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

Percentage Accurate: 69.6% → 77.1%

Time: 21.8s

Alternatives: 6

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: 69.6% 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: 77.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := \frac{a}{3 \cdot b}\\ t_2 := {\left(\sqrt[3]{z}\right)}^{2} \cdot \frac{-\sqrt[3]{z}}{\frac{3}{t}}\\ \mathbf{if}\;\cos \left(y - \frac{z \cdot t}{3}\right) \leq 0.988:\\ \;\;\;\;2 \cdot \left(\sqrt{x} \cdot \left(\cos y \cdot \cos t_2 - \sin y \cdot \sin t_2\right)\right) - t_1\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\left(x \cdot 4\right) \cdot {\cos y}^{2}} - t_1\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ a (* 3.0 b)))
        (t_2 (* (pow (cbrt z) 2.0) (/ (- (cbrt z)) (/ 3.0 t)))))
   (if (<= (cos (- y (/ (* z t) 3.0))) 0.988)
     (-
      (* 2.0 (* (sqrt x) (- (* (cos y) (cos t_2)) (* (sin y) (sin t_2)))))
      t_1)
     (- (sqrt (* (* x 4.0) (pow (cos y) 2.0))) t_1))))

C

assert(z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a / (3.0 * b);
	double t_2 = pow(cbrt(z), 2.0) * (-cbrt(z) / (3.0 / t));
	double tmp;
	if (cos((y - ((z * t) / 3.0))) <= 0.988) {
		tmp = (2.0 * (sqrt(x) * ((cos(y) * cos(t_2)) - (sin(y) * sin(t_2))))) - t_1;
	} else {
		tmp = sqrt(((x * 4.0) * pow(cos(y), 2.0))) - t_1;
	}
	return tmp;
}

Java

assert z < t;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a / (3.0 * b);
	double t_2 = Math.pow(Math.cbrt(z), 2.0) * (-Math.cbrt(z) / (3.0 / t));
	double tmp;
	if (Math.cos((y - ((z * t) / 3.0))) <= 0.988) {
		tmp = (2.0 * (Math.sqrt(x) * ((Math.cos(y) * Math.cos(t_2)) - (Math.sin(y) * Math.sin(t_2))))) - t_1;
	} else {
		tmp = Math.sqrt(((x * 4.0) * Math.pow(Math.cos(y), 2.0))) - t_1;
	}
	return tmp;
}

Julia

z, t = sort([z, t])
function code(x, y, z, t, a, b)
	t_1 = Float64(a / Float64(3.0 * b))
	t_2 = Float64((cbrt(z) ^ 2.0) * Float64(Float64(-cbrt(z)) / Float64(3.0 / t)))
	tmp = 0.0
	if (cos(Float64(y - Float64(Float64(z * t) / 3.0))) <= 0.988)
		tmp = Float64(Float64(2.0 * Float64(sqrt(x) * Float64(Float64(cos(y) * cos(t_2)) - Float64(sin(y) * sin(t_2))))) - t_1);
	else
		tmp = Float64(sqrt(Float64(Float64(x * 4.0) * (cos(y) ^ 2.0))) - t_1);
	end
	return tmp
end

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a / N[(3.0 * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[Power[N[Power[z, 1/3], $MachinePrecision], 2.0], $MachinePrecision] * N[((-N[Power[z, 1/3], $MachinePrecision]) / N[(3.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[Cos[N[(y - N[(N[(z * t), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], 0.988], N[(N[(2.0 * N[(N[Sqrt[x], $MachinePrecision] * N[(N[(N[Cos[y], $MachinePrecision] * N[Cos[t$95$2], $MachinePrecision]), $MachinePrecision] - N[(N[Sin[y], $MachinePrecision] * N[Sin[t$95$2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[Sqrt[N[(N[(x * 4.0), $MachinePrecision] * N[Power[N[Cos[y], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3))) < 0.98799999999999999

   1. Initial program 71.6%

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

      1. associate-*l* 71.6%

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

      2. fma-neg 71.6%

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

      3. remove-double-neg 71.6%

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

      4. fma-neg 71.6%

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

      5. remove-double-neg 71.6%

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

      6. associate-/l* 71.3%

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

      7. *-commutative 71.3%

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

   3. Simplified 71.3%

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

      1. add-cube-cbrt 71.7%

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

      2. *-un-lft-identity 71.7%

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

      3. times-frac 71.1%

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

      4. pow2 71.1%

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

   5. Applied egg-rr 71.1%

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

      1. /-rgt-identity 71.1%

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

      2. cancel-sign-sub-inv 71.1%

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

      3. cos-sum 73.1%

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

   7. Applied egg-rr 73.1%

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

   if 0.98799999999999999 < (cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3)))

   1. Initial program 59.4%

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

   2. Taylor expanded in z around 0 82.4%

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

      1. *-commutative 82.4%

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

      2. associate-*l* 82.4%

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

      3. *-commutative 82.4%

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

   4. Simplified 82.4%

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

      1. log1p-expm1-u 82.4%

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

   6. Applied egg-rr 82.4%

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

      1. log1p-expm1-u 82.4%

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

      2. add-log-exp 82.4%

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

      3. add-sqr-sqrt 76.3%

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

      4. sqrt-unprod 82.6%

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

      5. add-log-exp 82.6%

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

      6. add-log-exp 82.6%

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

      7. *-commutative 82.6%

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

      8. *-commutative 82.6%

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

      9. swap-sqr 82.6%

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

   8. Applied egg-rr 82.6%

      \[\leadsto \color{blue}{\sqrt{\left(x \cdot 4\right) \cdot {\cos y}^{2}}} - \frac{a}{b \cdot 3} \]
3. Recombined 2 regimes into one program.

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\cos \left(y - \frac{z \cdot t}{3}\right) \leq 0.988:\\ \;\;\;\;2 \cdot \left(\sqrt{x} \cdot \left(\cos y \cdot \cos \left({\left(\sqrt[3]{z}\right)}^{2} \cdot \frac{-\sqrt[3]{z}}{\frac{3}{t}}\right) - \sin y \cdot \sin \left({\left(\sqrt[3]{z}\right)}^{2} \cdot \frac{-\sqrt[3]{z}}{\frac{3}{t}}\right)\right)\right) - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\left(x \cdot 4\right) \cdot {\cos y}^{2}} - \frac{a}{3 \cdot b}\\ \end{array} \]

Alternative 2: 77.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := 2 \cdot \sqrt{x}\\ t_2 := \frac{a}{3 \cdot b}\\ t_3 := \frac{z}{\frac{3}{t}}\\ \mathbf{if}\;\cos \left(y - \frac{z \cdot t}{3}\right) \cdot t_1 \leq 2 \cdot 10^{+105}:\\ \;\;\;\;2 \cdot \left(\sqrt{x} \cdot \left(\cos y \cdot \cos t_3 + \sin y \cdot \sin t_3\right)\right) - t_2\\ \mathbf{else}:\\ \;\;\;\;t_1 \cdot \left|\cos y\right| - t_2\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* 2.0 (sqrt x))) (t_2 (/ a (* 3.0 b))) (t_3 (/ z (/ 3.0 t))))
   (if (<= (* (cos (- y (/ (* z t) 3.0))) t_1) 2e+105)
     (-
      (* 2.0 (* (sqrt x) (+ (* (cos y) (cos t_3)) (* (sin y) (sin t_3)))))
      t_2)
     (- (* t_1 (fabs (cos y))) t_2))))

C

assert(z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 2.0 * sqrt(x);
	double t_2 = a / (3.0 * b);
	double t_3 = z / (3.0 / t);
	double tmp;
	if ((cos((y - ((z * t) / 3.0))) * t_1) <= 2e+105) {
		tmp = (2.0 * (sqrt(x) * ((cos(y) * cos(t_3)) + (sin(y) * sin(t_3))))) - t_2;
	} else {
		tmp = (t_1 * fabs(cos(y))) - t_2;
	}
	return tmp;
}

Fortran

NOTE: z and t 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 = 2.0d0 * sqrt(x)
    t_2 = a / (3.0d0 * b)
    t_3 = z / (3.0d0 / t)
    if ((cos((y - ((z * t) / 3.0d0))) * t_1) <= 2d+105) then
        tmp = (2.0d0 * (sqrt(x) * ((cos(y) * cos(t_3)) + (sin(y) * sin(t_3))))) - t_2
    else
        tmp = (t_1 * abs(cos(y))) - t_2
    end if
    code = tmp
end function

Java

assert z < t;
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 t_2 = a / (3.0 * b);
	double t_3 = z / (3.0 / t);
	double tmp;
	if ((Math.cos((y - ((z * t) / 3.0))) * t_1) <= 2e+105) {
		tmp = (2.0 * (Math.sqrt(x) * ((Math.cos(y) * Math.cos(t_3)) + (Math.sin(y) * Math.sin(t_3))))) - t_2;
	} else {
		tmp = (t_1 * Math.abs(Math.cos(y))) - t_2;
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t, a, b):
	t_1 = 2.0 * math.sqrt(x)
	t_2 = a / (3.0 * b)
	t_3 = z / (3.0 / t)
	tmp = 0
	if (math.cos((y - ((z * t) / 3.0))) * t_1) <= 2e+105:
		tmp = (2.0 * (math.sqrt(x) * ((math.cos(y) * math.cos(t_3)) + (math.sin(y) * math.sin(t_3))))) - t_2
	else:
		tmp = (t_1 * math.fabs(math.cos(y))) - t_2
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t, a, b)
	t_1 = Float64(2.0 * sqrt(x))
	t_2 = Float64(a / Float64(3.0 * b))
	t_3 = Float64(z / Float64(3.0 / t))
	tmp = 0.0
	if (Float64(cos(Float64(y - Float64(Float64(z * t) / 3.0))) * t_1) <= 2e+105)
		tmp = Float64(Float64(2.0 * Float64(sqrt(x) * Float64(Float64(cos(y) * cos(t_3)) + Float64(sin(y) * sin(t_3))))) - t_2);
	else
		tmp = Float64(Float64(t_1 * abs(cos(y))) - t_2);
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 2.0 * sqrt(x);
	t_2 = a / (3.0 * b);
	t_3 = z / (3.0 / t);
	tmp = 0.0;
	if ((cos((y - ((z * t) / 3.0))) * t_1) <= 2e+105)
		tmp = (2.0 * (sqrt(x) * ((cos(y) * cos(t_3)) + (sin(y) * sin(t_3))))) - t_2;
	else
		tmp = (t_1 * abs(cos(y))) - t_2;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a / N[(3.0 * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z / N[(3.0 / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[Cos[N[(y - N[(N[(z * t), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * t$95$1), $MachinePrecision], 2e+105], N[(N[(2.0 * N[(N[Sqrt[x], $MachinePrecision] * N[(N[(N[Cos[y], $MachinePrecision] * N[Cos[t$95$3], $MachinePrecision]), $MachinePrecision] + N[(N[Sin[y], $MachinePrecision] * N[Sin[t$95$3], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision], N[(N[(t$95$1 * N[Abs[N[Cos[y], $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - t$95$2), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3)))) < 1.9999999999999999e105

   1. Initial program 79.7%

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

      1. associate-*l* 79.7%

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

      2. fma-neg 79.7%

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

      3. remove-double-neg 79.7%

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

      4. fma-neg 79.7%

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

      5. remove-double-neg 79.7%

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

      6. associate-/l* 79.5%

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

      7. *-commutative 79.5%

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

   3. Simplified 79.5%

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

      1. add-cube-cbrt 79.7%

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

      2. *-un-lft-identity 79.7%

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

      3. times-frac 79.2%

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

      4. pow2 79.2%

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

   5. Applied egg-rr 79.2%

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

      1. cos-diff 80.7%

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

      2. frac-times 81.0%

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

      3. unpow2 81.0%

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

      4. add-cube-cbrt 80.3%

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

      5. *-un-lft-identity 80.3%

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

      6. frac-times 80.3%

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

      7. unpow2 80.3%

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

      8. add-cube-cbrt 80.5%

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

      9. *-un-lft-identity 80.5%

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

   7. Applied egg-rr 80.5%

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

   if 1.9999999999999999e105 < (*.f64 (*.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3))))

   1. Initial program 31.4%

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

   2. Taylor expanded in z around 0 65.9%

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

      1. *-commutative 65.9%

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

      2. associate-*l* 65.9%

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

      3. *-commutative 65.9%

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

   4. Simplified 65.9%

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

      1. log1p-expm1-u 65.9%

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

   6. Applied egg-rr 65.9%

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

      1. log1p-expm1-u 65.9%

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

      2. add-sqr-sqrt 56.9%

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

      3. sqrt-unprod 66.2%

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

      4. pow2 66.2%

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

   8. Applied egg-rr 66.2%

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

      1. unpow2 66.2%

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

      2. rem-sqrt-square 66.2%

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

   10. Simplified 66.2%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\cos \left(y - \frac{z \cdot t}{3}\right) \cdot \left(2 \cdot \sqrt{x}\right) \leq 2 \cdot 10^{+105}:\\ \;\;\;\;2 \cdot \left(\sqrt{x} \cdot \left(\cos y \cdot \cos \left(\frac{z}{\frac{3}{t}}\right) + \sin y \cdot \sin \left(\frac{z}{\frac{3}{t}}\right)\right)\right) - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \left|\cos y\right| - \frac{a}{3 \cdot b}\\ \end{array} \]

Alternative 3: 76.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

assert(z < t);
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

NOTE: z and t 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 = (cos(y) * (2.0d0 * sqrt(x))) - (a / (3.0d0 * b))
end function

Java

assert z < t;
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

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

Julia

z, t = sort([z, t])
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

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

Wolfram

NOTE: z and t should be sorted in increasing order before calling this function.
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 66.7%

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

2. Taylor expanded in z around 0 75.1%

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

   1. *-commutative 75.1%

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

   2. associate-*l* 75.1%

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

   3. *-commutative 75.1%

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

4. Simplified 75.1%

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

5. Final simplification 75.1%

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

Alternative 4: 65.1% accurate, 2.0× speedup

Math

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

FPCore

NOTE: z and t 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(z < t);
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: z and t 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 z < t;
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

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

Julia

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

MATLAB

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

Wolfram

NOTE: z and t 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 66.7%

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

2. Taylor expanded in z around 0 75.1%

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

   1. *-commutative 75.1%

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

   2. associate-*l* 75.1%

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

   3. *-commutative 75.1%

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

4. Simplified 75.1%

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

5. Taylor expanded in y around 0 65.9%

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

6. Final simplification 65.9%

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

Alternative 5: 50.3% accurate, 43.4× speedup

Math

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

FPCore

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

C

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

Fortran

NOTE: z and t 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 * ((-0.3333333333333333d0) / b)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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. Taylor expanded in z around 0 75.1%

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

   1. *-commutative 75.1%

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

   2. associate-*l* 75.1%

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

   3. *-commutative 75.1%

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

4. Simplified 75.1%

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

5. Taylor expanded in x around 0 53.8%

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

   1. metadata-eval 53.8%

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

   2. distribute-lft-neg-in 53.8%

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

   3. metadata-eval 53.8%

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

   4. times-frac 54.2%

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

   5. *-lft-identity 54.2%

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

   6. *-commutative 54.2%

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

   7. *-rgt-identity 54.2%

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

   8. associate-*r/ 54.2%

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

   9. distribute-rgt-neg-in 54.2%

      \[\leadsto \color{blue}{a \cdot \left(-\frac{1}{b \cdot 3}\right)} \]

   10. distribute-neg-frac 54.2%

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

   11. metadata-eval 54.2%

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

   12. *-commutative 54.2%

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

   13. associate-/r* 54.1%

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

   14. metadata-eval 54.1%

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

7. Simplified 54.1%

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

8. Final simplification 54.1%

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

Alternative 6: 50.4% accurate, 43.4× speedup

Math

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

FPCore

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

Fortran

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

Python

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

Julia

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

MATLAB

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

Wolfram

NOTE: z and t 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 66.7%

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

2. Taylor expanded in z around 0 75.1%

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

   1. *-commutative 75.1%

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

   2. associate-*l* 75.1%

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

   3. *-commutative 75.1%

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

4. Simplified 75.1%

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

5. Taylor expanded in x around 0 53.8%

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

   1. metadata-eval 53.8%

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

   2. distribute-lft-neg-in 53.8%

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

   3. metadata-eval 53.8%

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

   4. times-frac 54.2%

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

   5. *-lft-identity 54.2%

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

   6. *-commutative 54.2%

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

   7. *-rgt-identity 54.2%

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

   8. associate-*r/ 54.2%

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

   9. distribute-rgt-neg-in 54.2%

      \[\leadsto \color{blue}{a \cdot \left(-\frac{1}{b \cdot 3}\right)} \]

   10. distribute-neg-frac 54.2%

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

   11. metadata-eval 54.2%

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

   12. *-commutative 54.2%

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

   13. associate-/r* 54.1%

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

   14. metadata-eval 54.1%

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

7. Simplified 54.1%

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

   1. clear-num 54.1%

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

   2. un-div-inv 54.2%

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

   3. div-inv 54.2%

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

   4. metadata-eval 54.2%

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

9. Applied egg-rr 54.2%

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

10. Final simplification 54.2%

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

Developer target: 73.8% 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 2023185 
(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))))