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

   1. *-commutative 78.2%

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

   2. metadata-eval 78.2%

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

   3. div-inv 78.3%

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

10. Applied egg-rr 78.3%

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

11. Final simplification 78.3%

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

Alternative 9: 53.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.6 \cdot 10^{-146}:\\ \;\;\;\;\frac{a}{b \cdot -3}\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-170}:\\ \;\;\;\;2 \cdot \sqrt{x} - a \cdot \frac{-0.3333333333333333}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{-0.3333333333333333 \cdot a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= a -3.6e-146)
   (/ a (* b -3.0))
   (if (<= a 6.5e-170)
     (- (* 2.0 (sqrt x)) (* a (/ -0.3333333333333333 b)))
     (/ (* -0.3333333333333333 a) b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (a <= -3.6e-146) {
		tmp = a / (b * -3.0);
	} else if (a <= 6.5e-170) {
		tmp = (2.0 * sqrt(x)) - (a * (-0.3333333333333333 / b));
	} 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 (a <= (-3.6d-146)) then
        tmp = a / (b * (-3.0d0))
    else if (a <= 6.5d-170) then
        tmp = (2.0d0 * sqrt(x)) - (a * ((-0.3333333333333333d0) / b))
    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 (a <= -3.6e-146) {
		tmp = a / (b * -3.0);
	} else if (a <= 6.5e-170) {
		tmp = (2.0 * Math.sqrt(x)) - (a * (-0.3333333333333333 / b));
	} else {
		tmp = (-0.3333333333333333 * a) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if a <= -3.6e-146:
		tmp = a / (b * -3.0)
	elif a <= 6.5e-170:
		tmp = (2.0 * math.sqrt(x)) - (a * (-0.3333333333333333 / b))
	else:
		tmp = (-0.3333333333333333 * a) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (a <= -3.6e-146)
		tmp = Float64(a / Float64(b * -3.0));
	elseif (a <= 6.5e-170)
		tmp = Float64(Float64(2.0 * sqrt(x)) - Float64(a * Float64(-0.3333333333333333 / b)));
	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 (a <= -3.6e-146)
		tmp = a / (b * -3.0);
	elseif (a <= 6.5e-170)
		tmp = (2.0 * sqrt(x)) - (a * (-0.3333333333333333 / b));
	else
		tmp = (-0.3333333333333333 * a) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[a, -3.6e-146], N[(a / N[(b * -3.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.5e-170], N[(N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] - N[(a * N[(-0.3333333333333333 / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(-0.3333333333333333 * a), $MachinePrecision] / b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.59999999999999978e-146

   1. Initial program 75.7%

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

      1. *-commutative 75.7%

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

      2. *-commutative 75.7%

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

      3. *-commutative 75.7%

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

      4. *-commutative 75.7%

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

      5. associate-/l* 76.1%

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

      6. *-commutative 76.1%

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

   3. Simplified 76.1%

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

   5. Taylor expanded in y around 0 67.9%

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\cos \left(-0.3333333333333333 \cdot \left(t \cdot z\right)\right)} - \frac{a}{3 \cdot b} \]
   6. Step-by-step derivation

      1. cos-neg 67.9%

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

   7. Simplified 67.9%

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

   8. Taylor expanded in t around 0 53.1%

      \[\leadsto \color{blue}{\left(-0.1111111111111111 \cdot \left(\left({t}^{2} \cdot {z}^{2}\right) \cdot \sqrt{x}\right) + 2 \cdot \sqrt{x}\right)} - \frac{a}{3 \cdot b} \]
   9. Step-by-step derivation

      1. +-commutative 53.1%

         \[\leadsto \color{blue}{\left(2 \cdot \sqrt{x} + -0.1111111111111111 \cdot \left(\left({t}^{2} \cdot {z}^{2}\right) \cdot \sqrt{x}\right)\right)} - \frac{a}{3 \cdot b} \]

      2. associate-*r* 53.1%

         \[\leadsto \left(2 \cdot \sqrt{x} + \color{blue}{\left(-0.1111111111111111 \cdot \left({t}^{2} \cdot {z}^{2}\right)\right) \cdot \sqrt{x}}\right) - \frac{a}{3 \cdot b} \]

      3. distribute-rgt-out 53.1%

         \[\leadsto \color{blue}{\sqrt{x} \cdot \left(2 + -0.1111111111111111 \cdot \left({t}^{2} \cdot {z}^{2}\right)\right)} - \frac{a}{3 \cdot b} \]

   10. Simplified 53.1%

       \[\leadsto \color{blue}{\sqrt{x} \cdot \left(2 + -0.1111111111111111 \cdot \left({t}^{2} \cdot {z}^{2}\right)\right)} - \frac{a}{3 \cdot b} \]

   11. Taylor expanded in a around inf 67.8%

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

       1. associate-*r/ 68.0%

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

       2. *-commutative 68.0%

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

       3. associate-/l* 67.9%

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

   13. Simplified 67.9%

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

       1. clear-num 67.9%

          \[\leadsto a \cdot \color{blue}{\frac{1}{\frac{b}{-0.3333333333333333}}} \]

       2. un-div-inv 67.9%

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

       3. div-inv 68.1%

          \[\leadsto \frac{a}{\color{blue}{b \cdot \frac{1}{-0.3333333333333333}}} \]

       4. metadata-eval 68.1%

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

   15. Applied egg-rr 68.1%

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

   if -3.59999999999999978e-146 < a < 6.50000000000000035e-170

   1. Initial program 61.8%

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

      1. *-commutative 61.8%

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

      2. *-commutative 61.8%

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

      3. *-commutative 61.8%

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

      4. *-commutative 61.8%

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

      5. associate-/l* 61.8%

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

      6. *-commutative 61.8%

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

   3. Simplified 61.8%

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

   5. Taylor expanded in z around 0 59.7%

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

   6. Taylor expanded in y around 0 43.1%

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

   7. Taylor expanded in a around 0 43.1%

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

      1. *-commutative 43.1%

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

      2. rem-square-sqrt 32.1%

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

      3. fabs-sqr 32.1%

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

      4. rem-square-sqrt 39.8%

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

      5. *-commutative 39.8%

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

      6. metadata-eval 39.8%

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

      7. times-frac 39.8%

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

      8. associate-*l/ 39.8%

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

      9. associate-/r/ 39.8%

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

      10. associate-*r/ 39.9%

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

      11. associate-/r* 39.9%

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

      12. metadata-eval 39.9%

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

      13. fabs-div 39.9%

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

      14. metadata-eval 39.9%

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

      15. metadata-eval 39.9%

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

      16. fabs-div 39.9%

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

      17. rem-square-sqrt 19.8%

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

      18. fabs-sqr 19.8%

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

      19. rem-square-sqrt 36.6%

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

      20. associate-/r/ 36.6%

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

      21. *-commutative 36.6%

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

   9. Simplified 36.6%

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

   if 6.50000000000000035e-170 < a

   1. Initial program 66.7%

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

      1. *-commutative 66.7%

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

      2. *-commutative 66.7%

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

      3. *-commutative 66.7%

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

      4. *-commutative 66.7%

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

      5. associate-/l* 66.5%

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

      6. *-commutative 66.5%

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

   3. Simplified 66.5%

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

   5. Taylor expanded in y around 0 60.2%

      \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\cos \left(-0.3333333333333333 \cdot \left(t \cdot z\right)\right)} - \frac{a}{3 \cdot b} \]
   6. Step-by-step derivation

      1. cos-neg 60.2%

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

   7. Simplified 60.2%

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

   8. Taylor expanded in t around 0 40.1%

      \[\leadsto \color{blue}{\left(-0.1111111111111111 \cdot \left(\left({t}^{2} \cdot {z}^{2}\right) \cdot \sqrt{x}\right) + 2 \cdot \sqrt{x}\right)} - \frac{a}{3 \cdot b} \]
   9. Step-by-step derivation

      1. +-commutative 40.1%

         \[\leadsto \color{blue}{\left(2 \cdot \sqrt{x} + -0.1111111111111111 \cdot \left(\left({t}^{2} \cdot {z}^{2}\right) \cdot \sqrt{x}\right)\right)} - \frac{a}{3 \cdot b} \]

      2. associate-*r* 40.1%

         \[\leadsto \left(2 \cdot \sqrt{x} + \color{blue}{\left(-0.1111111111111111 \cdot \left({t}^{2} \cdot {z}^{2}\right)\right) \cdot \sqrt{x}}\right) - \frac{a}{3 \cdot b} \]

      3. distribute-rgt-out 40.1%

         \[\leadsto \color{blue}{\sqrt{x} \cdot \left(2 + -0.1111111111111111 \cdot \left({t}^{2} \cdot {z}^{2}\right)\right)} - \frac{a}{3 \cdot b} \]

   10. Simplified 40.1%

       \[\leadsto \color{blue}{\sqrt{x} \cdot \left(2 + -0.1111111111111111 \cdot \left({t}^{2} \cdot {z}^{2}\right)\right)} - \frac{a}{3 \cdot b} \]

   11. Taylor expanded in a around inf 70.5%

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

       1. associate-*r/ 70.6%

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

       2. *-commutative 70.6%

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

       3. associate-/l* 70.6%

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

   13. Simplified 70.6%

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

       1. associate-*r/ 70.6%

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

   15. Applied egg-rr 70.6%

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

4. Final simplification 61.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.6 \cdot 10^{-146}:\\ \;\;\;\;\frac{a}{b \cdot -3}\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{-170}:\\ \;\;\;\;2 \cdot \sqrt{x} - a \cdot \frac{-0.3333333333333333}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{-0.3333333333333333 \cdot a}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 65.8% accurate, 2.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 68.7%

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

   1. *-commutative 68.7%

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

   2. *-commutative 68.7%

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

   3. *-commutative 68.7%

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

   4. *-commutative 68.7%

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

   5. associate-/l* 68.8%

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

   6. *-commutative 68.8%

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

3. Simplified 68.8%

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

5. Taylor expanded in z around 0 78.2%

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

6. Taylor expanded in y around 0 68.6%

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

7. Final simplification 68.6%

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

Alternative 11: 65.8% accurate, 2.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 68.7%

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

   1. *-commutative 68.7%

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

   2. *-commutative 68.7%

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

   3. *-commutative 68.7%

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

   4. *-commutative 68.7%

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

   5. associate-/l* 68.8%

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

   6. *-commutative 68.8%

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

3. Simplified 68.8%

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

5. Taylor expanded in z around 0 78.2%

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

6. Taylor expanded in a around 0 78.1%

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

   1. associate-*r/ 78.2%

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

8. Simplified 78.2%

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

   1. *-commutative 78.2%

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

   2. metadata-eval 78.2%

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

   3. div-inv 78.3%

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

10. Applied egg-rr 78.3%

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

11. Taylor expanded in y around 0 68.7%

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

12. Final simplification 68.7%

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

Alternative 12: 51.0% 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 68.7%

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

   1. *-commutative 68.7%

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

   2. *-commutative 68.7%

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

   3. *-commutative 68.7%

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

   4. *-commutative 68.7%

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

   5. associate-/l* 68.8%

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

   6. *-commutative 68.8%

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

3. Simplified 68.8%

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

5. Taylor expanded in y around 0 58.6%

   \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\cos \left(-0.3333333333333333 \cdot \left(t \cdot z\right)\right)} - \frac{a}{3 \cdot b} \]
6. Step-by-step derivation

   1. cos-neg 58.6%

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

7. Simplified 58.6%

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

8. Taylor expanded in t around 0 42.5%

   \[\leadsto \color{blue}{\left(-0.1111111111111111 \cdot \left(\left({t}^{2} \cdot {z}^{2}\right) \cdot \sqrt{x}\right) + 2 \cdot \sqrt{x}\right)} - \frac{a}{3 \cdot b} \]
9. Step-by-step derivation

   1. +-commutative 42.5%

      \[\leadsto \color{blue}{\left(2 \cdot \sqrt{x} + -0.1111111111111111 \cdot \left(\left({t}^{2} \cdot {z}^{2}\right) \cdot \sqrt{x}\right)\right)} - \frac{a}{3 \cdot b} \]

   2. associate-*r* 42.5%

      \[\leadsto \left(2 \cdot \sqrt{x} + \color{blue}{\left(-0.1111111111111111 \cdot \left({t}^{2} \cdot {z}^{2}\right)\right) \cdot \sqrt{x}}\right) - \frac{a}{3 \cdot b} \]

   3. distribute-rgt-out 42.5%

      \[\leadsto \color{blue}{\sqrt{x} \cdot \left(2 + -0.1111111111111111 \cdot \left({t}^{2} \cdot {z}^{2}\right)\right)} - \frac{a}{3 \cdot b} \]

10. Simplified 42.5%

    \[\leadsto \color{blue}{\sqrt{x} \cdot \left(2 + -0.1111111111111111 \cdot \left({t}^{2} \cdot {z}^{2}\right)\right)} - \frac{a}{3 \cdot b} \]

11. Taylor expanded in a around inf 55.4%

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

    1. associate-*r/ 55.5%

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

    2. *-commutative 55.5%

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

    3. associate-/l* 55.4%

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

13. Simplified 55.4%

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

14. Final simplification 55.4%

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

Alternative 13: 51.1% accurate, 43.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 68.7%

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

   1. *-commutative 68.7%

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

   2. *-commutative 68.7%

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

   3. *-commutative 68.7%

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

   4. *-commutative 68.7%

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

   5. associate-/l* 68.8%

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

   6. *-commutative 68.8%

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

3. Simplified 68.8%

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

5. Taylor expanded in y around 0 58.6%

   \[\leadsto \left(2 \cdot \sqrt{x}\right) \cdot \color{blue}{\cos \left(-0.3333333333333333 \cdot \left(t \cdot z\right)\right)} - \frac{a}{3 \cdot b} \]
6. Step-by-step derivation

   1. cos-neg 58.6%

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

7. Simplified 58.6%

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

8. Taylor expanded in t around 0 42.5%

   \[\leadsto \color{blue}{\left(-0.1111111111111111 \cdot \left(\left({t}^{2} \cdot {z}^{2}\right) \cdot \sqrt{x}\right) + 2 \cdot \sqrt{x}\right)} - \frac{a}{3 \cdot b} \]
9. Step-by-step derivation

   1. +-commutative 42.5%

      \[\leadsto \color{blue}{\left(2 \cdot \sqrt{x} + -0.1111111111111111 \cdot \left(\left({t}^{2} \cdot {z}^{2}\right) \cdot \sqrt{x}\right)\right)} - \frac{a}{3 \cdot b} \]

   2. associate-*r* 42.5%

      \[\leadsto \left(2 \cdot \sqrt{x} + \color{blue}{\left(-0.1111111111111111 \cdot \left({t}^{2} \cdot {z}^{2}\right)\right) \cdot \sqrt{x}}\right) - \frac{a}{3 \cdot b} \]

   3. distribute-rgt-out 42.5%

      \[\leadsto \color{blue}{\sqrt{x} \cdot \left(2 + -0.1111111111111111 \cdot \left({t}^{2} \cdot {z}^{2}\right)\right)} - \frac{a}{3 \cdot b} \]

10. Simplified 42.5%

    \[\leadsto \color{blue}{\sqrt{x} \cdot \left(2 + -0.1111111111111111 \cdot \left({t}^{2} \cdot {z}^{2}\right)\right)} - \frac{a}{3 \cdot b} \]

11. Taylor expanded in a around inf 55.4%

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

    1. associate-*r/ 55.5%

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

    2. *-commutative 55.5%

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

    3. associate-/l* 55.4%

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

13. Simplified 55.4%

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

    1. clear-num 55.4%

       \[\leadsto a \cdot \color{blue}{\frac{1}{\frac{b}{-0.3333333333333333}}} \]

    2. un-div-inv 55.5%

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

    3. div-inv 55.5%

       \[\leadsto \frac{a}{\color{blue}{b \cdot \frac{1}{-0.3333333333333333}}} \]

    4. metadata-eval 55.5%

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

15. Applied egg-rr 55.5%

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

16. Final simplification 55.5%

    \[\leadsto \frac{a}{b \cdot -3} \]
17. Add Preprocessing

Developer target: 74.4% 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 2024071 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, K"
  :precision binary64

  :alt
  (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))))