Main:z from

Percentage Accurate: 91.8% → 98.7%

Time: 35.7s

Alternatives: 16

Speedup: 1.3×

Specification

Math

\[\begin{array}{l} \\ \left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (+
  (+
   (+ (- (sqrt (+ x 1.0)) (sqrt x)) (- (sqrt (+ y 1.0)) (sqrt y)))
   (- (sqrt (+ z 1.0)) (sqrt z)))
  (- (sqrt (+ t 1.0)) (sqrt t))))

C

double code(double x, double y, double z, double t) {
	return (((sqrt((x + 1.0)) - sqrt(x)) + (sqrt((y + 1.0)) - sqrt(y))) + (sqrt((z + 1.0)) - sqrt(z))) + (sqrt((t + 1.0)) - sqrt(t));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (((sqrt((x + 1.0d0)) - sqrt(x)) + (sqrt((y + 1.0d0)) - sqrt(y))) + (sqrt((z + 1.0d0)) - sqrt(z))) + (sqrt((t + 1.0d0)) - sqrt(t))
end function

Java

public static double code(double x, double y, double z, double t) {
	return (((Math.sqrt((x + 1.0)) - Math.sqrt(x)) + (Math.sqrt((y + 1.0)) - Math.sqrt(y))) + (Math.sqrt((z + 1.0)) - Math.sqrt(z))) + (Math.sqrt((t + 1.0)) - Math.sqrt(t));
}

Python

def code(x, y, z, t):
	return (((math.sqrt((x + 1.0)) - math.sqrt(x)) + (math.sqrt((y + 1.0)) - math.sqrt(y))) + (math.sqrt((z + 1.0)) - math.sqrt(z))) + (math.sqrt((t + 1.0)) - math.sqrt(t))

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(Float64(sqrt(Float64(x + 1.0)) - sqrt(x)) + Float64(sqrt(Float64(y + 1.0)) - sqrt(y))) + Float64(sqrt(Float64(z + 1.0)) - sqrt(z))) + Float64(sqrt(Float64(t + 1.0)) - sqrt(t)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (((sqrt((x + 1.0)) - sqrt(x)) + (sqrt((y + 1.0)) - sqrt(y))) + (sqrt((z + 1.0)) - sqrt(z))) + (sqrt((t + 1.0)) - sqrt(t));
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(N[(N[Sqrt[N[(x + 1.0), $MachinePrecision]], $MachinePrecision] - N[Sqrt[x], $MachinePrecision]), $MachinePrecision] + N[(N[Sqrt[N[(y + 1.0), $MachinePrecision]], $MachinePrecision] - N[Sqrt[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[Sqrt[N[(z + 1.0), $MachinePrecision]], $MachinePrecision] - N[Sqrt[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[Sqrt[N[(t + 1.0), $MachinePrecision]], $MachinePrecision] - N[Sqrt[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 91.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(\left(\sqrt{x + 1} - \sqrt{x}\right) + \left(\sqrt{y + 1} - \sqrt{y}\right)\right) + \left(\sqrt{z + 1} - \sqrt{z}\right)\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (+
  (+
   (+ (- (sqrt (+ x 1.0)) (sqrt x)) (- (sqrt (+ y 1.0)) (sqrt y)))
   (- (sqrt (+ z 1.0)) (sqrt z)))
  (- (sqrt (+ t 1.0)) (sqrt t))))

C

double code(double x, double y, double z, double t) {
	return (((sqrt((x + 1.0)) - sqrt(x)) + (sqrt((y + 1.0)) - sqrt(y))) + (sqrt((z + 1.0)) - sqrt(z))) + (sqrt((t + 1.0)) - sqrt(t));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (((sqrt((x + 1.0d0)) - sqrt(x)) + (sqrt((y + 1.0d0)) - sqrt(y))) + (sqrt((z + 1.0d0)) - sqrt(z))) + (sqrt((t + 1.0d0)) - sqrt(t))
end function

Java

public static double code(double x, double y, double z, double t) {
	return (((Math.sqrt((x + 1.0)) - Math.sqrt(x)) + (Math.sqrt((y + 1.0)) - Math.sqrt(y))) + (Math.sqrt((z + 1.0)) - Math.sqrt(z))) + (Math.sqrt((t + 1.0)) - Math.sqrt(t));
}

Python

def code(x, y, z, t):
	return (((math.sqrt((x + 1.0)) - math.sqrt(x)) + (math.sqrt((y + 1.0)) - math.sqrt(y))) + (math.sqrt((z + 1.0)) - math.sqrt(z))) + (math.sqrt((t + 1.0)) - math.sqrt(t))

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(Float64(sqrt(Float64(x + 1.0)) - sqrt(x)) + Float64(sqrt(Float64(y + 1.0)) - sqrt(y))) + Float64(sqrt(Float64(z + 1.0)) - sqrt(z))) + Float64(sqrt(Float64(t + 1.0)) - sqrt(t)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (((sqrt((x + 1.0)) - sqrt(x)) + (sqrt((y + 1.0)) - sqrt(y))) + (sqrt((z + 1.0)) - sqrt(z))) + (sqrt((t + 1.0)) - sqrt(t));
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(N[(N[Sqrt[N[(x + 1.0), $MachinePrecision]], $MachinePrecision] - N[Sqrt[x], $MachinePrecision]), $MachinePrecision] + N[(N[Sqrt[N[(y + 1.0), $MachinePrecision]], $MachinePrecision] - N[Sqrt[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[Sqrt[N[(z + 1.0), $MachinePrecision]], $MachinePrecision] - N[Sqrt[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[Sqrt[N[(t + 1.0), $MachinePrecision]], $MachinePrecision] - N[Sqrt[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 98.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \sqrt{1 + y}\\ t_2 := \sqrt{1 + z}\\ t_3 := \sqrt{x + 1}\\ t_4 := \sqrt{1 + t}\\ \mathbf{if}\;t_3 - \sqrt{x} \leq 0.9999999999995:\\ \;\;\;\;\frac{1}{t_3 + \sqrt{x}} + \left(\left(t_1 - \sqrt{y}\right) + \left(t_4 + \left(\left(t_2 - \sqrt{z}\right) - \sqrt{t}\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{1}{t_2 + \sqrt{z}} + \left(1 + \frac{1}{t_1 + \sqrt{y}}\right)\right) + \frac{1}{t_4 + \sqrt{t}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (sqrt (+ 1.0 y)))
        (t_2 (sqrt (+ 1.0 z)))
        (t_3 (sqrt (+ x 1.0)))
        (t_4 (sqrt (+ 1.0 t))))
   (if (<= (- t_3 (sqrt x)) 0.9999999999995)
     (+
      (/ 1.0 (+ t_3 (sqrt x)))
      (+ (- t_1 (sqrt y)) (+ t_4 (- (- t_2 (sqrt z)) (sqrt t)))))
     (+
      (+ (/ 1.0 (+ t_2 (sqrt z))) (+ 1.0 (/ 1.0 (+ t_1 (sqrt y)))))
      (/ 1.0 (+ t_4 (sqrt t)))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = sqrt((1.0 + y));
	double t_2 = sqrt((1.0 + z));
	double t_3 = sqrt((x + 1.0));
	double t_4 = sqrt((1.0 + t));
	double tmp;
	if ((t_3 - sqrt(x)) <= 0.9999999999995) {
		tmp = (1.0 / (t_3 + sqrt(x))) + ((t_1 - sqrt(y)) + (t_4 + ((t_2 - sqrt(z)) - sqrt(t))));
	} else {
		tmp = ((1.0 / (t_2 + sqrt(z))) + (1.0 + (1.0 / (t_1 + sqrt(y))))) + (1.0 / (t_4 + sqrt(t)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = sqrt((1.0d0 + y))
    t_2 = sqrt((1.0d0 + z))
    t_3 = sqrt((x + 1.0d0))
    t_4 = sqrt((1.0d0 + t))
    if ((t_3 - sqrt(x)) <= 0.9999999999995d0) then
        tmp = (1.0d0 / (t_3 + sqrt(x))) + ((t_1 - sqrt(y)) + (t_4 + ((t_2 - sqrt(z)) - sqrt(t))))
    else
        tmp = ((1.0d0 / (t_2 + sqrt(z))) + (1.0d0 + (1.0d0 / (t_1 + sqrt(y))))) + (1.0d0 / (t_4 + sqrt(t)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = Math.sqrt((1.0 + y));
	double t_2 = Math.sqrt((1.0 + z));
	double t_3 = Math.sqrt((x + 1.0));
	double t_4 = Math.sqrt((1.0 + t));
	double tmp;
	if ((t_3 - Math.sqrt(x)) <= 0.9999999999995) {
		tmp = (1.0 / (t_3 + Math.sqrt(x))) + ((t_1 - Math.sqrt(y)) + (t_4 + ((t_2 - Math.sqrt(z)) - Math.sqrt(t))));
	} else {
		tmp = ((1.0 / (t_2 + Math.sqrt(z))) + (1.0 + (1.0 / (t_1 + Math.sqrt(y))))) + (1.0 / (t_4 + Math.sqrt(t)));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = math.sqrt((1.0 + y))
	t_2 = math.sqrt((1.0 + z))
	t_3 = math.sqrt((x + 1.0))
	t_4 = math.sqrt((1.0 + t))
	tmp = 0
	if (t_3 - math.sqrt(x)) <= 0.9999999999995:
		tmp = (1.0 / (t_3 + math.sqrt(x))) + ((t_1 - math.sqrt(y)) + (t_4 + ((t_2 - math.sqrt(z)) - math.sqrt(t))))
	else:
		tmp = ((1.0 / (t_2 + math.sqrt(z))) + (1.0 + (1.0 / (t_1 + math.sqrt(y))))) + (1.0 / (t_4 + math.sqrt(t)))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = sqrt(Float64(1.0 + y))
	t_2 = sqrt(Float64(1.0 + z))
	t_3 = sqrt(Float64(x + 1.0))
	t_4 = sqrt(Float64(1.0 + t))
	tmp = 0.0
	if (Float64(t_3 - sqrt(x)) <= 0.9999999999995)
		tmp = Float64(Float64(1.0 / Float64(t_3 + sqrt(x))) + Float64(Float64(t_1 - sqrt(y)) + Float64(t_4 + Float64(Float64(t_2 - sqrt(z)) - sqrt(t)))));
	else
		tmp = Float64(Float64(Float64(1.0 / Float64(t_2 + sqrt(z))) + Float64(1.0 + Float64(1.0 / Float64(t_1 + sqrt(y))))) + Float64(1.0 / Float64(t_4 + sqrt(t))));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = sqrt((1.0 + y));
	t_2 = sqrt((1.0 + z));
	t_3 = sqrt((x + 1.0));
	t_4 = sqrt((1.0 + t));
	tmp = 0.0;
	if ((t_3 - sqrt(x)) <= 0.9999999999995)
		tmp = (1.0 / (t_3 + sqrt(x))) + ((t_1 - sqrt(y)) + (t_4 + ((t_2 - sqrt(z)) - sqrt(t))));
	else
		tmp = ((1.0 / (t_2 + sqrt(z))) + (1.0 + (1.0 / (t_1 + sqrt(y))))) + (1.0 / (t_4 + sqrt(t)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[Sqrt[N[(1.0 + y), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[Sqrt[N[(1.0 + z), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$3 = N[Sqrt[N[(x + 1.0), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$4 = N[Sqrt[N[(1.0 + t), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[N[(t$95$3 - N[Sqrt[x], $MachinePrecision]), $MachinePrecision], 0.9999999999995], N[(N[(1.0 / N[(t$95$3 + N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t$95$1 - N[Sqrt[y], $MachinePrecision]), $MachinePrecision] + N[(t$95$4 + N[(N[(t$95$2 - N[Sqrt[z], $MachinePrecision]), $MachinePrecision] - N[Sqrt[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(1.0 / N[(t$95$2 + N[Sqrt[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(1.0 + N[(1.0 / N[(t$95$1 + N[Sqrt[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(1.0 / N[(t$95$4 + N[Sqrt[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 2: 98.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \sqrt{x + 1}\\ t_2 := \sqrt{1 + y}\\ \mathbf{if}\;\left(t_1 - \sqrt{x}\right) + \left(t_2 - \sqrt{y}\right) \leq 0.9999999999995:\\ \;\;\;\;\frac{1}{t_1 + \sqrt{x}}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{1}{\sqrt{1 + z} + \sqrt{z}} + \left(1 + \frac{1}{t_2 + \sqrt{y}}\right)\right) + \frac{1}{\sqrt{1 + t} + \sqrt{t}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (sqrt (+ x 1.0))) (t_2 (sqrt (+ 1.0 y))))
   (if (<= (+ (- t_1 (sqrt x)) (- t_2 (sqrt y))) 0.9999999999995)
     (/ 1.0 (+ t_1 (sqrt x)))
     (+
      (+
       (/ 1.0 (+ (sqrt (+ 1.0 z)) (sqrt z)))
       (+ 1.0 (/ 1.0 (+ t_2 (sqrt y)))))
      (/ 1.0 (+ (sqrt (+ 1.0 t)) (sqrt t)))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = sqrt((x + 1.0));
	double t_2 = sqrt((1.0 + y));
	double tmp;
	if (((t_1 - sqrt(x)) + (t_2 - sqrt(y))) <= 0.9999999999995) {
		tmp = 1.0 / (t_1 + sqrt(x));
	} else {
		tmp = ((1.0 / (sqrt((1.0 + z)) + sqrt(z))) + (1.0 + (1.0 / (t_2 + sqrt(y))))) + (1.0 / (sqrt((1.0 + t)) + sqrt(t)));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = sqrt((x + 1.0d0))
    t_2 = sqrt((1.0d0 + y))
    if (((t_1 - sqrt(x)) + (t_2 - sqrt(y))) <= 0.9999999999995d0) then
        tmp = 1.0d0 / (t_1 + sqrt(x))
    else
        tmp = ((1.0d0 / (sqrt((1.0d0 + z)) + sqrt(z))) + (1.0d0 + (1.0d0 / (t_2 + sqrt(y))))) + (1.0d0 / (sqrt((1.0d0 + t)) + sqrt(t)))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = Math.sqrt((x + 1.0));
	double t_2 = Math.sqrt((1.0 + y));
	double tmp;
	if (((t_1 - Math.sqrt(x)) + (t_2 - Math.sqrt(y))) <= 0.9999999999995) {
		tmp = 1.0 / (t_1 + Math.sqrt(x));
	} else {
		tmp = ((1.0 / (Math.sqrt((1.0 + z)) + Math.sqrt(z))) + (1.0 + (1.0 / (t_2 + Math.sqrt(y))))) + (1.0 / (Math.sqrt((1.0 + t)) + Math.sqrt(t)));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = math.sqrt((x + 1.0))
	t_2 = math.sqrt((1.0 + y))
	tmp = 0
	if ((t_1 - math.sqrt(x)) + (t_2 - math.sqrt(y))) <= 0.9999999999995:
		tmp = 1.0 / (t_1 + math.sqrt(x))
	else:
		tmp = ((1.0 / (math.sqrt((1.0 + z)) + math.sqrt(z))) + (1.0 + (1.0 / (t_2 + math.sqrt(y))))) + (1.0 / (math.sqrt((1.0 + t)) + math.sqrt(t)))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = sqrt(Float64(x + 1.0))
	t_2 = sqrt(Float64(1.0 + y))
	tmp = 0.0
	if (Float64(Float64(t_1 - sqrt(x)) + Float64(t_2 - sqrt(y))) <= 0.9999999999995)
		tmp = Float64(1.0 / Float64(t_1 + sqrt(x)));
	else
		tmp = Float64(Float64(Float64(1.0 / Float64(sqrt(Float64(1.0 + z)) + sqrt(z))) + Float64(1.0 + Float64(1.0 / Float64(t_2 + sqrt(y))))) + Float64(1.0 / Float64(sqrt(Float64(1.0 + t)) + sqrt(t))));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = sqrt((x + 1.0));
	t_2 = sqrt((1.0 + y));
	tmp = 0.0;
	if (((t_1 - sqrt(x)) + (t_2 - sqrt(y))) <= 0.9999999999995)
		tmp = 1.0 / (t_1 + sqrt(x));
	else
		tmp = ((1.0 / (sqrt((1.0 + z)) + sqrt(z))) + (1.0 + (1.0 / (t_2 + sqrt(y))))) + (1.0 / (sqrt((1.0 + t)) + sqrt(t)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[Sqrt[N[(x + 1.0), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[Sqrt[N[(1.0 + y), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[N[(N[(t$95$1 - N[Sqrt[x], $MachinePrecision]), $MachinePrecision] + N[(t$95$2 - N[Sqrt[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 0.9999999999995], N[(1.0 / N[(t$95$1 + N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(1.0 / N[(N[Sqrt[N[(1.0 + z), $MachinePrecision]], $MachinePrecision] + N[Sqrt[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(1.0 + N[(1.0 / N[(t$95$2 + N[Sqrt[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(1.0 / N[(N[Sqrt[N[(1.0 + t), $MachinePrecision]], $MachinePrecision] + N[Sqrt[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 3: 97.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 2.4 \cdot 10^{+31}:\\ \;\;\;\;\left(\frac{1}{\sqrt{1 + z} + \sqrt{z}} + \left(1 + \frac{1}{\sqrt{1 + y} + \sqrt{y}}\right)\right) + \left(\sqrt{1 + t} - \sqrt{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\sqrt{x + 1} + \sqrt{x}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= y 2.4e+31)
   (+
    (+
     (/ 1.0 (+ (sqrt (+ 1.0 z)) (sqrt z)))
     (+ 1.0 (/ 1.0 (+ (sqrt (+ 1.0 y)) (sqrt y)))))
    (- (sqrt (+ 1.0 t)) (sqrt t)))
   (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 2.4e+31) {
		tmp = ((1.0 / (sqrt((1.0 + z)) + sqrt(z))) + (1.0 + (1.0 / (sqrt((1.0 + y)) + sqrt(y))))) + (sqrt((1.0 + t)) - sqrt(t));
	} else {
		tmp = 1.0 / (sqrt((x + 1.0)) + sqrt(x));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= 2.4d+31) then
        tmp = ((1.0d0 / (sqrt((1.0d0 + z)) + sqrt(z))) + (1.0d0 + (1.0d0 / (sqrt((1.0d0 + y)) + sqrt(y))))) + (sqrt((1.0d0 + t)) - sqrt(t))
    else
        tmp = 1.0d0 / (sqrt((x + 1.0d0)) + sqrt(x))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 2.4e+31) {
		tmp = ((1.0 / (Math.sqrt((1.0 + z)) + Math.sqrt(z))) + (1.0 + (1.0 / (Math.sqrt((1.0 + y)) + Math.sqrt(y))))) + (Math.sqrt((1.0 + t)) - Math.sqrt(t));
	} else {
		tmp = 1.0 / (Math.sqrt((x + 1.0)) + Math.sqrt(x));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if y <= 2.4e+31:
		tmp = ((1.0 / (math.sqrt((1.0 + z)) + math.sqrt(z))) + (1.0 + (1.0 / (math.sqrt((1.0 + y)) + math.sqrt(y))))) + (math.sqrt((1.0 + t)) - math.sqrt(t))
	else:
		tmp = 1.0 / (math.sqrt((x + 1.0)) + math.sqrt(x))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (y <= 2.4e+31)
		tmp = Float64(Float64(Float64(1.0 / Float64(sqrt(Float64(1.0 + z)) + sqrt(z))) + Float64(1.0 + Float64(1.0 / Float64(sqrt(Float64(1.0 + y)) + sqrt(y))))) + Float64(sqrt(Float64(1.0 + t)) - sqrt(t)));
	else
		tmp = Float64(1.0 / Float64(sqrt(Float64(x + 1.0)) + sqrt(x)));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 2.4e+31)
		tmp = ((1.0 / (sqrt((1.0 + z)) + sqrt(z))) + (1.0 + (1.0 / (sqrt((1.0 + y)) + sqrt(y))))) + (sqrt((1.0 + t)) - sqrt(t));
	else
		tmp = 1.0 / (sqrt((x + 1.0)) + sqrt(x));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[y, 2.4e+31], N[(N[(N[(1.0 / N[(N[Sqrt[N[(1.0 + z), $MachinePrecision]], $MachinePrecision] + N[Sqrt[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(1.0 + N[(1.0 / N[(N[Sqrt[N[(1.0 + y), $MachinePrecision]], $MachinePrecision] + N[Sqrt[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[Sqrt[N[(1.0 + t), $MachinePrecision]], $MachinePrecision] - N[Sqrt[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(N[Sqrt[N[(x + 1.0), $MachinePrecision]], $MachinePrecision] + N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 4: 91.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \sqrt{1 + y} - \sqrt{y}\\ t_2 := \sqrt{x + 1} - \sqrt{x}\\ \mathbf{if}\;t \leq 2.4 \cdot 10^{+14}:\\ \;\;\;\;t_2 + \left(t_1 + \left(1 + \frac{1}{\sqrt{1 + t} + \sqrt{t}}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_2 + \left(t_1 - \left(\sqrt{z} - \sqrt{1 + z}\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (sqrt (+ 1.0 y)) (sqrt y)))
        (t_2 (- (sqrt (+ x 1.0)) (sqrt x))))
   (if (<= t 2.4e+14)
     (+ t_2 (+ t_1 (+ 1.0 (/ 1.0 (+ (sqrt (+ 1.0 t)) (sqrt t))))))
     (+ t_2 (- t_1 (- (sqrt z) (sqrt (+ 1.0 z))))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = sqrt((1.0 + y)) - sqrt(y);
	double t_2 = sqrt((x + 1.0)) - sqrt(x);
	double tmp;
	if (t <= 2.4e+14) {
		tmp = t_2 + (t_1 + (1.0 + (1.0 / (sqrt((1.0 + t)) + sqrt(t)))));
	} else {
		tmp = t_2 + (t_1 - (sqrt(z) - sqrt((1.0 + z))));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = sqrt((1.0d0 + y)) - sqrt(y)
    t_2 = sqrt((x + 1.0d0)) - sqrt(x)
    if (t <= 2.4d+14) then
        tmp = t_2 + (t_1 + (1.0d0 + (1.0d0 / (sqrt((1.0d0 + t)) + sqrt(t)))))
    else
        tmp = t_2 + (t_1 - (sqrt(z) - sqrt((1.0d0 + z))))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = Math.sqrt((1.0 + y)) - Math.sqrt(y);
	double t_2 = Math.sqrt((x + 1.0)) - Math.sqrt(x);
	double tmp;
	if (t <= 2.4e+14) {
		tmp = t_2 + (t_1 + (1.0 + (1.0 / (Math.sqrt((1.0 + t)) + Math.sqrt(t)))));
	} else {
		tmp = t_2 + (t_1 - (Math.sqrt(z) - Math.sqrt((1.0 + z))));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = math.sqrt((1.0 + y)) - math.sqrt(y)
	t_2 = math.sqrt((x + 1.0)) - math.sqrt(x)
	tmp = 0
	if t <= 2.4e+14:
		tmp = t_2 + (t_1 + (1.0 + (1.0 / (math.sqrt((1.0 + t)) + math.sqrt(t)))))
	else:
		tmp = t_2 + (t_1 - (math.sqrt(z) - math.sqrt((1.0 + z))))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(sqrt(Float64(1.0 + y)) - sqrt(y))
	t_2 = Float64(sqrt(Float64(x + 1.0)) - sqrt(x))
	tmp = 0.0
	if (t <= 2.4e+14)
		tmp = Float64(t_2 + Float64(t_1 + Float64(1.0 + Float64(1.0 / Float64(sqrt(Float64(1.0 + t)) + sqrt(t))))));
	else
		tmp = Float64(t_2 + Float64(t_1 - Float64(sqrt(z) - sqrt(Float64(1.0 + z)))));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = sqrt((1.0 + y)) - sqrt(y);
	t_2 = sqrt((x + 1.0)) - sqrt(x);
	tmp = 0.0;
	if (t <= 2.4e+14)
		tmp = t_2 + (t_1 + (1.0 + (1.0 / (sqrt((1.0 + t)) + sqrt(t)))));
	else
		tmp = t_2 + (t_1 - (sqrt(z) - sqrt((1.0 + z))));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[Sqrt[N[(1.0 + y), $MachinePrecision]], $MachinePrecision] - N[Sqrt[y], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[Sqrt[N[(x + 1.0), $MachinePrecision]], $MachinePrecision] - N[Sqrt[x], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, 2.4e+14], N[(t$95$2 + N[(t$95$1 + N[(1.0 + N[(1.0 / N[(N[Sqrt[N[(1.0 + t), $MachinePrecision]], $MachinePrecision] + N[Sqrt[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$2 + N[(t$95$1 - N[(N[Sqrt[z], $MachinePrecision] - N[Sqrt[N[(1.0 + z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 5: 96.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \sqrt{x + 1}\\ \mathbf{if}\;y \leq 3.9 \cdot 10^{-28}:\\ \;\;\;\;\left(\sqrt{1 + t} - \sqrt{t}\right) + \left(\left(\frac{1}{\sqrt{1 + z} + \sqrt{z}} + \left(1 + t_1\right)\right) - \sqrt{x}\right)\\ \mathbf{elif}\;y \leq 10^{+19}:\\ \;\;\;\;\left(t_1 + \sqrt{1 + y}\right) - \left(\sqrt{y} + \sqrt{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{t_1 + \sqrt{x}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (sqrt (+ x 1.0))))
   (if (<= y 3.9e-28)
     (+
      (- (sqrt (+ 1.0 t)) (sqrt t))
      (- (+ (/ 1.0 (+ (sqrt (+ 1.0 z)) (sqrt z))) (+ 1.0 t_1)) (sqrt x)))
     (if (<= y 1e+19)
       (- (+ t_1 (sqrt (+ 1.0 y))) (+ (sqrt y) (sqrt x)))
       (/ 1.0 (+ t_1 (sqrt x)))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = sqrt((x + 1.0));
	double tmp;
	if (y <= 3.9e-28) {
		tmp = (sqrt((1.0 + t)) - sqrt(t)) + (((1.0 / (sqrt((1.0 + z)) + sqrt(z))) + (1.0 + t_1)) - sqrt(x));
	} else if (y <= 1e+19) {
		tmp = (t_1 + sqrt((1.0 + y))) - (sqrt(y) + sqrt(x));
	} else {
		tmp = 1.0 / (t_1 + sqrt(x));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = sqrt((x + 1.0d0))
    if (y <= 3.9d-28) then
        tmp = (sqrt((1.0d0 + t)) - sqrt(t)) + (((1.0d0 / (sqrt((1.0d0 + z)) + sqrt(z))) + (1.0d0 + t_1)) - sqrt(x))
    else if (y <= 1d+19) then
        tmp = (t_1 + sqrt((1.0d0 + y))) - (sqrt(y) + sqrt(x))
    else
        tmp = 1.0d0 / (t_1 + sqrt(x))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = Math.sqrt((x + 1.0));
	double tmp;
	if (y <= 3.9e-28) {
		tmp = (Math.sqrt((1.0 + t)) - Math.sqrt(t)) + (((1.0 / (Math.sqrt((1.0 + z)) + Math.sqrt(z))) + (1.0 + t_1)) - Math.sqrt(x));
	} else if (y <= 1e+19) {
		tmp = (t_1 + Math.sqrt((1.0 + y))) - (Math.sqrt(y) + Math.sqrt(x));
	} else {
		tmp = 1.0 / (t_1 + Math.sqrt(x));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = math.sqrt((x + 1.0))
	tmp = 0
	if y <= 3.9e-28:
		tmp = (math.sqrt((1.0 + t)) - math.sqrt(t)) + (((1.0 / (math.sqrt((1.0 + z)) + math.sqrt(z))) + (1.0 + t_1)) - math.sqrt(x))
	elif y <= 1e+19:
		tmp = (t_1 + math.sqrt((1.0 + y))) - (math.sqrt(y) + math.sqrt(x))
	else:
		tmp = 1.0 / (t_1 + math.sqrt(x))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = sqrt(Float64(x + 1.0))
	tmp = 0.0
	if (y <= 3.9e-28)
		tmp = Float64(Float64(sqrt(Float64(1.0 + t)) - sqrt(t)) + Float64(Float64(Float64(1.0 / Float64(sqrt(Float64(1.0 + z)) + sqrt(z))) + Float64(1.0 + t_1)) - sqrt(x)));
	elseif (y <= 1e+19)
		tmp = Float64(Float64(t_1 + sqrt(Float64(1.0 + y))) - Float64(sqrt(y) + sqrt(x)));
	else
		tmp = Float64(1.0 / Float64(t_1 + sqrt(x)));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = sqrt((x + 1.0));
	tmp = 0.0;
	if (y <= 3.9e-28)
		tmp = (sqrt((1.0 + t)) - sqrt(t)) + (((1.0 / (sqrt((1.0 + z)) + sqrt(z))) + (1.0 + t_1)) - sqrt(x));
	elseif (y <= 1e+19)
		tmp = (t_1 + sqrt((1.0 + y))) - (sqrt(y) + sqrt(x));
	else
		tmp = 1.0 / (t_1 + sqrt(x));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[Sqrt[N[(x + 1.0), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[y, 3.9e-28], N[(N[(N[Sqrt[N[(1.0 + t), $MachinePrecision]], $MachinePrecision] - N[Sqrt[t], $MachinePrecision]), $MachinePrecision] + N[(N[(N[(1.0 / N[(N[Sqrt[N[(1.0 + z), $MachinePrecision]], $MachinePrecision] + N[Sqrt[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(1.0 + t$95$1), $MachinePrecision]), $MachinePrecision] - N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1e+19], N[(N[(t$95$1 + N[Sqrt[N[(1.0 + y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] - N[(N[Sqrt[y], $MachinePrecision] + N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(t$95$1 + N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 6: 91.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \sqrt{x + 1} - \sqrt{x}\\ \mathbf{if}\;t \leq 900000000000:\\ \;\;\;\;t_1 + {\left(\sqrt[3]{\frac{1}{\sqrt{1 + t} + \sqrt{t}} + 2}\right)}^{3}\\ \mathbf{else}:\\ \;\;\;\;t_1 + \left(\left(\sqrt{1 + y} - \sqrt{y}\right) - \left(\sqrt{z} - \sqrt{1 + z}\right)\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (sqrt (+ x 1.0)) (sqrt x))))
   (if (<= t 900000000000.0)
     (+ t_1 (pow (cbrt (+ (/ 1.0 (+ (sqrt (+ 1.0 t)) (sqrt t))) 2.0)) 3.0))
     (+ t_1 (- (- (sqrt (+ 1.0 y)) (sqrt y)) (- (sqrt z) (sqrt (+ 1.0 z))))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = sqrt((x + 1.0)) - sqrt(x);
	double tmp;
	if (t <= 900000000000.0) {
		tmp = t_1 + pow(cbrt(((1.0 / (sqrt((1.0 + t)) + sqrt(t))) + 2.0)), 3.0);
	} else {
		tmp = t_1 + ((sqrt((1.0 + y)) - sqrt(y)) - (sqrt(z) - sqrt((1.0 + z))));
	}
	return tmp;
}

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = Math.sqrt((x + 1.0)) - Math.sqrt(x);
	double tmp;
	if (t <= 900000000000.0) {
		tmp = t_1 + Math.pow(Math.cbrt(((1.0 / (Math.sqrt((1.0 + t)) + Math.sqrt(t))) + 2.0)), 3.0);
	} else {
		tmp = t_1 + ((Math.sqrt((1.0 + y)) - Math.sqrt(y)) - (Math.sqrt(z) - Math.sqrt((1.0 + z))));
	}
	return tmp;
}

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(sqrt(Float64(x + 1.0)) - sqrt(x))
	tmp = 0.0
	if (t <= 900000000000.0)
		tmp = Float64(t_1 + (cbrt(Float64(Float64(1.0 / Float64(sqrt(Float64(1.0 + t)) + sqrt(t))) + 2.0)) ^ 3.0));
	else
		tmp = Float64(t_1 + Float64(Float64(sqrt(Float64(1.0 + y)) - sqrt(y)) - Float64(sqrt(z) - sqrt(Float64(1.0 + z)))));
	end
	return tmp
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[Sqrt[N[(x + 1.0), $MachinePrecision]], $MachinePrecision] - N[Sqrt[x], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, 900000000000.0], N[(t$95$1 + N[Power[N[Power[N[(N[(1.0 / N[(N[Sqrt[N[(1.0 + t), $MachinePrecision]], $MachinePrecision] + N[Sqrt[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 2.0), $MachinePrecision], 1/3], $MachinePrecision], 3.0], $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(N[(N[Sqrt[N[(1.0 + y), $MachinePrecision]], $MachinePrecision] - N[Sqrt[y], $MachinePrecision]), $MachinePrecision] - N[(N[Sqrt[z], $MachinePrecision] - N[Sqrt[N[(1.0 + z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 7: 89.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \sqrt{x + 1}\\ \mathbf{if}\;z \leq 4.2 \cdot 10^{-31}:\\ \;\;\;\;\left(\sqrt{1 + t} - \sqrt{t}\right) + 3\\ \mathbf{elif}\;z \leq 13500000000000:\\ \;\;\;\;\left(1 + \left(t_1 + \sqrt{1 + z}\right)\right) - \left(\sqrt{x} + \frac{z - y}{\sqrt{z} - \sqrt{y}}\right)\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+219}:\\ \;\;\;\;t_1 + \left(\sqrt{1 + y} - \left(\sqrt{y} + \sqrt{x}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{t_1 + \sqrt{x}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (sqrt (+ x 1.0))))
   (if (<= z 4.2e-31)
     (+ (- (sqrt (+ 1.0 t)) (sqrt t)) 3.0)
     (if (<= z 13500000000000.0)
       (-
        (+ 1.0 (+ t_1 (sqrt (+ 1.0 z))))
        (+ (sqrt x) (/ (- z y) (- (sqrt z) (sqrt y)))))
       (if (<= z 1.8e+219)
         (+ t_1 (- (sqrt (+ 1.0 y)) (+ (sqrt y) (sqrt x))))
         (/ 1.0 (+ t_1 (sqrt x))))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = sqrt((x + 1.0));
	double tmp;
	if (z <= 4.2e-31) {
		tmp = (sqrt((1.0 + t)) - sqrt(t)) + 3.0;
	} else if (z <= 13500000000000.0) {
		tmp = (1.0 + (t_1 + sqrt((1.0 + z)))) - (sqrt(x) + ((z - y) / (sqrt(z) - sqrt(y))));
	} else if (z <= 1.8e+219) {
		tmp = t_1 + (sqrt((1.0 + y)) - (sqrt(y) + sqrt(x)));
	} else {
		tmp = 1.0 / (t_1 + sqrt(x));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = sqrt((x + 1.0d0))
    if (z <= 4.2d-31) then
        tmp = (sqrt((1.0d0 + t)) - sqrt(t)) + 3.0d0
    else if (z <= 13500000000000.0d0) then
        tmp = (1.0d0 + (t_1 + sqrt((1.0d0 + z)))) - (sqrt(x) + ((z - y) / (sqrt(z) - sqrt(y))))
    else if (z <= 1.8d+219) then
        tmp = t_1 + (sqrt((1.0d0 + y)) - (sqrt(y) + sqrt(x)))
    else
        tmp = 1.0d0 / (t_1 + sqrt(x))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = Math.sqrt((x + 1.0));
	double tmp;
	if (z <= 4.2e-31) {
		tmp = (Math.sqrt((1.0 + t)) - Math.sqrt(t)) + 3.0;
	} else if (z <= 13500000000000.0) {
		tmp = (1.0 + (t_1 + Math.sqrt((1.0 + z)))) - (Math.sqrt(x) + ((z - y) / (Math.sqrt(z) - Math.sqrt(y))));
	} else if (z <= 1.8e+219) {
		tmp = t_1 + (Math.sqrt((1.0 + y)) - (Math.sqrt(y) + Math.sqrt(x)));
	} else {
		tmp = 1.0 / (t_1 + Math.sqrt(x));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = math.sqrt((x + 1.0))
	tmp = 0
	if z <= 4.2e-31:
		tmp = (math.sqrt((1.0 + t)) - math.sqrt(t)) + 3.0
	elif z <= 13500000000000.0:
		tmp = (1.0 + (t_1 + math.sqrt((1.0 + z)))) - (math.sqrt(x) + ((z - y) / (math.sqrt(z) - math.sqrt(y))))
	elif z <= 1.8e+219:
		tmp = t_1 + (math.sqrt((1.0 + y)) - (math.sqrt(y) + math.sqrt(x)))
	else:
		tmp = 1.0 / (t_1 + math.sqrt(x))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = sqrt(Float64(x + 1.0))
	tmp = 0.0
	if (z <= 4.2e-31)
		tmp = Float64(Float64(sqrt(Float64(1.0 + t)) - sqrt(t)) + 3.0);
	elseif (z <= 13500000000000.0)
		tmp = Float64(Float64(1.0 + Float64(t_1 + sqrt(Float64(1.0 + z)))) - Float64(sqrt(x) + Float64(Float64(z - y) / Float64(sqrt(z) - sqrt(y)))));
	elseif (z <= 1.8e+219)
		tmp = Float64(t_1 + Float64(sqrt(Float64(1.0 + y)) - Float64(sqrt(y) + sqrt(x))));
	else
		tmp = Float64(1.0 / Float64(t_1 + sqrt(x)));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = sqrt((x + 1.0));
	tmp = 0.0;
	if (z <= 4.2e-31)
		tmp = (sqrt((1.0 + t)) - sqrt(t)) + 3.0;
	elseif (z <= 13500000000000.0)
		tmp = (1.0 + (t_1 + sqrt((1.0 + z)))) - (sqrt(x) + ((z - y) / (sqrt(z) - sqrt(y))));
	elseif (z <= 1.8e+219)
		tmp = t_1 + (sqrt((1.0 + y)) - (sqrt(y) + sqrt(x)));
	else
		tmp = 1.0 / (t_1 + sqrt(x));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[Sqrt[N[(x + 1.0), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[z, 4.2e-31], N[(N[(N[Sqrt[N[(1.0 + t), $MachinePrecision]], $MachinePrecision] - N[Sqrt[t], $MachinePrecision]), $MachinePrecision] + 3.0), $MachinePrecision], If[LessEqual[z, 13500000000000.0], N[(N[(1.0 + N[(t$95$1 + N[Sqrt[N[(1.0 + z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[Sqrt[x], $MachinePrecision] + N[(N[(z - y), $MachinePrecision] / N[(N[Sqrt[z], $MachinePrecision] - N[Sqrt[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.8e+219], N[(t$95$1 + N[(N[Sqrt[N[(1.0 + y), $MachinePrecision]], $MachinePrecision] - N[(N[Sqrt[y], $MachinePrecision] + N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(t$95$1 + N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 8: 88.5% accurate, 2.0× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \sqrt{x + 1}\\ \mathbf{if}\;z \leq 5.5 \cdot 10^{-28}:\\ \;\;\;\;\left(\sqrt{1 + t} - \sqrt{t}\right) + 3\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+29}:\\ \;\;\;\;1 + \left(\sqrt{1 + z} + \left(t_1 - \left(\sqrt{z} + \sqrt{x}\right)\right)\right)\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+219}:\\ \;\;\;\;t_1 + \left(\sqrt{1 + y} - \left(\sqrt{y} + \sqrt{x}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{t_1 + \sqrt{x}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (sqrt (+ x 1.0))))
   (if (<= z 5.5e-28)
     (+ (- (sqrt (+ 1.0 t)) (sqrt t)) 3.0)
     (if (<= z 4.2e+29)
       (+ 1.0 (+ (sqrt (+ 1.0 z)) (- t_1 (+ (sqrt z) (sqrt x)))))
       (if (<= z 1.8e+219)
         (+ t_1 (- (sqrt (+ 1.0 y)) (+ (sqrt y) (sqrt x))))
         (/ 1.0 (+ t_1 (sqrt x))))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = sqrt((x + 1.0));
	double tmp;
	if (z <= 5.5e-28) {
		tmp = (sqrt((1.0 + t)) - sqrt(t)) + 3.0;
	} else if (z <= 4.2e+29) {
		tmp = 1.0 + (sqrt((1.0 + z)) + (t_1 - (sqrt(z) + sqrt(x))));
	} else if (z <= 1.8e+219) {
		tmp = t_1 + (sqrt((1.0 + y)) - (sqrt(y) + sqrt(x)));
	} else {
		tmp = 1.0 / (t_1 + sqrt(x));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = sqrt((x + 1.0d0))
    if (z <= 5.5d-28) then
        tmp = (sqrt((1.0d0 + t)) - sqrt(t)) + 3.0d0
    else if (z <= 4.2d+29) then
        tmp = 1.0d0 + (sqrt((1.0d0 + z)) + (t_1 - (sqrt(z) + sqrt(x))))
    else if (z <= 1.8d+219) then
        tmp = t_1 + (sqrt((1.0d0 + y)) - (sqrt(y) + sqrt(x)))
    else
        tmp = 1.0d0 / (t_1 + sqrt(x))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = Math.sqrt((x + 1.0));
	double tmp;
	if (z <= 5.5e-28) {
		tmp = (Math.sqrt((1.0 + t)) - Math.sqrt(t)) + 3.0;
	} else if (z <= 4.2e+29) {
		tmp = 1.0 + (Math.sqrt((1.0 + z)) + (t_1 - (Math.sqrt(z) + Math.sqrt(x))));
	} else if (z <= 1.8e+219) {
		tmp = t_1 + (Math.sqrt((1.0 + y)) - (Math.sqrt(y) + Math.sqrt(x)));
	} else {
		tmp = 1.0 / (t_1 + Math.sqrt(x));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = math.sqrt((x + 1.0))
	tmp = 0
	if z <= 5.5e-28:
		tmp = (math.sqrt((1.0 + t)) - math.sqrt(t)) + 3.0
	elif z <= 4.2e+29:
		tmp = 1.0 + (math.sqrt((1.0 + z)) + (t_1 - (math.sqrt(z) + math.sqrt(x))))
	elif z <= 1.8e+219:
		tmp = t_1 + (math.sqrt((1.0 + y)) - (math.sqrt(y) + math.sqrt(x)))
	else:
		tmp = 1.0 / (t_1 + math.sqrt(x))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = sqrt(Float64(x + 1.0))
	tmp = 0.0
	if (z <= 5.5e-28)
		tmp = Float64(Float64(sqrt(Float64(1.0 + t)) - sqrt(t)) + 3.0);
	elseif (z <= 4.2e+29)
		tmp = Float64(1.0 + Float64(sqrt(Float64(1.0 + z)) + Float64(t_1 - Float64(sqrt(z) + sqrt(x)))));
	elseif (z <= 1.8e+219)
		tmp = Float64(t_1 + Float64(sqrt(Float64(1.0 + y)) - Float64(sqrt(y) + sqrt(x))));
	else
		tmp = Float64(1.0 / Float64(t_1 + sqrt(x)));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = sqrt((x + 1.0));
	tmp = 0.0;
	if (z <= 5.5e-28)
		tmp = (sqrt((1.0 + t)) - sqrt(t)) + 3.0;
	elseif (z <= 4.2e+29)
		tmp = 1.0 + (sqrt((1.0 + z)) + (t_1 - (sqrt(z) + sqrt(x))));
	elseif (z <= 1.8e+219)
		tmp = t_1 + (sqrt((1.0 + y)) - (sqrt(y) + sqrt(x)));
	else
		tmp = 1.0 / (t_1 + sqrt(x));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[Sqrt[N[(x + 1.0), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[z, 5.5e-28], N[(N[(N[Sqrt[N[(1.0 + t), $MachinePrecision]], $MachinePrecision] - N[Sqrt[t], $MachinePrecision]), $MachinePrecision] + 3.0), $MachinePrecision], If[LessEqual[z, 4.2e+29], N[(1.0 + N[(N[Sqrt[N[(1.0 + z), $MachinePrecision]], $MachinePrecision] + N[(t$95$1 - N[(N[Sqrt[z], $MachinePrecision] + N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.8e+219], N[(t$95$1 + N[(N[Sqrt[N[(1.0 + y), $MachinePrecision]], $MachinePrecision] - N[(N[Sqrt[y], $MachinePrecision] + N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(t$95$1 + N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 9: 85.4% accurate, 2.0× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \sqrt{x + 1}\\ \mathbf{if}\;z \leq 0.56:\\ \;\;\;\;\left(\sqrt{1 + t} - \sqrt{t}\right) + 3\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+219}:\\ \;\;\;\;t_1 + \left(\sqrt{1 + y} - \left(\sqrt{y} + \sqrt{x}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{t_1 + \sqrt{x}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (sqrt (+ x 1.0))))
   (if (<= z 0.56)
     (+ (- (sqrt (+ 1.0 t)) (sqrt t)) 3.0)
     (if (<= z 1.8e+219)
       (+ t_1 (- (sqrt (+ 1.0 y)) (+ (sqrt y) (sqrt x))))
       (/ 1.0 (+ t_1 (sqrt x)))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = sqrt((x + 1.0));
	double tmp;
	if (z <= 0.56) {
		tmp = (sqrt((1.0 + t)) - sqrt(t)) + 3.0;
	} else if (z <= 1.8e+219) {
		tmp = t_1 + (sqrt((1.0 + y)) - (sqrt(y) + sqrt(x)));
	} else {
		tmp = 1.0 / (t_1 + sqrt(x));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = sqrt((x + 1.0d0))
    if (z <= 0.56d0) then
        tmp = (sqrt((1.0d0 + t)) - sqrt(t)) + 3.0d0
    else if (z <= 1.8d+219) then
        tmp = t_1 + (sqrt((1.0d0 + y)) - (sqrt(y) + sqrt(x)))
    else
        tmp = 1.0d0 / (t_1 + sqrt(x))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = Math.sqrt((x + 1.0));
	double tmp;
	if (z <= 0.56) {
		tmp = (Math.sqrt((1.0 + t)) - Math.sqrt(t)) + 3.0;
	} else if (z <= 1.8e+219) {
		tmp = t_1 + (Math.sqrt((1.0 + y)) - (Math.sqrt(y) + Math.sqrt(x)));
	} else {
		tmp = 1.0 / (t_1 + Math.sqrt(x));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = math.sqrt((x + 1.0))
	tmp = 0
	if z <= 0.56:
		tmp = (math.sqrt((1.0 + t)) - math.sqrt(t)) + 3.0
	elif z <= 1.8e+219:
		tmp = t_1 + (math.sqrt((1.0 + y)) - (math.sqrt(y) + math.sqrt(x)))
	else:
		tmp = 1.0 / (t_1 + math.sqrt(x))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = sqrt(Float64(x + 1.0))
	tmp = 0.0
	if (z <= 0.56)
		tmp = Float64(Float64(sqrt(Float64(1.0 + t)) - sqrt(t)) + 3.0);
	elseif (z <= 1.8e+219)
		tmp = Float64(t_1 + Float64(sqrt(Float64(1.0 + y)) - Float64(sqrt(y) + sqrt(x))));
	else
		tmp = Float64(1.0 / Float64(t_1 + sqrt(x)));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = sqrt((x + 1.0));
	tmp = 0.0;
	if (z <= 0.56)
		tmp = (sqrt((1.0 + t)) - sqrt(t)) + 3.0;
	elseif (z <= 1.8e+219)
		tmp = t_1 + (sqrt((1.0 + y)) - (sqrt(y) + sqrt(x)));
	else
		tmp = 1.0 / (t_1 + sqrt(x));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[Sqrt[N[(x + 1.0), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[z, 0.56], N[(N[(N[Sqrt[N[(1.0 + t), $MachinePrecision]], $MachinePrecision] - N[Sqrt[t], $MachinePrecision]), $MachinePrecision] + 3.0), $MachinePrecision], If[LessEqual[z, 1.8e+219], N[(t$95$1 + N[(N[Sqrt[N[(1.0 + y), $MachinePrecision]], $MachinePrecision] - N[(N[Sqrt[y], $MachinePrecision] + N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(t$95$1 + N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 10: 85.2% accurate, 3.9× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 0.56:\\ \;\;\;\;\left(\sqrt{1 + t} - \sqrt{t}\right) + 3\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+219}:\\ \;\;\;\;1 + \left(\sqrt{1 + y} - \sqrt{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\sqrt{x + 1} + \sqrt{x}}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z 0.56)
   (+ (- (sqrt (+ 1.0 t)) (sqrt t)) 3.0)
   (if (<= z 1.8e+219)
     (+ 1.0 (- (sqrt (+ 1.0 y)) (sqrt y)))
     (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 0.56) {
		tmp = (sqrt((1.0 + t)) - sqrt(t)) + 3.0;
	} else if (z <= 1.8e+219) {
		tmp = 1.0 + (sqrt((1.0 + y)) - sqrt(y));
	} else {
		tmp = 1.0 / (sqrt((x + 1.0)) + sqrt(x));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= 0.56d0) then
        tmp = (sqrt((1.0d0 + t)) - sqrt(t)) + 3.0d0
    else if (z <= 1.8d+219) then
        tmp = 1.0d0 + (sqrt((1.0d0 + y)) - sqrt(y))
    else
        tmp = 1.0d0 / (sqrt((x + 1.0d0)) + sqrt(x))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 0.56) {
		tmp = (Math.sqrt((1.0 + t)) - Math.sqrt(t)) + 3.0;
	} else if (z <= 1.8e+219) {
		tmp = 1.0 + (Math.sqrt((1.0 + y)) - Math.sqrt(y));
	} else {
		tmp = 1.0 / (Math.sqrt((x + 1.0)) + Math.sqrt(x));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if z <= 0.56:
		tmp = (math.sqrt((1.0 + t)) - math.sqrt(t)) + 3.0
	elif z <= 1.8e+219:
		tmp = 1.0 + (math.sqrt((1.0 + y)) - math.sqrt(y))
	else:
		tmp = 1.0 / (math.sqrt((x + 1.0)) + math.sqrt(x))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= 0.56)
		tmp = Float64(Float64(sqrt(Float64(1.0 + t)) - sqrt(t)) + 3.0);
	elseif (z <= 1.8e+219)
		tmp = Float64(1.0 + Float64(sqrt(Float64(1.0 + y)) - sqrt(y)));
	else
		tmp = Float64(1.0 / Float64(sqrt(Float64(x + 1.0)) + sqrt(x)));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= 0.56)
		tmp = (sqrt((1.0 + t)) - sqrt(t)) + 3.0;
	elseif (z <= 1.8e+219)
		tmp = 1.0 + (sqrt((1.0 + y)) - sqrt(y));
	else
		tmp = 1.0 / (sqrt((x + 1.0)) + sqrt(x));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[z, 0.56], N[(N[(N[Sqrt[N[(1.0 + t), $MachinePrecision]], $MachinePrecision] - N[Sqrt[t], $MachinePrecision]), $MachinePrecision] + 3.0), $MachinePrecision], If[LessEqual[z, 1.8e+219], N[(1.0 + N[(N[Sqrt[N[(1.0 + y), $MachinePrecision]], $MachinePrecision] - N[Sqrt[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(N[Sqrt[N[(x + 1.0), $MachinePrecision]], $MachinePrecision] + N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 11: 61.8% accurate, 3.9× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} t_1 := \sqrt{x + 1} - \sqrt{x}\\ \mathbf{if}\;y \leq 3.9:\\ \;\;\;\;1 + t_1\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (sqrt (+ x 1.0)) (sqrt x)))) (if (<= y 3.9) (+ 1.0 t_1) t_1)))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double t_1 = sqrt((x + 1.0)) - sqrt(x);
	double tmp;
	if (y <= 3.9) {
		tmp = 1.0 + t_1;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = sqrt((x + 1.0d0)) - sqrt(x)
    if (y <= 3.9d0) then
        tmp = 1.0d0 + t_1
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double t_1 = Math.sqrt((x + 1.0)) - Math.sqrt(x);
	double tmp;
	if (y <= 3.9) {
		tmp = 1.0 + t_1;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	t_1 = math.sqrt((x + 1.0)) - math.sqrt(x)
	tmp = 0
	if y <= 3.9:
		tmp = 1.0 + t_1
	else:
		tmp = t_1
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	t_1 = Float64(sqrt(Float64(x + 1.0)) - sqrt(x))
	tmp = 0.0
	if (y <= 3.9)
		tmp = Float64(1.0 + t_1);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	t_1 = sqrt((x + 1.0)) - sqrt(x);
	tmp = 0.0;
	if (y <= 3.9)
		tmp = 1.0 + t_1;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[Sqrt[N[(x + 1.0), $MachinePrecision]], $MachinePrecision] - N[Sqrt[x], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, 3.9], N[(1.0 + t$95$1), $MachinePrecision], t$95$1]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 12: 86.1% accurate, 3.9× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \begin{array}{l} \mathbf{if}\;z \leq 0.56:\\ \;\;\;\;\left(\sqrt{1 + t} - \sqrt{t}\right) + 3\\ \mathbf{else}:\\ \;\;\;\;1 + \left(\sqrt{1 + y} - \sqrt{y}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t)
 :precision binary64
 (if (<= z 0.56)
   (+ (- (sqrt (+ 1.0 t)) (sqrt t)) 3.0)
   (+ 1.0 (- (sqrt (+ 1.0 y)) (sqrt y)))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 0.56) {
		tmp = (sqrt((1.0 + t)) - sqrt(t)) + 3.0;
	} else {
		tmp = 1.0 + (sqrt((1.0 + y)) - sqrt(y));
	}
	return tmp;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= 0.56d0) then
        tmp = (sqrt((1.0d0 + t)) - sqrt(t)) + 3.0d0
    else
        tmp = 1.0d0 + (sqrt((1.0d0 + y)) - sqrt(y))
    end if
    code = tmp
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= 0.56) {
		tmp = (Math.sqrt((1.0 + t)) - Math.sqrt(t)) + 3.0;
	} else {
		tmp = 1.0 + (Math.sqrt((1.0 + y)) - Math.sqrt(y));
	}
	return tmp;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	tmp = 0
	if z <= 0.56:
		tmp = (math.sqrt((1.0 + t)) - math.sqrt(t)) + 3.0
	else:
		tmp = 1.0 + (math.sqrt((1.0 + y)) - math.sqrt(y))
	return tmp

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	tmp = 0.0
	if (z <= 0.56)
		tmp = Float64(Float64(sqrt(Float64(1.0 + t)) - sqrt(t)) + 3.0);
	else
		tmp = Float64(1.0 + Float64(sqrt(Float64(1.0 + y)) - sqrt(y)));
	end
	return tmp
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= 0.56)
		tmp = (sqrt((1.0 + t)) - sqrt(t)) + 3.0;
	else
		tmp = 1.0 + (sqrt((1.0 + y)) - sqrt(y));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := If[LessEqual[z, 0.56], N[(N[(N[Sqrt[N[(1.0 + t), $MachinePrecision]], $MachinePrecision] - N[Sqrt[t], $MachinePrecision]), $MachinePrecision] + 3.0), $MachinePrecision], N[(1.0 + N[(N[Sqrt[N[(1.0 + y), $MachinePrecision]], $MachinePrecision] - N[Sqrt[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 13: 64.8% accurate, 4.0× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ 1 + \left(\sqrt{1 + y} - \sqrt{y}\right) \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t) :precision binary64 (+ 1.0 (- (sqrt (+ 1.0 y)) (sqrt y))))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	return 1.0 + (sqrt((1.0 + y)) - sqrt(y));
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = 1.0d0 + (sqrt((1.0d0 + y)) - sqrt(y))
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	return 1.0 + (Math.sqrt((1.0 + y)) - Math.sqrt(y));
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	return 1.0 + (math.sqrt((1.0 + y)) - math.sqrt(y))

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	return Float64(1.0 + Float64(sqrt(Float64(1.0 + y)) - sqrt(y)))
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp = code(x, y, z, t)
	tmp = 1.0 + (sqrt((1.0 + y)) - sqrt(y));
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := N[(1.0 + N[(N[Sqrt[N[(1.0 + y), $MachinePrecision]], $MachinePrecision] - N[Sqrt[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 14: 35.2% accurate, 4.0× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \sqrt{x + 1} - \sqrt{x} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t) :precision binary64 (- (sqrt (+ x 1.0)) (sqrt x)))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	return sqrt((x + 1.0)) - sqrt(x);
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = sqrt((x + 1.0d0)) - sqrt(x)
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	return Math.sqrt((x + 1.0)) - Math.sqrt(x);
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	return math.sqrt((x + 1.0)) - math.sqrt(x)

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	return Float64(sqrt(Float64(x + 1.0)) - sqrt(x))
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp = code(x, y, z, t)
	tmp = sqrt((x + 1.0)) - sqrt(x);
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := N[(N[Sqrt[N[(x + 1.0), $MachinePrecision]], $MachinePrecision] - N[Sqrt[x], $MachinePrecision]), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 15: 34.5% accurate, 7.7× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ \left(1 + x \cdot 0.5\right) - \sqrt{x} \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t) :precision binary64 (- (+ 1.0 (* x 0.5)) (sqrt x)))

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	return (1.0 + (x * 0.5)) - sqrt(x);
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (1.0d0 + (x * 0.5d0)) - sqrt(x)
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	return (1.0 + (x * 0.5)) - Math.sqrt(x);
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	return (1.0 + (x * 0.5)) - math.sqrt(x)

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	return Float64(Float64(1.0 + Float64(x * 0.5)) - sqrt(x))
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp = code(x, y, z, t)
	tmp = (1.0 + (x * 0.5)) - sqrt(x);
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := N[(N[(1.0 + N[(x * 0.5), $MachinePrecision]), $MachinePrecision] - N[Sqrt[x], $MachinePrecision]), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 16: 34.0% accurate, 823.0× speedup

Math

\[\begin{array}{l} [x, y, z, t] = \mathsf{sort}([x, y, z, t])\\ \\ 1 \end{array} \]

FPCore

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
(FPCore (x y z t) :precision binary64 1.0)

C

assert(x < y && y < z && z < t);
double code(double x, double y, double z, double t) {
	return 1.0;
}

Fortran

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = 1.0d0
end function

Java

assert x < y && y < z && z < t;
public static double code(double x, double y, double z, double t) {
	return 1.0;
}

Python

[x, y, z, t] = sort([x, y, z, t])
def code(x, y, z, t):
	return 1.0

Julia

x, y, z, t = sort([x, y, z, t])
function code(x, y, z, t)
	return 1.0
end

MATLAB

x, y, z, t = num2cell(sort([x, y, z, t])){:}
function tmp = code(x, y, z, t)
	tmp = 1.0;
end

Wolfram

NOTE: x, y, z, and t should be sorted in increasing order before calling this function.
code[x_, y_, z_, t_] := 1.0

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Developer target: 99.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(\frac{1}{\sqrt{x + 1} + \sqrt{x}} + \frac{1}{\sqrt{y + 1} + \sqrt{y}}\right) + \frac{1}{\sqrt{z + 1} + \sqrt{z}}\right) + \left(\sqrt{t + 1} - \sqrt{t}\right) \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (+
  (+
   (+
    (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
    (/ 1.0 (+ (sqrt (+ y 1.0)) (sqrt y))))
   (/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z))))
  (- (sqrt (+ t 1.0)) (sqrt t))))

C

double code(double x, double y, double z, double t) {
	return (((1.0 / (sqrt((x + 1.0)) + sqrt(x))) + (1.0 / (sqrt((y + 1.0)) + sqrt(y)))) + (1.0 / (sqrt((z + 1.0)) + sqrt(z)))) + (sqrt((t + 1.0)) - sqrt(t));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (((1.0d0 / (sqrt((x + 1.0d0)) + sqrt(x))) + (1.0d0 / (sqrt((y + 1.0d0)) + sqrt(y)))) + (1.0d0 / (sqrt((z + 1.0d0)) + sqrt(z)))) + (sqrt((t + 1.0d0)) - sqrt(t))
end function

Java

public static double code(double x, double y, double z, double t) {
	return (((1.0 / (Math.sqrt((x + 1.0)) + Math.sqrt(x))) + (1.0 / (Math.sqrt((y + 1.0)) + Math.sqrt(y)))) + (1.0 / (Math.sqrt((z + 1.0)) + Math.sqrt(z)))) + (Math.sqrt((t + 1.0)) - Math.sqrt(t));
}

Python

def code(x, y, z, t):
	return (((1.0 / (math.sqrt((x + 1.0)) + math.sqrt(x))) + (1.0 / (math.sqrt((y + 1.0)) + math.sqrt(y)))) + (1.0 / (math.sqrt((z + 1.0)) + math.sqrt(z)))) + (math.sqrt((t + 1.0)) - math.sqrt(t))

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(Float64(1.0 / Float64(sqrt(Float64(x + 1.0)) + sqrt(x))) + Float64(1.0 / Float64(sqrt(Float64(y + 1.0)) + sqrt(y)))) + Float64(1.0 / Float64(sqrt(Float64(z + 1.0)) + sqrt(z)))) + Float64(sqrt(Float64(t + 1.0)) - sqrt(t)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (((1.0 / (sqrt((x + 1.0)) + sqrt(x))) + (1.0 / (sqrt((y + 1.0)) + sqrt(y)))) + (1.0 / (sqrt((z + 1.0)) + sqrt(z)))) + (sqrt((t + 1.0)) - sqrt(t));
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(N[(1.0 / N[(N[Sqrt[N[(x + 1.0), $MachinePrecision]], $MachinePrecision] + N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(1.0 / N[(N[Sqrt[N[(y + 1.0), $MachinePrecision]], $MachinePrecision] + N[Sqrt[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(1.0 / N[(N[Sqrt[N[(z + 1.0), $MachinePrecision]], $MachinePrecision] + N[Sqrt[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[Sqrt[N[(t + 1.0), $MachinePrecision]], $MachinePrecision] - N[Sqrt[t], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2023350 
(FPCore (x y z t)
  :name "Main:z from "
  :precision binary64

  :herbie-target
  (+ (+ (+ (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))) (/ 1.0 (+ (sqrt (+ y 1.0)) (sqrt y)))) (/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))) (- (sqrt (+ t 1.0)) (sqrt t)))

  (+ (+ (+ (- (sqrt (+ x 1.0)) (sqrt x)) (- (sqrt (+ y 1.0)) (sqrt y))) (- (sqrt (+ z 1.0)) (sqrt z))) (- (sqrt (+ t 1.0)) (sqrt t))))