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

Percentage Accurate: 69.8% → 77.5%

Time: 18.0s

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: 69.8% 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: 77.5% accurate, 0.3× speedup

Math

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

FPCore

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

C

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

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = a / (3.0d0 * b)
    t_2 = 2.0d0 * sqrt(x)
    t_3 = t * (z / 3.0d0)
    if ((t_2 * cos((y - ((z * t) / 3.0d0)))) <= 2d+151) then
        tmp = ((sin(t_3) * (t_2 * sin(y))) + (cos(t_3) * (t_2 * cos(y)))) - t_1
    else
        tmp = t_2 - t_1
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a / N[(3.0 * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(z / 3.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$2 * N[Cos[N[(y - N[(N[(z * t), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2e+151], N[(N[(N[(N[Sin[t$95$3], $MachinePrecision] * N[(t$95$2 * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[Cos[t$95$3], $MachinePrecision] * N[(t$95$2 * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(t$95$2 - t$95$1), $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))))) < 2.00000000000000003e151

   1. Initial program 81.5%

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

      1. cos-diff N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\left(2 \cdot \sqrt{x}\right) \cdot \left(\cos y \cdot \cos \left(\frac{z \cdot t}{3}\right) + \sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\left(2 \cdot \sqrt{x}\right) \cdot \left(\sin y \cdot \sin \left(\frac{z \cdot t}{3}\right) + \cos y \cdot \cos \left(\frac{z \cdot t}{3}\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      3. distribute-rgt-in N/A

         \[\leadsto \mathsf{\_.f64}\left(\left(\left(\sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right) \cdot \left(2 \cdot \sqrt{x}\right) + \left(\cos y \cdot \cos \left(\frac{z \cdot t}{3}\right)\right) \cdot \left(2 \cdot \sqrt{x}\right)\right), \mathsf{/.f64}\left(\color{blue}{a}, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{+.f64}\left(\left(\left(\sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right) \cdot \left(2 \cdot \sqrt{x}\right)\right), \left(\left(\cos y \cdot \cos \left(\frac{z \cdot t}{3}\right)\right) \cdot \left(2 \cdot \sqrt{x}\right)\right)\right), \mathsf{/.f64}\left(\color{blue}{a}, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

   4. Applied egg-rr 82.6%

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

   if 2.00000000000000003e151 < (*.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

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \color{blue}{\cos y}\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]
   4. Step-by-step derivation

      1. cos-lowering-cos.f64 52.2%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

   5. Simplified 52.2%

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

   6. Taylor expanded in y around 0

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(2 \cdot \sqrt{x}\right)}, \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(2, \left(\sqrt{x}\right)\right), \mathsf{/.f64}\left(\color{blue}{a}, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      2. sqrt-lowering-sqrt.f64 55.9%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

   8. Simplified 55.9%

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

4. Final simplification 79.1%

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

Alternative 2: 77.5% accurate, 0.3× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a / N[(3.0 * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(z / 3.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$2 * N[Cos[N[(y - N[(N[(z * t), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2e+151], N[(N[(t$95$2 * N[(N[Cos[t$95$3], $MachinePrecision] * N[Cos[y], $MachinePrecision] + N[(N[Sin[t$95$3], $MachinePrecision] * N[Sin[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(t$95$2 - t$95$1), $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))))) < 2.00000000000000003e151

   1. Initial program 81.5%

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

      1. cos-diff N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \left(\cos y \cdot \cos \left(\frac{z \cdot t}{3}\right) + \sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \left(\cos \left(\frac{z \cdot t}{3}\right) \cdot \cos y + \sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      3. fma-define N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \left(\mathsf{fma}\left(\cos \left(\frac{z \cdot t}{3}\right), \cos y, \sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      4. fma-lowering-fma.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{fma.f64}\left(\cos \left(\frac{z \cdot t}{3}\right), \cos y, \left(\sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      5. cos-lowering-cos.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{fma.f64}\left(\mathsf{cos.f64}\left(\left(\frac{z \cdot t}{3}\right)\right), \cos y, \left(\sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      6. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{fma.f64}\left(\mathsf{cos.f64}\left(\left(\frac{t \cdot z}{3}\right)\right), \cos y, \left(\sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      7. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{fma.f64}\left(\mathsf{cos.f64}\left(\left(t \cdot \frac{z}{3}\right)\right), \cos y, \left(\sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{fma.f64}\left(\mathsf{cos.f64}\left(\mathsf{*.f64}\left(t, \left(\frac{z}{3}\right)\right)\right), \cos y, \left(\sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{fma.f64}\left(\mathsf{cos.f64}\left(\mathsf{*.f64}\left(t, \mathsf{/.f64}\left(z, 3\right)\right)\right), \cos y, \left(\sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      10. cos-lowering-cos.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{fma.f64}\left(\mathsf{cos.f64}\left(\mathsf{*.f64}\left(t, \mathsf{/.f64}\left(z, 3\right)\right)\right), \mathsf{cos.f64}\left(y\right), \left(\sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{fma.f64}\left(\mathsf{cos.f64}\left(\mathsf{*.f64}\left(t, \mathsf{/.f64}\left(z, 3\right)\right)\right), \mathsf{cos.f64}\left(y\right), \mathsf{*.f64}\left(\sin y, \sin \left(\frac{z \cdot t}{3}\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      12. sin-lowering-sin.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{fma.f64}\left(\mathsf{cos.f64}\left(\mathsf{*.f64}\left(t, \mathsf{/.f64}\left(z, 3\right)\right)\right), \mathsf{cos.f64}\left(y\right), \mathsf{*.f64}\left(\mathsf{sin.f64}\left(y\right), \sin \left(\frac{z \cdot t}{3}\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      13. sin-lowering-sin.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{fma.f64}\left(\mathsf{cos.f64}\left(\mathsf{*.f64}\left(t, \mathsf{/.f64}\left(z, 3\right)\right)\right), \mathsf{cos.f64}\left(y\right), \mathsf{*.f64}\left(\mathsf{sin.f64}\left(y\right), \mathsf{sin.f64}\left(\left(\frac{z \cdot t}{3}\right)\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{fma.f64}\left(\mathsf{cos.f64}\left(\mathsf{*.f64}\left(t, \mathsf{/.f64}\left(z, 3\right)\right)\right), \mathsf{cos.f64}\left(y\right), \mathsf{*.f64}\left(\mathsf{sin.f64}\left(y\right), \mathsf{sin.f64}\left(\left(\frac{t \cdot z}{3}\right)\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      15. associate-/l* N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{fma.f64}\left(\mathsf{cos.f64}\left(\mathsf{*.f64}\left(t, \mathsf{/.f64}\left(z, 3\right)\right)\right), \mathsf{cos.f64}\left(y\right), \mathsf{*.f64}\left(\mathsf{sin.f64}\left(y\right), \mathsf{sin.f64}\left(\left(t \cdot \frac{z}{3}\right)\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{fma.f64}\left(\mathsf{cos.f64}\left(\mathsf{*.f64}\left(t, \mathsf{/.f64}\left(z, 3\right)\right)\right), \mathsf{cos.f64}\left(y\right), \mathsf{*.f64}\left(\mathsf{sin.f64}\left(y\right), \mathsf{sin.f64}\left(\mathsf{*.f64}\left(t, \left(\frac{z}{3}\right)\right)\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      17. /-lowering-/.f64 82.6%

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{fma.f64}\left(\mathsf{cos.f64}\left(\mathsf{*.f64}\left(t, \mathsf{/.f64}\left(z, 3\right)\right)\right), \mathsf{cos.f64}\left(y\right), \mathsf{*.f64}\left(\mathsf{sin.f64}\left(y\right), \mathsf{sin.f64}\left(\mathsf{*.f64}\left(t, \mathsf{/.f64}\left(z, 3\right)\right)\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

   4. Applied egg-rr 82.6%

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

   if 2.00000000000000003e151 < (*.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

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \color{blue}{\cos y}\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]
   4. Step-by-step derivation

      1. cos-lowering-cos.f64 52.2%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

   5. Simplified 52.2%

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

   6. Taylor expanded in y around 0

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(2 \cdot \sqrt{x}\right)}, \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(2, \left(\sqrt{x}\right)\right), \mathsf{/.f64}\left(\color{blue}{a}, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      2. sqrt-lowering-sqrt.f64 55.9%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

   8. Simplified 55.9%

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

4. Final simplification 79.1%

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

Alternative 3: 77.5% accurate, 0.3× speedup

Math

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

FPCore

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

C

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

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = a / (3.0d0 * b)
    t_2 = 2.0d0 * sqrt(x)
    t_3 = t * (z / 3.0d0)
    if ((t_2 * cos((y - ((z * t) / 3.0d0)))) <= 2d+151) then
        tmp = (t_2 * ((sin(t_3) * sin(y)) + (cos(t_3) * cos(y)))) - t_1
    else
        tmp = t_2 - t_1
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a / N[(3.0 * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(z / 3.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(t$95$2 * N[Cos[N[(y - N[(N[(z * t), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], 2e+151], N[(N[(t$95$2 * N[(N[(N[Sin[t$95$3], $MachinePrecision] * N[Sin[y], $MachinePrecision]), $MachinePrecision] + N[(N[Cos[t$95$3], $MachinePrecision] * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(t$95$2 - t$95$1), $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))))) < 2.00000000000000003e151

   1. Initial program 81.5%

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

      1. cos-diff N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \left(\cos y \cdot \cos \left(\frac{z \cdot t}{3}\right) + \sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \left(\sin y \cdot \sin \left(\frac{z \cdot t}{3}\right) + \cos y \cdot \cos \left(\frac{z \cdot t}{3}\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{+.f64}\left(\left(\sin y \cdot \sin \left(\frac{z \cdot t}{3}\right)\right), \left(\cos y \cdot \cos \left(\frac{z \cdot t}{3}\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\sin y, \sin \left(\frac{z \cdot t}{3}\right)\right), \left(\cos y \cdot \cos \left(\frac{z \cdot t}{3}\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      5. sin-lowering-sin.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{sin.f64}\left(y\right), \sin \left(\frac{z \cdot t}{3}\right)\right), \left(\cos y \cdot \cos \left(\frac{z \cdot t}{3}\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      6. sin-lowering-sin.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{sin.f64}\left(y\right), \mathsf{sin.f64}\left(\left(\frac{z \cdot t}{3}\right)\right)\right), \left(\cos y \cdot \cos \left(\frac{z \cdot t}{3}\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{sin.f64}\left(y\right), \mathsf{sin.f64}\left(\left(\frac{t \cdot z}{3}\right)\right)\right), \left(\cos y \cdot \cos \left(\frac{z \cdot t}{3}\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      8. associate-/l* N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{sin.f64}\left(y\right), \mathsf{sin.f64}\left(\left(t \cdot \frac{z}{3}\right)\right)\right), \left(\cos y \cdot \cos \left(\frac{z \cdot t}{3}\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{sin.f64}\left(y\right), \mathsf{sin.f64}\left(\mathsf{*.f64}\left(t, \left(\frac{z}{3}\right)\right)\right)\right), \left(\cos y \cdot \cos \left(\frac{z \cdot t}{3}\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{sin.f64}\left(y\right), \mathsf{sin.f64}\left(\mathsf{*.f64}\left(t, \mathsf{/.f64}\left(z, 3\right)\right)\right)\right), \left(\cos y \cdot \cos \left(\frac{z \cdot t}{3}\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{sin.f64}\left(y\right), \mathsf{sin.f64}\left(\mathsf{*.f64}\left(t, \mathsf{/.f64}\left(z, 3\right)\right)\right)\right), \mathsf{*.f64}\left(\cos y, \cos \left(\frac{z \cdot t}{3}\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      12. cos-lowering-cos.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{sin.f64}\left(y\right), \mathsf{sin.f64}\left(\mathsf{*.f64}\left(t, \mathsf{/.f64}\left(z, 3\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{cos.f64}\left(y\right), \cos \left(\frac{z \cdot t}{3}\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      13. cos-lowering-cos.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{sin.f64}\left(y\right), \mathsf{sin.f64}\left(\mathsf{*.f64}\left(t, \mathsf{/.f64}\left(z, 3\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{cos.f64}\left(y\right), \mathsf{cos.f64}\left(\left(\frac{z \cdot t}{3}\right)\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{sin.f64}\left(y\right), \mathsf{sin.f64}\left(\mathsf{*.f64}\left(t, \mathsf{/.f64}\left(z, 3\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{cos.f64}\left(y\right), \mathsf{cos.f64}\left(\left(\frac{t \cdot z}{3}\right)\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      15. associate-/l* N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{sin.f64}\left(y\right), \mathsf{sin.f64}\left(\mathsf{*.f64}\left(t, \mathsf{/.f64}\left(z, 3\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{cos.f64}\left(y\right), \mathsf{cos.f64}\left(\left(t \cdot \frac{z}{3}\right)\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      16. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{sin.f64}\left(y\right), \mathsf{sin.f64}\left(\mathsf{*.f64}\left(t, \mathsf{/.f64}\left(z, 3\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{cos.f64}\left(y\right), \mathsf{cos.f64}\left(\mathsf{*.f64}\left(t, \left(\frac{z}{3}\right)\right)\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      17. /-lowering-/.f64 82.6%

          \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{sin.f64}\left(y\right), \mathsf{sin.f64}\left(\mathsf{*.f64}\left(t, \mathsf{/.f64}\left(z, 3\right)\right)\right)\right), \mathsf{*.f64}\left(\mathsf{cos.f64}\left(y\right), \mathsf{cos.f64}\left(\mathsf{*.f64}\left(t, \mathsf{/.f64}\left(z, 3\right)\right)\right)\right)\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

   4. Applied egg-rr 82.6%

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

   if 2.00000000000000003e151 < (*.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

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \color{blue}{\cos y}\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]
   4. Step-by-step derivation

      1. cos-lowering-cos.f64 52.2%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

   5. Simplified 52.2%

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

   6. Taylor expanded in y around 0

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(2 \cdot \sqrt{x}\right)}, \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(2, \left(\sqrt{x}\right)\right), \mathsf{/.f64}\left(\color{blue}{a}, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      2. sqrt-lowering-sqrt.f64 55.9%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

   8. Simplified 55.9%

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

4. Final simplification 79.1%

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

Alternative 4: 72.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z, t, a, b] = \mathsf{sort}([x, y, z, t, a, b])\\ \\ \begin{array}{l} t_1 := \frac{a}{3 \cdot b}\\ t_2 := 2 \cdot \sqrt{x}\\ t_3 := t\_2 - t\_1\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-88}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-151}:\\ \;\;\;\;t\_2 \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ a (* 3.0 b))) (t_2 (* 2.0 (sqrt x))) (t_3 (- t_2 t_1)))
   (if (<= t_1 -5e-88) t_3 (if (<= t_1 5e-151) (* t_2 (cos y)) t_3))))

C

assert(x < y && y < z && z < t && t < a && a < b);
double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a / (3.0 * b);
	double t_2 = 2.0 * sqrt(x);
	double t_3 = t_2 - t_1;
	double tmp;
	if (t_1 <= -5e-88) {
		tmp = t_3;
	} else if (t_1 <= 5e-151) {
		tmp = t_2 * cos(y);
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = a / (3.0d0 * b)
    t_2 = 2.0d0 * sqrt(x)
    t_3 = t_2 - t_1
    if (t_1 <= (-5d-88)) then
        tmp = t_3
    else if (t_1 <= 5d-151) then
        tmp = t_2 * cos(y)
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t && t < a && a < b;
public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a / (3.0 * b);
	double t_2 = 2.0 * Math.sqrt(x);
	double t_3 = t_2 - t_1;
	double tmp;
	if (t_1 <= -5e-88) {
		tmp = t_3;
	} else if (t_1 <= 5e-151) {
		tmp = t_2 * Math.cos(y);
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

[x, y, z, t, a, b] = sort([x, y, z, t, a, b])
def code(x, y, z, t, a, b):
	t_1 = a / (3.0 * b)
	t_2 = 2.0 * math.sqrt(x)
	t_3 = t_2 - t_1
	tmp = 0
	if t_1 <= -5e-88:
		tmp = t_3
	elif t_1 <= 5e-151:
		tmp = t_2 * math.cos(y)
	else:
		tmp = t_3
	return tmp

Julia

x, y, z, t, a, b = sort([x, y, z, t, a, b])
function code(x, y, z, t, a, b)
	t_1 = Float64(a / Float64(3.0 * b))
	t_2 = Float64(2.0 * sqrt(x))
	t_3 = Float64(t_2 - t_1)
	tmp = 0.0
	if (t_1 <= -5e-88)
		tmp = t_3;
	elseif (t_1 <= 5e-151)
		tmp = Float64(t_2 * cos(y));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

x, y, z, t, a, b = num2cell(sort([x, y, z, t, a, b])){:}
function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a / (3.0 * b);
	t_2 = 2.0 * sqrt(x);
	t_3 = t_2 - t_1;
	tmp = 0.0;
	if (t_1 <= -5e-88)
		tmp = t_3;
	elseif (t_1 <= 5e-151)
		tmp = t_2 * cos(y);
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, t, a, and b should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a / N[(3.0 * b), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 - t$95$1), $MachinePrecision]}, If[LessEqual[t$95$1, -5e-88], t$95$3, If[LessEqual[t$95$1, 5e-151], N[(t$95$2 * N[Cos[y], $MachinePrecision]), $MachinePrecision], t$95$3]]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 a (*.f64 b #s(literal 3 binary64))) < -5.00000000000000009e-88 or 5.00000000000000003e-151 < (/.f64 a (*.f64 b #s(literal 3 binary64)))

   1. Initial program 81.2%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \color{blue}{\cos y}\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]
   4. Step-by-step derivation

      1. cos-lowering-cos.f64 89.6%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

   5. Simplified 89.6%

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

   6. Taylor expanded in y around 0

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(2 \cdot \sqrt{x}\right)}, \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]
   7. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(2, \left(\sqrt{x}\right)\right), \mathsf{/.f64}\left(\color{blue}{a}, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

      2. sqrt-lowering-sqrt.f64 85.2%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

   8. Simplified 85.2%

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

   if -5.00000000000000009e-88 < (/.f64 a (*.f64 b #s(literal 3 binary64))) < 5.00000000000000003e-151

   1. Initial program 48.8%

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

   3. Taylor expanded in z around 0

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \color{blue}{\cos y}\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]
   4. Step-by-step derivation

      1. cos-lowering-cos.f64 51.3%

         \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

   5. Simplified 51.3%

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

   6. Taylor expanded in x around inf

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

      1. associate-*r* N/A

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

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(2 \cdot \sqrt{x}\right), \color{blue}{\cos y}\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \left(\sqrt{x}\right)\right), \cos \color{blue}{y}\right) \]

      4. sqrt-lowering-sqrt.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \cos y\right) \]

      5. cos-lowering-cos.f64 51.3%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{cos.f64}\left(y\right)\right) \]

   8. Simplified 51.3%

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

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{a}{3 \cdot b} \leq -5 \cdot 10^{-88}:\\ \;\;\;\;2 \cdot \sqrt{x} - \frac{a}{3 \cdot b}\\ \mathbf{elif}\;\frac{a}{3 \cdot b} \leq 5 \cdot 10^{-151}:\\ \;\;\;\;\left(2 \cdot \sqrt{x}\right) \cdot \cos y\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{x} - \frac{a}{3 \cdot b}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 76.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 70.7%

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

3. Taylor expanded in z around 0

   \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \color{blue}{\cos y}\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]
4. Step-by-step derivation

   1. cos-lowering-cos.f64 77.2%

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

5. Simplified 77.2%

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

   1. associate-/l/ N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{cos.f64}\left(y\right)\right), \left(\frac{\frac{a}{3}}{\color{blue}{b}}\right)\right) \]

   2. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{/.f64}\left(\left(\frac{a}{3}\right), \color{blue}{b}\right)\right) \]

   3. /-lowering-/.f64 77.2%

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{/.f64}\left(\mathsf{/.f64}\left(a, 3\right), b\right)\right) \]

7. Applied egg-rr 77.2%

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

Alternative 6: 76.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 70.7%

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

3. Taylor expanded in z around 0

   \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \color{blue}{\cos y}\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]
4. Step-by-step derivation

   1. cos-lowering-cos.f64 77.2%

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

5. Simplified 77.2%

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

6. Final simplification 77.2%

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

Alternative 7: 76.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 70.7%

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

3. Taylor expanded in z around 0

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

   1. sub-neg N/A

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

   2. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\left(2 \cdot \left(\sqrt{x} \cdot \cos y\right)\right), \color{blue}{\left(\mathsf{neg}\left(\frac{1}{3} \cdot \frac{a}{b}\right)\right)}\right) \]

   3. associate-*r* N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\left(2 \cdot \sqrt{x}\right) \cdot \cos y\right), \left(\mathsf{neg}\left(\color{blue}{\frac{1}{3} \cdot \frac{a}{b}}\right)\right)\right) \]

   4. *-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\left(\sqrt{x} \cdot 2\right) \cdot \cos y\right), \left(\mathsf{neg}\left(\color{blue}{\frac{1}{3}} \cdot \frac{a}{b}\right)\right)\right) \]

   5. associate-*l* N/A

      \[\leadsto \mathsf{+.f64}\left(\left(\sqrt{x} \cdot \left(2 \cdot \cos y\right)\right), \left(\mathsf{neg}\left(\color{blue}{\frac{1}{3} \cdot \frac{a}{b}}\right)\right)\right) \]

   6. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\left(\sqrt{x}\right), \left(2 \cdot \cos y\right)\right), \left(\mathsf{neg}\left(\color{blue}{\frac{1}{3} \cdot \frac{a}{b}}\right)\right)\right) \]

   7. sqrt-lowering-sqrt.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(2 \cdot \cos y\right)\right), \left(\mathsf{neg}\left(\color{blue}{\frac{1}{3}} \cdot \frac{a}{b}\right)\right)\right) \]

   8. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{*.f64}\left(2, \cos y\right)\right), \left(\mathsf{neg}\left(\frac{1}{3} \cdot \color{blue}{\frac{a}{b}}\right)\right)\right) \]

   9. cos-lowering-cos.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{*.f64}\left(2, \mathsf{cos.f64}\left(y\right)\right)\right), \left(\mathsf{neg}\left(\frac{1}{3} \cdot \frac{a}{\color{blue}{b}}\right)\right)\right) \]

   10. distribute-lft-neg-in N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{*.f64}\left(2, \mathsf{cos.f64}\left(y\right)\right)\right), \left(\left(\mathsf{neg}\left(\frac{1}{3}\right)\right) \cdot \color{blue}{\frac{a}{b}}\right)\right) \]

   11. metadata-eval N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{*.f64}\left(2, \mathsf{cos.f64}\left(y\right)\right)\right), \left(\frac{-1}{3} \cdot \frac{\color{blue}{a}}{b}\right)\right) \]

   12. *-commutative N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{*.f64}\left(2, \mathsf{cos.f64}\left(y\right)\right)\right), \left(\frac{a}{b} \cdot \color{blue}{\frac{-1}{3}}\right)\right) \]

   13. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{*.f64}\left(2, \mathsf{cos.f64}\left(y\right)\right)\right), \mathsf{*.f64}\left(\left(\frac{a}{b}\right), \color{blue}{\frac{-1}{3}}\right)\right) \]

   14. /-lowering-/.f64 77.1%

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{*.f64}\left(2, \mathsf{cos.f64}\left(y\right)\right)\right), \mathsf{*.f64}\left(\mathsf{/.f64}\left(a, b\right), \frac{-1}{3}\right)\right) \]

5. Simplified 77.1%

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

Alternative 8: 65.9% accurate, 2.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 70.7%

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

3. Taylor expanded in z around 0

   \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \color{blue}{\cos y}\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]
4. Step-by-step derivation

   1. cos-lowering-cos.f64 77.2%

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{cos.f64}\left(y\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

5. Simplified 77.2%

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

6. Taylor expanded in y around 0

   \[\leadsto \mathsf{\_.f64}\left(\color{blue}{\left(2 \cdot \sqrt{x}\right)}, \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]
7. Step-by-step derivation

   1. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(2, \left(\sqrt{x}\right)\right), \mathsf{/.f64}\left(\color{blue}{a}, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

   2. sqrt-lowering-sqrt.f64 67.2%

      \[\leadsto \mathsf{\_.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, 3\right)\right)\right) \]

8. Simplified 67.2%

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

9. Final simplification 67.2%

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

Alternative 9: 50.8% accurate, 43.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 70.7%

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

3. Taylor expanded in a around inf

   \[\leadsto \color{blue}{\frac{-1}{3} \cdot \frac{a}{b}} \]
4. Step-by-step derivation

   1. *-commutative N/A

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

   2. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\left(\frac{a}{b}\right), \color{blue}{\frac{-1}{3}}\right) \]

   3. /-lowering-/.f64 54.1%

      \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(a, b\right), \frac{-1}{3}\right) \]

5. Simplified 54.1%

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

   1. associate-*l/ N/A

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

   2. clear-num N/A

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

   3. metadata-eval N/A

      \[\leadsto \frac{1}{\frac{b}{a \cdot \left(\mathsf{neg}\left(\frac{1}{3}\right)\right)}} \]

   4. distribute-rgt-neg-in N/A

      \[\leadsto \frac{1}{\frac{b}{\mathsf{neg}\left(a \cdot \frac{1}{3}\right)}} \]

   5. metadata-eval N/A

      \[\leadsto \frac{1}{\frac{b}{\mathsf{neg}\left(a \cdot \frac{1}{3}\right)}} \]

   6. div-inv N/A

      \[\leadsto \frac{1}{\frac{b}{\mathsf{neg}\left(\frac{a}{3}\right)}} \]

   7. distribute-neg-frac2 N/A

      \[\leadsto \frac{1}{\mathsf{neg}\left(\frac{b}{\frac{a}{3}}\right)} \]

   8. associate-/r/ N/A

      \[\leadsto \frac{1}{\mathsf{neg}\left(\frac{b}{a} \cdot 3\right)} \]

   9. associate-*l/ N/A

      \[\leadsto \frac{1}{\mathsf{neg}\left(\frac{b \cdot 3}{a}\right)} \]

   10. distribute-neg-frac2 N/A

       \[\leadsto \mathsf{neg}\left(\frac{1}{\frac{b \cdot 3}{a}}\right) \]

   11. clear-num N/A

       \[\leadsto \mathsf{neg}\left(\frac{a}{b \cdot 3}\right) \]

   12. associate-/r* N/A

       \[\leadsto \mathsf{neg}\left(\frac{\frac{a}{b}}{3}\right) \]

   13. distribute-neg-frac2 N/A

       \[\leadsto \frac{\frac{a}{b}}{\color{blue}{\mathsf{neg}\left(3\right)}} \]

   14. /-lowering-/.f64 N/A

       \[\leadsto \mathsf{/.f64}\left(\left(\frac{a}{b}\right), \color{blue}{\left(\mathsf{neg}\left(3\right)\right)}\right) \]

   15. /-lowering-/.f64 N/A

       \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(a, b\right), \left(\mathsf{neg}\left(\color{blue}{3}\right)\right)\right) \]

   16. metadata-eval 54.2%

       \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(a, b\right), -3\right) \]

7. Applied egg-rr 54.2%

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

Alternative 10: 50.8% accurate, 43.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 70.7%

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

3. Taylor expanded in a around inf

   \[\leadsto \color{blue}{\frac{-1}{3} \cdot \frac{a}{b}} \]
4. Step-by-step derivation

   1. *-commutative N/A

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

   2. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\left(\frac{a}{b}\right), \color{blue}{\frac{-1}{3}}\right) \]

   3. /-lowering-/.f64 54.1%

      \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(a, b\right), \frac{-1}{3}\right) \]

5. Simplified 54.1%

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

   1. associate-*l/ N/A

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

   2. metadata-eval N/A

      \[\leadsto \frac{a \cdot \left(\mathsf{neg}\left(\frac{1}{3}\right)\right)}{b} \]

   3. distribute-rgt-neg-in N/A

      \[\leadsto \frac{\mathsf{neg}\left(a \cdot \frac{1}{3}\right)}{b} \]

   4. metadata-eval N/A

      \[\leadsto \frac{\mathsf{neg}\left(a \cdot \frac{1}{3}\right)}{b} \]

   5. div-inv N/A

      \[\leadsto \frac{\mathsf{neg}\left(\frac{a}{3}\right)}{b} \]

   6. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\left(\mathsf{neg}\left(\frac{a}{3}\right)\right), \color{blue}{b}\right) \]

   7. distribute-neg-frac2 N/A

      \[\leadsto \mathsf{/.f64}\left(\left(\frac{a}{\mathsf{neg}\left(3\right)}\right), b\right) \]

   8. /-lowering-/.f64 N/A

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(a, \left(\mathsf{neg}\left(3\right)\right)\right), b\right) \]

   9. metadata-eval 54.2%

      \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(a, -3\right), b\right) \]

7. Applied egg-rr 54.2%

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

Alternative 11: 50.8% accurate, 43.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 70.7%

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

3. Taylor expanded in a around inf

   \[\leadsto \color{blue}{\frac{-1}{3} \cdot \frac{a}{b}} \]
4. Step-by-step derivation

   1. *-commutative N/A

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

   2. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\left(\frac{a}{b}\right), \color{blue}{\frac{-1}{3}}\right) \]

   3. /-lowering-/.f64 54.1%

      \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(a, b\right), \frac{-1}{3}\right) \]

5. Simplified 54.1%

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

   1. associate-*l/ N/A

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

   2. clear-num N/A

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

   3. metadata-eval N/A

      \[\leadsto \frac{1}{\frac{b}{a \cdot \left(\mathsf{neg}\left(\frac{1}{3}\right)\right)}} \]

   4. distribute-rgt-neg-in N/A

      \[\leadsto \frac{1}{\frac{b}{\mathsf{neg}\left(a \cdot \frac{1}{3}\right)}} \]

   5. metadata-eval N/A

      \[\leadsto \frac{1}{\frac{b}{\mathsf{neg}\left(a \cdot \frac{1}{3}\right)}} \]

   6. div-inv N/A

      \[\leadsto \frac{1}{\frac{b}{\mathsf{neg}\left(\frac{a}{3}\right)}} \]

   7. distribute-neg-frac2 N/A

      \[\leadsto \frac{1}{\mathsf{neg}\left(\frac{b}{\frac{a}{3}}\right)} \]

   8. associate-/r/ N/A

      \[\leadsto \frac{1}{\mathsf{neg}\left(\frac{b}{a} \cdot 3\right)} \]

   9. associate-*l/ N/A

      \[\leadsto \frac{1}{\mathsf{neg}\left(\frac{b \cdot 3}{a}\right)} \]

   10. distribute-neg-frac2 N/A

       \[\leadsto \mathsf{neg}\left(\frac{1}{\frac{b \cdot 3}{a}}\right) \]

   11. clear-num N/A

       \[\leadsto \mathsf{neg}\left(\frac{a}{b \cdot 3}\right) \]

   12. distribute-neg-frac2 N/A

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

   13. /-lowering-/.f64 N/A

       \[\leadsto \mathsf{/.f64}\left(a, \color{blue}{\left(\mathsf{neg}\left(b \cdot 3\right)\right)}\right) \]

   14. distribute-rgt-neg-in N/A

       \[\leadsto \mathsf{/.f64}\left(a, \left(b \cdot \color{blue}{\left(\mathsf{neg}\left(3\right)\right)}\right)\right) \]

   15. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, \color{blue}{\left(\mathsf{neg}\left(3\right)\right)}\right)\right) \]

   16. metadata-eval 54.2%

       \[\leadsto \mathsf{/.f64}\left(a, \mathsf{*.f64}\left(b, -3\right)\right) \]

7. Applied egg-rr 54.2%

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

Alternative 12: 50.7% accurate, 43.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 70.7%

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

3. Taylor expanded in a around inf

   \[\leadsto \color{blue}{\frac{-1}{3} \cdot \frac{a}{b}} \]
4. Step-by-step derivation

   1. *-commutative N/A

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

   2. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\left(\frac{a}{b}\right), \color{blue}{\frac{-1}{3}}\right) \]

   3. /-lowering-/.f64 54.1%

      \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(a, b\right), \frac{-1}{3}\right) \]

5. Simplified 54.1%

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

   1. associate-*l/ N/A

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

   2. associate-/l* N/A

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

   3. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(a, \color{blue}{\left(\frac{\frac{-1}{3}}{b}\right)}\right) \]

   4. /-lowering-/.f64 54.2%

      \[\leadsto \mathsf{*.f64}\left(a, \mathsf{/.f64}\left(\frac{-1}{3}, \color{blue}{b}\right)\right) \]

7. Applied egg-rr 54.2%

   \[\leadsto \color{blue}{a \cdot \frac{-0.3333333333333333}{b}} \]
8. Add Preprocessing

Developer Target 1: 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 2024163 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, K"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< z -1379333748723514100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (* (* 2 (sqrt x)) (cos (- (/ 1 y) (/ (/ 3333333333333333/10000000000000000 z) t)))) (/ (/ a 3) b)) (if (< z 35162906135559870000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (* (* (sqrt x) 2) (cos (- y (* (/ t 3) z)))) (/ (/ a 3) b)) (- (* (cos (- y (/ (/ 3333333333333333/10000000000000000 z) t))) (* 2 (sqrt x))) (/ (/ a b) 3)))))

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