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

Percentage Accurate: 69.9% → 77.3%

Time: 29.8s

Alternatives: 12

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: 69.9% 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: 77.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := \frac{a}{3 \cdot b}\\ t_2 := 2 \cdot \sqrt{x}\\ t_3 := z \cdot \left(t \cdot 0.3333333333333333\right)\\ \mathbf{if}\;t_2 \cdot \cos \left(y - \frac{z \cdot t}{3}\right) \leq 5 \cdot 10^{+51}:\\ \;\;\;\;\left(t_2 \cdot \left(\cos y \cdot \cos t_3\right) + t_2 \cdot \left(\sin t_3 \cdot \sin y\right)\right) - t_1\\ \mathbf{else}:\\ \;\;\;\;\sqrt{{\cos y}^{2} \cdot \left(x \cdot 4\right)} - t_1\\ \end{array} \end{array} \]

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 (* 2.0 (sqrt x)))
        (t_3 (* z (* t 0.3333333333333333))))
   (if (<= (* t_2 (cos (- y (/ (* z t) 3.0)))) 5e+51)
     (- (+ (* t_2 (* (cos y) (cos t_3))) (* t_2 (* (sin t_3) (sin y)))) t_1)
     (- (sqrt (* (pow (cos y) 2.0) (* x 4.0))) 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 = 2.0 * sqrt(x);
	double t_3 = z * (t * 0.3333333333333333);
	double tmp;
	if ((t_2 * cos((y - ((z * t) / 3.0)))) <= 5e+51) {
		tmp = ((t_2 * (cos(y) * cos(t_3))) + (t_2 * (sin(t_3) * sin(y)))) - t_1;
	} else {
		tmp = sqrt((pow(cos(y), 2.0) * (x * 4.0))) - t_1;
	}
	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 = a / (3.0d0 * b)
    t_2 = 2.0d0 * sqrt(x)
    t_3 = z * (t * 0.3333333333333333d0)
    if ((t_2 * cos((y - ((z * t) / 3.0d0)))) <= 5d+51) then
        tmp = ((t_2 * (cos(y) * cos(t_3))) + (t_2 * (sin(t_3) * sin(y)))) - t_1
    else
        tmp = sqrt(((cos(y) ** 2.0d0) * (x * 4.0d0))) - t_1
    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 = a / (3.0 * b);
	double t_2 = 2.0 * Math.sqrt(x);
	double t_3 = z * (t * 0.3333333333333333);
	double tmp;
	if ((t_2 * Math.cos((y - ((z * t) / 3.0)))) <= 5e+51) {
		tmp = ((t_2 * (Math.cos(y) * Math.cos(t_3))) + (t_2 * (Math.sin(t_3) * Math.sin(y)))) - t_1;
	} else {
		tmp = Math.sqrt((Math.pow(Math.cos(y), 2.0) * (x * 4.0))) - t_1;
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t, a, b):
	t_1 = a / (3.0 * b)
	t_2 = 2.0 * math.sqrt(x)
	t_3 = z * (t * 0.3333333333333333)
	tmp = 0
	if (t_2 * math.cos((y - ((z * t) / 3.0)))) <= 5e+51:
		tmp = ((t_2 * (math.cos(y) * math.cos(t_3))) + (t_2 * (math.sin(t_3) * math.sin(y)))) - t_1
	else:
		tmp = math.sqrt((math.pow(math.cos(y), 2.0) * (x * 4.0))) - 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(2.0 * sqrt(x))
	t_3 = Float64(z * Float64(t * 0.3333333333333333))
	tmp = 0.0
	if (Float64(t_2 * cos(Float64(y - Float64(Float64(z * t) / 3.0)))) <= 5e+51)
		tmp = Float64(Float64(Float64(t_2 * Float64(cos(y) * cos(t_3))) + Float64(t_2 * Float64(sin(t_3) * sin(y)))) - t_1);
	else
		tmp = Float64(sqrt(Float64((cos(y) ^ 2.0) * Float64(x * 4.0))) - t_1);
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a / (3.0 * b);
	t_2 = 2.0 * sqrt(x);
	t_3 = z * (t * 0.3333333333333333);
	tmp = 0.0;
	if ((t_2 * cos((y - ((z * t) / 3.0)))) <= 5e+51)
		tmp = ((t_2 * (cos(y) * cos(t_3))) + (t_2 * (sin(t_3) * sin(y)))) - t_1;
	else
		tmp = sqrt(((cos(y) ^ 2.0) * (x * 4.0))) - t_1;
	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[(a / N[(3.0 * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(t * 0.3333333333333333), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$2 * N[Cos[N[(y - N[(N[(z * t), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 5e+51], N[(N[(N[(t$95$2 * N[(N[Cos[y], $MachinePrecision] * N[Cos[t$95$3], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t$95$2 * N[(N[Sin[t$95$3], $MachinePrecision] * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[Sqrt[N[(N[Power[N[Cos[y], $MachinePrecision], 2.0], $MachinePrecision] * N[(x * 4.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - t$95$1), $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)))) < 5e51

   1. Initial program 77.7%

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

      1. add-exp-log 49.5%

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

      2. *-commutative 49.5%

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

      3. div-inv 48.9%

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

      4. metadata-eval 48.9%

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

   3. Applied egg-rr 48.9%

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

   5. Applied egg-rr 79.5%

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

   if 5e51 < (*.f64 (*.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3))))

   1. Initial program 45.9%

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

   2. Taylor expanded in z around 0 71.6%

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

      1. add-sqr-sqrt 65.0%

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

      2. sqrt-unprod 71.7%

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

      3. *-commutative 71.7%

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

      4. *-commutative 71.7%

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

      5. swap-sqr 71.7%

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

      6. pow2 71.7%

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

      7. *-commutative 71.7%

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

      8. *-commutative 71.7%

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

      9. swap-sqr 71.7%

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

      10. add-sqr-sqrt 71.6%

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

      11. metadata-eval 71.6%

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

   4. Applied egg-rr 71.6%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) \leq 5 \cdot 10^{+51}:\\ \;\;\;\;\left(\left(2 \cdot \sqrt{x}\right) \cdot \left(\cos y \cdot \cos \left(z \cdot \left(t \cdot 0.3333333333333333\right)\right)\right) + \left(2 \cdot \sqrt{x}\right) \cdot \left(\sin \left(z \cdot \left(t \cdot 0.3333333333333333\right)\right) \cdot \sin y\right)\right) - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{{\cos y}^{2} \cdot \left(x \cdot 4\right)} - \frac{a}{3 \cdot b}\\ \end{array} \]

Alternative 2: 77.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := \frac{a}{3 \cdot b}\\ t_2 := 2 \cdot \sqrt{x}\\ t_3 := \left(z \cdot t\right) \cdot 0.3333333333333333\\ \mathbf{if}\;t_2 \cdot \cos \left(y - \frac{z \cdot t}{3}\right) \leq 10^{+100}:\\ \;\;\;\;t_2 \cdot \left(\cos y \cdot \cos t_3 + \sin y \cdot \sin t_3\right) - t_1\\ \mathbf{else}:\\ \;\;\;\;\sqrt{{\cos y}^{2} \cdot \left(x \cdot 4\right)} - t_1\\ \end{array} \end{array} \]

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 (* 2.0 (sqrt x)))
        (t_3 (* (* z t) 0.3333333333333333)))
   (if (<= (* t_2 (cos (- y (/ (* z t) 3.0)))) 1e+100)
     (- (* t_2 (+ (* (cos y) (cos t_3)) (* (sin y) (sin t_3)))) t_1)
     (- (sqrt (* (pow (cos y) 2.0) (* x 4.0))) 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 = 2.0 * sqrt(x);
	double t_3 = (z * t) * 0.3333333333333333;
	double tmp;
	if ((t_2 * cos((y - ((z * t) / 3.0)))) <= 1e+100) {
		tmp = (t_2 * ((cos(y) * cos(t_3)) + (sin(y) * sin(t_3)))) - t_1;
	} else {
		tmp = sqrt((pow(cos(y), 2.0) * (x * 4.0))) - t_1;
	}
	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 = a / (3.0d0 * b)
    t_2 = 2.0d0 * sqrt(x)
    t_3 = (z * t) * 0.3333333333333333d0
    if ((t_2 * cos((y - ((z * t) / 3.0d0)))) <= 1d+100) then
        tmp = (t_2 * ((cos(y) * cos(t_3)) + (sin(y) * sin(t_3)))) - t_1
    else
        tmp = sqrt(((cos(y) ** 2.0d0) * (x * 4.0d0))) - t_1
    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 = a / (3.0 * b);
	double t_2 = 2.0 * Math.sqrt(x);
	double t_3 = (z * t) * 0.3333333333333333;
	double tmp;
	if ((t_2 * Math.cos((y - ((z * t) / 3.0)))) <= 1e+100) {
		tmp = (t_2 * ((Math.cos(y) * Math.cos(t_3)) + (Math.sin(y) * Math.sin(t_3)))) - t_1;
	} else {
		tmp = Math.sqrt((Math.pow(Math.cos(y), 2.0) * (x * 4.0))) - t_1;
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t, a, b):
	t_1 = a / (3.0 * b)
	t_2 = 2.0 * math.sqrt(x)
	t_3 = (z * t) * 0.3333333333333333
	tmp = 0
	if (t_2 * math.cos((y - ((z * t) / 3.0)))) <= 1e+100:
		tmp = (t_2 * ((math.cos(y) * math.cos(t_3)) + (math.sin(y) * math.sin(t_3)))) - t_1
	else:
		tmp = math.sqrt((math.pow(math.cos(y), 2.0) * (x * 4.0))) - 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(2.0 * sqrt(x))
	t_3 = Float64(Float64(z * t) * 0.3333333333333333)
	tmp = 0.0
	if (Float64(t_2 * cos(Float64(y - Float64(Float64(z * t) / 3.0)))) <= 1e+100)
		tmp = Float64(Float64(t_2 * Float64(Float64(cos(y) * cos(t_3)) + Float64(sin(y) * sin(t_3)))) - t_1);
	else
		tmp = Float64(sqrt(Float64((cos(y) ^ 2.0) * Float64(x * 4.0))) - t_1);
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a / (3.0 * b);
	t_2 = 2.0 * sqrt(x);
	t_3 = (z * t) * 0.3333333333333333;
	tmp = 0.0;
	if ((t_2 * cos((y - ((z * t) / 3.0)))) <= 1e+100)
		tmp = (t_2 * ((cos(y) * cos(t_3)) + (sin(y) * sin(t_3)))) - t_1;
	else
		tmp = sqrt(((cos(y) ^ 2.0) * (x * 4.0))) - t_1;
	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[(a / N[(3.0 * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(z * t), $MachinePrecision] * 0.3333333333333333), $MachinePrecision]}, If[LessEqual[N[(t$95$2 * N[Cos[N[(y - N[(N[(z * t), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 1e+100], N[(N[(t$95$2 * 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] - t$95$1), $MachinePrecision], N[(N[Sqrt[N[(N[Power[N[Cos[y], $MachinePrecision], 2.0], $MachinePrecision] * N[(x * 4.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] - t$95$1), $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)))) < 1.00000000000000002e100

   1. Initial program 77.8%

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

      1. cos-diff 79.7%

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

      2. div-inv 79.7%

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

      3. metadata-eval 79.7%

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

      4. div-inv 79.5%

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

      5. metadata-eval 79.5%

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

   3. Applied egg-rr 79.5%

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

   if 1.00000000000000002e100 < (*.f64 (*.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3))))

   1. Initial program 33.5%

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

   2. Taylor expanded in z around 0 68.9%

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

      1. add-sqr-sqrt 61.4%

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

      2. sqrt-unprod 68.9%

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

      3. *-commutative 68.9%

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

      4. *-commutative 68.9%

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

      5. swap-sqr 68.9%

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

      6. pow2 68.9%

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

      7. *-commutative 68.9%

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

      8. *-commutative 68.9%

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

      9. swap-sqr 68.9%

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

      10. add-sqr-sqrt 68.9%

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

      11. metadata-eval 68.9%

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

   4. Applied egg-rr 68.9%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(2 \cdot \sqrt{x}\right) \cdot \cos \left(y - \frac{z \cdot t}{3}\right) \leq 10^{+100}:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \left(\cos y \cdot \cos \left(\left(z \cdot t\right) \cdot 0.3333333333333333\right) + \sin y \cdot \sin \left(\left(z \cdot t\right) \cdot 0.3333333333333333\right)\right) - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{{\cos y}^{2} \cdot \left(x \cdot 4\right)} - \frac{a}{3 \cdot b}\\ \end{array} \]

Alternative 3: 71.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} t_1 := \frac{a}{3 \cdot b}\\ \mathbf{if}\;t_1 \leq -2 \cdot 10^{-107} \lor \neg \left(t_1 \leq 5 \cdot 10^{-54}\right):\\ \;\;\;\;2 \cdot \sqrt{x} - t_1\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot \left(2 \cdot \cos y\right)\\ \end{array} \end{array} \]

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))))
   (if (or (<= t_1 -2e-107) (not (<= t_1 5e-54)))
     (- (* 2.0 (sqrt x)) t_1)
     (* (sqrt x) (* 2.0 (cos y))))))

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 tmp;
	if ((t_1 <= -2e-107) || !(t_1 <= 5e-54)) {
		tmp = (2.0 * sqrt(x)) - t_1;
	} else {
		tmp = sqrt(x) * (2.0 * cos(y));
	}
	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) :: tmp
    t_1 = a / (3.0d0 * b)
    if ((t_1 <= (-2d-107)) .or. (.not. (t_1 <= 5d-54))) then
        tmp = (2.0d0 * sqrt(x)) - t_1
    else
        tmp = sqrt(x) * (2.0d0 * cos(y))
    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 = a / (3.0 * b);
	double tmp;
	if ((t_1 <= -2e-107) || !(t_1 <= 5e-54)) {
		tmp = (2.0 * Math.sqrt(x)) - t_1;
	} else {
		tmp = Math.sqrt(x) * (2.0 * Math.cos(y));
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t, a, b):
	t_1 = a / (3.0 * b)
	tmp = 0
	if (t_1 <= -2e-107) or not (t_1 <= 5e-54):
		tmp = (2.0 * math.sqrt(x)) - t_1
	else:
		tmp = math.sqrt(x) * (2.0 * math.cos(y))
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t, a, b)
	t_1 = Float64(a / Float64(3.0 * b))
	tmp = 0.0
	if ((t_1 <= -2e-107) || !(t_1 <= 5e-54))
		tmp = Float64(Float64(2.0 * sqrt(x)) - t_1);
	else
		tmp = Float64(sqrt(x) * Float64(2.0 * cos(y)));
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a / (3.0 * b);
	tmp = 0.0;
	if ((t_1 <= -2e-107) || ~((t_1 <= 5e-54)))
		tmp = (2.0 * sqrt(x)) - t_1;
	else
		tmp = sqrt(x) * (2.0 * cos(y));
	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[(a / N[(3.0 * b), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e-107], N[Not[LessEqual[t$95$1, 5e-54]], $MachinePrecision]], N[(N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(N[Sqrt[x], $MachinePrecision] * N[(2.0 * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 a (*.f64 b 3)) < -2e-107 or 5.00000000000000015e-54 < (/.f64 a (*.f64 b 3))

   1. Initial program 76.4%

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

   2. Taylor expanded in z around 0 88.2%

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

   3. Taylor expanded in y around 0 85.7%

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

   if -2e-107 < (/.f64 a (*.f64 b 3)) < 5.00000000000000015e-54

   1. Initial program 51.3%

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

      1. fma-neg 51.3%

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

      2. distribute-frac-neg 51.3%

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

      3. *-commutative 51.3%

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

   3. Simplified 51.3%

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

   4. Taylor expanded in z around 0 52.3%

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

      1. associate-*r/ 52.3%

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

   6. Applied egg-rr 52.3%

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

   7. Taylor expanded in a around 0 52.3%

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

      1. *-commutative 52.3%

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

      2. associate-*l* 52.3%

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

   9. Simplified 52.3%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{a}{3 \cdot b} \leq -2 \cdot 10^{-107} \lor \neg \left(\frac{a}{3 \cdot b} \leq 5 \cdot 10^{-54}\right):\\ \;\;\;\;2 \cdot \sqrt{x} - \frac{a}{3 \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot \left(2 \cdot \cos y\right)\\ \end{array} \]

Alternative 4: 76.2% accurate, 1.0× speedup

Math

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

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) (cos y))) (* -0.3333333333333333 (/ a b))))

C

assert(z < t);
double code(double x, double y, double z, double t, double a, double b) {
	return (2.0 * (sqrt(x) * cos(y))) + (-0.3333333333333333 * (a / 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) * cos(y))) + ((-0.3333333333333333d0) * (a / 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) * Math.cos(y))) + (-0.3333333333333333 * (a / b));
}

Python

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

Julia

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

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp = code(x, y, z, t, a, b)
	tmp = (2.0 * (sqrt(x) * cos(y))) + (-0.3333333333333333 * (a / 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[(N[Sqrt[x], $MachinePrecision] * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(-0.3333333333333333 * N[(a / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 67.4%

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

   1. fma-neg 67.4%

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

   2. distribute-frac-neg 67.4%

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

   3. *-commutative 67.4%

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

3. Simplified 67.4%

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

4. Taylor expanded in z around 0 75.3%

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

5. Final simplification 75.3%

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

Alternative 5: 76.3% accurate, 1.0× speedup

Math

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

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) (* 2.0 (* (sqrt x) (cos y)))))

C

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

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) + (2.0d0 * (sqrt(x) * cos(y)))
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) + (2.0 * (Math.sqrt(x) * Math.cos(y)));
}

Python

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

Julia

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

MATLAB

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

Derivation

1. Initial program 67.4%

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

   1. fma-neg 67.4%

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

   2. distribute-frac-neg 67.4%

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

   3. *-commutative 67.4%

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

3. Simplified 67.4%

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

4. Taylor expanded in z around 0 75.3%

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

   1. associate-*r/ 75.3%

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

6. Applied egg-rr 75.3%

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

7. Final simplification 75.3%

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

Alternative 6: 76.3% accurate, 1.0× speedup

Math

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

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)) (cos y)) (/ 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)) * cos(y)) - (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)) * cos(y)) - (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)) * Math.cos(y)) - (a / (3.0 * b));
}

Python

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

Julia

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

z, t = num2cell(sort([z, t])){:}
function tmp = code(x, y, z, t, a, b)
	tmp = ((2.0 * sqrt(x)) * cos(y)) - (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[(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 67.4%

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

2. Taylor expanded in z around 0 75.3%

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

3. Final simplification 75.3%

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

Alternative 7: 65.3% accurate, 2.0× speedup

Math

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

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)) (* -0.3333333333333333 (/ a b))))

C

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

Python

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

Julia

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

MATLAB

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

Derivation

1. Initial program 67.4%

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

   1. fma-neg 67.4%

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

   2. distribute-frac-neg 67.4%

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

   3. *-commutative 67.4%

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

3. Simplified 67.4%

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

4. Taylor expanded in z around 0 75.3%

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

5. Taylor expanded in y around 0 65.1%

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

6. Final simplification 65.1%

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

Alternative 8: 65.4% accurate, 2.0× speedup

Math

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

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (+ (* 2.0 (sqrt x)) (/ (* a -0.3333333333333333) 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 * -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 = (2.0d0 * sqrt(x)) + ((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 (2.0 * Math.sqrt(x)) + ((a * -0.3333333333333333) / b);
}

Python

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

Julia

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

MATLAB

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

Derivation

1. Initial program 67.4%

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

   1. fma-neg 67.4%

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

   2. distribute-frac-neg 67.4%

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

   3. *-commutative 67.4%

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

3. Simplified 67.4%

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

4. Taylor expanded in z around 0 75.3%

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

   1. associate-*r/ 75.3%

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

6. Applied egg-rr 75.3%

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

7. Taylor expanded in y around 0 65.1%

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

8. Final simplification 65.1%

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

Alternative 9: 65.5% 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 67.4%

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

2. Taylor expanded in z around 0 75.3%

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

3. Taylor expanded in y around 0 65.1%

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

4. Final simplification 65.1%

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

Alternative 10: 51.7% accurate, 2.1× speedup

Math

\[\begin{array}{l} [z, t] = \mathsf{sort}([z, t])\\ \\ \begin{array}{l} \mathbf{if}\;b \leq 2.35 \cdot 10^{+91}:\\ \;\;\;\;\frac{a \cdot -0.3333333333333333}{b}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{x}\\ \end{array} \end{array} \]

FPCore

NOTE: z and t should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 2.35e+91) (/ (* a -0.3333333333333333) b) (* 2.0 (sqrt x))))

C

assert(z < t);
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 2.35e+91) {
		tmp = (a * -0.3333333333333333) / b;
	} else {
		tmp = 2.0 * sqrt(x);
	}
	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) :: tmp
    if (b <= 2.35d+91) then
        tmp = (a * (-0.3333333333333333d0)) / b
    else
        tmp = 2.0d0 * sqrt(x)
    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 tmp;
	if (b <= 2.35e+91) {
		tmp = (a * -0.3333333333333333) / b;
	} else {
		tmp = 2.0 * Math.sqrt(x);
	}
	return tmp;
}

Python

[z, t] = sort([z, t])
def code(x, y, z, t, a, b):
	tmp = 0
	if b <= 2.35e+91:
		tmp = (a * -0.3333333333333333) / b
	else:
		tmp = 2.0 * math.sqrt(x)
	return tmp

Julia

z, t = sort([z, t])
function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 2.35e+91)
		tmp = Float64(Float64(a * -0.3333333333333333) / b);
	else
		tmp = Float64(2.0 * sqrt(x));
	end
	return tmp
end

MATLAB

z, t = num2cell(sort([z, t])){:}
function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= 2.35e+91)
		tmp = (a * -0.3333333333333333) / b;
	else
		tmp = 2.0 * sqrt(x);
	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_] := If[LessEqual[b, 2.35e+91], N[(N[(a * -0.3333333333333333), $MachinePrecision] / b), $MachinePrecision], N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 2.3499999999999999e91

   1. Initial program 68.4%

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

   2. Taylor expanded in z around 0 77.7%

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

      1. div-inv 77.6%

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

      2. *-commutative 77.6%

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

   4. Applied egg-rr 77.6%

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

   5. Taylor expanded in x around 0 61.0%

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

      1. associate-*r/ 61.0%

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

   7. Simplified 61.0%

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

   if 2.3499999999999999e91 < b

   1. Initial program 62.1%

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

      1. fma-neg 62.1%

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

      2. distribute-frac-neg 62.1%

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

      3. *-commutative 62.1%

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

   3. Simplified 62.1%

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

   4. Taylor expanded in z around 0 63.3%

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

   5. Taylor expanded in y around 0 38.9%

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

   6. Taylor expanded in a around 0 27.8%

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

4. Final simplification 55.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 2.35 \cdot 10^{+91}:\\ \;\;\;\;\frac{a \cdot -0.3333333333333333}{b}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{x}\\ \end{array} \]

Alternative 11: 50.6% accurate, 43.4× speedup

Math

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

FPCore

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

C

assert(z < t);
double code(double x, double y, double z, double t, double a, double b) {
	return -0.3333333333333333 * (a / 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 = (-0.3333333333333333d0) * (a / b)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Derivation

1. Initial program 67.4%

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

2. Taylor expanded in z around 0 75.3%

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

   1. div-inv 75.2%

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

   2. *-commutative 75.2%

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

4. Applied egg-rr 75.2%

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

5. Taylor expanded in x around 0 53.2%

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

6. Final simplification 53.2%

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

Alternative 12: 50.6% accurate, 43.4× speedup

Math

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

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

Derivation

1. Initial program 67.4%

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

2. Taylor expanded in z around 0 75.3%

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

   1. div-inv 75.2%

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

   2. *-commutative 75.2%

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

4. Applied egg-rr 75.2%

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

5. Taylor expanded in x around 0 53.2%

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

   1. associate-*r/ 53.2%

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

7. Simplified 53.2%

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

8. Final simplification 53.2%

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

Developer target: 74.1% 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 2023287 
(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))))