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

Percentage Accurate: 69.5% → 77.2%

Time: 36.1s

Alternatives: 8

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: 69.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 77.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := z \cdot \left(t \cdot 0.3333333333333333\right)\\ t_2 := \frac{a}{3 \cdot b}\\ t_3 := 2 \cdot \sqrt{x}\\ \mathbf{if}\;t\_3 \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - t\_2 \leq 2 \cdot 10^{+151}:\\ \;\;\;\;\left(t\_3 \cdot \left(\cos y \cdot \cos t\_1\right) + t\_3 \cdot \left(\sin y \cdot \sin t\_1\right)\right) - t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3 - t\_2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (* t 0.3333333333333333)))
        (t_2 (/ a (* 3.0 b)))
        (t_3 (* 2.0 (sqrt x))))
   (if (<= (- (* t_3 (cos (- y (/ (* z t) 3.0)))) t_2) 2e+151)
     (- (+ (* t_3 (* (cos y) (cos t_1))) (* t_3 (* (sin y) (sin t_1)))) t_2)
     (- t_3 t_2))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (t * 0.3333333333333333);
	double t_2 = a / (3.0 * b);
	double t_3 = 2.0 * sqrt(x);
	double tmp;
	if (((t_3 * cos((y - ((z * t) / 3.0)))) - t_2) <= 2e+151) {
		tmp = ((t_3 * (cos(y) * cos(t_1))) + (t_3 * (sin(y) * sin(t_1)))) - t_2;
	} else {
		tmp = t_3 - t_2;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
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 = z * (t * 0.3333333333333333d0)
    t_2 = a / (3.0d0 * b)
    t_3 = 2.0d0 * sqrt(x)
    if (((t_3 * cos((y - ((z * t) / 3.0d0)))) - t_2) <= 2d+151) then
        tmp = ((t_3 * (cos(y) * cos(t_1))) + (t_3 * (sin(y) * sin(t_1)))) - t_2
    else
        tmp = t_3 - t_2
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (t * 0.3333333333333333);
	double t_2 = a / (3.0 * b);
	double t_3 = 2.0 * Math.sqrt(x);
	double tmp;
	if (((t_3 * Math.cos((y - ((z * t) / 3.0)))) - t_2) <= 2e+151) {
		tmp = ((t_3 * (Math.cos(y) * Math.cos(t_1))) + (t_3 * (Math.sin(y) * Math.sin(t_1)))) - t_2;
	} else {
		tmp = t_3 - t_2;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = z * (t * 0.3333333333333333)
	t_2 = a / (3.0 * b)
	t_3 = 2.0 * math.sqrt(x)
	tmp = 0
	if ((t_3 * math.cos((y - ((z * t) / 3.0)))) - t_2) <= 2e+151:
		tmp = ((t_3 * (math.cos(y) * math.cos(t_1))) + (t_3 * (math.sin(y) * math.sin(t_1)))) - t_2
	else:
		tmp = t_3 - t_2
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(t * 0.3333333333333333))
	t_2 = Float64(a / Float64(3.0 * b))
	t_3 = Float64(2.0 * sqrt(x))
	tmp = 0.0
	if (Float64(Float64(t_3 * cos(Float64(y - Float64(Float64(z * t) / 3.0)))) - t_2) <= 2e+151)
		tmp = Float64(Float64(Float64(t_3 * Float64(cos(y) * cos(t_1))) + Float64(t_3 * Float64(sin(y) * sin(t_1)))) - t_2);
	else
		tmp = Float64(t_3 - t_2);
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (t * 0.3333333333333333);
	t_2 = a / (3.0 * b);
	t_3 = 2.0 * sqrt(x);
	tmp = 0.0;
	if (((t_3 * cos((y - ((z * t) / 3.0)))) - t_2) <= 2e+151)
		tmp = ((t_3 * (cos(y) * cos(t_1))) + (t_3 * (sin(y) * sin(t_1)))) - t_2;
	else
		tmp = t_3 - t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(t * 0.3333333333333333), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a / N[(3.0 * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(t$95$3 * N[Cos[N[(y - N[(N[(z * t), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], 2e+151], N[(N[(N[(t$95$3 * N[(N[Cos[y], $MachinePrecision] * N[Cos[t$95$1], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$3 * N[(N[Sin[y], $MachinePrecision] * N[Sin[t$95$1], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], N[(t$95$3 - t$95$2), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (*.f64 (*.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3)))) (/.f64 a (*.f64 b 3))) < 2.00000000000000003e151

   1. Initial program 80.4%

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

      1. *-commutative 80.4%

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

      2. *-commutative 80.4%

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

      3. associate-/l* 80.1%

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

      4. *-commutative 80.1%

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

   3. Simplified 80.1%

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

      1. add-log-exp 27.9%

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

      2. add-log-exp 27.9%

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

      3. associate-/l* 27.5%

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

      4. exp-to-pow 27.5%

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

      5. exp-prod 27.5%

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

      6. associate-/l* 27.9%

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

      7. add-sqr-sqrt 24.4%

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

      8. sqrt-unprod 27.7%

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

      9. frac-times 27.2%

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

      10. metadata-eval 27.2%

          \[\leadsto \log \left({\left({\left(e^{2}\right)}^{\left(\sqrt{x}\right)}\right)}^{\cos \left(y - \frac{z}{\sqrt{\frac{\color{blue}{9}}{t \cdot t}}}\right)}\right) - \frac{a}{3 \cdot b} \]

      11. metadata-eval 27.2%

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

      12. frac-times 27.7%

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

      13. sqrt-unprod 25.1%

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

      14. add-sqr-sqrt 27.9%

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

      15. associate-/r/ 27.4%

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

   6. Applied egg-rr 27.5%

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

   8. Applied egg-rr 81.7%

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

   if 2.00000000000000003e151 < (-.f64 (*.f64 (*.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3)))) (/.f64 a (*.f64 b 3)))

   1. Initial program 41.6%

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

      1. *-commutative 41.6%

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

      2. *-commutative 41.6%

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

      3. associate-/l* 41.6%

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

      4. *-commutative 41.6%

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

   3. Simplified 41.6%

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

   5. Taylor expanded in z around 0 75.6%

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

      1. *-commutative 75.6%

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

      2. *-commutative 75.6%

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

      3. associate-*l* 75.6%

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

      4. *-commutative 75.6%

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

   7. Simplified 75.6%

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

   8. Taylor expanded in y around 0 76.6%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) - \frac{a}{3 \cdot b} \leq 2 \cdot 10^{+151}:\\ \;\;\;\;\left(\left(2 \cdot \sqrt{x}\right) \cdot \left(\cos y \cdot \cos \left(z \cdot \left(t \cdot 0.3333333333333333\right)\right)\right) + \left(2 \cdot \sqrt{x}\right) \cdot \left(\sin y \cdot \sin \left(z \cdot \left(t \cdot 0.3333333333333333\right)\right)\right)\right) - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{x} - \frac{a}{3 \cdot b}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 76.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \left(2 \cdot \cos y\right) \cdot {x}^{0.5} - \frac{a}{3 \cdot b} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (- (* (* 2.0 (cos y)) (pow x 0.5)) (/ a (* 3.0 b))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	return ((2.0 * cos(y)) * pow(x, 0.5)) - (a / (3.0 * b));
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
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 * cos(y)) * (x ** 0.5d0)) - (a / (3.0d0 * b))
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	return ((2.0 * Math.cos(y)) * Math.pow(x, 0.5)) - (a / (3.0 * b));
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	return ((2.0 * math.cos(y)) * math.pow(x, 0.5)) - (a / (3.0 * b))

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(2.0 * cos(y)) * (x ^ 0.5)) - Float64(a / Float64(3.0 * b)))
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp = code(x, y, z, t, a, b)
	tmp = ((2.0 * cos(y)) * (x ^ 0.5)) - (a / (3.0 * b));
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(2.0 * N[Cos[y], $MachinePrecision]), $MachinePrecision] * N[Power[x, 0.5], $MachinePrecision]), $MachinePrecision] - N[(a / N[(3.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 71.2%

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

   1. *-commutative 71.2%

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

   2. *-commutative 71.2%

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

   3. associate-/l* 70.9%

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

   4. *-commutative 70.9%

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

3. Simplified 70.9%

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

5. Taylor expanded in z around 0 78.9%

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

   1. *-commutative 78.9%

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

   2. *-commutative 78.9%

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

   3. associate-*l* 78.9%

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

   4. *-commutative 78.9%

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

7. Simplified 78.9%

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

   1. expm1-log1p-u 69.4%

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

   2. expm1-udef 54.3%

      \[\leadsto \color{blue}{\left(e^{\mathsf{log1p}\left(\cos y \cdot \left(2 \cdot \sqrt{x}\right)\right)} - 1\right)} - \frac{a}{3 \cdot b} \]

   3. *-commutative 54.3%

      \[\leadsto \left(e^{\mathsf{log1p}\left(\color{blue}{\left(2 \cdot \sqrt{x}\right) \cdot \cos y}\right)} - 1\right) - \frac{a}{3 \cdot b} \]

   4. associate-*l* 54.3%

      \[\leadsto \left(e^{\mathsf{log1p}\left(\color{blue}{2 \cdot \left(\sqrt{x} \cdot \cos y\right)}\right)} - 1\right) - \frac{a}{3 \cdot b} \]

9. Applied egg-rr 54.3%

   \[\leadsto \color{blue}{\left(e^{\mathsf{log1p}\left(2 \cdot \left(\sqrt{x} \cdot \cos y\right)\right)} - 1\right)} - \frac{a}{3 \cdot b} \]
10. Step-by-step derivation

    1. expm1-def 69.4%

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

    2. expm1-log1p-u 78.9%

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

    3. associate-*r* 78.9%

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

    4. *-commutative 78.9%

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

    5. associate-*r* 78.9%

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

    6. add-sqr-sqrt 78.7%

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

    7. associate-*r* 78.7%

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

    8. pow1/2 78.7%

       \[\leadsto \left(\left(\cos y \cdot 2\right) \cdot \sqrt{\color{blue}{{x}^{0.5}}}\right) \cdot \sqrt{\sqrt{x}} - \frac{a}{3 \cdot b} \]

    9. sqrt-pow1 78.8%

       \[\leadsto \left(\left(\cos y \cdot 2\right) \cdot \color{blue}{{x}^{\left(\frac{0.5}{2}\right)}}\right) \cdot \sqrt{\sqrt{x}} - \frac{a}{3 \cdot b} \]

    10. metadata-eval 78.8%

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

    11. pow1/2 78.8%

        \[\leadsto \left(\left(\cos y \cdot 2\right) \cdot {x}^{0.25}\right) \cdot \sqrt{\color{blue}{{x}^{0.5}}} - \frac{a}{3 \cdot b} \]

    12. sqrt-pow1 78.8%

        \[\leadsto \left(\left(\cos y \cdot 2\right) \cdot {x}^{0.25}\right) \cdot \color{blue}{{x}^{\left(\frac{0.5}{2}\right)}} - \frac{a}{3 \cdot b} \]

    13. metadata-eval 78.8%

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

11. Applied egg-rr 78.8%

    \[\leadsto \color{blue}{\left(\left(\cos y \cdot 2\right) \cdot {x}^{0.25}\right) \cdot {x}^{0.25}} - \frac{a}{3 \cdot b} \]
12. Step-by-step derivation

    1. associate-*l* 78.7%

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

    2. *-commutative 78.7%

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

    3. pow-sqr 78.9%

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

    4. metadata-eval 78.9%

       \[\leadsto \left(2 \cdot \cos y\right) \cdot {x}^{\color{blue}{0.5}} - \frac{a}{3 \cdot b} \]

13. Simplified 78.9%

    \[\leadsto \color{blue}{\left(2 \cdot \cos y\right) \cdot {x}^{0.5}} - \frac{a}{3 \cdot b} \]

14. Final simplification 78.9%

    \[\leadsto \left(2 \cdot \cos y\right) \cdot {x}^{0.5} - \frac{a}{3 \cdot b} \]
15. Add Preprocessing

Alternative 3: 76.2% accurate, 1.0× speedup

Math

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

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (- (* (* 2.0 (sqrt x)) (cos y)) (/ a (* 3.0 b))))

C

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

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = ((2.0d0 * sqrt(x)) * cos(y)) - (a / (3.0d0 * b))
end function

Java

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

Python

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

Julia

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

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp = code(x, y, z, t, a, b)
	tmp = ((2.0 * sqrt(x)) * cos(y)) - (a / (3.0 * b));
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] * N[Cos[y], $MachinePrecision]), $MachinePrecision] - N[(a / N[(3.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 71.2%

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

   1. *-commutative 71.2%

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

   2. *-commutative 71.2%

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

   3. associate-/l* 70.9%

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

   4. *-commutative 70.9%

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

3. Simplified 70.9%

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

5. Taylor expanded in z around 0 78.9%

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

   1. *-commutative 78.9%

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

   2. *-commutative 78.9%

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

   3. associate-*l* 78.9%

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

   4. *-commutative 78.9%

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

7. Simplified 78.9%

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

8. Final simplification 78.9%

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

Alternative 4: 65.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq 2.9 \cdot 10^{+110}:\\ \;\;\;\;2 \cdot \sqrt{x} - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt{x} \cdot \cos y\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 2.9e+110)
   (- (* 2.0 (sqrt x)) (/ a (* 3.0 b)))
   (* 2.0 (* (sqrt x) (cos y)))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 2.9e+110) {
		tmp = (2.0 * sqrt(x)) - (a / (3.0 * b));
	} else {
		tmp = 2.0 * (sqrt(x) * cos(y));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (b <= 2.9d+110) then
        tmp = (2.0d0 * sqrt(x)) - (a / (3.0d0 * b))
    else
        tmp = 2.0d0 * (sqrt(x) * cos(y))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 2.9e+110) {
		tmp = (2.0 * Math.sqrt(x)) - (a / (3.0 * b));
	} else {
		tmp = 2.0 * (Math.sqrt(x) * Math.cos(y));
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 2.9e+110:
		tmp = (2.0 * math.sqrt(x)) - (a / (3.0 * b))
	else:
		tmp = 2.0 * (math.sqrt(x) * math.cos(y))
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 2.9e+110)
		tmp = Float64(Float64(2.0 * sqrt(x)) - Float64(a / Float64(3.0 * b)));
	else
		tmp = Float64(2.0 * Float64(sqrt(x) * cos(y)));
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 2.9e+110)
		tmp = (2.0 * sqrt(x)) - (a / (3.0 * b));
	else
		tmp = 2.0 * (sqrt(x) * cos(y));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 2.9e+110], N[(N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] - N[(a / N[(3.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[Sqrt[x], $MachinePrecision] * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 2.9e110

   1. Initial program 73.6%

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

      1. *-commutative 73.6%

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

      2. *-commutative 73.6%

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

      3. associate-/l* 73.5%

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

      4. *-commutative 73.5%

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

   3. Simplified 73.5%

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

   5. Taylor expanded in z around 0 83.2%

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

      1. *-commutative 83.2%

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

      2. *-commutative 83.2%

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

      3. associate-*l* 83.2%

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

      4. *-commutative 83.2%

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

   7. Simplified 83.2%

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

   8. Taylor expanded in y around 0 72.0%

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

   if 2.9e110 < b

   1. Initial program 60.8%

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

      1. *-commutative 60.8%

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

      2. *-commutative 60.8%

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

      3. associate-/l* 60.1%

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

      4. *-commutative 60.1%

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

   3. Simplified 60.1%

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

   5. Taylor expanded in z around 0 60.5%

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

      1. *-commutative 60.5%

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

      2. *-commutative 60.5%

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

      3. associate-*l* 60.5%

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

      4. *-commutative 60.5%

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

   7. Simplified 60.5%

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

   8. Taylor expanded in a around 0 60.4%

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

      1. associate-*r/ 60.5%

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

   10. Simplified 60.5%

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

   11. Taylor expanded in a around 0 50.9%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 2.9 \cdot 10^{+110}:\\ \;\;\;\;2 \cdot \sqrt{x} - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt{x} \cdot \cos y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 65.0% accurate, 2.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ 2 \cdot \sqrt{x} + a \cdot \frac{-0.3333333333333333}{b} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (+ (* 2.0 (sqrt x)) (* a (/ -0.3333333333333333 b))))

C

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

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = (2.0d0 * sqrt(x)) + (a * ((-0.3333333333333333d0) / b))
end function

Java

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

Python

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

Julia

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

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp = code(x, y, z, t, a, b)
	tmp = (2.0 * sqrt(x)) + (a * (-0.3333333333333333 / b));
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := N[(N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] + N[(a * N[(-0.3333333333333333 / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 71.2%

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

   1. *-commutative 71.2%

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

   2. *-commutative 71.2%

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

   3. associate-/l* 70.9%

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

   4. *-commutative 70.9%

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

3. Simplified 70.9%

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

5. Taylor expanded in z around 0 78.9%

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

   1. *-commutative 78.9%

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

   2. *-commutative 78.9%

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

   3. associate-*l* 78.9%

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

   4. *-commutative 78.9%

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

7. Simplified 78.9%

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

8. Taylor expanded in y around 0 64.1%

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

   1. cancel-sign-sub-inv 64.1%

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

   2. metadata-eval 64.1%

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

   3. associate-*r/ 64.1%

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

   4. associate-*l/ 64.0%

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

   5. *-commutative 64.0%

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

10. Simplified 64.0%

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

11. Final simplification 64.0%

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

Alternative 6: 65.1% accurate, 2.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ 2 \cdot \sqrt{x} - \frac{a}{3 \cdot b} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b) :precision binary64 (- (* 2.0 (sqrt x)) (/ a (* 3.0 b))))

C

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

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
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

assert x < y && y < z && z < t && t < a && a < b;
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

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

Julia

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

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp = code(x, y, z, t, a, b)
	tmp = (2.0 * sqrt(x)) - (a / (3.0 * b));
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
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 71.2%

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

   1. *-commutative 71.2%

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

   2. *-commutative 71.2%

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

   3. associate-/l* 70.9%

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

   4. *-commutative 70.9%

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

3. Simplified 70.9%

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

5. Taylor expanded in z around 0 78.9%

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

   1. *-commutative 78.9%

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

   2. *-commutative 78.9%

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

   3. associate-*l* 78.9%

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

   4. *-commutative 78.9%

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

7. Simplified 78.9%

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

8. Taylor expanded in y around 0 64.1%

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

9. Final simplification 64.1%

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

Alternative 7: 50.0% accurate, 43.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ -0.3333333333333333 \cdot \frac{a}{b} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b) :precision binary64 (* -0.3333333333333333 (/ a b)))

C

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

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = (-0.3333333333333333d0) * (a / b)
end function

Java

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

Python

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

Julia

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

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp = code(x, y, z, t, a, b)
	tmp = -0.3333333333333333 * (a / b);
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := N[(-0.3333333333333333 * N[(a / b), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 71.2%

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

   1. *-commutative 71.2%

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

   2. *-commutative 71.2%

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

   3. associate-/l* 70.9%

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

   4. *-commutative 70.9%

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

3. Simplified 70.9%

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

5. Taylor expanded in z around 0 78.9%

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

   1. *-commutative 78.9%

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

   2. *-commutative 78.9%

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

   3. associate-*l* 78.9%

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

   4. *-commutative 78.9%

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

7. Simplified 78.9%

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

8. Taylor expanded in x around 0 47.1%

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

9. Final simplification 47.1%

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

Alternative 8: 50.1% accurate, 43.4× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \frac{a}{b \cdot -3} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b) :precision binary64 (/ a (* b -3.0)))

C

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

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
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

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

Python

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

Julia

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

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp = code(x, y, z, t, a, b)
	tmp = a / (b * -3.0);
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := N[(a / N[(b * -3.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 71.2%

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

   1. *-commutative 71.2%

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

   2. *-commutative 71.2%

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

   3. associate-/l* 70.9%

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

   4. *-commutative 70.9%

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

3. Simplified 70.9%

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

5. Taylor expanded in z around 0 78.9%

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

   1. *-commutative 78.9%

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

   2. *-commutative 78.9%

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

   3. associate-*l* 78.9%

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

   4. *-commutative 78.9%

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

7. Simplified 78.9%

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

8. Taylor expanded in x around 0 47.1%

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

   1. associate-*r/ 47.1%

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

   2. associate-*l/ 47.0%

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

   3. *-commutative 47.0%

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

10. Simplified 47.0%

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

    1. clear-num 47.0%

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

    2. un-div-inv 47.1%

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

    3. div-inv 47.2%

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

    4. metadata-eval 47.2%

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

12. Applied egg-rr 47.2%

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

13. Final simplification 47.2%

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

Developer target: 73.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024031 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, K"
  :precision binary64

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

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