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

Percentage Accurate: 70.7% → 77.9%

Time: 31.7s

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: 70.7% 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: 77.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot t}{3}\\ t_2 := 2 \cdot \sqrt{x}\\ t_3 := \frac{a}{3 \cdot b}\\ \mathbf{if}\;t\_2 \cdot \cos \left(y - t\_1\right) \leq 10^{+149}:\\ \;\;\;\;t\_2 \cdot \left(\cos y \cdot \cos t\_1 + \sin y \cdot \sin t\_1\right) - t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_2 \cdot \log \left(e^{\cos y}\right) - t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* z t) 3.0)) (t_2 (* 2.0 (sqrt x))) (t_3 (/ a (* 3.0 b))))
   (if (<= (* t_2 (cos (- y t_1))) 1e+149)
     (- (* t_2 (+ (* (cos y) (cos t_1)) (* (sin y) (sin t_1)))) t_3)
     (- (* t_2 (log (exp (cos y)))) t_3))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * t) / 3.0;
	double t_2 = 2.0 * sqrt(x);
	double t_3 = a / (3.0 * b);
	double tmp;
	if ((t_2 * cos((y - t_1))) <= 1e+149) {
		tmp = (t_2 * ((cos(y) * cos(t_1)) + (sin(y) * sin(t_1)))) - t_3;
	} else {
		tmp = (t_2 * log(exp(cos(y)))) - t_3;
	}
	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 = (z * t) / 3.0d0
    t_2 = 2.0d0 * sqrt(x)
    t_3 = a / (3.0d0 * b)
    if ((t_2 * cos((y - t_1))) <= 1d+149) then
        tmp = (t_2 * ((cos(y) * cos(t_1)) + (sin(y) * sin(t_1)))) - t_3
    else
        tmp = (t_2 * log(exp(cos(y)))) - t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * t) / 3.0;
	double t_2 = 2.0 * Math.sqrt(x);
	double t_3 = a / (3.0 * b);
	double tmp;
	if ((t_2 * Math.cos((y - t_1))) <= 1e+149) {
		tmp = (t_2 * ((Math.cos(y) * Math.cos(t_1)) + (Math.sin(y) * Math.sin(t_1)))) - t_3;
	} else {
		tmp = (t_2 * Math.log(Math.exp(Math.cos(y)))) - t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z * t) / 3.0
	t_2 = 2.0 * math.sqrt(x)
	t_3 = a / (3.0 * b)
	tmp = 0
	if (t_2 * math.cos((y - t_1))) <= 1e+149:
		tmp = (t_2 * ((math.cos(y) * math.cos(t_1)) + (math.sin(y) * math.sin(t_1)))) - t_3
	else:
		tmp = (t_2 * math.log(math.exp(math.cos(y)))) - t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z * t) / 3.0)
	t_2 = Float64(2.0 * sqrt(x))
	t_3 = Float64(a / Float64(3.0 * b))
	tmp = 0.0
	if (Float64(t_2 * cos(Float64(y - t_1))) <= 1e+149)
		tmp = Float64(Float64(t_2 * Float64(Float64(cos(y) * cos(t_1)) + Float64(sin(y) * sin(t_1)))) - t_3);
	else
		tmp = Float64(Float64(t_2 * log(exp(cos(y)))) - t_3);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z * t) / 3.0;
	t_2 = 2.0 * sqrt(x);
	t_3 = a / (3.0 * b);
	tmp = 0.0;
	if ((t_2 * cos((y - t_1))) <= 1e+149)
		tmp = (t_2 * ((cos(y) * cos(t_1)) + (sin(y) * sin(t_1)))) - t_3;
	else
		tmp = (t_2 * log(exp(cos(y)))) - t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z * t), $MachinePrecision] / 3.0), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a / N[(3.0 * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$2 * N[Cos[N[(y - t$95$1), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 1e+149], N[(N[(t$95$2 * N[(N[(N[Cos[y], $MachinePrecision] * N[Cos[t$95$1], $MachinePrecision]), $MachinePrecision] + N[(N[Sin[y], $MachinePrecision] * N[Sin[t$95$1], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$3), $MachinePrecision], N[(N[(t$95$2 * N[Log[N[Exp[N[Cos[y], $MachinePrecision]], $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - t$95$3), $MachinePrecision]]]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64))))) < 1.00000000000000005e149

   1. Initial program 84.1%

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

      1. add-cube-cbrt 83.9%

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

      2. associate-/l* 84.1%

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

      3. pow2 84.1%

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

   4. Applied egg-rr 84.1%

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

      1. cos-diff 85.3%

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

      2. associate-*r/ 84.9%

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

      3. unpow2 84.9%

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

      4. add-cube-cbrt 85.3%

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

      5. *-commutative 85.3%

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

      6. associate-*r/ 85.2%

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

      7. unpow2 85.2%

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

      8. add-cube-cbrt 85.3%

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

      9. *-commutative 85.3%

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

   6. Applied egg-rr 85.3%

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

   if 1.00000000000000005e149 < (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64)))))

   1. Initial program 3.2%

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

   3. Taylor expanded in z around 0 59.1%

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

      1. add-log-exp 59.1%

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

   5. Applied egg-rr 59.1%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) \leq 10^{+149}:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \left(\cos y \cdot \cos \left(\frac{z \cdot t}{3}\right) + \sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right) - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \log \left(e^{\cos y}\right) - \frac{a}{3 \cdot b}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 77.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z \cdot t}{3}\\ t_2 := \frac{a}{3 \cdot b}\\ t_3 := 2 \cdot \sqrt{x}\\ \mathbf{if}\;t\_3 \cdot \cos \left(y - t\_1\right) \leq 2 \cdot 10^{+152}:\\ \;\;\;\;t\_3 \cdot \left(\cos y \cdot \cos t\_1 + \sin y \cdot \sin \left(t \cdot \frac{z}{3}\right)\right) - t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3 - t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (* z t) 3.0)) (t_2 (/ a (* 3.0 b))) (t_3 (* 2.0 (sqrt x))))
   (if (<= (* t_3 (cos (- y t_1))) 2e+152)
     (-
      (* t_3 (+ (* (cos y) (cos t_1)) (* (sin y) (sin (* t (/ z 3.0))))))
      t_2)
     (- t_3 t_2))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * t) / 3.0;
	double t_2 = a / (3.0 * b);
	double t_3 = 2.0 * sqrt(x);
	double tmp;
	if ((t_3 * cos((y - t_1))) <= 2e+152) {
		tmp = (t_3 * ((cos(y) * cos(t_1)) + (sin(y) * sin((t * (z / 3.0)))))) - t_2;
	} else {
		tmp = t_3 - t_2;
	}
	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 = (z * t) / 3.0d0
    t_2 = a / (3.0d0 * b)
    t_3 = 2.0d0 * sqrt(x)
    if ((t_3 * cos((y - t_1))) <= 2d+152) then
        tmp = (t_3 * ((cos(y) * cos(t_1)) + (sin(y) * sin((t * (z / 3.0d0)))))) - t_2
    else
        tmp = t_3 - t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z * t) / 3.0;
	double t_2 = a / (3.0 * b);
	double t_3 = 2.0 * Math.sqrt(x);
	double tmp;
	if ((t_3 * Math.cos((y - t_1))) <= 2e+152) {
		tmp = (t_3 * ((Math.cos(y) * Math.cos(t_1)) + (Math.sin(y) * Math.sin((t * (z / 3.0)))))) - t_2;
	} else {
		tmp = t_3 - t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z * t) / 3.0
	t_2 = a / (3.0 * b)
	t_3 = 2.0 * math.sqrt(x)
	tmp = 0
	if (t_3 * math.cos((y - t_1))) <= 2e+152:
		tmp = (t_3 * ((math.cos(y) * math.cos(t_1)) + (math.sin(y) * math.sin((t * (z / 3.0)))))) - t_2
	else:
		tmp = t_3 - t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z * t) / 3.0)
	t_2 = Float64(a / Float64(3.0 * b))
	t_3 = Float64(2.0 * sqrt(x))
	tmp = 0.0
	if (Float64(t_3 * cos(Float64(y - t_1))) <= 2e+152)
		tmp = Float64(Float64(t_3 * Float64(Float64(cos(y) * cos(t_1)) + Float64(sin(y) * sin(Float64(t * Float64(z / 3.0)))))) - t_2);
	else
		tmp = Float64(t_3 - t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z * t) / 3.0;
	t_2 = a / (3.0 * b);
	t_3 = 2.0 * sqrt(x);
	tmp = 0.0;
	if ((t_3 * cos((y - t_1))) <= 2e+152)
		tmp = (t_3 * ((cos(y) * cos(t_1)) + (sin(y) * sin((t * (z / 3.0)))))) - t_2;
	else
		tmp = t_3 - t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z * t), $MachinePrecision] / 3.0), $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[(t$95$3 * N[Cos[N[(y - t$95$1), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2e+152], N[(N[(t$95$3 * N[(N[(N[Cos[y], $MachinePrecision] * N[Cos[t$95$1], $MachinePrecision]), $MachinePrecision] + N[(N[Sin[y], $MachinePrecision] * N[Sin[N[(t * N[(z / 3.0), $MachinePrecision]), $MachinePrecision]], $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 #s(literal 2 binary64) (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64))))) < 2.0000000000000001e152

   1. Initial program 83.4%

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

      1. add-cube-cbrt 83.4%

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

      2. associate-/l* 83.5%

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

      3. pow2 83.5%

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

   4. Applied egg-rr 83.5%

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

      1. cos-diff 84.6%

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

      2. associate-*r/ 84.3%

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

      3. unpow2 84.3%

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

      4. add-cube-cbrt 84.6%

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

      5. *-commutative 84.6%

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

      6. associate-*r/ 84.5%

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

      7. unpow2 84.5%

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

      8. add-cube-cbrt 84.6%

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

      9. *-commutative 84.6%

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

   6. Applied egg-rr 84.6%

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

   8. Applied egg-rr 84.6%

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

      1. associate-/l* 84.7%

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

   10. Simplified 84.7%

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

   if 2.0000000000000001e152 < (*.f64 (*.f64 #s(literal 2 binary64) (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) #s(literal 3 binary64)))))

   1. Initial program 0.0%

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

   3. Taylor expanded in z around 0 61.0%

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

   4. Taylor expanded in y around 0 61.3%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) \leq 2 \cdot 10^{+152}:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \left(\cos y \cdot \cos \left(\frac{z \cdot t}{3}\right) + \sin y \cdot \sin \left(t \cdot \frac{z}{3}\right)\right) - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{x} - \frac{a}{3 \cdot b}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 72.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 2 \cdot \sqrt{x}\\ t_2 := \frac{a}{3 \cdot b}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{-61} \lor \neg \left(t\_2 \leq 2 \cdot 10^{-55}\right):\\ \;\;\;\;t\_1 - t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1 \cdot \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* 2.0 (sqrt x))) (t_2 (/ a (* 3.0 b))))
   (if (or (<= t_2 -2e-61) (not (<= t_2 2e-55))) (- t_1 t_2) (* t_1 (cos y)))))

C

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 tmp;
	if ((t_2 <= -2e-61) || !(t_2 <= 2e-55)) {
		tmp = t_1 - t_2;
	} else {
		tmp = t_1 * cos(y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 2.0d0 * sqrt(x)
    t_2 = a / (3.0d0 * b)
    if ((t_2 <= (-2d-61)) .or. (.not. (t_2 <= 2d-55))) then
        tmp = t_1 - t_2
    else
        tmp = t_1 * cos(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = 2.0 * Math.sqrt(x);
	double t_2 = a / (3.0 * b);
	double tmp;
	if ((t_2 <= -2e-61) || !(t_2 <= 2e-55)) {
		tmp = t_1 - t_2;
	} else {
		tmp = t_1 * Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = 2.0 * math.sqrt(x)
	t_2 = a / (3.0 * b)
	tmp = 0
	if (t_2 <= -2e-61) or not (t_2 <= 2e-55):
		tmp = t_1 - t_2
	else:
		tmp = t_1 * math.cos(y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(2.0 * sqrt(x))
	t_2 = Float64(a / Float64(3.0 * b))
	tmp = 0.0
	if ((t_2 <= -2e-61) || !(t_2 <= 2e-55))
		tmp = Float64(t_1 - t_2);
	else
		tmp = Float64(t_1 * cos(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = 2.0 * sqrt(x);
	t_2 = a / (3.0 * b);
	tmp = 0.0;
	if ((t_2 <= -2e-61) || ~((t_2 <= 2e-55)))
		tmp = t_1 - t_2;
	else
		tmp = t_1 * cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a / N[(3.0 * b), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$2, -2e-61], N[Not[LessEqual[t$95$2, 2e-55]], $MachinePrecision]], N[(t$95$1 - t$95$2), $MachinePrecision], N[(t$95$1 * N[Cos[y], $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 a (*.f64 b #s(literal 3 binary64))) < -2.0000000000000001e-61 or 1.99999999999999999e-55 < (/.f64 a (*.f64 b #s(literal 3 binary64)))

   1. Initial program 82.0%

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

   3. Taylor expanded in z around 0 91.9%

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

   4. Taylor expanded in y around 0 88.3%

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

   if -2.0000000000000001e-61 < (/.f64 a (*.f64 b #s(literal 3 binary64))) < 1.99999999999999999e-55

   1. Initial program 60.5%

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

   3. Taylor expanded in z around 0 61.0%

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

      1. log1p-expm1-u 61.0%

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

   5. Applied egg-rr 61.0%

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

      1. log1p-expm1-u 61.0%

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

      2. *-commutative 61.0%

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

      3. *-commutative 61.0%

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

      4. associate-*r* 61.0%

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

   7. Applied egg-rr 61.0%

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

   8. Taylor expanded in x around inf 57.8%

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

      1. *-commutative 57.8%

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

      2. *-commutative 57.8%

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

      3. associate-*l* 57.8%

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

   10. Simplified 57.8%

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

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{a}{3 \cdot b} \leq -2 \cdot 10^{-61} \lor \neg \left(\frac{a}{3 \cdot b} \leq 2 \cdot 10^{-55}\right):\\ \;\;\;\;2 \cdot \sqrt{x} - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 76.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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

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

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

Julia

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

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

Wolfram

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

Derivation

1. Initial program 73.9%

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

3. Taylor expanded in z around 0 80.3%

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

4. Final simplification 80.3%

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

Alternative 5: 65.2% accurate, 2.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 73.9%

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

3. Taylor expanded in z around 0 80.3%

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

4. Taylor expanded in y around 0 68.8%

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

5. Final simplification 68.8%

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

Alternative 6: 65.1% accurate, 2.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 73.9%

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

3. Taylor expanded in z around 0 80.3%

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

4. Taylor expanded in y around 0 68.7%

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

Alternative 7: 50.0% accurate, 43.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 73.9%

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

3. Taylor expanded in z around 0 80.3%

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

4. Taylor expanded in a around inf 54.9%

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

   1. metadata-eval 54.9%

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

   2. distribute-lft-neg-in 54.9%

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

   3. associate-*r/ 54.9%

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

   4. *-commutative 54.9%

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

   5. associate-*r/ 54.9%

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

   6. metadata-eval 54.9%

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

   7. associate-*r/ 54.9%

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

   8. distribute-rgt-neg-in 54.9%

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

   9. associate-*r/ 54.9%

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

   10. metadata-eval 54.9%

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

   11. distribute-neg-frac 54.9%

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

   12. metadata-eval 54.9%

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

6. Simplified 54.9%

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

   1. clear-num 54.8%

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

   2. un-div-inv 54.9%

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

   3. div-inv 55.0%

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

   4. metadata-eval 55.0%

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

8. Applied egg-rr 55.0%

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

Alternative 8: 49.9% accurate, 43.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 73.9%

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

3. Taylor expanded in z around 0 80.3%

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

4. Taylor expanded in a around inf 54.9%

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

5. Final simplification 54.9%

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

Developer target: 74.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024096 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, K"
  :precision binary64

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

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